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Reliability, validity, and utility of composite measures used in the 1981 and 1985 Denver air quality surveys

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Reliability, validity, and utility of composite measures used in the 1981 and 1985 Denver air quality surveys
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Smith, Phillip Heywood
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105 leaves : forms ; 28 cm

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Air quality management -- Public opinion -- Colorado -- Denver Metropolitan Area ( lcsh )
Air quality management -- Public opinion ( fast )
Colorado -- Denver Metropolitan Area ( fast )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Includes bibliographical references (leaves 74-83).
General Note:
Submitted in partial fulfillment of the requirements for the degree, Master of Arts, Department of Sociology.
Statement of Responsibility:
by Phillip Heywood Smith.

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University of Colorado Denver
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Full Text
BIOPHYSICAL PARAMETERS IMPLEMENTING
GROWTH CONTROL IN PHYCOMYCES
by
Martin Eliot Smith
A.A.S., Ferris State College, 1978
B.S., University of Colorado at Denver, 1988
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado at Denver in Partial fulfillment
of the requirements for the degree of
Master of Science
Department of Mechanical Engineering
1990


This thesis for the Master of Science
degree by
Martin Eliot Smith
has been approved for the
Department of
Mechanical Engineering
by
Date.


FIGURES
Figure 1.1. Sporangiophore Morphology......................6
Figure 1.2. Sporangiophore Development.....................7
Figure 1.3. Pressure Probe Schematic Diagram...............8
Figure 2.1. July 1 1989 Experiment........................13
Figure 2.1. August 3 1989 Experiment......................14
Figure 3.1. July 1 1989 Experiment........................22
Figure 3.2. June 2 1990 Experiment........................26
Figure 3.3. Histographic Summary of Data..................28
Figure 4.1. July 12 1989 Observations.....................32
Figure 4.2. September 10 1989 Observations................32
Figure 4.3. September 6 1989 Observations.................33
Figure 5.1. Two Probe Experiment Pressure Trace...........39
vi


TABLES
Table 2.1. Summary of Experiments...................16
Table 3.1. Values of e..............................25
Table 5.1 Pressure Probe Output....................38
vii


ACKNOWLEDGEMENT
How shall we believe you, then, good legislators, when you
say, 'We allow none to be educated but the free'? For the
philosophers say 'We allow none to be free but the wise'; that is,
God does not allow it. -Epictetus (Disclosures, II.i.)
Thanks to ...
My Friends: Lillith Justine Graeme, Donna Moxley, Julianne
Stall, and others, for their support.
Dr. J. Kenneth E. Ortega, who thinks first, and always makes
the time to do the job right; and the other members of the thesis
commitee: Dr. William H. Clohessy, Dr. John A. Trapp.
The crew in the lab for technical support, feedback,
independent reproduction of results, and physical assistance with
some of the more demanding experiments: (in chronological order)
Keith J. Manica, Edwin G. Zehr, Mark A. Espinosa, Scott A. Bell, and
A. Jeanette Erazo.
Mark A. Espinosa, for the Chapter One graphics; Allen E.
Johnson, statistician extraodinaire; and Hannah J Kelminson, for
editorial assistance.
The Club Natural Philosophy for encouraging student interest in
research within a difficult environment.
Ed Lipson and Walt Shropshire for taking time to visit our lab
and contribute some of their experience.
This work was supported by the National Science Foundation
(Grant # DCB-8801717 to Dr. J.K.E.Ortega), and indirectly by the
University of Colorado (Colorado Graduate Grant), and the UCD College
of Engineering (Deans Scholarship).
viii


CHAPTER ONE
INTRODUCTION
General
The most vital and pervasive interaction between man and the
biosphere is agriculture. Science has impacted agriculture mainly
through the application of principles discovered in the field of
plant physiology. Past improvements in farming have resulted from
improved understanding and control of the plant's external
environment, mechanization, and trial and error breeding. The field
of plant physiology has focused on efforts to describe and understand
the morphology, growth, development properties and behaviors of
plants.
At the other extreme, biochemistry and physical chemistry seek
to produce a detailed understanding of the mechanisms by which light
and simple molecules are converted into life. Indeed genetic
manipulation is now beginning to describe biological systems in
unprecedented detail. As scientists attempt to extend microscopic
mechanisms to macroscopic behaviors, they have discovered limitations
in predicting and describing large-scale phenomena. It follows that
before the extrapolation of these microscopic mechanisms can be
successful in modeling macroscopic behaviors, the intermediate scale
of cell function must be understood. It is not sufficient to
describe macroscopic behaviors on a purely qualitative level, the
transition to quantitative modeling must be made. Only through
quantitative modeling can the individual parameters be isolated and
studied. It is now possible to do so on the scale of the plant cell
itself, that is to model the biophysical aspects of the transport of
water, the behavior of the cell wall, and the effects of cell wall


growth and sensory responses (Ortega 1990). This type of study is
particularly well suited to engineering and material science. When
the governing principles are discovered and enough data are compiled,
complete systems models may be developed and integrated with
microscopic data. Only then can biology become a truly quantitative
science.
A major objective of the work in our laboratory is to construct
a quantitative model which describe and predict plant cell growth
rate and its regulation. Previous work (Lockhart 1965) has produced
two equations termed the Growth Equations which have been
subsequently augmented (Ortega 1985; Ortega et al. 1988a). This
thesis will specifically study the changes in cell wall properties
throughout different stages of cell development. The results can be
used to determine the magnitude and behavior of parameters in one of
the Growth Equations.
Theory
The rate of cell enlargement is the result of two simultaneous
and interrelated physical processes: the net rate of extension of the
cell wall, and the net rate of water uptake. Lockhart (1965)
proposed that these processes could be modeled with two equations
under equilibrium conditions. First, the irreversible cell wall
extension is modeled as a Newtonian dashpot. Plastic deformation of
the cell wall results from the application of a force via constant
turgor pressure, P. Ortega (1985) augmented this equation with a
term to account for reversible extension the case of variable P.
The resulting equation is similar to that of a linear Maxwell model,
that is an elastic and viscous element in series:
4 = - Equation 1.1
2


Where V is the relative rate of change of volume of the cell wall
chamber, Vc is the volume of the cell wall chamber, t is time, <}) is
relative irreversible cell wall extensibility, Pc is the critical
turgor pressure (or Y the yield threshold), and e is the volumetric
elastic modulus. Equation 1.1 then states that the relative rate of
change in volume of the cell wall chamber is the sum of plastic cell
wall deformation (proportional to P) and elastic cell wall
deformation (proportional to the change in P).
The second equation models the net rate of water uptake.
Lockhart's (1965) equation assumed that the cell's growth rate is
directly proportional to the rate of water uptake. Ortega et al.
(1988a) augmented this equation to include water loss through
transpiration:
v = = l(cAII P) T. Equation 1.2
Vdt
Where V is the volume of the cell contents (mostly water), L is the
relative hydraulic conductance of the cell membrane, a is the solute
reflection coefficient, AH is the osmotic pressure difference in the
uptake region of the cell membrane, and T is the relative
transpiration rate. Equation 1.2 states that the relative rate of
change of volume of the cell contents is equal to the difference
between the osmotic water uptake and the transpiration water loss.
These two equations are coupled by P and equal to one another
because the volume of the cell wall chamber is equal to the volume of
the cell contents. Taken together these equations are referred to as
the "augmented growth equations" (Ortega et al. 1988a, 1988b; Ortega
1990).
3


The terms in the equations are quite difficult to evaluate in a
multicellular plant. A single plant cell in a multicellular plant
might be only 10(i/n in diameter, with its function and behavior
closely related to its physical position within the plant. Material
and water are exchanged with surrounding cells, while transpiration
and water uptake occur in numerous pores and capillary channels. The
cell might also grow in highly irregular directions while under
tension, compression, torsion and shear loads (Zimmermann 1978).
Under such conditions it is difficult to isolate the governing
parameters. To avoid these problems work has been done on single
celled plants (Cerda-Olmedo and Lipson 1987). In an isolated single
cell plant the volumetric growth, and turgor pressure can be directly
measured in vivo without altering the plant's normal growth (Cosgrove
et al. 1987, Ortega et al. 1988a, 1988b, 1989). Water uptake and
transpiration can also be controlled within qualitative extremes
(Ortega et al. 1988a). Furthermore, stress may be applied to the
cell wall mechanically or by changing turgor (Ortega 1976, Ortega et
al. 1988b, 1989).
The algal cells Nitella (Green 1968; Green et al. 1970) and
Chora (Dainty et al. 1974) as well as the fungal cell Phycomyces
(Cosgrove et al. 1987; Ortega et al. 1975, 1976, 1988a, 1988b, and
1989) have been studied by in vivo creep and relaxation tests. In
the in vivo creep test a fixed stress or stress rate change is
applied to the cell wall and the resulting change in strain (growth)
rate is measured. In the relaxation test a fixed strain is imposed
on the cell wall and the resulting stress decay rate (turgor pressure
change) is measured. In vivo creep measurements have been conducted
on stage IVb sporangiophores of Phycomyces blakesleeanus by Ortega et
al.(1989) using a pressure probe technique, and on Nitella by Green
4


(1968) and Green et al. (1970) using changes in osmotic pressure.
The results obtained are consistent with the Maxwell model over the
specified range, and give numerical values for the wall extensibility
and yield threshold. The in vivo stress relaxation tests were
conducted by Ortega (1976) using an Instron tension/ compression
machine, and using a pressure probe technique (Ortega et al. 1989).
Some of these measurements have also provided numerical values for
yield threshold.
Phvcomvces Blakesleeanus. Development and Morphology
The sporangiophores of Phycomyces blakesleeanus are an ideal
organism for macroscopic experimental work on plant cell mechanics
(Bergman et al. 1969; Cerda-Olmedo and Lipson 1987). The Phycomyces
sporangiophore is a single-celled fungus which can grow up to 100 mm
in length and is typically 200 (xm in diameter. With large growth
rates (up to 80 min-1) and rapid sensory response times (10 to 30
minutes) experiments can be completed in reasonable time frames and
with readily available equipment.
The sporangiophore is a cylindrical, multi-nucleated, single
cell (see Figure 1.1). A large cylindrical vacuole runs the length
of the sporangiophore, the contents are approximately 85% water (-
Olmedo and Lipson 1987). Specifically the vacuole is filled with
cell sap and the products of metabolic activity. The contents of the
vacuole are separated from the cytoplasm by a membrane called the
tonoplast. The tonoplast has very little mechanical strength and
serves primarily as a valve, pumping materials into and out of the
vacuole as needed. Surrounding the tonoplast is a cytoplasmic layer
containing all major organelles; this where the majority of metabolic
activity takes place. Finally the cell membrane and thick cell wall
5


separate the cell contents from the outside world. The cell wall is
a composite material made of chitin microfibril imbedded in an
amorphous chitosan matrix. Mechanically, the cell wall is the
strongest part of the cell and provides its principal means of
support and protection. Water is released through the cell wall and
transpires into the atmosphere. It has been observed (Cosgrove et
al. 1987) that the porous cell wall acts as an additional reservoir
of water for the cell.
Phycomyces exhibits five distinct stages of growth three of
which are relevant to this paper (Bergman et al. 1969; Cerda-Olmedo
and Lipson 1987, see Figure 1.2). After inoculation on an
appropriate growth media (see Appendix A), a thick mat of interlaced
hyphae grow out across the media forming a mycelium. Two to three
days after inoculation aerial hyphae begin to grow upward forming the
stage I sporangiophore. The stage I sporangiophore is a circular
cylinder typically 200 jim in diameter tapering to an apical tip.
Longitudinal growth in this stage occurs between the apical tip and
500 to 1500nm below (termed the "growing zone"), at a rate of
between 5 and 20 (im min'1. Points on the cell wall in the growing
zone move around the cell and upward in a left hand spiral (termed
6


"left-handed spiral growth").
After several hours longitudinal growth slows and the top of
the sporangiophore forms a sphere or sporangium. The period of
spherical growth is termed stage II. After the sporangium is formed
there is a period during which little or no growth occurs; this is
termed stage III. After a few hours growth resumes in a right hand
spiral (stage IVa). About 90 minutes later growth reverses into a
left hand spiral without interruption of growth (stage IVb). The
reversal of rotation has been analyzed to yield subtle details of the
cell wall's behavior (Ortega 1976). Longitudinal growth in stage IVa
begins slowly and accelerates reaching maximum values in stage IVb
where growth rates can be as high as 80 (xm min-1. As stage IV
progresses, the sporangium changes color from a bright yellow to
green then darkening to black as approximately 10s spores mature
within the sporangium. When the sporangium is broken the spores are
7


released and the sporangiophore generally dies. The total life cycle
described here involves about four or five days.
Pressure Probe
The pressure probe technique for measuring turgor pressure is
well established (Zimmermann et al., 1978; Cosgrove et al., 1987;
Ortega et al., 1988a, 1988b and 1989). The pressure probe (see
figure 1.3 and Appendix A) consists of a glass micro-capillary and
pressure chamber filled with an incompressible and biologically inert
silicone oil. The pressure in the chamber is measured with a
pressure transducer in contact with the oil. The chamber volume can
be adjusted by advancing and retracting a control rod (plunger).
When the plant cell is impaled by the micro-capillary the turgor
pressure pushes cell sap from the vacuole into the capillary and a
visible oil/cell sap interface is formed. If the micro-capillary is
correctly sized and very stable, sap escaping between the capillary
8


and cell wall will quickly seal preventing leaks. Advancing the
control rod allows the interface to be moved, displacing the cell sap
from the capillary. When the interface is adjacent to the cell wall,
the pressure in the chamber is equal to the turgor pressure. Should
the interface become stuck the measured pressure would be in error.
Frequent movement of the interface will generally ensure that
pressure measurements remain accurate while reducing precision only
slightly.
Thesis Preview
In Chapter Two, In vivo creep experiments are conducted wherein
the cell wall extensibility and yield threshold of stage I
sporangiophores of P. blakesleeanus are measured and compared to
previously obtained values for stage IVb using the same In vivo creep
technique (Ortega et al. 1989). It is shown that growth rate is a
function of the cell wall extensibility, and that the cell wall
extensibility is a function of the length of the growing zone.
Extensibility per unit length of the growing zone appears to be
nearly constant.
In Chapter Three experiments are conducted wherein the
volumetric elastic modulus of growing stages I and IVb
sporangiophores of P. blakesleeanus are measured and compared with
previously measured values from non-growing stage III
sporangiophores. The use of methods proposed by Ortega (1985) but as
yet untested, to calculate the elastic modulus of growing cells, are
used and evaluated. The method appears to be most successful when
steps in pressure are given with long time intervals between steps.
In Chapter Four the results of a study of stage I growing zones
are presented. The length of the growing zone is found to be greater
9


than had been previously thought. Previously developed techniques
for measuring the length of the growing zone are shown to be
insufficient. The dynamic behavior of the growing zone is found to
be more complex than previously described.
In Chapter Five an independent test of the pressure probe
technique is presented which supports the validity of the technique.
The dynamic response of the pressure probe/ sporangiophore system is
examined. The test has potentially important applications for
further experimentation.
10


CHAPTER TWO
CELL WALL EXTENSIBILITY
Introduction
Considering equilibrium growth (constant P) in the longitudinal
direction only, the Augmented Growth Equation for cell wall extension
(Equation 1.1) can be written for the growing zone (see Appendix C)
as
1 dV
Vg dt
1 dl
lg dt
4>g(P ~ Pe)
Defining m as the irreversible wall extensibility equal to §glff, and
assuming that m and Pc are constant, I may discretize derivatives
and take the differential.
aA = A(mP) A (mPc)
At c
Now, solving for m,
m = A (-A ) y Equation 2.1
At A P
With m known, Pc may be found.
P_ = P ( ) Equation 2.2
c Atm
as was shown by Ortega et al. (1989). The equations are now in a
form amenable to experimentation. The longitudinal growth rate and
its changes can be measured with a micrometer, the turgor pressure
and its changes can be measured with a pressure probe.


Materials and Methods
A detailed description of all apparatus used in these
experiments, and the procedures for growing sporangiophores and
measuring their turgor pressure is provided in Appendix A.
Experimental Protocol
Stage I sporangiophores of Phycomyces were selected and placed
under a broadband cool light at 21 + 1 'C. A growth scope (see
Appendix A) was used to measure changes in length. The length of the
sporangiophore was monitored for at least one half hour until steady
state growth was observed.
When steady state growth occurred, length measurements were
taken every 1 or 2 minutes. If the growth rate remained steady for
10 to 20 minutes, the sporangiophore was impaled and turgor pressure
was measured with the pressure probe. The growth rate was monitored
for an additional 5 to 10 minutes to ensure that it had not been
influenced by the measurement of P. At the end of this time a step
up in pressure was produced by injecting oil into the sporangiophore.
With the pressure held at a fixed value, growth measurements were
continued for at least 30 minutes.
Results
Figures 2.1 and 2.2 show two typical experiments. The turgor
pressure, is plotted in the upper graph (a). The lower graph (b) in
each figure is a plot of length versus time. The main events in the
protocol are marked an the graphs as they occurred in time. Figures
2.1 b and 2.2 b show an increase in growth rate (slope) following the
step increase in turgor pressure. These results are typical of the
eight experiments conducted by me and the seventeen experiments
analyzed herein (the remaining experiments were conducted by Scott A.
12


TURGOR
a) Turgor pressure trace
STEP UP EXPERIMENT JULY 01, 1989
L£N5TH
b) Growth rate versus time
Figure 2.1. July 1 1989 Experiment
13


a) Turgor pressure trace
STEP UP EXPERIMENT AUGUST 3, T989
TCTOt LEN5TH
'..OB 1 1 1 I 1 1 1 1 1 1 1 ^
1 1 1 i i i i i i 1 X
i i i i i i i i i i i
i i i i i i i rtrn i
i I i i i i i j*r i i i
1X3 E 1 1 1 1 1 1 L^l 1 1 1
i i I i i ii r i i
J _ i i i i i >r i i i i i
i i i i s i i i i i i
1 1 I IV 1 1 1 1 1 1 1
1 1 S\ 1 1 1 1 1 1 1
1 L^l 1 1 I 1 I 1 1 1
CLS6 - k'i i i i i i i i i i
0 20 40 f o BO 100 120
Tim* (min)
1 5TEP1
IMPALE
b) Growth rate versus time
Figure 2.2. August 3 1989 Experiment
14


Bell, A. Jeannette Erazo, Mark A. Espinosa, and Edwin Zehr)
Analysis
The extensibility was calculated using the difference in the
average growth rate for a period of 5 or 10 minutes before and after
the step and dividing that value by AP (see Equation 2.1). For
example in the experiment shown in Figure 2.1 the averaged growth
rate increases by 0.3 [1/77 min-1 after a step of 0.010 MPa yielding an
m value via Equation 2.1 of 46.9\im MPa'1 Min''1. Table 2.1 summarizes
the results of these experiments. The value obtained for the
extensibility m, in the 17 experiments analyzed is 116 +
19 n MPa'1 min-1 (mean + standard error).
Pc was calculated using the average growth rate for the period
before the step up since the growth rate, m, P and Pc, are constant
for this period. Extending the above example from the Figure 2.1
experiment, P was measured as .390 MPa yielding a Pc via Equation
2.2 of .249. Table 2.1 summarizes these results also. The mean
value obtained for Pc, in the 17 experiments analyzed is 0.4 + 0.03
MPa with n = 17. Finally, <|>ff may be calculated given lg. From
growing zone measurements lg is taken to be approximately 0.70 mm
(see Chapter Four).
As was reported for stage IVb's (Ortega et al. 1989), a
decrease in steady state rate growth was seen to occur after
sufficiently large steps in pressure (greater then 0.02 MPa).
Similar decreases can be seen in some of the stage I experiments
discussed herein. Data from such experiments result in negative
values of m and were not used in the analysis presented here. These
experiments indicate that in stage I's the threshold of pressure
15


above which steady state growth rate drops is between 0.010 MPa and
0.006 MPa, less than that of stage IVb's.
Discussion
Ortega et al. (1989) measured m, Pc, and in stage IVb
sporangiophores of Phycomyces, these values together with those we
obtained for stage I sporangiophores are shown in Table 2.1. The
values of m obtained for stage I are approximately one tenth of those
obtained for stage IVb. However when divided by the length of the
growing zone (lg) to obtain y the resulting values differ by only a
factor of two.
Table 2.1 Summary of experiments
Parameter (Units) Staae I m Staae IVb (2)
Mean + SE (3) Mean + SE
(urn min' 7.1 + 0.7 34.1 + 3.1
m (\im MPa . 116 + 19 997 + 164
PQ {MPa) 0.4 + 0.03 0.26 + 0.01
P Pc {MPa) 0.08 + 0.01 0.05 0.01
lg {mm) -0.7 -3.0
n 17 20
(1) Experiments analyzed herein
(2) Ortega et al. 1989
(3) SE is Standard Error
Conclusion
The relevance of these results is that, of the parameters in
the growth equations (Equations 1.1 and 1.2), the length of the
growing zone appears to be important in the control of growth rate
16


between stages. This simplifies manipulation of the equations by
establishing lg as an independent parameter in the equations.
Essentially m becomes a dependent parameter driven by the change in
lg. The position and importance of lg in the equations, where it
originally did not exist, is therefore established. Knowing this,
one can now focus on this parameter in biochemical work to determine
how the plant controls its growth rate. Clearly this result does not
apply itself to plant cells which grow along their entire length.
Due to the importance of lg in the equations its precise value
should be determined to refine the values calculated herein.
Additional work is called for to determine whether the length of
growing zone also changes during growth rate changes associated with
sensory responses. Unfortunately, sensory responses in Phycomyces
are transient and not sufficiently reproducible to easily determine m
dynamically. Reliable determination of a change in lg during the
sensory response may be possible although the material presented in
Chapter Four indicates that the steady state length of the growing
zone is itself a dynamic parameter.
17


CHAPTER THREE
VOLUMETRIC ELASTIC MODULUS
Introduction
In studies of water relations in plants the hydraulic
conductance L is frequently measured by observation of elastic
changes in volume due to water uptake and transpiration (Zimmermann
et al. 1978). In order to accurately assess L, accurate measures of
the volumetric elastic modulus e must be made.
Manipulating Equation 1.1 (see Appendix C for details), the
volumetric elastic modulus can be solved for in terms of the known
variables: growth rate and turgor pressure as follows....
e=
dP
dt

Equation 3.1
By observing the steady state growth and monitoring P, a state of
constant P can be found wherein dP/dt is zero. Given this, the
relative plastic extension rate can be found...
(P-P.)=-^
1 dl
which is easily measured in discretized form...
(PPe) = steady
10 AC state
Assuming that this is constant, e can now be determined and plotted
as a function of turgor pressure by...
A P 7
e,
A t'
'2 A 1 r Al I
At L At
Equation 3.2
As was shown by Ortega in 1985. In the case of zero growth
(AI/A t) ss is zero and the equation simplifies to...


Ah
e,= -A-l- = Equation 3.3
1 AI A 1
A t
(subscripts 1 and 2 are added for later reference only).
Experimentally, by supplying a series of discrete pressure steps on
fixed time intervals and measuring the resulting change in length, e
may be determined as a function of P. These equations clearly
show that the values obtained for growing versus non growing cells
should be determined by different methods. Zimmermann et al. (1978)
notes that in plasticly deformable (growing) cells it is necessary to
either produce instantaneous steps in P and measure instantaneous
changes in 1 or, if the steps are not instantaneous, the plastic
deformation occurring during the step interval must be accounted for.
Zimmermann also notes potential errors due to hysteresis effects and
"changes in cell volume and pressure due to water flow" may be
relevant in longer time intervals for growing plants. Unfortunately
in the literature this distinction of growth is rarely made.
Zimmermann et al. (1978) lists e values for 23 species of plants
obtained from a variety of techniques. Zimmermann's paper only once
notes whether the cell in question was growing and no note is made as
to whether plastic deformation was accounted for. Ortega (1985)
presents an explicit equation for handling the plastic deformation
when measurements are made over finite time intervals. In this
chapter I will develop and conduct experiments to measure e using
the equation developed by Ortega (1985) (Equation 3.2) and compare
the values obtained with and without the growth rate compensation to
evaluate its importance.
19


Materials and Methods
As has been previously reported for Phycomyces (Gammow et al.
1977, 1981, 1986, 1987; Lafay et al. 1985) growth rates fluctuate on
short time scales. It must be remembered that the steady state
growth rate is only an approximation to the actual growth rate. From
a physical standpoint, the natural variation in steady state growth
rate over short time intervals can cause the denominator of Equation
3.2 to approach zero or go negative. Such a circumstance would lead
to extreme and nonphysical values of e2. From a mathematical
standpoint however,
4>(p pc) At <
A2
1
a short time interval is preferred to ensure that
(Ortega 1985; Zimmermann 1978). Also, Ortega et
al. (1989) reported that sufficiently large pressure step ups cause a
decrease in steady state growth. Since the reported drop takes a few
minutes to occur it might be possible to make many rapid steps before
the steady state drop becomes significant. Two step interval sizes
are evaluated in the stage I experiments.
Experimental Protocol
Stage I and stage IVb sporangiophores were selected and placed
under a biologically inert, cool, constant biaxial light at 21 + 1
"C. The growth rate was monitored at five minute intervals for one
half hour. After this adaptation period the sporangiophore's apical
tip was monitored until constant growth was observed.
When constant growth rate was seen, length measurements were
taken every minute. If the growth rate remained constant for 10 to
20 minutes, the sporangiophore was impaled with the pressure probe
and P was measured. For an additional 5 to 10 minutes the growth
20


rate was monitored to ensure that it was not changed by the
measurement of P. At the end of this time the pressure was stepped
up using the pressure probe. If no oil was seen to move into the
cell vacuole the pressure in the probe was increased (spiked) until
oil was seen to move into the cell at which time the pressure was
rapidly backed down. Equal pressure steps were made at 15 or 20
second intervals (here after referred to as 'short interval
experiments'). In other experiments (long interval experiments) a
single pressure step or multiple steps on intervals of greater then 1
minute were conducted. Short interval experiments were conducted on
stage I sporangiophores only. In both cases 1 was measured
immediately after each step.
Results
Figure 3.1 shows a typical stage I long interval experiment. P
is plotted on top in MPa versus time in minutes. The lower graph is a
plot of growth rate (dl/dt) versus time on the same time scale. The
principal events in the protocol are marked on the graphs as they
occurred in time. The growth rate graph shows responses following
the steps. This result is typical of the 19 experiments analyzed
herein which yield 21 values of e for stage I sporangiophores. Two
short interval stage I experiments are also analyzed which yield 62
values for e.
Figure 3.2 shows a typical stage IVb experiment similarly
plotted. This result is typical of the 12 experiments conducted
which yield 68 values for stage IVb's.
e may be calculated by averaging the growth rate for 10
minutes before the step and subtracting this from the change in
length which occurs after the step. For example in the experiment
21


dl/dl (um/mln)
a) Turgor pressure trace
STEP UP EXPERIMENT 1 JULY, 1989
LSiSm CHANSZ
b) Growth rate versus time
Figure 3.1. July 1 1989 Experiment
22


a) Turgor pressure trace
Z
c
*
e
£5
STEP UP EXPERIMENT 7 JUNE, 1290
DS.TA I
50
45
40
50
20 ~.i
15 -
90
94
95
I 102
HUi (min)
105
110
b) Growth rate versus time IMPALE
Figure 3.2. June 7 1990 Experiment
5TEP 1
!
1
1
1 \ 1
V
j s
/ \ A] 1
/ V A ! ' V
114
23


shown in Figure 3.2 the steady state growth rate of 20 urn min"1
increases by 22 urn min"1 during a step up of .512 MPa yielding an
elastic modulus via Equation 3.3 of ex = 23.73 MPa and via Equation
3.2 of e2 = 45.50 MPa.
Both experiments shown above illustrate the dramatic variation
in growth rate. In Figure 3.2 for example the growth rate varies by
+ 50% of its steady state value before the cell was impaled. Indeed
of the 150 e values collected from growing cells 57 of them are
negative and 4 of them are greater than 1000 MPa. Before analysis
can proceed therefore it is necessary to establish some limits on
acceptable values of e. The requirement of limits is an intrinsic
part of this method for calculating e.
Analysis and Discussion
The two largest epsilon values in the survey conducted by
Zimmermann et al. (1978) are 120 and 77 MPa. Ortega et al. (1988a)
measured e for the non growing stage III sporangiophores and found
the following relation...
e = emax ~ O e'kp Equation 3.4
Where emax was measured between 80 and 160 MPa. In the growing zone
the cell wall will be softer than in the non-growing wall, this will
produce higher extensions and therefore smaller e's in growing
cells. e2 therefore should be less than 160 MPa for stage I and
stage IVb sporangiophores, greater values will be discarded. In
Table 3.1 averages and standard deviations for the e values obtained
are listed by stage and interval size (for stage I only). The number
of values (n) used in each calculation is also listed along with
24


percentages indicating how many points were not thrown out.
Experiments performed with small time intervals between steps
produced more out of range values of e2 then those with larger time
intervals (See Table 3.1). In the small interval experiments, the
response to the pressure step was frequently no larger than the
TABLE 3.1 VALUES OF e
STAGE/ e2 N
INTERVAL AVG. STD. AVG. STD % OF TOTAL
STAGE 1/ <1 MIN 39.17 12.39 78.19 30.72 19 31%
>1 min 13.86 16.67 50.98 48.77 19 90%
m > 0 13.13 11.40 50.53 38.65 14 82%
STAGE IVb 19.71 8.55 74.32 32.81 45 66%
m > 0 21.22 8.02 61.52 27.89 12 18%
steady state growth rate. This results in the denominator of
Equation 3.2 being close to zero or even negative. In the short
interval stage I experiments 69% of all the data had to be thrown out
based on the 160 MPa limit. For the stage I's the short and long
interval techniques produced slightly different values for e2 and
greatly different values of ex. Because of the large percentage of
data points thrown out, data from the short interval experiments will
not be considered further.
To determine statistically if ex is significantly different
from e2 I will conduct a t-test on the stage IVb data. If the data
are not highly skewed a paired t-test will predict the probability
that the two data sets are identical. With the limit of 160 MPa, e2
exhibits a skewness (see Appendix D) of Sk =.068 + .35 which implies
25


a Z value of 0.19, this indicates that the probability of a normal
distribution is greater than 99%. With this limit a paired t-test
gives a probability of less than .001 that the two values are the
same with 45 data points. Using a broader limit of 0 now highly skewed with Sk =3.95 + .33 implying a Z value of 12.00.
In general absolute Z values of over 2.58 are not normally
distributed. This violates the t-test assumption that both data sets
are normally distributed or that 90% of the data lie within two
standard deviations of the mean. It is not possible therefore to use
the t-test in the 0 reason to assume that e2 should be normally distributed, the low
skew resulting from the 150 MPa limit intuitively reenforces the
assumption that the limit is valid.
Ortega et al. (1989) showed that the steady state growth rate
of stage IVb sporangiophores of phycomyces respond differently to
different sized step ups in pressure. Specifically it was found that
pressure step ups with magnitudes between 0.02 MPa and 0.031 MPa
produced temporary decreases in steady state growth rate and larger
steps produced permanent decreases. As was reported in Chapter Two,
similar behavior can be seen in stage I's. It can therefore be
argued that all multiple step experiments in which the step size
exceeds the limit of 0.02 MPa in stage IVb's and .01 MPa in stage
I's, require careful control experiments to determine exactly how the
steady state growth rate changes after the step. That assumes that
the changes in growth rate are repeatably precise enough to allow
meaningful calculations. For long interval experiments one could
argue against keeping successive steps in pressure unless it could be
shown that some specific steady state growth rate could be measured
after the first step. This most often occurs when m is positive. If
26


I consider only the data from steps where m remains positive (where
the growth rate does not decrease) I calculate the additional epsilon
values shown in Table 3.1 in the columns labeled m > 0.
Graphically illustrated in Figure 3.3 are normal distribution
based on the long interval data in Table 3.1. e is shown as
obtained in the long interval experiments for stage I (top), and
stage IVb (bottom). The data sorted on positive values of m are also
shown (lower curves).
Conclusion
The graphs in Figure 3.3 summarize the experiments and show
that the method which accounts for growth rates (e2) produces larger
values then that method which does not (ex) as predicted by Equation
3.2. A statistical t-test of the data gives a high probability that
the difference is significant. The data from the positive m
experiments are not significantly different from the values obtained
in the long interval experiments overall. In multiple step
experiments it is therefore not necessary to account for a change in
growth rate due to the previous pressure steps. I conclude therefore
that for the stage I e = e2 = 50.98 MPa + 48.77 MPa and for the stage
IVb e = 76.26 MPa +, 37.05 MPa.Most of the variation in e predicted by
Equation 3.4 occurs for P less than 0.2 MPa (Ortega et al. 1988a).
Unfortunately I found no sporangiophores with such small values of P.
This and the large standard deviations in the data make an e v.s. P
curve fit a stressful exercise in optimism. In Chapter Five,
existing methods for reducing P are reviewed and a new method is
developed and evaluated. These methods could make it possible to
determine if e is indeed a function of P in stage I and IVb
27


EPSILON SUMMARY. STAGE I
EPSILON SUMMARY, STAGE IVb
b) Stage IVb
Figure 3.3. Histographic summary of results
28


sporangiophores.
Due to the large number of rejected data points, I conclude
that for stage I sporangiophores, long time intervals (> 1 minute)
are required between step ups for success.
Zimmermann et al. (1978) states that pressure step ups should
not exceed 0.1 MPa if reliable measures of e as a function of P are
to be made. The stage I experiments were conducted with pressure
step-ups ranging in size from .007 MPa to .555 MPa and no clear
effects of pressure step size is visible in the data. The stage IVb
experiments were all conducted with pressure step-ups of 0.512 MPa or
0.535 MPa. That the large step sizes did not clearly impair the
experiments is probably due to the experiments being conducted in the
flat part of the e v.s. P curve.
If lg could be measured precisely, one could differentiate e
values inside and outside of the growing zone to build a differential
model of the cell. Consideration of this subject is presented in
Chapter Four.

29


CHAPTER FOUR
DYNAMICS OF THE STAGE I GROWING ZONE
Introduction
Previously several investigators (Gammow et. al 1977, 1981,
1986, 1987, Lafay et al. 1985) have measured growth velocities on
stage IVb sporangiophores. The method involved monitoring the
position of a single marker placed on the cell wall relative to the
top of the sporangiophore. Over time a marker placed near the top of
the cell can be seen to move downward.through the growing zone (G.Z.)
(upward through space) as material is added above. lg was
determined by finding the distance from the top of the G.Z. to the
point at which the marker's velocity became zero relative to a fixed
frame. In these papers and others going back to the 1930's (Castle
1940, Oort 1931) growth rate of the sporangiophore has been seen as
highly variable about a mean value.
Materials and Methods
In order to determine lg in the stage I, several corn starch
markers were placed on the stalk (see Appendix A) and monitored over
time. Since the stage I growing zone extends to near the apical tip
of the sporangiophore, lg may be determined by observing the
distance from the tip to a marker when that marker stops moving in
height. By using multiple markers scattered throughout the G.Z., it
should be possible to get some redundancy in the estimates of lg, to
reduce uncertainty, and to save time.


Results
Figures 4.1 4.3 show the results of the marker analysis. The
position of each marker relative to its position at time zero is
plotted versus time. At the bottom of each graph the initial
distance from each marker to the apical tip of the sporangiophore is
recorded in In Figure 4.1 a stage I to stage II transition
occurs where the expected behavior of the G.Z. is observed. Two
markers below the G.Z. initially (at 719 and 919 pm) remain in
approximately the same position for 80 minutes. The next marker
upward (initially at 523 Jim) moves up indicating that
523nm < lg < 719(im. The transition to stage II was first visible at
40 minutes and the G.Z. quickly moves up the stalk as the third
marker leaves the G.Z. at about 50 minutes, and the next two markers
stop moving at about 60 minutes. Typical values of lg ranged around
0.7 mm + 0.3 mm.
Figure 4.2 however shows a much different behavior more nearly
typical of the observations in general. Two markers within the
growing zone slow to zero growth rate at approximetly 50 to 60
minutes indicating an lg of approximately 680 and 420 \im.
Interestingly, the markers then begin to move downward indicating
that the sporangiophore has begun to shrink locally. The lower
markers move downward almost from the beginning of the experiment.
The total downward movement of 120 \im is far greater then the errors
in the measurements. In 28 experiments, this type of shrinking
behavior can be observed. These observation are also supported by 11
separate qualitative observations of pressure probe needles which
31


STAGE I OBSERVATIONS, JULY 12, 19B9
Figure 4.1. July 12 1989 Observations
-10 10 30 SO 7C BO 110 130 ISO 170
HC (min)
a TOP + 213 404 A 1E7S X 47S6 V 10 300
Figure 4.2. September 10 1989 Observations
32


STAGE ONE OBSERVATIONS, SEPT 6, 19B9
Figure 4.3 September 6 1989 Observations
bend down by 20 to 100 [im while impaled within a sporangiophore.
In Figures 4.2 and 4.3 sudden "jumps" in length can be seen
occurring over the entire monitored length of the sporangiophore.
For example in Figure 4.2 the lowest marker (10800 Jim below the tip)
moves upward by approximately 70 urn at 80 minutes while the top of
the sporangiophore moves upward by twice as much. This is repeated
at 160 minutes when the lowest marker moves up by approximately 50
jxm. Figure 4.3 shows a single jump at 20 minutes of between 40 and
100 jim. Initially it was believed that this was caused by a
movement in our equipment. Careful checking against a fixed target
ruled this out. Of the 31 marker experiments performed on stage I's
by myself 12 show some jumps in length. Since my initial observation
of this phenomena, numerous repeated observations have been
independently made in our lab. The effect is quite striking when
seen in a micro scope as the cell elongates by hundreds of
micrometers in 20 seconds to one minute. On two occasions these
33


jumps in length occurred while the sporangiophore was impaled and
turgor pressure was being monitored. In both cases P climbed slowly
by up to 0.01 MPa over a minute before the jump then dropped
abruptly. In most cases the steady state growth rate appears nearly
unchanged after the jump.
Analysis and Conclusion
The observation of a local shrinking zone at the base of the
stage I growing zone appears to be unique and has an important
implication for measurement of lg. With this region of local
contraction in length it is clearly not valid to measure the length
of the growing zone at the point of zero absolute marker velocity.
Since points below the zero velocity point may be moving downward it
follows that the intervening region must be elongating. Therefore I
conclude that the stage I growing zone is longer than previously
believed. This will produce corresponding errors in sizes of I
conclude therefore that the previous method of measuring lg, that is
by following a marker until it stops, is inadequate. This calls into
question all previous calculations of §g in growing sporangiophores.
Additional observations are called for define lg precisely in light
of these conclusions.
The jumps in length are interesting because they present a wide
array of theoretical problems. Current theories of plastic cell wall
deformation (Ortega 1976) describe growth as driven by enzymatic
breakdown of the cell wall. A jump would then require a rapid
increase in enzyme levels throughout the cell. Much more rapid than
existing transport mechanisms. If the jumps were to be described in
terms of elastic deformation, one would expect to see the steady
state P increasing, the jumps reversing themselves, or again have to
34


explain how e might change throughout the cell very quickly. While
P was monitored in only two cases, the similar behavior in each of
those cases is very suggestive. Further, since the cell returns to a
similar steady state growth rate after the jump, it appears as though
the mechanisms of normal growth are not involved in the jump. Such
behavior could be described by a static friction component within the
cell which allows elongation when P exceeds some critical level.
Since the behavior has only been observed in stage I's, which are
generally thicker then stage IVb's it might be that this is part of
the mechanism by which the stage I looses its excess width. It might
therefore be that the current growth equations could be augmented to
include a dependence on developmental stage and radius.
Once lg was known with accuracy, one could then examine
whether lg was an important parameter in sensory responses.
Further, my work has already shown that lg is important in plastic
deformation of the cell. If lg were precisely known one could then
determine how much elastic deformation occurred within the G.Z. as
opposed to within the non-growing zone; that is one could begin to
develop differential models of cell development.
35


CHAPTER FIVE
VERIFICATION OF THE PRESSURE PROBE TECHNIQUE
THE TWO PROBE EXPERIMENT
Introduction
Although theoretically the pressure probe should accurately
measure pressure, the technique has never been independently
verified. The time required for the cell to feel a change in
pressure applied from a pressure probe has never been determined. In
Chapters Two and Three (as in all of the pressure probe related
literature cited) it has been assumed not only that the probe read
true static pressure, but that instantaneous step changes in turgor
could be made.
Ortega (1988a) measures the values of e for stage Ill's and
found they follow Equation 3.4. Since the most significant changes
in e were seen to occur at low P it is frequently of interest to
reduce P within the cell. Two methods to produce steps down in P
require eliminating the rate of net water uptake by plucking, or
increasing the rate of transpiration. In such experiments P may
decay rapidly over many minutes or slowly over two hours (Ortega
1988, 1989) reaching some new equilibrium level. In practice it is
very difficult to hold turgor for an hour in stage IVb
sporangiophores and, due to the higher viscosity of cell sap,
extremely difficult in stage I and stage III sporangiophores. Also
in reducing the net water uptake, the pressure drop obtained is not
predictable and is limited in magnitude. In practice it is possible
to drop P by pulling the interface back into the pressure probe.


Unfortunately it is not possible to continuously monitor P with the
pressure probe's needle full of sap because the sap quickly thickens
and plugs the needle.
A third method of dropping P, raising the external atmospheric
pressure (Cosgrove 1988), requires baric isolation of the cell. For
this the apparatus must be contained within a pressure vessel which
is quite cumbersome for moderately complex experiments.
To address both the pressure probe's legitimacy and the low P
response questions, a sporangiophore could be impaled with two
pressure probes simultaneously. With one pressure probe used to pull
sap out of the cell, the second could continue to monitor P even of
the first became plugged. In such an experiment it could be
determined firstly if both pressure probes recorded the same value of
P in different parts of the cell, secondly if a step change in P by
one probe produced a rapid change in P as measured by a second, and
finally if e as a function of P followed Equation 3.4 for low values
of P.
Materials and Methods
Nine experiments were conducted in which P was measured in a
sporangiophore with two pressure probes simultaneously. In each case
a sporangiophore was impaled with one pressure probe and turgor
pressure was determined. Turgor was monitored with the first probe
for a period of a few minutes. If turgor was not constant
(indicating a leak or non equilibrium condition) the experiment was
terminated. To prevent the first probe from loosing control of its
interface and dumping oil into the cell, the pressure in the second
probe was brought up to just under the P value reported by the first
probe before the second impaled. After the second probe succeeded in
37


establishing an interface for a few minutes, one of the probes was
used to pull back its interface in an attempt to reduce P. The other
probe continued to monitor P.
Results
Figure 5.1 shows the output of the pressure probes during one
of the nine experiments in milli-Volts (mV) versus time. The
calibrations for the probes are listed in Appendix B. The value of
equilibrium turgor pressure measured in both of the probes for each
experiment can be seen in Table 5.1. Attempts to pull down the
pressure were only moderately successful. When a large volume of
cell sap enters the capillary, the sap tends to solidify within the
probe. Shown in Figure 5.1 is the July 10, 1990, experiment wherein
probe III pulls down the pressure by 8 mV (.20 MPa) and probe II
quickly decays by 11 mV (.18 MPa) to a new equilibrium value. Probe
II was then used to step up from the new equilibrium pressure while
probe III jammed and no longer recorded true turgor. The response by
probe II follows the pressure in probe III very closely. In other
experiments the similarity in dynamic response was not as clear.
These experiments were conducted by me, Scott A. Bell, and Mark A.
Espinosa.
Analysis and Discussion
The main difficulty in performing these experiments is finding
a workable geometry and two highly experienced and skilled pressure
probe operators.
38


39


Table 5.1 Pressure probe output
Date Probe II Probe III
MPa MPa
6/21/90 .339 .395
6/25/90 .365 .351
7/10/90 .367 .361
7/11/90 .423 .408
7/12/90 .456 .433
7/13/90 .428 .433
7/16/90a .450 .420
7/16/90b .459 .433
7/18/90 .525 .521
The standard method of analysis for data such as these is the
linear regression. A linear regression will produce a straight line
which best fits the data. The ideal regression equation obtained if
both pressure probes measured exactly the same data is PTII = PXI. A
reduced major axis linear regression of the data in Table 5.1 gives a
linear regression equation of Pjrr = .9875Pri- .007629 which is quite
close to the expected ideal. The regression gives a coefficient of
correlation between the data and the equation of 0.972 and a
probability of less than 0.0005 that PJT PJTJ. This indicates that
the pressure measured in both probes may be taken to be the same.
Conclusion
Based on the linear regression I conclude that the static
pressure measured by the pressure probe in one part of the cell is
indeed the correct value of turgor throughout the cell. From turgor
pressure traces similar to Figure 4.1 it appears likely that a change
40


in pressure created by one probe can be felt throughout the cell
within a very few seconds. Ideally additional control experiments
would be conducted with step increases in pressure to more precisely
determine the dynamics of the probe/sporangiophore.
This two probe technique adds a fourth method to reduce
pressure which, in theory, could yield a precise range of pressure
drops extending to zero. The technique could be of great use in
experiments to determine the extent to which the values of e follow
Equation 3.4 for low values of P since this is where the most
significant changes in e are thought to occur (Ortega 1988a). We
did not perform enough experiments to unambiguously determine e with
all necessary controls. For example, after dropping P one would in
principle like to determine precisely the effect on steady state
growth before beginning the pressure steps (as was done for step ups
in P by Ortega 1989 et al.). Although we did not conduct enough such
control experiments to produce reliable values for e, we have shown
that such experiments can be done.
41


APPENDIX A
GENERAL TECHNIQUES AND EQUIPMENT
Innoculation. Incubation, and Maintaenance
Growth media
The growth media is prepaired by combining 2.5 g of vitamin B
with 25 g of Potato Dextrose Agar, 7 drops of vegitable oil and 250
ml of distilled water. The solution is thouroughly mixed then heated
slowly to a boil. After boiling for four minutes the liquid is
poured into 2.5 cm shell vials. The vials are then sterilized in a
steroclave and allowed to cool slowly at room temperature. After
solidifying the vials are refridgerated untill needed. Unused vials
are cleaned and refilled after two weeks.
Innoculation and Growth
A concentrated solution of spores in distilled water (generaly
105 to 107 spores per ml) is diluted to obtain approximately 5 to 10
spores per drop. The resulting solution is heat shocked at 48C for
10 minutes and one drop is placed into each vial. The vials are
maintained at 20C in uniform cool white light and high humidity.
After stage IV sporangiophores appear the sporangiophores are plucked
back daily to leave only stage I's.
Growth Measurement
Marker Placement
To mark the sporangiophore, a small pair of tweezers was used
to grasp a quantity of cornstarch. By steadying the hand on the
pressure probe and stereo scope, small groups of starch granules


could be accurately placed on to the sporangiophore without
disturbing it. Marking is done before any growth measurements are
made so that the sporangiophore may be moved in the visual field of
the stereo scope with out affecting growth measurements. It is
essential that the markers consist of small numbers of granules. In
a large group, the adhesion of the group can cause errors in readings
because the motion of the marker may be due to motion of the
sporangiophore far from where the measurement is made. In addition,
large groups of granules in an active growing region will breakup and
spread out during growth producing ambiguity.
Measurement
Measurement of the marker position proceeds largely as
described below with one important modification. It is necessary in
measuring the marker positions that a sketch of the markers be made
indicating which part of a group of granules is to be measured.
Erroneous data would be generated if, for example, in alternate
measurements, the top and bottom of a group of granules were taken as
the same point.
Growth Scope
Growth measurements are made using a microscope attached to a
three axis micro-positioner. The micro-positioner is a Line Tool Co.
three axis stage (H-LH) with large barrel one inch metric micrometer
heads in the x and y directions (along the horizon, see figure A.l).
In the z direction (vertical) a Mitutoia digital micrometer is used.
A Bausch & Lomb microscope (48X) with cross hair is mounted to the
stage via a custom bracket. Two additional Narisige positioners are
used in the custom bracket to provide course adjustment in the y and
z directions. The three axis stage is mounted to the work station
43


via a single screw which permits further course adjustment (rotation)
in the X and Y directions.
Setup
Initially the X and Y axes micro-positioners are each set at
10,000um and the 2 axis digital micro-positioner is set near mid-
range. The stage is then rotated until aligned with the target. Next
the Z axis coarse adjustment is moved until the target appears in the
scope, then it is locked down. The image is then focused with the y
axis coarse adjustment. Finally at five seconds before the minuet,
the digital z axis is adjusted until the target is on the cross hair
and zeroed.
Measurements
Because the principal objective of the measurements was to
ascertain when the growth rate is steady, the initial measurements
were made in the following manner. At five seconds before the end of
the designated time interval the X, Y and Z axes are adjusted until
the target on the cross hair. The new position of each adjustment
screw is recorded and the Z axis positioner is zeroed. If marker
locations are desired, the distance from the principal target (the
top of the sporangiophore) to each marker is obtained by adjusting
the X, Y, and Z axes until the marker is in the cross hair, and
recording their positions. At the beginning of each experiment, the
width of the stalk is also measured at 1500 micrometers from the top,
using the difference in the X axis positions of each side. This
technique gives the operator the change in length during each time
interval and makes it quite simple to determine when growth is steady
and when the trop rate is excessive. There are three principal
disadvantages of this technique. First, it requires a good deal of
44


calculation to reconstruct the absolute position of the markers in
time, thus increasing the likelihood of error. Second, when the
growth-rate is small the accumulated error in round-off with each
zeroing becomes significant. Finally, the "Jump" behavior (described
in Chapter Four) cannot be distinguished from the operator forgetting
to zero the Z axis manipulator. Although understanding or describing
the "Jump" behavior was not the initial objective of this work, it
appears to be a significant part of the sporangiophore's behavior,
and therefore is worthy of study.
To eliminate the problems discussed above, the Z axis
positioner was not zeroed in later experiments. This required an
already busy experimentalist to calculate delta l's as the experiment
progressed and was deemed a reasonable trade-off.
Estimated Accuracy
+ 0.5 \im Z axis when measuring changes in length
+ 2.0 (Jim Z axis when measuring marker positions
+ 1.0 |im X axis
+ 5.0 Jim Y axis
Total Length Measurenent
Total length measurement was made by 'eyeballing' the
sporangiophor with one of several verniers. Although the instruments
could be read to + 50 Jim, uncertanty in the position of the agar and
mycleum probably limit these numbers by as much as + 2 mm.
Light Source
Schoelly Fiber Optic GMBH, Denelinger, West Germany Flexilux
90; HLU light source 90/w with a two-armed swan neck light guide.
45


Pressure Probe
Description
The pressure probe is mounted on a Line Tool Co. three axes
micro-positioning stage(H-RH) which in turn is mounted on a 2 inch to
9 inch scissor jack. The Probe body consist of three plexiglass
blocks glued firmly together. Through these blocks two small holes
have been drilled for oil channels. The first channel runs the
entire length of the block and holds a control rod (musical
instrument wire .053 inch Dia.). The second channel intersects and
is runs perpendicular to the first. The second channel is tapped to
mate with the pressure transducer (XT-190-300G). A small circular
depression is cut into the body around the top of the second channel
to provide an "O-Ring" seat for sealing the pressure transducer. The
'back' of the first channel is tapped to accept a threaded plug. The
plug is drilled concentrically to admit the control rod. On the
front of the first channel a cylindrical plexiglass block is glued
onto the main block and drilled concentrically. The cylinder is
threaded to admit a cap. This cylinder is the principal weakness of
the probe as the glue has given way on occasion resulting in small
leaks which dramatically affect the function of the probe.
The pressure transducer is a Klute semiconductor strain gauge.
(Max pressure 300 psig, input voltage 10.0 volts, output Z 420 ohms.
Because the transducer is a resistive device, a small climb in
pressure can be seen when the heat produced by the transducer heats
the oil and causes small thermal expansion. In fact the sealed probe
is a very sensitive thermometer and changes in room temperature are
easily seen when checking the probe for leaks.
Seals on both ends of the first channel are made with 1/8 inch
thick neoprene rubber cut into .285 inch discs and drilled
concentrically .035 Dia. When the cap and plug are tightened
46


against the seals into the probe body, all air is forced out and all
mating parts are put in compression. Errors in the concentricity of
all holes associated with the first channel, its plug, and cap result
in reduced life of the neoprene seals. Fortunately the seals are
cheep, easy to manufacture, and simple to change.
Calibration
The pressure probe is calibrated by supplying static air
pressure via a Norgren air regulator R08-300-RGMA to the probe. Air
pressure is monitored on a Heist bourdon tube pressure gauge CMM-
66101. The pressure transducer output is monitored on a six digit
Hewlet Packard multimeter 3490A (only the four most significant
digits are recorded) and an OnmiScribe chart recorder D5000. The
voltage of the pressure probe power source is also recorded.
Pressure is stepped up in five psi increments from room pressure and
the multimeter output is recorded after the system stabilizes at each
new pressure. When maximum line pressure is reached, the pressure is
stepped down and a second set of readings are taken at identical
points as the first group. The two sets of values are averaged and
fit to a linear curve. This provides the slope and intercept of the
Pressure v.s. millivolt calibration curve. The pressure probe is
recalibrated whenever the transducer is replaced and after and major
maintenance.
Needles
Micro capillary needles are produced using a KOPF vertical
pipette puller 720 which produces a consistently shaped needle from a
1.0 mm OD x 0.5 mm ID glass capillary.
47



Loading
To load the pressure probe the foam control knob is removed
followed by the rear probe mount screw, this allows the probe to
rotate approximately 70 degrees from vertical. The probe cap is then
removed and the old needle discarded. The front probe seal is
inspected and replaced if severely deformed or fragmenting. A 5cc
syringe with a 1cm needle is used to fill the probe channel with
paraffin oil while the control rod is backed out. Great care must be
taken to ensure that no air is entrained in the syringe before
filling the probe. As long as the probe is inclined and the syringe
needle tip is below the oil surface within the channel, no air can
become trapped in the probe channel as it is filled. As the syringe
needle is withdrawn a continuous flow of oil ensures that the probe
body is completely filled.
To fill the glass micro-capillary needle, a 2 inch by .002 OD
syringe needle is placed on a 5cc syringe loaded with 200 centi-stoke
oil (Dow Corning 200). All air is purged from the syringe and its
needle. A micro capillary needle is then chosen and measured. If
the micro-capillary is longer then the syringe needle it is broken
off, this is essential to minimize entrained air. The micro
capillary is inserted into the pressure probe cap and its seal. The
long syringe needle is then inserted into the capillary needle and
the capillary is filled. Some time must be allowed to pass to allow
all air to flow out of the capillary. Finally the syringe is
withdrawn while a continuous flow of oil from the syringe ensures no
air is left in the capillary. Once the capillary is loaded it is
simply inverted and the probe cap is screwed onto the probe body.
Surface tension and the oil displaced by the capillary within the
probe body prevent the final possible influx of air into the system.
48


Operation
When the pressure probe is first powered up the control rod is
moved in until an output of approximately 80 mV is obtained. The
release of stored elastic energy causes the pressure to decay
initially. The probe is allowed to sit until the pressure decay
stops. This provides a frequent check on the integrity of the
pressure seals in the probe. When the time to use the probe arrives,
the glass microcapillary needle is opened by brushing a tissue across
the tip. The size of this opening is absolutely critical to
achieving a successful experiment. If the needle is too small the
cell sap will coagulate and plug the tip. If the needle is too large
the pressure in the sporangiophore will decay rapidly, either because
of a leak or due to some "injury response" associated with the loss
of volume. The size of the needle can be accurately gauged based
upon the pressure decay rate when the needle is opened.
After the probe is ready it is aligned with the target
sporangiophore and the needle is brought in contact with it. The
silicon oil, which flows freely and rapidly back down the needle, is
immediately wicked onto the sporangiophore when oil contact is made.
The time at which oil contact occurred was recorded in order to
determine if the oil interfered with the growth rate (by reducing
surface transpiration of water). No such interference was seen.
When the probe's pressure is decayed below the minimum likely
turgor pressure, the needle is gently driven into the sporangiophore.
Since the cell sap in the cell is at a higher pressure then the oil,
the oil is forced back and sap flows into the probe needle. With
luck an oil/cell sap interface is visible in the needle and can be
driven back to the cell wall by adjusting the control rod.
Alternately, the oil and sap may mix, in which case the experiment
must be terminated. Once the pressure in the probe is sufficient to
49


hold the interface at the cell wall, the pressure probe is reading
equilibrium turgor pressure. If the interface should become immobile
then it could support a pressure gradient and therefore, the measured
pressure would not be accurate. To prevent this, the interface is
held slightly away from the cell wall and constantly moved back and
forth slightly to ensure that it is loose.
In the coarse of this work it was frequently necessary to
increase the pressure within the cell slightly. Frequently when
doing this it was found that the interface would move down the needle
and become stuck at the tip. It was found that a small over pressure
initially which forced oil into the cell, would insure that the
needle remained open without adversely affecting the growth.
Accuracy
See Chapter Five.
Electronics
The pressure probe is powered by a 10 volt DC regulated power
supply. The pressure probe output is monitored on a Hewlit Packard
six digit multimeter (3490A) and an OmniScribe strip chart recorder
D5000.
50


APPENDIX B
SUMMARY OF RESULTS
Stage I Experiments
Step up experiments with single steps or multiple steps over
intervals greater then 1 minute.
DATE P A P m e2
UNITS MPa MPa MPa MPa
MPa min
1989
10/25 .4472 .0260 23.1 30.62 306.24
10/13 .4495 .0256 101.6 438.59 1075.79
10/8 .0256 7.8
10/6 .3740 .0256 26.43 45.01
10/1 .4175 .0384 49.55 208.13
9/29 .3996 .0064 3.84 8.35
9/20 .5399 .0064 7.20 19.13
.0064 9.42 40.82
8/3 .5272 .0064 109.4 4.04 28.85
.0077 4.54 22.03
7/30 .0077 13.0
7/27 .3843 .0064 3.30 4.36
7/25 .5374 .0102 284.1 12.43 124.31
.0076 14.39 105.18
7/23 .4302 .0077 519.5 4.10 35.87
7/22 .4111 .0077 389.6 7.92 31.19
7/02 .5610 .0102 500.0+* 8.86 48.14
.0096 7.69 35.79
7/01 .0064 46.9+
6/06 .4596 .0111 31.25* 8.92 107.04
6/03 .4209 .0111 14.82 42.71
.0555 6.22 9.19
5/31 .3592 .0155 39.26 128.04
.0422 72.66 185.89
.0444 35.06 48.63
5/17 .0179 37.9+
+ Second step also yielded a phi value
* Additional dataGZ
Step up experiments with multiple steps over intervals less then 1
minute.
10/13 .4495 .0128
10/25
9/20


Stage IVb Experiments
One Half Bar steps (0. 512 unless otherwise noted)
on 60 Second intervals
DATE P c equl dl dt equl dl afcei ei
MPa MPa MPa
min min
(1990) 5/30a .545 32.2 75 15.20 83.6*
5/30b .560 37.4 63 36.15 112.2
5/31 .545 20.3 168 6.70 22.8
6/la .521 29.8 78 11.16 18.1
6/lb .567 36.9 54 19.34 61.1
6/6 .566 25.2 36 27.73 92.4
6/7 .497 19.6 41 23.73 45.5
6/8a .535 20.6 33 18.77 50.0*
6/8b .524 18.6 33 29.17 66.8
9/8a .500 22.5 34 28.6 92.6*#
9/8b .486 27.0 50 21.82 54.0#
9/8c .409 33.0 66 16.24 39.1#
N = 12
1 Noncompensated values (Equation 3.3)
2 Growth compensated values (Equation 3.2)
Values from first step only
#Step size 0.536 Bar
52


Two Probe Experiments
DATE PROBE II PROBE III
OPERATORS
mV MPa mV MPa
6/21/90 28.5 .399 21.5 .395 SAB, MAE
6/25/90 25.9 .365 18.9 .351 SAB, MAE
7/10/90b 30.4 .367 22.3 .361 SAB, MAE
7/11/90 33.0 .427 23.8 .408 SAB, MES
7/12/90 26.0 .456 19.5 .433 MAE, MES
7/13/90 30.8 .428 23.8 .433 SAB, MAE
7/16/90a 32.5 .450 24.0 .420 SAB, MES
7/16/90b 33.2 .459 23.8 .433 SAB, MES
7/18/90 38.4 .525 29.0 .521 SAB, MAE
OPERATORS
SAB Scott : A. Bell
MAE Mark A. Espinosa
MES Martin E. Smith
PROBE CALIBRATIONS
Probe II P = 0.0128 * V + 0.0338 MPa
Probe III P = 0.0168 * V + 0.0666 MPa
Where V is output voltage in mV, P is i turgor pressure in MPa
MES
53


THE LENGTH OF THE GROWING ZONE
6/ 1/89
6/ 2/89
6/ 3/89
6/ 5/89
6/ 6/89
6/ 8/89
6/10/89
6/28/89
2 experiments
2 experiments
2 experiments
7/ 1/89
7/12/89
7/13/89
7/15/89
7/16/89
7/19/89
7/20/89
3 experiments
2 experiments
2 experiments
8/ 4/89
9/ 06/89
10/ 8/89
DISCONTINUOUS INSTANTANEOUS CHANGES IN GROWTH RATE
"JUMPS"
3/19/89
4/ 4/89
4/ 5/89
5/16/89
5/18/89
5/30/89
5 31/89
6/ 3/89
6/ 9/89
6/12/89
6/27/89


APPENDIX C
DERIVATIONS
Chapter II
A^Z=d>(p-p)+A dP
V dt c> e dt
Equation 1.1
At constant P
dP
dt
0
For a sporangiophore changes in radius r are much much smaller then
changes in length 1, so that...
1 dV_ 1 d(nz2l) 1 dl
V dt nr2l dt 1 dt
Then Equation 1.1 becomes...

Equation 2.1
Since the growing zone is defined as the region where all
irreversible extension occurs...
= 4>*
Assuming that lg is approximetly constant and solving for the
irreversible extension rate ..


We may define the relative irreversible extension rate m as...
Then
-f-(P-Pc)
Equation A
Discretizing the derivative we may now solve for Pc
Pc=P-(-|4-)
c At m
Equation 2.3
Taking the differential of Equation A...
A-^-=A {mP) A (mPc)
dt c
Again discretizing the derivative and assuming that m and Pc are
constant I may solve for m
m=
a<44>
A P
Equation 2.2
Chapter III

5^(p-p=)+tI
Equation 1.1
Substituting 1 for Vc as before and isolating the right hand term...


1 dP
e dt
Unlike the previous experience with plastic deformation in Chapter 2,
elastic deformation occures over the entire length of the
sporangiophore. The value of e is probably different in the growing
zone then it is in the nongrowing zone. Due to the problems involved
56


in measureing the length of the growing zone (see Chapter 5) we may
only know the BULK value of e at this time. Since the change in
length durring an experiment is on the order of one in one hundred,
we may take 1 to be a constant 10. Now, solving for e
e=
dP
dt
AL-i, (P-P )
1 dt c>
Equation 3.1
Substituting in and assuming no growth i get eg 3.2
t Test
Staticstics
t =
X-V0
Vn
Where X is the mean of the test data, p.0 is the mean of the control
data, a is the standard deviation of the test data, and n is the
number of samples.
Skewness
Sk = 3 SJ-M)
CT
Where Sk is the skewness, and M is the median of the data.
Z
Z= M
s
Where s is the standard error of Sk.
57


GLOSSARY / SYMBOLS
G.Z. Growing zone The total region of plant cell involved in
growth.
In Vivo Within a living organism.
L Hydraulic Conductance The ability to conduct water, inverse
of hydraulic Resistance.
I Length Length of the sporangiophor from the mycleum to the
tip, in micro-meters.
lg Length of the growing zone.
10 Initial length of the sporangiophore at time zero
m Irreversible cell wall extensibility A measure of the ability
of the cell wall to deform plastically, or relative plastic
strain rate over stress.
T Relative Transpiration Rate Evaporative water loss per unit
length and time.
P Turgor Pressure Gauge pressure of the plant cell sap.
Pc Critical Turgor Pressure Minimum turgor pressure required to
elicit growth. Analogous to static friction.
Relative Per unit length or per unit volume.
t Time.
V Volume of the cell contents.
Vc Volume of the cell wall chamber.
v Relative rate of volumetric expansion of the cell wall chamber.
Y Yield threshold - Same as Pc.
A Delta Discreet, finite changes in a variable.
II Osmotic Pressure The pressure that must be applied to a
solution to just prevent osmosis. (Webester, 1973)
e Volumetric elastic modulus A measure of the ability of a
material to deform reversibility, or elastic strain over
stress.
H micro 10'6.
a Solute Reflection Coefficient Average osmotic efficiency of
all solutes: Oso^l..


a Solute Reflection Coefficient Average osmotic efficiency of
all solutes:
]) Relative irreversible cell wall extensibility m divided by
the total length of the sporangiophor.
(j)ff Irreversible cell wall extensibility relative to the length of
the growing zone m divided by the length of the growing zone.
59


I
BIBLIOGRAPHY
Bergman K, Burke PV, Cerda-Olmedo E, David CN, Delbruck M, Foster KW,
Goodell EW, Heisenberg ZM, Meissner G, Zalokar M, Dennison DS,
and Shropshire W, Jr. (1969) Phycomyces Bacteriological Reviews
33:99-157
Castle ES (1940) Discontinous growth of single plant cells measured
at short intervals, and the theory of intussusception. J. Cell
Comp. Physol. 15:285-298
Cerda-Olmedo E ,Lipson E (1987) A biograph of Phycomyces. In
E Cerda-Olmedo, E Lipson, eds, Phycomyces, Cold Springs Harbor
Laboratory, Cold Springs Harbor, pp 7-26
Cosgrove DJ (1988) Mechanisms of rapid suppression of cell expansion
in cucumber hypoctyls. Planta 176:109-116
Cosgrove DJ, Ortega JKE, and Shropshire W 1987 Pressure probe
study of the water relations of Phycomyces Blakesleeanus
sporangiophores. Biophys. J. 51:413-423
Dainty J, Vinters H, Tyree MT (1974) Membrane transport in plants.
Zimmermann and Dainty, eds, PP 59-63 Springer-Verlag Berlin,
Heidelberg, New York.
Gammow IR, Bottger B (1977) Phycomyces: Distribution of growth
velocities in the growing zone. Plant Physol. 59:901-906
Gammow IR, Bottger B (1981) Phycomyces'. Irregular growth patterns in
stage IVb sporangiophores. J. Gen. Physol. 77:65-75
Gammow IR, Geer GA, Bottger B (1986) Phycomyces: Fine structure
analysis of the growing zone. Plant Physol. 80:721-726
Gammow RI, Ruiz-Herrera J, Fischer EP, (1987) The cell wall of
Phycomyces. In E Cerda-Olmedo, E Lipson, eds, Phycomyces, Cold
Springs Harbor Laboratory, Cold Springs Harbor, pp 223-246
Green PB (1968) Growth physics in Nitella: A method for in vivo
analysis of extensibility based on a micro-manometer technique
for turgor pressure. Plant Physol. 43:1169-1184
Green PB, Erickson RO, and Buggy J (1970) Metabolic and physical
control of cell elongation rate. 47:423-430
Lafay JF, Matricon J (1985) Observation of growth ,rate fluctuations
in Phycomyces Blakesleeanus using a high resolution automated
measuring system. Physol. Ve'g. 23:929-934
Lockhart JA (1965) An analysis of irreversible plant cell
elongation. J. Theor. Biol. 8:264-275


Ortega JKE, (1976) Phycomycess The mechanical and structural dynamics
of cell wall growth. PhD Thesis. University of Colorado,
Boulder
Ortega JKE, (1985) Augmented growth equations for cell wall
expansion. Plant Physol. 87:11-14
Ortega JKE, (1990) Governing equations for plant cell growth. Physio.
Plantarum 79: 116-121
Ortega JKE, Gamow RI (1976) An increase in mechanical extensibility
during the period of light-stimulated growth.
J. Plant Physol. 57:456-457
Ortega JKE, Gamow RI and Ahlquist CN (1975) Phycomyces: A change in
mechanical properties after a light stimulus. J. Plant Physol.
55:333-337
Ortega JKE, Keanini RG, and Manica KJ (1988a) Pressure probe
technique to study transpiration in Phycomyces sporangiophores.
Plant Physol. 87:11-14
Ortega JKE, Manica KJ, and Keanini RG (1988b) Phycomyces: Turgor
pressure behavior during the light and avoidance growth
responses. Photochemistry and Photobiology 48:697-703
Ortega JKE, Smith ME, Erazo AJ, Espinosa MA, Bell SA, Zehr EG (1991).
Comparisons of cell wall extensibilities in Phycomyces. Physio.
Plantarum, in press
Ortega JKE, Zehr EG, and Keanini RG (1989) In vivo creep and stress
relaxation experiments to determine the wall extensibility and
yield threshold for the sporangiophores of Phycomyces. Biophys.
J. 56:465-475
Zimmermann U, Steudle E (1978) Physical aspects of water relations of
plant cells. Adv. Bot. Res. 6:45-117

61


Full Text

PAGE 1

BIOPHYSICAL PARAMETERS IMPLEMENTING GROWTH CONTROL IN PHYCOMYCES by Martin Eliot Smith A.A.s., Ferris State College, 1978 B.S., University of Colorado at Denver, 1988 A thesis submitted to the Faculty of the Graduate School of the University of Colorado at Denver in Partial fulfillment of the requirements for the degree of Master of Science Department of Mechanical Engineering 1990

PAGE 2

This thesis for the Master of Science degree by Martin Eliot Smith has been approved for the Department of Mechanical Engineering by

PAGE 3

FIGURES Figure 1.1. Sporangiophore Morphology .......... 6 Figure 1.2. Sporangiophore Development ... ? Figure 1.3. Pressure Probe Schematic Diagram ... 8 Figure 2.1. July 1 1989 Experiment 13 Figure 2.1. August 3 1989 Experiment 14 Figure 3 .1. July 1 1989 Experiment .... 22 Figure 3.2. June 2 1990 Experiment . 2 6 Figure 3.3. Histographic Summary of Data . 28 Figure 4.1. July 12 1989 Observations ..................... 32 Figure 4.2. September 10 1989 Observations 32 Figure 4.3. September 6 1989 Observations . 33 Figure 5.1. Two Probe Experiment Pressure Trace ..... 39 vi

PAGE 4

Table 2 .1. Table 3 .1. Table 5.1 TABLES Summary of Experiments .. l6 Values of e ..... 25 Pressure Probe Output ... 38 vii

PAGE 5

ACKNOWLEDGEMENT How shall we believe you, then, good when you say, 'We allow none to be educated but the free'? For the philosophers say 'We allow none to be free but the wise'; that is, God does not allow it. -Epictetus (Disclosures, II.i.) Thanks to . My Friends: Lillith Justine Graeme, Donna Moxley, Julianne Stall, and others, for their support. Dr. J. Kenneth E. Ortega, who thinks first, and always makes the time to do the job right; and the other members of the thesis commitee: Dr. William H. Clohessy, Dr. John A. Trapp. The crew in the lab for technical support, feedback, independent reproduction of results, and physical assistance with some of the more demanding experiments: (in chronological order) Keith J. Manica, Edwin G. Zehr, Mark A. Espinosa, Scott A. Bell, and A. Jeanette Erazo. Mark A. Espinosa, for the Chapter One graphics; Allen E. Johnson, statistician extraodinaire; and Hannah J Kelminson, for editorial assistance. The Club Natural Philosophy for encouraging student interest in research within a difficult environment. Ed Lipson and Walt Shropshire for taking time to visit our lab and contribute some of their experience. This work was supported by National Science Foundation (Grant# DCB-8801717 to Dr. J.K.E.Ortega), and indirectly by the University of Colorado (Colorado Graduate Grant), and the UCD College of Engineering (Deans Scholarship). viii

PAGE 6

CHAPTER ONE INTRODUCTION General The most vital and pervasive interaction between man and the biosphere is agriculture. Science has impacted agriculture mainly through the application of principles discovered in the field of plant physiology. Past improvements in farming have resulted from improved understanding and control of the plant's external environment, mechanization, and trial and error breeding. The field of plant physiology has focused on efforts to describe and understand the morphology, growth, development properties and behaviors of plants. At the other extreme, biochemistry and physical chemistry seek to produce a detailed understanding of the mechanisms by which light and simple molecules are converted into life. Indeed genetic manipulation is now beginning to describe biological systems in unprecedented detail. As scientists attempt to extend microscopic mechanisms to macroscopic behaviors, they have discovered limitations in predicting and describing large-scale phenomena. It follows that before the extrapolation of these microscopic mechanisms can be successful in modeling macroscopic behaviors, the intermediate scale of cell function must be understood. It is not sufficient to describe macroscopic behaviors on a purely qualitative level, the transition to quantitative modeling must be made. Only through quantitative modeling can the individual parameters be isolated and studied. It is now possible to do so on the scale of the plant cell itself, that is to model the biophysical aspects of the transport of water, the behavior of the cell wall, and the effects of cell wall

PAGE 7

growth and sensory responses (Ortega 1990). This type of study is J particularly well suited to engineering and material science. When the governing principles are discovered and enough data are compiled, complete systems models may be developed and integrated with microscopic data. Only then can biology become a truly quantitative science. A major objective of the work in our laboratory is to construct a quantitative model which describe and predict plant cell growth rate and its regulation. Previous work (Lockhart 1965) has produced two equations termed the Growth Equations which have been subsequently augmented (Ortega 19851 Ortega et al. 1988a). This thesis will specifically study the changes in cell wall properties throughout different stages of cell development. The results can be used to determine the magnitude and behavior of parameters in one of the Growth Equations. Theory The rate of cell enlargement is the result of two simultaneous and interrelated physical processes: the net rate of extension of the cell wall, and the net rate of water uptake. Lockhart (1965) proposed that these processes could be modeled with two equations under equilibrium conditions. First, the irreversible cell wall extension is modeled as a Newtonian dashpot. Plastic deformation of the cell wall results from the application of a force via constant turgor pressure, P. Ortega (1985) augmented this equation with a term to account for reversible extension--the case of variable P. The resulting equation is similar to that of a linear Maxwell model, that is an elastic and viscous element in series: 1 dP cJ> ( P P c) + edt 2 Equation 1.1

PAGE 8

Where v is the relative rate of change of volume of the cell wall chamber, Vc is the volume of the cell wall chamber, t is time, is relative irreversible cell wall extensibility, Pc is the critical turgor pressure (or Y the yield threshold), and e is the volumetric elastic modulus. Equation 1.1 then states that the relative rate of change in volume of the cell wall chamber is the sum of plastic cell wall deformation (proportional to P) and elastic cell wall deformation (proportional to the change in P). The second equation models the net rate of water uptake. Lockhart's (1965) equation assumed that the cell's growth rate is directly proportional to the rate of water uptake. Ortega et al. (1988a) augmented this equation to include water loss through transpiration: v = = L (a an -P) t. Equation 1. 2 Where Vis the volume of the cell contents (mostly water), Lis the relative hydraulic conductance of the cell membrane, a is the solute reflection coefficient, an is the osmotic pressure difference in the uptake region of the cell membrane, and T is the relative transpiration rate. Equation 1.2 states that the relative rate of change of volume of the cell contents is equal to the difference between the osmotic water uptake and the transpiration water loss. These two equations are coupled by P and equal to one another because the volume of the cell wall chamber is equal to the volume of the cell contents. Taken together these equations are referred to as the "augmented growth equations" (Ortega et al. 1988a, 1988b; ortega 1990). 3

PAGE 9

The terms in the equations are quite difficult to evaluate in a multicellular plant. A single plant cell in a multicellular plant might be only in diameter, with its function and behavior closely related to its physical position within the plant. Material and water are exchanged with surrounding cells, while transpiration and water uptake occur in numerous pores and capillary channels. The cell might also grow in highly irregular directions while under tension, compression, torsion and shear loads (Zimmermann 1978). Under such conditions it is difficult to isolate the governing parameters. To avoid these problems work has been done on single celled plants (Cerda-Olmedo and Lipson 1987). In an isolated single cell plant the volumetric growth, and turgor pressure can be directly measured in vivo without altering the plant's normal growth (Cosgrove et al. 1987, Ortega et al. 198Ba, 1988b, 1989). Water uptake and transpiration can also be controlled within qualitative extremes (Ortega et al. 1988a). Furthermore, stress may be applied to the cell wall mechanically or by changing turgor (Ortega 1976, Ortega et al. 1988b, 1989). The algal cells Nitella (Green 1968; Green et al. 1970) and Chora (Dainty et al. 1974) as well as the fungal cell Phycomyces (Cosgrove et al. 1987; Ortega et al. 1975, 1976, 1988a, 198Bb, and 1989) have been studied by in vivo creep and relaxation tests. In the in vivo creep test a fixed stress or stress rate change is applied to the cell wall and the resulting change in strain (growth) rate is measured. In the relaxation test a fixed strain is imposed on the cell wall and the resulting stress decay rate (turgor pressure change) is measured. In vivo creep measurements have been conducted on stage IVb sporangiophores of Phycomyces blakesleeanus by Ortega et al.(1989) using a pressure probe technique, and on Nitella by Green 4

PAGE 10

(1968) and Green et al. (1970) using changes in osmotic pressure. The results obtained are consistent with the Maxwell model over the specified range, and give numerical values for the wall extensibility and yield threshold. The in vivo stress relaxation tests were conducted by Ortega (1976) using an Instron tension/ compression machine, and using a pressure probe technique (Ortega et al. 1989). Some of these measurements have also provided numerical values for yield threshold. Phycomyces Blakesleeanus, Development and Morphology The sporangiophores of Phycomyces blakesleeanus are an ideal organism for macroscopic experimental work on plant cell mechanics (Bergman et al. 1969; Cerda-Olmedo and Lipson 1987). The Phycomyces sporangiophore is a single-celled fungus which can grow up to 100 mm in length and is typically 200 in diameter. With large growth rates (up to 80 and rapid sensory response times (10 to 30 minutes) experiments can be completed in reasonable time frames and with readily available equipment. The sporangiophore is a cylindrical, multi-nucleated, single cell (see Figure 1.1). A large cylindrical vacuole runs the iength of the sporangiophore, the contents are approximately 85% water (Olmedo and Lipson 1987). Specifically the vacuole is filled with cell sap and the products of metabolic activity. The contents of the vacuole are separated from the cytoplasm by a membrane called the tonoplast. The tonoplast has very little mechanical strength and serves primarily as a valve, pumping materials into and out of the vacuole as needed. Surrounding the tonoplast is a cytoplasmic layer containing all major organelles; this where the majority of metabolic activity takes place. Finally the cell membrane and thick cell wall 5

PAGE 11

separate the cell contents from the outside world. The cell wall is a composite material made of chitin microfibril imbedded in an amorphous chitosan matrix. Mechanically, the cell wall is the strongest part of the cell and provides its principal means of support and protection. Water is released through the cell wall and transpires into the atmosphere. It has been observed (Cosgrove et TONOPLAST SPORAGWM Figure 1.1 Sporangiophore Morphology CYTOPLASM LAYER al. 1987) that the porous cell wall acts as an additional reservoir of water for the cell. Phycomyces exhibits five distinct stages of growth three of which are relevant to this paper (Bergman et al. 1969; Cerda-Olmedo and Lipson 1987, see Figure 1.2). After inoculation on an appropriate growth media (see Appendix A), a thick mat of interlaced hyphae grow out across the media forming a mycelium. Two to three days after inoculation aerial hyphae begin to grow upward forming the stage I sporangiophore. The stage I sporangiophore is a circular cylinder typically 200 in diameter tapering to an apical tip. Longitudinal growth in this stage occurs between the apical tip and 500 to 1500j.1m below (termed the "growing zone"), at a rate of between 5 and 20 j.lmmin-1 Points on the cell wall in the growing zone move around the cell and upward in a left hand spiral (termed 6

PAGE 12

STAGE IVb STAGE IVa STAGE III STAGE II APICAL TIP Figure 1.2 Sporangiophore Development "left-handed spiral growth"). After several hours longitudinal growth slows and the top of the sporangiophore forms a sphere or sporangium. The period of spherical growth is termed stage II. After the sporangium is formed there is a period during which little or no growth occurs; this is termed stage III. After a few hours growth resumes in a right hand spiral {stage IVa). About 90 minutes later growth reverses into a left hand spiral without interruption of growth {stage IVb). The reversal of rotation has been analyzed to yield subtle details of the cell wall's behavior {Ortega 1976). Longitudinal growth in stage IVa begins slowly and accelerates reaching maximum values in stage IVb where growth rates can be as high as 80 As stage IV progresses, the sporangium changes color from a bright yellow to green then darkening to black as approximately 105 spores mature within the sporangium. When the sporangium is broken the spores are 7

PAGE 13

released and the sporangiophore generally dies. The total life cycle described here involves about four or five days. Pressure Probe The pressure probe technique for measuring turgor pressure is well established (Zimmermann et al., 1978; Cosgrove et al., 1987; Ortega et al., 1988a, 1988b and 1989). The pressure probe (see figure 1.3 and Appendix A) consists of a glass micro-capillary and pressure chamber filled with an incompressible and biologically inert silicone oil. The pressure in the chamber is measured with a PRESSURE TRANSDUCER 0-RING SEAL SILICON OIL PLASTIC BODY Figure 1.3 Pressure Probe Schematic Diagram pressure transducer in contact with the oil. The chamber volume can be adjusted by advancing and retracting a control rod (plunger). When the plant cell is impaled by the micro-capillary the turgor pressure pushes cell sap from the vacuole into the capillary and a visible oil/cell sap interface is formed. If the micro-capillary is correctly sized and very stable, sap escaping between the capillary 8

PAGE 14

and cell wall will quickly seal preventing leaks. Advancing the control rod allows the interface to be moved, displacing the cell sap from the capillary. When the interface is adjacent to the cell wall, the pressure in the chamber is equal to the turgor pressure. Should the interface become stuck the measured pressure would be in error. Frequent movement of the interface will generally ensure that pressure measurements remain accurate while reducing precision only slightly. Thesis Preview In Chapter Two, in vivo creep experiments are conducted wherein the cell wall extensibility and yield threshold of stage I sporangiophores of P. blakesleeanus are measured and compared to previously obtained values for stage IVb using the same in vivo creep technique (Ortega et al. 1989). It is shown that growth rate is a function of the cell wall extensibility, and that the cell wall extensibility is a function of the length of the growing zone. Extensibility per unit length of the growing zone appears to be nearly constant. In Chapter Three experiments are conducted wherein the volumetric elastic modulus of growing stages I and IVb sporangiophores of P. blakesleeanus are measured and compared with previously measured values from non-growing stage III sporangiophores. The use of methods proposed by Ortega (1985) but as yet untested, to calculate the elastic modulus of growing cells, are used and evaluated. The method appears to be most successful when steps in pressure are given with long time intervals between steps. In Chapter Four the results of a study of stage I growing zones are presented. The length of the growing zone is found to be greater 9

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than had been previously thought. Previously developed techniques for measuring the length of the growing zone are shown to be insufficient. The dynamic behavior of the growing zone is found to be more complex than previously described. In Chapter Five an independent test of the pressure probe technique is presented which supports the validity of the technique. The dynamic response of the pressure probe/ sporangiophore system is examined. The test has potentially important applications for further experimentation. 10

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CHAPTER TWO CELL WALL EXTENSIBILITY Introduction Considering equilibrium growth (constant P) in the longitudinal direction only, the Augmented Growth Equation for cell wall extension (Equation 1.1) can be written for the growing zone (see Appendix C) as 1 dV 1 dl = = lg dt Defining m as the irreversible wall extensibility equal to $glg, and assuming that m and Pc are constant, I may discretize derivatives and take the differential. Now, solving for m, Equation 2.1 With m known, Pc may be found. p = p -( ill ) J:. c ll.t m Equation 2.2 as was shown by Ortega et al. (1989). The equations are now in a form amenable to experimentation. The longitudinal growth rate and its changes can be measured with a micrometer, the turgor pressure and its changes can be measured with a pressure probe.

PAGE 17

Materials. and Methods A detailed description of all apparatus used in these experiments, and the procedures for growing sporangiophores and measuring their turgor pressure is provided in Appendix A. Experimental Protocol Stage I sporangiophores of Phycomyces were selected and placed under a broadband cool light at 21 1 DC. A growth scope (see Appendix A) was used to measure changes in length. The length of the sporangiophore was monitored for at least one half hour until steady state growth was observed. When steady state growth occurred, length measurements were taken every 1 or 2 minutes. If the growth rate remained steady for 10 to 20 minutes, the sporangiophore was impaled and turgor pressure was measured with the pressure probe. The growth rate was monitored for an additional 5 to 10 minutes to ensure that it had not been influenced by the measurement of P. At the end of this time a step up in pressure was produced by injecting oil into the sporangiophore. With the pressure held at a fixed value, growth measurements were continued for at least 30 minutes. Results Figures 2.1 and 2.2 show two typical experiments. The turgor pressure, is plotted in the upper graph (a). The lower graph (b) in each figure is a plot of length versus time. The main events in the protocol are marked an the graphs as they occurred in time. Figures 2.1 b and 2.2 b show an increase in growth rate (slope) following the step increase in turgor pressure. These results are typical of the eight experiments conducted by me and the seventeen experiments analyzed herein (the remaining experiments were conducted by Scott A. 12

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..... E u ..., !. ::: !l a: 0 (.!) a: :::> ll a) Turgor pressure trace t' STEP U? EX?ERIMENT JULY 01, 1989 I I I I I I I [; I I I I I I 1//f I I I I I I 1e I I ' I I I I lA I I I I I vr I I I I I I I I I V1 I I I I I I I ' 100 ,40 160 1BO lame {min) 1 STEP 1 5TEP 2 IMPALE b) Growth rate versus time Figure 2.1. July 1 1989 Experiment 13

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a) Turgor pressure trace ST::? U? 8C?::RilvENT AUGUST 3, 1989 I I I I I I I I I I I 1/ I I I I I I I I I I I.A I I I I I I I I I l......f I I I I I I I I I ,...( I I I I i I I I I W'"'l ..... I I I I I I I VI I 0 I I I I I I I I I/! I I I I I / I I I I I l? I I I I I 1/1 I I I I 1/1 VI I . :ZO I I I I I I I I f 1 so o40 To-lmin) I I 5TEP .1 IMPALE b) Growth rate versus time I I I I I I I eo Figure 2.2. August 3 1989 Experiment 14 I I r I I I I I I I I I I I I 100 I I I I I I I I I I I

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Bell, A. Jeannette Erazo, Mark A. Espinosa, and Edwin Zehr). Analysis The extensibility was calculated using the difference in the average growth rate for a period of 5 or 10 minutes before and after the step and dividing that value by llP (see Equation 2.1). For example in the experiment shown in Figure 2.1 the averaged growth rate increases by 0.3 min-1 after a step of 0.010 MPa yielding an m value via Equation 2.1 of 46. 9!-Lm MPa -l Min-1 Table 2.1 summarizes the results of these experiments. The value obtained for the extensibility m, in the 17 experiments analyzed is 116 19!-L MPa-1 min-1 (mean standard error). Pc was calculated using the average growth rate for the period before the step up since the growth rate, m, P and Pc, are constant for this period. Extending the above example from the Figure 2.1 experiment, P was measured as .390 MPa yielding a Pc via Equation 2.2 of .249. Table 2.1 summarizes these results also. The mean value obtained for Pc, in the 17 experiments analyzed is 0.4 0.03 MPa with n = 17. Finally, may be calculated given lg. From growing zone measurements lg is taken to be approximately 0.70 mm (see Chapter Four). As was reported for stage IVb's (Ortega et al. 1989), a decrease in steady state rate growth was seen to occur after sufficiently large steps in pressure (greater then 0.02 MPa). Similar decreases can be seen in some of the stage I experiments discussed herein. Data from such experiments result in negative values of m and were not used in the analysis presented here. These experiments indicate that in stage I's the threshold of pressure 15

PAGE 21

above which steady state growth rate drops is between 0.010 MPa and 0.006 MPa, less than that of stage IVb's. Discussion Ortega et al. (1989) measured m, and g in stage IVb sporangiophores of Phycomyces, these values together with those we obtained for stage I sporangiophores are shown in Table 2.1. The values of m obtained for stage I are approximately one tenth of those obtained for stage IVb. However when divided by the length of the growing zone (lg) to obtain g the resulting values differ by only a factor of two. Table 2.1 Summary of experiments Parameter Stage I ( 1) Stage IVb (2) (Units) Mean + SE (3) Mean + SE dl (llm min 7.1 0.7 34.1 3.1 dt m (J..Lm MPa-1 116 19 997 164 Pc (MPa) 0.4 0.03 0.26 + 0.01 p -Pr: (MPa) 0.08 0.01 0.05 + 0.01 g (MPa-1 mil -0.16 -o. 33 lg (mm) -0.7 -3.0 n 17 20 (1) Experiments analyzed herein (2) Ortega et al. 1989 (3) SE is Standard Error Conclusion The relevance of these results is that, of the parameters in the growth equations (Equations 1.1 and 1.2), the length of the growing zone appears to be important in the control of growth rate 16

PAGE 22

between stages. This simplifies manipulation of the equations by establishing lg as an independent parameter in the equations. Essentially m becomes a dependent parameter driven by the change in lg. The position and importance of lg in the equations, where it originally did not exist, is therefore established. Knowing this, one can now focus on this parameter in biochemical work to determine how the plant controls its growth rate. Clearly this result does not apply itself to plant cells which grow along their entire length. Due to the importance of lg in the equations its precise value should be determined to refine the values calculated herein. Additional work is called for to determine whether the length of growing zone also changes during growth rate changes associated with sensory responses. Unfortunately, sensory responses in Phycomyces are transient and not sufficiently reproducible to easily determine m dynamically. Reliable determination of a change in lg during the sensory response may be possible although the material presented in Chapter Four indicates that the steady state length of the growing zone is itself a dynamic parameter. 17

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CHAPTER THREE VOLUMETRIC ELASTIC MODULUS Introduction In studies of water relations in plants the hydraulic conductance L is frequently measured by observation of elastic changes in volume due to water uptake and transpiration (Zimmermann et al. 1978). In order to accurately assess L, accurate measures of the volumetric elastic modulus e must be made. Manipulating Equation 1.1 (see Appendix c for details), the volumetric elastic modulus can be solved for in terms of the known variables: growth rate and turgor pressure as follows . dP dt __!_ d1 -cj> (P-P ) 10 dt c Equation 3.1 By observing the steady state growth and monitoring P, a state of constant P can be found wherein dP/dt is zero. Given this, the relative plastic extension rate can be found cj> (P-P ) =__!_ d1 c 10 dt which is easily measured in discretized form cl> ( P-P c> = [ __!_ 1!.1 ) steady 10 I!. t scac& Assuming that this is constant, now be determined and plotted as a function of turgor pressure by I!.Pl 1!. t 0 2 = 1!. t-[ ll t Iss Equation 3.2 As was shown by Ortega in 1985. In the case of zero growth (!!l.l/!!l.t)55 is zero and the equation simplifies to ...

PAGE 24

flp Ttlo Ill !lt (subscripts 1 and 2 are added for later reference only). Equation 3.3 Experimentally, by supplying a series of discrete pressure steps on fixed time intervals and meas.uring the resulting change in length, e may be determined as a function of P. These equations clearly show that the values obtained for growing versus non growing cells should be determined by different methods. Zimmermann et al. (1978) notes that in plasticly deformable (growing) cells it is necessary to either produce instantaneous steps in P and measure instantaneous changes in 1 or, if the steps are not instantaneous, the plastic deformation occurring during the step interval must be accounted for. Zimmermann also notes potential errors due to hysteresis effects and "changes in cell volume and pressure due to water flow" may be relevant in longer time intervals for growing plants. Unfortunately in the literature this distinction of growth is rarely made. Zimmermann et al. (1978) lists e values for 23 species of plants obtained from a variety of techniques. Zimmermann's paper only once notes whether the cell in question was growing and no note is made as to whether plastic deformation was accounted for. Ortega (1985) presents an explicit equation for handling the plastic deformation when measurements are made over finite time intervals. In this chapter I will develop and conduct experiments to measure e using the equation developed by Ortega (1985) (Equation 3.2) and compare the values obtained with and without the growth rate compensation to evaluate its importance. 19

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Materials and Methods As has been previously reported for Phycomyces (Gammow et al. 1977, 1981, 1986, 1987; Lafay et al. 1985) growth rates fluctuate on short time scales. It must be remembered that the steady state growth rate is only an approximation to the actual growth rate. From a physical standpoint, the natural variation in steady state growth rate over short time intervals can cause the denominator of Equation 3.2 to approach zero or go negative. Such a circumstance would lead to extreme and nonphysical values of e2 From a mathematical standpoint however, a short time interval is preferred to ensure that (PPc) 11 t < 11} (Ortega 1985; Zimmermann 1978). Also, Ortega et al. (1989) reported that sufficiently large pressure step ups cause a decrease in steady state growth. Since the reported drop takes a few minutes to occur it might be possible to make many rapid steps before the steady state drop becomes significant. are evaluated in the stage I experiments. Experimental Protocol Two step interval sizes Stage I and stage IVb sporangiophores were selected and placed under a biologically inert, cool, constant biaxial light at 21 1 C. The growth rate was monitored at five minute intervals for one half hour. After this adaptation period the sporangiophore's apical tip was monitored until constant growth was observed. When constant growth rate was seen, length measurements were taken every minute. If the growth rate remained constant for 10 to 20 minutes, the sporangiophore was impaled with the pressure probe and P was measured. For an additional 5 to 10 minutes the growth 20

PAGE 26

rate was monitored to ensure that it was not changed by the measurement of P. At the end of this time the pressure was stepped up using the pressure probe. If no oil was seen to move into the cell vacuole the pressure in the probe was increased (spiked) until oil was seen to move into the cell at which time the pressure was rapidly backed down. Equal pressure steps were made at 15 or 20 second intervals (here after referred to as 'short interval experiments'). In other experiments (long interval experiments) a single pressure step or multiple steps on intervals of greater then 1 minute were conducted. Short interval experiments were conducted on stage I sporangiophores only. In both cases 1 was measured immediately after each step. Results Figure 3.1 shows a typical stage I long interval experiment. P is plotted on top in MPa versus time in minutes. The lower graph is a plot of growth rate (dl/dt) versus time on the same time scale. The principal events in the protocol are marked on the graphs as they occurred in time. The growth rate graph shows responses following the steps. This result is typical of the 19 experiments analyzed herein which yield 21 values of e for stage I sporangiophores. Two short interval stage I experiments are also analyzed which yield 62 values for e. Figure 3.2 shows a typical stage IVb experiment similarly plotted. This result is typical of the 12 experiments conducted which yield 68 values for stage IVb's. e may be calculated by averaging the growth rate for 10 minutes before the step and subtracting this from the change in length which occurs after the step. For example in the experiment 21

PAGE 27

E .:. "D a) Turgor pressure trace ST::? U? EX?::RIMENT 1 JULY, 1989 ,, ,0 t a & $ 1\ I I \/ r\ II .._ ._...... 1 3 70 I 't' I I A IJ I \ ll 1\ I n ':1. l I 90 t 130 (lhil'\) I s+EPi IMPALE J b) Growth rate versus time I } I 1 1/ v v I . 170 I STEPZ Figure 3.1. July 1 1989 Experiment 22 -I\ Vl! I ,90

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a) Turgor pressure trace ST::? U? EXPERIMENT 7 JUNE, i 990 I I T I I 50 "? -'0 1 .:. ... s 30 "'I :s 20 ,s I 1\ I I Ill L_ I I I II I/\ ....... 11\ 1\ /'1 \ v VI' l/\1 v tl ' 0 . 90 S'4 98 i 1C:Z ,06 ,D 114 1'1/IZ (mln) I b) Growth rate versus time IMPALE STEP 1 Figure 3.2. June 7 1990 Experiment 23

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shown in Figure 3.2 the steady state growth rate of 20 increases by 22 during a step up of .512 MPa yielding an elastic modulus via Equation 3.3 of e1 = 23.73 MPa and via Equation 3.2 of e2 = 45.50 MPa. Both experiments shown above illustrate the dramatic variation in growth rate. In Figure 3.2 for example the growth rate varies by 50% of its steady state value before the cell was impaled. Indeed of the 150 e values collected from growing cells 57 of them are negative and 4 of them are greater than 1000 MPa. Before analysis can proceed therefore it is necessary to establish some limits on acceptable values of e. The requirement of limits is an intrinsic part of this method for calculating e. Analysis and Discussion The two largest epsilon values in the survey conducted by Zimmermann et al. (1978) are 120 and 77 MPa. Ortega et al. (1988a) measured e for the non growing stage III sporangiophores and found the following relation . e = max (E1r,ax 0 ) e-kP Equation 3. 4 Where emax was measured between 80 and 160 MPa. In the growing zone the cell wall will be softer than in the non-growing wall, this will produce higher extensions and therefore smaller e's in growing cells. e2 therefore should be less than 160 MPa for stage I and stage IVb sporangiophores, greater values will be discarded. In Table 3.1 averages and standard deviations for the e values obtained are listed by stage and interval size (for stage I only). The number of values (n) used in each calculation is also listed along with 24

PAGE 30

percentages indicating how many points were not thrown out. Experiments performed with small time intervals between steps produced more out of range values of e2 then those with larger time intervals (See Table 3.1). In the small interval experiments, the response to the pressure step was frequently no larger than the TABLE 3.1 VALUES OF e STAGE/ N el INTERVAL AVG. STD. AVG. STD % OF TOTAL STAGE I/ 39.17 12.39 78.19 30.72 19 31% <1 MIN >1 min 13.86 16.67 50.98 48.77 19 90% m > 0 13.13 11.40 50.53 38.65 14 82% STAGE IVb 19.71 8.55 74.32 32.81 45 66% m > 0 21.22 8.02 61.52 27.89 12 18% steady state growth rate. This results in the denominator of Equation 3.2 being close to zero or even negative. In the short interval stage I experiments 69% of all the data had to be thrown out based on the 160 MPa limit. For the stage I's the short and long interval techniques produced slightly different values for e2 and greatly different values of e1 Because of the large percentage of data points thrown out, data from the short interval experiments will not be considered further. To determine statistically if e1 is significantly different from e2 I will conduct a t-test on the stage IVb data. If the data are not highly skewed a paired t-test will predict the probability that the two data sets are identical. With the limit of 160 MPa, e2 exhibits a skewness (see Appendix D) of Sk =.068 .35 which implies 25

PAGE 31

a Z value of 0.19, this indicates that the probability of a normal distribution is greater than 99%. With this limit a paired t-test gives a probability of less than .001 that the two values are the same with 45 data points. Using a broader limit of 0<2<1000 2 is now highly skewed with Sk =3.96 .33 implying a Z value of 12.00. In general absolute Z values of over 2.58 are not normally distributed. This violates the t-test assumption that both data sets are normally distributed or that 90% of the data lie within two standard deviations of the mean. It is not possible therefore to use the t-test in the 0<2<1000 case. While there is no theoretical reason to assume that 2 should be normally distributed, the low skew resulting from the 160 MPa limit intuitively reenforces the assumption that the limit is valid. Ortega et al. (1989) showed that the steady state growth rate of stage IVb sporangiophores of phycomyces respond differently to different sized step ups in pressure. Specifically it was found that pressure step ups with magnitudes between 0.02 MPa and 0.031 MPa produced temporary decreases in steady state growth rate and larger steps produced permanent decreases. As was reported in Chapter Two, similar behavior can be seen in stage I's. It can therefore be argued that all multiple step experiments in which the step size exceeds the limit of 0.02 MPa in stage IVb's and .01 MPa in stage I's, require careful control experiments to determine exactly how the steady state growth rate changes after the step. That assumes that the changes in growth rate are repeatably precise enough to allow meaningful calculations. For long interval experiments one could argue against keeping successive steps in pressure unless it could be shown that some specific steady state growth rate could be measured after the first step. This most often occurs when m is positive. If 26

PAGE 32

I consider only the data from steps where m remains positive (where the growth rate does not decrease) I calculate the additional epsilon values shown in Table 3.1 in the columns labeled m > 0. Graphically illustrated in Figure 3.3 are normal distribution based on the long interval data in Table 3.1. e is shown as obtained in the long interval experiments for stage I (top), and stage IVb (bottom). The data sorted on positive values of mare also shown (lower curves). Conclusion The graphs in Figure 3.3 summarize the experiments and show that the method which accounts for growth rates (e2 ) produces larger values then that method which does not (e1 ) as predicted by Equation 3.2. A statistical t-test of the data gives a high probability that the difference is significant. The data from the positive m experiments are not significantly different from the values obtained in the long interval experiments overall. In multiple step experiments it is therefore not necessary to account for a change in growth rate due to the previous pressure steps. I conclude therefore that for the stage I e = = 50.98 MPa 48.77 MPa and for the stage IVb e = 76.26 MPa 37.05 MPa.Most of the variation in e predicted by Equation 3.4 occurs for Pless than 0.2 MPa (Ortega et al. 1988a). Unfortunately I found no sporangiophores with such small values of P. This and the large standard deviations in the data make an e v.s. P curve fit a stressful exercise in optimism. In Chapter Five, existing methods for reducing P are reviewed and a new method is developed and evaluated. These methods could make it possible to determine if e is indeed a function of P in stage I and IVb 27

PAGE 33

EPSILON SUMMARY. STAGE I 1.7 t.S 1.8 1.4 1.3 1.2 1.1 o$. 2n >a I u o.a 0.7 o.a Q.ll A.4 0.3 0.2 0.1 D D a) Stage I EPSILON SUMMARY. STAGE IVb 7 I I I 2 b) Stage IVb Figure 3.3. Histographic summary of results 28

PAGE 34

sporangiophores. Due to the large number of rejected data points, I conclude that for stage I sporangiophores, long time intervals 1 minute) are required between step ups for success. Zimmermann et al. (1978) states that pressure step ups should not exceed 0.1 MPa if reliable measures of e as a function of P are to be made. The stage I experiments were conducted with pressure step-ups ranging in size from .007 MPa to .555 MPa and no clear effects of pressure step size is visible in the data. The stage IVb experiments were all conducted with pressure step-ups of 0.512 MPa or 0.536 MPa. That the large step sizes did not clearly impair the experiments is probably due to the experiments being conducted in the flat part of the v.s. P curve. If lg could be measured precisely, one could differentiate e values inside and outside of the growing zone to build a differential model of the cell. Consideration of this subject is presented in Chapter Four. 29

PAGE 35

CHAPTER FOUR DYNAMICS OF THE STAGE I GROWING ZONE Introduction Previously several investigators (Gammow et. al 1977, 1981, 1986, 1987, Lafay et al. 1985) have measured growth velocities on stage IVb sporangiophores. The method involved monitoring the position of a single marker placed on the cell wall relative to the top of the sporangiophore. Over ti6e a marker placed near the top of the cell can be seen to move downward through the growing zone (G.Z.) (upward through space) as material is added above. lg was determined by finding the distance from the top of the G.Z. to the point at which the marker's velocity became zero relative to a fixed frame. In these papers and others going back to the 1930's (Castle 1940, Oort 1931) growth rate of the sporangiophore has been seen as highly variable about a mean value. Materials and Methods In order to determine lg in the stage I, several corn starch markers were placed on the stalk (see Appendix A) and monitored over time. Since the stage I growing zone extends to near the apical tip of the sporangiophore, lg may be determined by observing the distance from the tip to a marker when that marker stops moving in height. By using multiple markers scattered throughout the G.Z., it should be possible to get some redundancy in the estimates of lg, to reduce uncertainty, and to save time.

PAGE 36

Results Figures 4.1 -4.3 show the results of the marker analysis. The position of each marker relative to its position at time zero is plotted versus time. At the bottom of each graph the initial distance from each marker to the apical tip of the sporangiophore is recorded in In Figure a stage I to stage II transition occurs where the expected behavior of the G.Z. is observed. Two markers below the G.Z. initially (at 719 and 919 remain in approximately the same position for 80 minutes. The next marker upward (initially at 523 moves up indicating that < lg < The transition to stage II was first visible at 40 minutes and the G.Z. quickly moves up the stalk as the third marker leaves the G.Z. at about 50 minutes, and the next two markers stop moving at about 60 minutes. Typical values of lg ranged around 0.7 mm 0.3 mm. Figure 4.2 however shows a much different behavior more nearly typical of the observations in general. Two markers within the growing zone slow to zero growth rate at approximetly 50 to 60 minutes indicating an lg of approximately 680 and 420 Interestingly, the markers then begin to move downward indicating that the sporangiophore has begun to shrink locally. The lower markers move downward almost from the beginning of the experiment. The total downward movement of 120 is far greater then the errors in the measurements. In 28 experiments, this type of shrinking behavior can be observed. These observation are also supported by 11 separate qualitative observations of pressure probe needles which 31

PAGE 37

STAGE I OBSERVATIONS, JULY 12, 1989 v t .... v I i UIO v / !,_....-' v -0 -100 10 10 11 (min) A ezs + 171 11151 Figure 4.1. July 12 1989 Observations t ... II I g TOf' STAGE ONE OBSERVATIONS, SEPT 1 0, 1 989 1.1 I I D.l c.e 0.7 u D.l D.4 u C.2 D.1 c L.,...--' / ...... v ....... --1-""P""' '""""''' -D.1 -Co2 -10 10 10 + ..... J / r7 ...... ""''' 70 10 11 (min) A 1&71 I 7 v / ....... v v ...... 1 I I 110 110 170 10 318 Figure 4.2. September 10 1989 Observations 32

PAGE 38

ICIO 8110 7DO .... IDO I 100 400 ; -200 1DO I) -100 a 'niP Figure 4.3 STAGE ONE OBSERVATIONS, SEPT 6, 1989 A ........ 0 + 12 l/ j.ooo"" ,__ 10 1K (!111ft) .... .) / v It' [.........-10 X September 6 1989 Observations 7 v v _.....-[7 1DO bend down by 20 to 100 while impaled within a sporangiophore. In Figures 4.2 and 4.3 sudden "jumps" in length can be seen occurring over the entire monitored length of the sporangiophore. For example in Figure 4.2 the lowest marker (10800 below the tip) moves upward by approximately 70 at 80 minutes while the top of the sporangiophore moves upward by twice as much. This is repeated at 160 minutes when the lowest marker moves up by approximately SO Figure 4.3 shows a single jump at 20 minutes of between 40 and 100 Initially it was believed that this was caused by a movement in our equipment. Careful checking against a fixed target ruled this out. Of the 31 marker experiments performed on stage I's by myself 12 show some jumps in length. Since my initial observation of this phenomena, numerous repeated observations have been independently made in our lab. The effect is quite striking when seen in a micro scope as the cell elongates by hundreds of micrometers in 20 seconds to one minute. On two occasions these 33

PAGE 39

jumps in length occurred while the sporangiophore was impaled and turgor pressure was being monitored. In both cases P climbed slowly by up to 0.01 MPa over a minute before the jump then dropped abruptly. In most cases the steady state growth rate appears nearly unchanged after the jump. Analysis and Conclusion The observation of a local shrinking zone at the base of the stage I growing zone appears to be unique and has an important implication for measurement of lg. With this region of local contraction in length it is clearly not valid to measure the length of the growing zone at the point of zero absolute marker velocity. Since points below the zero velocity point may be moving downward it follows that the intervening region must be elongating. Therefore I conclude that the stage I growing zone is longer than previously believed. This will produce corresponding errors in sizes of I conclude therefore that the previous method of measuring lg, that is by following a marker until it stops, is inadequate. This calls into question all previous calculations of in growing sporangiophores. Additional observations are called for define lg precisely in light of these conclusions. The jumps in length are interesting because they present a wide array of theoretical problems. current theories of plastic cell wall deformation (Ortega 1976) describe growth as driven by enzymatic breakdown of the cell wall. A jump would then require a rapid increase in enzyme levels throughout the cell. Much more rapid than existing transport mechanisms. If the jumps were to be described in terms of elastic deformation, one would expect to see the steady state P increasing, the jumps reversing themselves, or again have to 34

PAGE 40

explain how might change throughout the cell very quickly. While P was monitored in only two cases, the similar behavior in each of those cases is very suggestive. Further, since the cell returns to a similar steady state growth rate after the jump, it appears as though the mechanisms of normal growth are not involved in the jump. Such behavior could be described by a static friction component within the cell which allows elongation when P exceeds some critical level. Since the behavior has only been observed in stage I's, which are generally thicker then stage IVb's it might be that this is part of the mechanism by which the stage I looses its excess width. It might therefore be that the current growth eqUations could be augmented to include a dependence on developmental stage and radius. Once lg was known with accuracy, one could then examine whether lg was an important parameter in sensory responses. Further, my work has already shown that lg is important in plastic deformation of the cell. If lg were precisely known one could then determine how much elastic deformation occurred within the G.Z. as opposed to within the non-growing zone; that is one could begin to develop differential models of cell development. 35

PAGE 41

CHAPTER FIVE VERIFICATION OF THE PRESSURE PROBE TECHNIQUE THE TWO PROBE EXPERIMENT Introduction Although theoretically the pressure probe should accurately measure pressure, the technique has never been independently verified. The time required for the cell to feel a change in pressure applied from a pressure probe has never been determined. In Chapters Two and Three (as in all of the pressure probe related literature cited) it has been assumed not only that the probe read true static pressure, but that instantaneous step changes in turgor could be made. Ortega (1988a) measures the values of e for stage III's and found they follow Equation 3.4. Since the most significant changes in e were seen to occur at low P it is frequently of interest to reduce P within the cell. Two methods to produce steps down in P require eliminating the rate of net water uptake by plucking, or increasing the rate of transpiration. In such experiments P may decay rapidly over many minutes or slowly over two hours (Ortega 1988, 1989) reaching some new equilibrium level. In practice it is very difficult to hold turgor for an hour in stage IVb sporangiophores and, due to the higher viscosity of cell sap, extremely difficult in stage I and stage III sporangiophores. Also in reducing the net water uptake, the pressure drop obtained is not predictable and is limited in magnitude. In practice it is possible to drop P by pulling the interface back into the pressure probe.

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Unfortunately it is not possible to continuously monitor P with the pressure probe's needle full of sap because the sap quickly thickens and plugs the needle. A third method of dropping P, raising the external atmospheric pressure (Cosgrove 1988), requires baric isolation of the cell. For this the apparatus must be contained within a pressure vessel which is quite cumbersome for moderately complex experiments. To address both the pressure probe's legitimacy and the low P response questions, a sporangiophore could be impaled with two pressure probes simultaneously. With one pressure probe used to pull sap out of the cell, the second could continue to monitor P even of the first became plugged. In such an experiment it could be determined firstly if both pressure probes recorded the same value of P in different parts of the cell, secondly if a step change in P by one probe produced a rapid change in P as measured by a second, and finally if as a function of P followed Equation 3.4 for low values of P. Materials and Methods Nine experiments were conducted in which P was measured in a sporangiophore with two pressure probes simultaneously. In each case a sporangiophore was impaled with one pressure probe and turgor pressure was determined. Turgor was monitored with the first probe for a period of a few minutes. If turgor was not constant (indicating a leak or non equilibrium condition) the experiment was terminated. To prevent the first probe from loosing control of its interface and dumping oil into the cell, the pressure in the second probe was brought up to just under the P value reported by the first probe before the second impaled. After the second probe succeeded in 37

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establishing an interface for a few minutes, one of the probes was used to pull back its interface in an attempt to reduce P. The other probe continued to monitor P. Results Figure 5.1 shows the output of the pressure probes during one of the nine experiments in milli-Volts (mV) versus time. The calibrations for the probes are listed in Appendix B. The value of equilibrium turgor pressure measured in both of the probes for each experiment can be seen in Table 5.1. Attempts to pull down the pressure were only moderately successful. When a large volume of cell sap enters the capillary, the sap tends to solidify within the probe. Shown in Figure 5.1 is the July 10, 1990, experiment wherein probe III pulls down the pressure by 8 mV (.20 MPa) and probe II quickly decays by 11 mV (.18 MPa) to a new equilibrium value. Probe II was then used to step up from the new equilibrium pressure while probe III jammed and no longer recorded true turgor. The response by probe II follows the pressure in probe III very closely. In other experiments the similarity in dynamic response was not as clear. These experiments were conducted by me, Scott A. Bell, and Mark A. Espinosa. Analysis and Discussion The main difficulty in performing these experiments is finding a workable geometry and two highly experienced and skilled pressure probe operators. 38

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PROBE 1li \ 1 PROBtli: ... .... ----"" \,.. 0 TIME Figure 5.1 Two Probe Experiment Pressure Trace 39

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Table 5.1 Pressure probe output Date Probe II Probe III MPa MPa 6/21/90 .339 .395 6/25/90 .365 .351 7/10/90 .367 .361 7/11/90 .423 .408 7/12/90 .456 .433 7/13/90 .428 .433 7/16/90a .450 .420 7/16/90b .459 .433 7/18/90 .525 .521 The standard method of analysis for data such as these is the linear regression. A linear regression will produce a straight line which best fits the data. The ideal regression equation obtained if both pressure probes measured exactly the same data is Pxxx = PII. A reduced major axis linear regression of the data in Table 5.1 gives a linear regression equation of PIII = 9875PII-. 007629 which is quite close to the expected ideal. The regression gives a coefficient of correlation between the data and the equation of 0.972 and a probability of less than 0.0005 that PII "# PIIx This indicates that the pressure measured in both probes may be taken to be the same. Conclusion Based on the linear regression I conclude that the static pressure measured by the pressure probe in one part of the cell is indeed the correct value of turgor throughout the cell. From turgor pressure traces similar to Figure 4.1 it appears likely that a change 40

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in pressure created by one probe can be felt throughout the cell within a very few seconds. Ideally additional control experiments would be conducted with step increases in to more precisely determine the dynamics of the probe/sporangiophore. This two probe technique adds a fourth method to reduce pressure which, in theory, could yield a precise range of pressure drops extending to zero. The technique could be of great use in experiments to determine the extent to which the values of e follow Equation 3.4 for low values of P since this is where the most significant changes in e are thought to occur (Ortega 1988a). We did not perform enough experiments to unambiguously determine e with all necessary controls. For example, after dropping P one would in principle like to determine precisely the effect on steady state growth before beginning the pressure steps (as was done for step ups in P by Ortega 1989 et al.). Although we did not conduct enough such control experiments to produce reliable values for e, we have shown that such experiments can be done. 41

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APPENDIX A GENERAL TECHNIQUES AND EQUIPMENT Innoculation, Incubation, and Maintaenance Growth media The growth media is prepaired by combining 2.5 g of vitamin B with 25 g of Potato Dextrose Agar, 7 drops of vegitable oil and 250 ml of distilled water. The solution is thouroughly mixed then heated slowly to a boil. After boiling for four minutes the liquid is poured into 2.5 em shell vials. The vials are then sterilized in a steroclave and allowed to cool slowly at room temperature. After solidifying the vials are refridgerated untill needed. Unused vials are cleaned and refilled after two weeks. Innoculation and Growth A concentrated solution of spores in distilled water (generaly 105 to 107 spores per ml) is diluted to obtain approximately 5 to 10 spores per drop. The resulting solution is heat shocked at 48C for 10 minutes and one drop is placed into each vial. The vials are maintained at 20C in uniform cool white light and high humidity. After stage IV sporangiophores appear the sporangiophores are plucked back daily to leave only stage I's. Growth Measurement Marker Placement To mark the sporangiophore, a small pair of tweezers was used to grasp a quantity of cornstarch. By steadying the hand on the pressure probe and stereo scope, small groups of starch granules

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could be accurately placed on to the sporangiophore without disturbing it. Marking is done before any growth measurements are made so that the sporangiophore may be moved in the visual field of the stereo scope with out affecting growth measurements. It is essential that the markers consist of small numbers of granules. In a large group, the adhesion of the group can cause errors in readings because the motion of the marker may be due to motion of the sporangiophore far from where the measurement is made. In addition, large groups of granules in an active growing region will breakup and spread out during growth producing ambiguity. Measurement Measurement of the marker position proceeds largely as described below with one important modification. It is necessary in measuring the marker positions that a sketch of the markers be made indicating which part of a group of granules is to be measured. Erroneous data would be generated if, for example, in alternate measurements, the top and bottom of a group of granules were taken as the same point. Growth Scope Growth measurements are made using a microscope attached to a three axis micro-positioner. The micro-positioner is a Line Tool Co. three axis stage (H-LH) with large barrel one inch metric micrometer heads in the x andy directions (along the horizon, see figure A.l). In the z direction (vertical) a Mitutoia digital micrometer is used. A Bausch & Lomb microscope (48X) with cross hair is mounted to the stage via a custom bracket. Two additional Narisige positioners are used in the custom bracket to provide course adjustment in the y and z directions. The three axis stage is mounted to the work station 43

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via a single screw which permits further course adjustment (rotation) in the X and Y directions. Initially the X and Y axes micro-positioners are each set at lO,OOOum and the z axis digital micro-positioner is set near midrange. The stage is then rotated until aligned with the target. Next the Z axis coarse adjustment is moved until the target appears in the scope, then it is locked down. The image is then focused with the y axis coarse adjustment. Finally at five seconds before the minuet, the digital z axis is adjusted until the target is on the cross hair and zeroed. Measurements Because the principal objective of the measurements was to ascertain when the growth rate is steady, the initial measurements were made in the following manner. At five seconds before the end of the designated time interval the X, Y and z axes are adjusted until the target on the cross hair. The new position of each adjustment screw is recorded and the Z axis positioner is zeroed. If marker locations are desired, the distance from the principal target (the top of the sporangiophore) to each marker is obtained by adjusting the X, Y, and Z axes until the marker is in the cross hair, and recording their positions. At the beginning of each experiment, the width of the stalk is also measured at 1500 micrometers from the top, using the difference in the X axis positions of each side. This technique gives the operator the change in length during each time interval and makes it quite simple to determine when growth is steady and when the trap rate is excessive. There are three principal disadvantages of this technique. First, it requires a good deal of 44

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calculation to reconstruct the absolute position of the markers in time, thus increasing the likelihood of error. Second, when the growth-rate is small the accumulated error in round-off with each zeroing becomes significant. Finally, the "Jump" behavior (described in Chapter Four) cannot be distinguished from the operator forgetting to zero the z axis manipulator. Although understanding or describing the "Jump" behavior was not the initial objective of this work, it appears to be a significant part of the sporangiophore's behavior, and therefore is worthy of study. To eliminate the problems discussed above, the Z axis positioner was not zeroed in later experiments. This required an already busy experimentalist to calculate delta l's as the experiment progressed and was deemed a reasonable trade-off. Estimated Accuracy + 0.5 IJ.m z axis when measuring changes in length 2.0 IJ.m z axis when measuring marker positions + 1.0 IJ.m X axis 5.0 llm y axis Total Length Measurenent Total length measurement was made by 'eyeballing' the sporangiophor with one of several verniers. Although the instruments could be read to 50 !J.m, uncertanty in the position of the agar and mycleum probably limit these numbers by as much as 2 mm. Light Source Schoelly Fiber Optic GMBH, Denelinger, West Germany Flexilux 90; HLU light source 90/w with a two-armed swan neck light guide. 45

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Pressure Probe Description The pressure probe is mounted on a Line Tool Co. three axes micro-positioning stage(H-RH) which in turn is mounted on a 2 inch to 9 inch scissor jack. The Probe body consist of three plexiglass blocks glued firmly Through these blocks two small holes have been drilled for oil channels. The first channel runs the entire length of the block and holds a control rod (musical instrument wire .053 inch Dia.). The second channel intersects and is runs perpendicular to the first. The second channel is tapped to mate with the pressure transducer (XT-190-300G). A small circular depression is cut into the body around the top of the second channel to provide an "0-Ring" seat for sealing the pressure transducer. The 'back' of the first channel is tapped to accept a threaded plug. The plug is drilled concentrically to admit the control rod. On the front of the first channel a cylindrical plexiglass block is glued onto the main block and drilled concentrically. The cylinder is threaded to admit a cap. This cylinder is the principal weakness of the probe as the glue has given way on occasion resulting in small leaks which dramatically affect the function of the probe. The pressure transducer is a Klute semiconductor strain gauge. (Max pressure 300 psig, input voltage 10.0 volts, output Z 420 ohms. Because the transducer is a resistive device, a small climb in pressure can be seen when the heat produced by the transducer heats the oil and causes small thermal expansion. In fact the sealed probe is a very sensitive thermometer and changes in room temperature are easily seen when checking the probe for leaks. Seals on both ends of the first channel are made with 1/8 inch thick neoprene rubber cut into .285 inch discs and drilled concentrically .035 Dia. When the cap and plug are tightened 46

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against the seals into the probe body, all air is forced out and all mating parts are put in compression. Errors in the concentricity of all holes associated with the first channel, its plug, and cap result in reduced life of the neoprene seals. Fortunately the seals are cheep, easy to manufacture, and simple to change. Calibration The pressure probe is calibrated by supplying static air pressure via a Norgren air regulator ROB-300-RGMA to the probe. Air pressure is monitored on a Heist bourdon tube pressure gauge CMM-66101. The pressure transducer output is monitored on a six digit Hewlet Packard multimeter 3490A (only the four most significant digits are recorded) and an OnmiScribe chart recorder DSOOO. The voltage of the pressure probe power source is also recorded. Pressure is stepped up in five psi increments from room pressure and the multimeter output is recorded after the system stabilizes at each new pressure. When maximum line pressure is reached, the pressure is stepped down and a second set of readings are taken at identical points as the first group. The two sets of values are averaged and fit to a linear curve. This provides the slope and intercept of the Pressure v.s. millivolt calibration curve. The pressure probe is recalibrated whenever the transducer is replaced and after and major maintenance. Needles Micro capillary needles are produced using a KOPF vertical pipette puller 720 which produces a consistently shaped needle from a 1.0 mm OD x 0.5 mm ID glass capillary. 47

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Loading To load the pressure probe the foam control knob is removed followed by the rear probe mount screw, this allows the probe to rotate approximately 70 degrees from vertical. The probe cap is then removed and the old needle discarded. The front probe seal is inspected and replaced if severely deformed or fragmenting. A Sec syringe with a lcm needle is used to fill the probe channel with paraffin oil while the control rod is backed out. Great care must be taken to ensure that no air is entrained in the syringe before filling the probe. As long as the probe is inclined and the syringe needle tip is below the oil surface within the channel, no air can become trapped in the probe channel as it is filled. As the syringe needle is withdrawn a continuous flow of oil ensures that the probe body is completely filled. To fill the glass micro-capillary needle, a 2 inch by .002 OD syringe needle is placed on a Sec syringe loaded with 200 centi-stoke oil (Dow corning 200). All air is purged from the syringe and its needle. A micro capillary needle is then chosen and measured. If the micro-capillary is longer then the syringe needle it is broken off, this is essential to minimize entrained air. The micro capillary is inserted into the pressure probe cap and its seal. The long syringe needle is then inserted into the capillary needle and the capillary is filled. Some time must be allowed to pass to allow all air to flow out of the capillary. Finally the syringe is withdrawn while a continuous flow of oil from the syringe ensures no air is left in the capillary. Once the capillary is loaded it is simply inverted and the probe cap is screwed onto the probe body. Surface tension and the oil displaced by the capillary within the probe body prevent the final possible influx of air into the system. 48

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Operation When the pressure probe is first powered up the control rod is moved in until an output of approximately 80 mV is obtained. The release of stored elastic energy causes the pressure to decay initially. The probe is allowed to sit until the pressure decay stops. This provides a frequent check on the integrity of the pressure seals in the probe. When the time to use the probe arrives, the glass microcapillary needle is opened by brushing a tissue across the tip. The size of this opening is absolutely critical to achieving a successful experiment. If the needle is too small the cell sap will coagulate and plug the tip. If the needle is too large the pressure in the sporangiophore will decay rapidly, either because of a leak or due to some "injury response" associated with the loss of volume. The size of the needle can be accurately gauged based upon the pressure decay rate when the needle is opened. After the probe is ready it is aligned with the target sporangiophore and the needle is brought in contact with it. The silicon oil, which flows freely and rapidly back down the needle, is immediately wicked onto the sporangiophore when oil contact is made. The time at which oil contact occurred was recorded in order to determine if the oil interfered with the growth rate (by reducing surface transpiration of water). No such interference was seen. When the probe's pressure is decayed below the minimum likely turgor pressure, the needle is gently driven into the sporangiophore. Since the cell sap in the cell is at a higher pressure then the oil, the oil is forced back and sap flows into the probe needle. With luck an oil/cell sap interface is visible in the needle and can be driven back to the cell wall by adjusting the control rod. Alternately, the oil and sap may mix, in which case the experiment must be terminated. Once the pressure in the probe is sufficient to 49

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hold the interface at the cell wall, the pressure probe is reading equilibrium turgor pressure. If the interface should become immobile then it could support a pressure gradient and therefore, the measured pressure would not be accurate. To prevent this, the interface is held slightly away from the cell wall and constantly moved back and forth slightly to ensure that it is loose. In the coarse of this work it was frequently necessary to increase the pressure within the cell slightly. Frequently when doing this it was found that the interface would move down the needle and become stuck at the tip. It was found that a small over pressure initially which forced oil into the cell, would insure that the needle remained open without adversely affecting the growth. Accuracy See Chapter Five. Electronics The pressure probe is powered by a 10 volt DC regulated power supply. The pressure probe output is monitored on a Hewlit Packard six digit multimeter (3490A) and an Omniscribe strip chart recorder DSOOO. 50

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APPENDIX B SUMMARY OF RESULTS Stage I Experiments Step up experiments with single steps or multiple steps over intervals greater then 1 minute. DATE p fl.p m UNITS MPa MPa fl MPa min 1989 10/25 .4472 .0260 23.1 10/13 .4495 .0256 101.6 10/8 .0256 7.8 10/6 .3740 .0256 10/1 .4175 .0384 9/29 .3996 .0064 9/20 .5399 .0064 .0064 8/3 .5272 .0064 109.4 .0077 7/30 .0077 13.0 7/27 .3843 .0064 7/25 .5374 .0102 284.1 .0076 7/23 .4302 .0077 519.5 7/22 .4111 .0077 389.6 7/02 .5610 .0102 500.0+* .0096 7/01 .0064 46.9+ 6/06 .4596 .0111 31. 25* 6/03 .4209 .0111 .0555 5/31 .3592 .0155 .0422 .0444 5/17 .0179 37.9+ + Second step also yielded a phi value Additional data--GZ e:l MPa MPa 30.62 306.24 438.59 1075.79 26.43 45.01 49.55 208.13 3.84 8.35 7.20 19.13 9.42 40.82 4.04 28.85 4.54 22.03 3.30 4.36 12.43 124.31 14.39 105.18 4.10 35.87 7.92 31.19 8.86 48.14 7.69 35.79 8.92 107.04 14.82 42.71 6.22 9.19 39.26 128.04 72.66 185.89 35.06 48.63 Step up experiments with multiple steps over intervals less then 1 minute. 10/13 .4495 .0128 10/25 9/20

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Stage IVb Experiments One Half Bar steps (0.512 unless otherwise on 60 second intervals DATE Pequl dl dl dt equl dt after MPa _L _L min min (1990) 5/30a .545 32.2 75 5/30b .560 37.4 63 5/31 .545 20.3 168 6/1a .521 29.8 78 6/lb .567 36.9 54 6/6 .566 25.2 36 6/7 .497 19.6 41 6/8a .535 20.6 33 6/8b .524 18.6 33 9/8a .500 22.5 34 9/8b .486 27.0 50 9/8c .409 33.0 66 N = 12 1 Noncompensated values (Equation 3.3) 2 Growth compensated values (Equation 3.2) Values from first step only #Step size 0.536 Bar 52 noted) MPa 15.20 36.15 6.70 11.16 19.34 27.73 23.73 18.77 29.17 28.6 21.82 16.24 MPa 83.6* 112.2 22.8 18.1 61.1 92.4 45.5 50.0* 66.8 92.6*# 54.0# 39.1#

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Two Probe Experiments DATE PROBE II PROBE III OPERATORS mv MPa mV MPa 6/21/90 28.5 .399 21.5 .395 SAB, MAE, MES 6/25/90 25.9 .365 18.9 .351 SAB, MAE 7/10/90b 30.4 .367 22.3 .361 SAB, MAE 7/11/90 33.0 .427 23.8 .408 SAB, MES 7/12/90 26.0 .456 19.5 .433 MAE, MES 7/13/90 30.8 .428. 23.8 .433 SAB, MAE 7/16/90a 32.5 .450 24.0 .420 SAB, MES 7/16/90b 33.2 .459 23.8 .433 SAB, MES 7/18/90 38.4 .525 29.0 .521 SAB, MAE OPERATORS SAB Scott A. Bell MAE -Mark A. Espinosa MES -Martin E. smith PROBE CALIBRATIONS Probe II p = 0.0128 v + 0.0338 MPa Probe III p = 0.0168 v + 0.0666 MPa Where V is output voltage in mV, P is turgor pressure in MPa 53

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THE LENGTH OF THE GROWING ZONE 6/ 1/89 6/ 2/89 6/ 3/89 2 experiments 6/ 5/89 2 experiments 6/ 6/89 6/ 8/89 6/10/89 6/28/89 2 experiments 7/ 1/89 7/12/89 7/13/89 7/15/89 3 experiments 7/16/89 7/19/89 2 experiments 7/20/89 2 experiments 8/ 4/89 9/ 06/89 10/ 8/89 DISCONTINUOUS INSTANTANEOUS CHANGES IN GROWTH RATE "JUMPS" 3/19/89 4/ 4/89 4/ 5/89 5/16/89 5/18/89 5/30/89 5 31/89 6/ 3/89 6/ 9/89 6/12/89 6/27/89 54

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At constant p APPENDIX C DERIVATIONS Chapter II dP=D dt Equation 1.1 For a sporangiophore changes in radius r are much much smaller then changes in length 1, so that Then Equation 1.1 becomes . l:_ dl ="' (P-P ) 1 dt 'f' c Equation 2 .1 Since the growing zone is defined as the region where all irreversible extension occurs Assuming that lg is approximetly constant and solving for the irreversible extension rate cilg 1 dl ---= Ql (P-P) lg dt g c

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We may define the relative irreversible extension rate mas Then d1 -=m(P-P) dt c Discretizing the derivative we may now solve for Pc !:d 1 p =P-(-)c t:.t m Taking the differential of Equation A d1 !:.-=!:. (mP) -!:. (mP ) dt c Equation A Equation 2.3 Again discretizing the derivative and assuming that m and Pc are constant I may solve for m !:. ( 1::.1 ) m= t:. t f::.p Equation 2.2 Chapter III 1 dVc 1 dP ---=cj>(P-P) +--Vc dt c e: dt Equation 1.1 Substituting 1 for Vc as before and isolating the right hand term 1 d1 1 dP ---<1> (P-P ) =--1 dt c e: dt Unlike the previous experience with plastic deformation in Chapter 2, elastic deformation occures over the entire length of the sporangiophore. The value of e: is probably different in the growing zone then it is in the nongrowing zone. Due to the problems involved 56

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in measureing the length of the growing zone (see Chapter 5) we may only know the BULK value of e at this time. Since the change in length durring an experiment is on the order of one in one hundred, we may take 1 to be a constant 10 Now, solving for e dP dt; 1 dl l dt -4> (P-P c> Equation 3.1 Substituting in and assuming no growth i get eq 3.2 t Test Staticstics t = X-J.Lo y'n 0 Where X is the mean of the test data, J.l0 is the mean of the control data, o is the standard deviation of the test data, and n is the number of samples. Skewness Sk = 3 (X-M) 0 Where Sk is the skewness, and M is the median of the data. z z = Sk s Where s is the standard error of Sk. 57

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GLOSSARY / SYMBOLS G.Z. Growing zone -The total region of plant cell involved in growth. In Vivo -Within a living organism. L Hydraulic conductance -The ability to conduct water, inverse of hydraulic Resistance. 1 Length -Length of the sporangiophor from the mycleum to the tip, in micro-meters. lg Length of the growing zone. 10 Initial length of the sporangiophore at time zero m Irreversible cell wall extensibility -A measure of the ability of the cell wall to deform plastically, or relative plastic strain rate over stress. T Relative Transpiration Rate -Evaporative water loss per unit length and time. P Turgor Pressure -Gauge pressure of the plant cell sap. Pc Critical Turgor Pressure -Minimum turgor pressure required to elicit growth. Analogous to static friction. Relative Per unit length or per unit volume. t Time. V Volume of the cell contents. Vc Volume of the cell wall chamber. v Relative rate of volumetric expansion of the cell wall chamber. Y Yield threshold Same as Pc. Delta -Discreet, finite changes in a variable. ll Osmotic Pressure -The pressure that must be applied to a solution to just prevent osmosis. (Webester, 1973) e Volumetric elastic modulus -A measure of the ability of a material to deform reversibility, or elastic strain over stress. J.1. micro 10-6 o Solute Reflection Coefficient -Average osmotic efficiency of all solutes: .

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cr Solute Reflection Coefficient -Average osmotic efficiency of all solutes: . Relative irreversible cell wall extensibility -rn divided by the total length of the sporangiophor. Irreversible cell wall extensibility relative to the length of the growing zone -rn divided by the length of the growing zone. 59

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BIBLIOGRAPHY Bergman K, Burke PV, Cerda-Olmedo E, David CN, Delbruck M, Foster KW, Goodell EW, Heisenberg ZM, Meissner G, Zalokar M, Dennison DS, and Shropshire W, Jr. (1969) Phycomyces Bacteriological Reviews 33:99-157 Castle ES {1940) Discontinous growth of single plant cells measured at short intervals, and the theory of intussusception. J. Cell Camp. Physol. 15:285-298 Cerda-Olmedo E ,Lipson E {1987) A biograph of Phycomyces. In E Cerda-Olmedo, E Lipson, eds, Phycomyces, Cold Springs Harbor Laboratory, Cold Springs Harbor, pp 7-26 Cosgrove DJ {1988) Mechanisms of rapid suppression of cell expansion in cucumber hypoctyls. Planta 176:109-116 Cosgrove DJ, Ortega JKE, and Shropshire W 1987 Pressure probe study of the water relations of Phycomyces Blakesleeanus sporangiophores. Biophys. J. 51:413-423 Dainty J, Vinters H, Tyree MT (1974) Membrane transport in plants. Zimmermann and Dainty, eds, PP 59-63 Springer-Verlag Berlin, Heidelberg, New York. Gammow IR, Bottger B {1977) Phycomyces: Distribution of growth velocities in the growing zone. Plant Physol. 59:901-906 Gammow IR, Bottger B {1981) Phycomyces: Irregular growth patterns in stage IVb sporangiophores. J. Gen. Physol. 77:65-75 Gammow IR, Geer GA, Bottger B {1986) Phycomyces: Fine structure analysis of the growing zone. Plant Physol. 80:721-726 Gammow RI, Ruiz-Herrera J, Fischer EP, (1987) The cell wall of Phycomyces. In E Cerda-Olmedo, E Lipson, eds, Phycomyces, Cold Springs Harbor Laboratory, Cold Springs Harbor, pp 223-246 Green PB (1968) Growth physics in Nitella: A method for in vivo analysis of extensibility based on a micro-manometer technique for turgor pressure. Plant Physol. 43:1169-1184 I Green PB, Erickson RO, and Buggy J {1970) Metabolic and physical control of cell elongation rate. 47:423-430 Lafay JF, Matricon J {1985) Observation of growth ,rate fluctuations in Phycomyces Blakesleeanus using a high resolution automated measuring system. Physol. Ve'g. 23:929-934 Lockhart JA {1965) elongation. An analysis of irreversible plant cell J. Theor. Biol. 8:264-275

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Ortega JKE, (1976) Phycomyces: The mechanical and structural dynamics of cell wall growth. PhD Thesis. University of Colorado, Boulder Ortega JKE, (1985) Augmented growth equations for cell wall expansion. Plant Physol. 87:11-14 Ortega JKE, (1990) Governing equations for plant cell growth. Physlo. Plantarum 79: 116-121 Ortega JKE, Gamow RI (1976) An increase in mechanical extensibility during the period of light-stimulated growth. J. Plant Physol. 57:456-457 Ortega JKE, Gamow RI and Ahlquist CN (1975) Phycomyces: A change in mechanical properties after a light stimulus. J. Plant Physol. 55:333-337 ortega JKE, Keanini RG, and Manica KJ (1988a) Pressure probe technique to study transpiration in Phycomyces sporangiophores. Plant Physol. 87:11-14 Ortega JKE, Manica KJ, and Keanini RG (1988b) Phycomyces: Turgor pressure behavior during the light and avoidance growth responses. Photochemistry and Photobiology 48:697-703 Ortega JKE, Smith ME, Erazo AJ, Espinosa MA, Bell SA, Zehr EG (1991). Comparisons of cell wall extensibilities in Phycomyces. Physic. Plantarum, in press Ortega JKE, Zehr EG, and Keanini RG (1989) In vivo creep and stress relaxation experiments to determine the wall extensibility and yield threshold for the sporangiophores of Phycomyces. Biophys. J. 56:465-475 Zimmermann U, Steudle E (1978) Physical aspects of water relations of plant cells. Adv. Bot. Res. 6:45-117 61