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Phycomyces

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Phycomyces turgor pressure and growth behavior during creep, stress relaxation, and the light growth response
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Keanini, Russell Guy
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x, 92 leaves : illustrations ; 29 cm

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Phycomycetes -- Growth ( lcsh )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Includes bibliographical references (leaves 88-90).
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Submitted in partial fulfillment of the requirements for the degree of Master of Science, Department of Mechanical Engineering.
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by Russell Guy Keanini.

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|University of Colorado Denver
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Auraria Library
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Full Text
PHYCOMYCES: TURGOR PRESSURE AND
GROWTH BEHAVIOR DURING CREEP,
STRESS RELAXATION, AND THE
LIGHT GROWTH RESPONSE
by
Russell Guy Keanini
B.Sc., Colorado School of Mines, 1983
A thesis submitted to the
Graduate School of the
University of Colorado at Denver
for the degree of
Master of Science
Department of Mechanical Entineering
1987


This thesis for the Master of Science degree by
Russell Guy Keanini
has been approved for the
Department of
Mechanical Engineering
by
Date
i )fl7


Keanini, Russell Guy (M.S., Mechanical Engineering)
Phycomyces: Turgor Pressure and Growth Behavior During Creep,
Stress Relaxation, and the Light Growth Response
Thesis directed by Assistant Professor J. Kenneth E. Ortega
The growth response of Phycomyces during pressure, induced
creep was investigated using a new technique in which the pressure
probe was used to inject inert silicon oil into the cell vacuole.
The stage IVb sporangiophere. responds according to the Augmented
Growth Equation during pressure step-ups of less than approximately
0.02 MPa, and according to the Generalized Growth Equation during
step-ups greater than 0.02 MPa, but less than 0.10 MPa. The
sporangiophore's growth response to turgor step-ups larger than 0.02
MPa appears to be the previously reported negative stretch response.
Cell wall extensibilities which were measured in 7 creep tests
ranged from 0.00135 to 0.0583 MPa1 min'1 and averaged 0.0205 MPa'1
min'1. The corresponding Pc values ranged from 0.162 to 0.440 MPa
and averaged 0.262 MPa.
Stress relaxation tests using a pressure probe indicate that
turgor pressure in Phycomyces decays according to the Augmented
Growth Equation to an ultimate Pc of approximately 0.1 MPa. Results
from these tests also provide additional support for the previously
proposed two compartment model of cell water uptake in Phycomyces.
Cell turgor pressure was continuously measured with a pressure
probe during Phycomyces' positive and negative light growth re-
sponses It was found that turgor pressure remained essentially
constant during both responses. These responses apparently result
solely from altered cell wall extensibility.


ACKNOWLEDGEMENT
I wish to thank John Trapp and William Clohessy for serving
on my committee.
I wish to thank Keith Manica for his fine technical support.
I wish to thank Pauline LeBlanc for typing this thesis.
I wish to express special thanks to my advisor Ken Ortega
for his guidance and mentorship.
I wish to thank my brother and sister, David Keanini and
Roseann Dashkowitz for their encouragement and support.
I wish to thank my parents, Russ and Pat Keanini for their
moral and financial support.
Last, I wish to express special appreciation to my wife
Yvette for her continued support and encouragement.


VI.
CONTENTS (continued)
CHAPTER
SECTION 4 ANALYSIS AND DISCUSSION..................... 39
Data Selection Criteria................................... 39
Creep Control Experiment................................. 41
Phycomyces Growth Response to Pressure
Step-ups Smaller Than 0.02 MPa....................... 41
A Qualitative Model of Sporangiophore Growth........... 42
Estimating Extensibility and Critical Pressure............ 43
Comparison of Experimental and Theoritical
Creep Responses to Pressure Step-ups Smaller
Than 0.02 MPa......................................... 46
Modeling Sporangiophore Growth with the
Augmented Growth Equation............................... 48
Phycomyces' Growth Response to Pressure
Step-ups Between 0.02 and 0.10 MPa and the
Negative Stretch Response............................... 53
Self-stabilizing Growth Following a Large
Pressure Step-up....................................... 55
SECTION 5 CONCLUSIONS.................................... 60
III. STRESS RELAXATION IN PHYCOMYCES
SECTION 1 INTRODUCTION.................................. 63
SECTION 2 MATERIALS AND METHODS.......................... 64
SECTION 3 RESULTS........................................ 67
SECTION 4 DISCUSSION AND ANALYSIS..................... 69
Theoretical Pressure Decay During Wall
Stress Relaxation...................................... 69
Comparison Between Theoretical and
Experimental Stress Relaxation.......................... 72
Discussion of Stress Relaxation Results................... 74
Extracellular Water in Phycomyces......................... 77
SECTION 5 CONCLUSIONS.................................... 78
IV. TURGOR PRESSURE BEHAVIOR DURING THE LIGHT
GROWTH RESPONSE
SECTION 1 INTRODUCTION................................... 80
SECTION 2 MATERIALS AND METHODS....................... 81


CONTENTS
CHAPTER
I. INTRODUCTION................................................. 1
SECTION 1 GENERAL INTRODUCTION......................... 1
The Significance of Turgor Pressure........................ 3
SECTION 2 SPORANGIOPHORE DEVELOPMENT AND DESCRIPTION.. 4
Sporangiophore Description................................. 7
SECTION 3 SENSORY RESPONSES OF PHYCOMYCES.............. 9
Light Growth Response..................................... 10
Mechanical Stretch Response.............................. 13
SECTION 4 PLANT CELL GROWTH.............................. 14
SECTION 5 TURGOR PRESSURE MEASUREMENT..................... 17
SECTION 6 THESIS PREVIEW.................................. 18
II. IN VIVO CREEP GROWTH RESPONSE OF PHYCOMYCES
SECTION 1 INTRODUCTION.................................... 22
SECTION 2 MATERIALS AND METHODS........................... 25
Pressure Probe............................................ 25
Pressure Probe Insertion and Turgor
Pressure Measurement.................................... 27
Creep Experimental Procedure.............................. 28
SECTION 3 CREEP TEST RESULTS.............................. 29
Creep Responses in Terms of Growth........................ 34
Creep Response in Experiments Exhibiting Altered
and Unaltered Growth Rate Following Probe
Insertion............................................... 36
Creep Control Experiments................................ 37


vii
CONTENTS (continued)
CHAPTER
SECTION 3 - RESULTS..................................... 82
SECTION 4 - DISCUSSION.................................... 83
BIBLIOGRAPHY...................................................... 88
APPENDIX A
91


TABLES
TABLE
1. Extensibilities and Critical Pressures Calculated
From Creep Experiments...............................
45


FIGURES
FIGURE
1. Stages of Sporangiophiore Development....................... 6
2. Description of Stage IVb Sporangiophore...................... 8
3. Typical Positive and Negative Light Growth Responses.... 12
4. Typical Positive and Negative Stretch Responses............. 15
5. Description of Pressure Probe............................... 26
6. Representative Creep Response to Turgor Pressure
Step-up Smaller than 0.02 MPa.......................... 30
7. Representative Creep Response to Turgor Pressure
Step-up Smaller than 0.02 MPa.......................... 31
8. Representative Creep Response to Turgor Pressure
Step-up Larger than 0.02 MPa........................... 32
9. Representative Creep Response to Turgor Pressure
Step-up Larger than 0.02 MPa........................... 33
10. Increasing Creep Response Magnitude with Increasing
Pressure Step-up Size.................................. 35
11. Representative Creep Response to Small Pressure
Step-ups in a Cell Affected by Probe Insertion......... 36
12. Representative Creep Control Experiment.................. 40
13. Comparison Between Experimental Creep Response
to Small Pressure Step-Ups and the Theoretical
Response Predicted by the Growth Equation.............. 49
14. Comparison Between Experimental Creep Response
to Small Pressure Step-Ups and the Theoretical
Response Predicted by the Growth Equation........ 50
15. Comparison Between Experimental Creep Response
to Small Pressure Step-Ups and the Theoretical
Response Predicted by the Augmented Growth Equation...
52


X
FIGURES (Continued)
FIGURE
16. Comparison Between Experimental Creep Response
to Large Pressure Step-Ups and the Theoretical
Response Predicted by the Self-stabilization
Equation.............................................. 58
17. Comparison Between Experimental Creep Response
to Large Pressure Step-Ups and the Theoretical
Response Predicted by the Self-stabilization
Equation............................................... 59
18. Description of Environmental Chamber.................... 65
19. Experimental Pressure Decay During Wall Stress
Relaxation in a Slowly Growing Cell....................... 68
20. Experimental Pressure Decay During Wall Stress
Relaxation in a Non-growing Cell...............;...... 70
21. Comparison Between Experimental Pressure Decay
During Wall Stress Relaxation and the Decay
Predicted by the Augmented Growth Equation
in a Non-growing Cell................................... 73
22. Comparison Between Experimental Pressure Decay
During Wall Stress Relaxation and the Decay
Predicted by the Augmented Growth Equation
in a Slowly Growing Cell.............................. 75
23. Representative Turgor Pressure Behavior During
the Positive Light Growth Response.................... 84
24. Representative Turgor Pressure Behavior During
the Negative Light Growth Response........................ 85


CHAPTER I
INTRODUCTION
SECTION 1
GENERAL INTRODUCTION
The sporangiophore of Phycomyces blakesleeanus is a large
single-celled fungus which alters its growth rate and/or direction
of growth in response to light, humidity, wind and gravity, and in
response to nearby objects and externally induced mechanical strain
(3). Phycomyces has been studied extensively for the past 120
years, largely due to its enormous size and its spectacular
responses to light. It is a favored system of many sensory physio-
logists interested in sensory transduction, i.e., the biochemical
reactions occurring between the reception of a sensory stimulus
(e.g., a change in light fluence) and the corresponding sensory
response (3,13,14).
Phycomyces has also been extensively studied by workers
interested in the mechanisms of plant cell growth. Using Instron
tension and compression machines and pressure chambers, these
investigators have applied external stresses and strains to the
sporangiophore in order to characterize its mechanical and material
properties (1,3,4,16,26,29,30). Additionally, two models of


sporangiophore growth in terms of these externally applied stresses
and strains have been proposed (2,27,38).
A central goal of modern plant physiology, and of biology in
general, is to foot these sciences on a mathematical foundation
based on physical principals. Although it has long been recognized
that mathematical theories lend themselves to testing, reformu-
lation, and generalization, the complexity of biological systems has
of necessity kept biology somewhat qualitative. However, as new
technology has developed, and more importantly, as investigators
from other disciplines, such as engineering and physics, have become
increasingly involved in biological research, much progress has been
made toward realizing this goal.
An ultimate goal of plant physiology is the qualitative and
quantitative understanding of plant growth. Such an understanding
might, for example, be used to increase crop yields in harsh
environments with fewer resources. However, before the complex
process of plant growth can be modeled, a solid quantitative
understanding of plant cell growth and behavior must be established.
The growth of cells in higher plants, which are perhaps of
most economic significance, is difficult to study, however. These
cells are generally quite small and fragile and are situated well
within the plant mileau. An individual cell can be in hydraulic
contact with hundreds of other cells so that its osmotic behavior,
for example, is impossible to characterize due to apoplastic (i.e.,
external) water. To adequately model cell growth and behavior then,
isolated cells are required.


The sporangiophore of Phycomyces is an ideal system for
studying plant cell biophysics. It is large, and due to its sturdy
cell wall, very durable and easily handled. Additionally, while
Phycomyces is a fungus, it is sufficiently similar in morphology and
growth behavior to higher cells that an understanding of sporan-
giophore growth provides useful knowledge in understanding higher
plant cell growth. A motivation for studying the growth physics of
Phycomyces is thus apparent.
The Significance of Turgor Pressure
The present view of plant cell growth holds that cells grow
after being irreversibly strained by turgor pressure, the cell's
internal hydrostatic pressure in excess of atmospheric pressure
(33). Turgor pressure is a very important biophysical parameter.
In addition to driving cell wall extension, it regulates cell water
uptake (24), provides structural support for the cell, and may
control solute transport across intracellular membranes (10). As an
indication of turgor's importance in plant cell growth, the most
widely accepted theory of cell growth is based fundamentally on this
parameter (24).
Turgor magnitude is determined by a number of interrelated
factors: the solute concentration within the aqueous cell solution;
the hydraulic conductance of the cell wall and membranes; the
mechanical properties of the cell wall; apoplastic water reserves;
and the metabolic activity of the cell (8,12).
A knowledge of turgor pressure behavior during cell growth
may then be used in the following ways. First,some of the physics


underlying cell extension (specifically, turgor's role in growth)
can be elucidated. Second, a better understanding of the biological
processes occurring during growth, e.g. water uptake, may be
obtained. Third, a mathematical relationship between turgor and
cell growth can either be formulated or, using existing models,
adapted to the cell being studied.
A knowledge of turgor pressure behavior during sporan-
giophore growth may be used to determine what biophysical processes
occur during a sensory stimulated growth response. This information
in turn might elucidate the final steps in a given sensory transduc-
tion chain. A knowledge of turgor behavior during growth can
suggest physical explanations for dynamic and steady-state cell
growth. Finally, such knowledge can help uncover the biomechanical
and metabolic events occurring during various growth responses and
during steady growth. For these reasons, a study of the turgor
pressure and growth behavior of Phycomyces during steady and sensory
stimulated growth is important.
SECTION 2
SPORANGIOPHORE DEVELOPMENT AND DESCRIPTION
Sporangiophores of Phycomyces blakesleeanus are normally
grown from vegetative spores. The spores are small, ellipsoid (8-13
by 5-7.5 (im), multinucleated, single cells enclosed within a thick
cell wall (3).
Under suitable conditions, these spores germinate. They
then begin to swell and vacuolize. After approximately 5 hours, one


to three tip-growing hyphae emerge from the spore. These hyphae
branch and spread rapidly to form a coenocytic mycelium. Two to
three days following spore germination, a few hyphael tips within
the mycelium begin to grow vertically against gravity, forming
aerial hyphae or incipient sporangiophores.
Sporangiophore development is divided into five stages, as
first described by Errera (3) (see Figure 1).
Stage 1 development lasts approximately 9 hours. The
sporangiophore elongates at 1 to 2 mm/hr to a length of 1 to 4 cm.
The region of growth (growing zone) extends from the apical tip to
1.5 nun below, and remains approximately constant in length through-
out this first stage. As extension occurs, the sporangium rotates
at 30 degrees/min in the clockwise direction when viewed from above
(27). It is believed that this rotation results when stiff micro-
fibrils within the viscoelastic growing zone wall are passively
reoriented during cell wall growth (32).
Stage 11 development begins when the apical tip of the stage
1 sporangiophore undergoes spherical expansion. During spherical
growth, sporangiophore elongation and rotation cease. The formation
of a yellow spherical spore sac, or sporangium, 0.5 mm in diameter,
marks the end of stage 11.
During stage 111, no visible growth or rotation occurs. The
sporangium remains a bright yellow as putative spore formation takes
place within (27).
The gradual resumption of sporangiophore elongation and
rotation signals the initiation of stage lVa development. The


IENCIM !mm>
-iU
13
12
It
10
10
12 14
TIME (hr)
16 18
Figure 1 : The five stages of sprongiophore development.
The elapsed time from the initiation of stage
I is shown on the abscissa. This drawing was
taken from Ortega's Ph.D. dissertation (1976).


sporangium quickly turns dark brown or black and is observed to now
rotate in the counterclockwise direction (viewed from overhead).
Elongational growth accelerates while counterclockwise rotation
slowly decelerates to zero during the 90 minute interval that
constitutes stage lVa.
The reversal of rotation to the clockwise direction marks
the beginning of the final stage of sporangiophore development,
stage lVb. The rotational rate accelerates and stabilizes at
720/hr within the first half hour of this stage while the elonga-
tional growth rate stabilizes at approximately 3 ram/hr. These rates
are then maintained throughout the remainder of the sporangiophores
useful life (approximately 1 to 2 days), which usually ends when the
stalk folds over under its own weight.
Sporangiophore Description
Most experimental work in Phycomyces is performed using
stage IVb sporangiophores. During stage lVb, all observable
growth takes place in a fixed growing zone which extends from 0.1 mm
to 2.5 mm below the sporangium (see Figure 2 for a schematic
description of the stage IVb sporangiophore). The growing zone's
cell wall is extensible and deforms plastically when strained in the
longitudinal direction (26). In addition, cell wall elongational
growth rates within the growing zone decrease nearly exponentially
or possibly linearly with distance from the sporangium until the
non-growing zone of the cell stalk is reached (26,36). The cell
wall in the non-growing zone is covered by a waxy cuticle. It
deforms elastically when subjected to a longitudinal load (3,16,22).


8
Figure 2 : Schematic description of a typical
stage IVb sporangiophore.


A central vacuole, about 40 /xm in diameter, extends from
the sporangiophore's basal tip to the columella under the spor-
angium. The vacuo'le is an aqueous solution, containing cellular
waste products and solutes (3). It may be involved in regulating
water transport through the cell via solute transport across its
enclosing membrane, the tonoplast (3). The columella is a closed,
pear shaped extension of the cell wall that forms during stage 11.
A membrane enclosed cytoplasmic envelope, 30 pm thick in the
growing zone and about 5 jum thick in the non-growing zone,surrounds
the vacuole. The cytoplasm contains nuclei, mitochondria, lipid
droplets and other particles (3). It also contains strands of
protoplasm which transport these subcellular particles up and down
the length of the sporangiophore in a process called protoplasmic
streaming (3). The plasmallema, a membrane, separates the cell wall
from the cytoplasm. The cell wall is approximately 0.6 /im thick and
is essentially composed of stiff chitin microfibrils, about 20 nm
thick, embedded in an amorphous gel-like polysacharidic matrix of
chitosan (3,26).
SECTION 3
SENSORY RESPONSES OF PHYCOMYCES
Phycomyces responds to a variety of sensory stimuli by
altering its elongational growth rate and/or its direction of
growth. In general, a stimulus applied symmetrically with the
growth axis (i.e., the sporangiophore's longitudinal axis) produces
a change in the elongational growth rate only, while an asymmetric


10
stimulus induces differential growth rates on opposite flanks of the
growing zone wall. This asymmetric growth results in cell troping.
For example, when a barrier is placed 0 to 3 mm from the sporangio-
phore's growing zone, the sporangiophore will grow away from the
barrier at 1 to 2 degrees/min until the sporangiophore is skewed 50
degrees from the barrier (avoidance response). In contrast, when
two barriers are placed symmetrically on either side of the growing
zone, the elongational growth rate increases for approximately 5
minutes and then returns to the prestimulus rate (avoidance growth
response). Other examples of this phenomenon are the symmetric and
asymmetric light responses and the symmetric and asymmetric mechan-
ical stretch responses. The symmetric light responses (positive and
negative light growth responses) and the assymetric light response
(phototropic response) are elicited by altering the blue light flu-
ence rate either symmetrically or asymmetrically, respectively,
about the sporangiophore's longitudinal axis. The symmetric mechan-
ical stretch responses (negative and positive stretch responses) and
the asymmetric (bend) response are elicited, respectively, by apply-
ing (or removing) external longitudinal loads, or by applying a
lateral force to the sporangium (3,16). Since the symmetric light
growth responses and the mechanical stretch responses are relevant
to this study, they will each be discussed in further detail below.
Light Growth Response
The sporangiophore's light growth response is a transient
period of altered elongational growth rate that occurs following a
change in the' ambient blue light fluence rate. The positive light


11
growth response, a transient increase in growth rate, can be
elicited by stepping up the blue light fluence rate, while the
negative light growth response, a transient decrease in growth rate,
is effected by a stepping down the blue light fluence rate. Typical
positive and negative light growth responses are shown in Figure 3.
Experimentally, the positive response can be elicited by
first adapting the sporangiophore to two bilateral, equal fluence
light sources that are positioned symmetrically about the spor-
angiophore 's vertical axis. To avoid phototropic hunting, in which
the sporangiophore oscillates between the two light sources, the
light sources are usually positioned at an angle to the spor-
angiophore, optimally 60 degrees (18). The adaptation period allows
growth to stabilize at the basal rate of approximately 3 mm/hr.
Following this initial adaptation period, the light fluence rates of
both sources are stepped up simultaneously.
As indicated in Figure 3, the elongational growth rate
increases by approximately 100% about 3 to 4 minutes after the light
step-up. During the next 4 to 15 minutes, the growth rate remains
higher than the prestimulus rate, with the maximum rate occurring
approximately 5 minutes after the stimulus (3). Growth then
gradually returns to the basal rate 15 minutes following the
stimulus.
Ortega et al., have shown that the sporangiophore's mechan-
ical, extensibility increases during the light growth response (30).
He and others have also observed increased cell wall extensibility
during sensory growth responses to humidity (4) and nearby objects


Growth Roto |um/min)
Tim* (min]
Growth Roto |m/min)
Nogotivo
Figure 3 : Typical positive and negative light growth
response. These responses are ellicited by
stepping up (positive response) or stepping
down (negative response) the adapting blue
light fluence rate.


(28). A question which has remained unanswered until this inves-
tigation however, is whether the period of increased growth observed
during these responses results solely from altered cell wall
extensibility or whether turgor pressure changes also play a role.
This information is vital in understanding the penultimate
transduction event in these sensory responses. In addition, this
information may provide insight into the cell's adaptation process.
For example, does the return to the basal growth rate, which is
observed in any symmetric growth response, reflect a purely
biochemical process or is the cell wall perhaps strain hardened by
higher turgor pressure, inducing in turn, slower growth?
Mechanical Stretch Response
A mechanical stretch response is a transient alteration in
sporangiophore growth rate induced by the addition or removal of a
longitudinal load, or a transient change in growth direction
elicited by applying a lateral force to the sporangium (3,16).
Dennison and Roth first reported the positive and negative stretch
responses in 1967 (16). They found that hanging a weight heavier
than 0.5 mg from the sporangium of an inverted sporangiophore caused
dramatic slowing in elongational growth during the immediate five
minute period following the stimulus. Growth then slowly
reapproached the prestimulus rate during the subsequent 40 to 60
minute period. They also found that the period of depressed growth
increased with increasing load. In contrast, loads smaller than 0.5
mg caused an almost immediate increase in growth rate.


14
These workers also found that when a load is hung for 60
minutes from a sporangiophore and then removed, the sporangiophore's
growth rate doubles within 2 minutes of load removal (positive
stretch response). After five minutes of accelerated growth, the
sporangiophore gradually assumes its prestimulus growth rate (see
Figure 4).
SECTION 4
PLANT CELL GROWTH
A plant cell is thought to grow after the following bio-
physical and biochemical events occur. First, enzymatic action on
the cell wall is thought to cause stress relaxation within the cell
wall. Since at any instant the stress exerted by turgor pressure is
balanced by the reaction force of the cell wall, then any enzymatic
stress relaxation induces incremental turgor decay. A turgor
decrease, in turn, increases the driving potential for cell water
uptake (24,8,33), causing an incremental influx of water into the
cell. This influx of water causes the cell to expand until the
mechanical extensibility of the cell wall is exhausted. This cycle
is repeated hundreds of thousands of times during the life of the
cell. Evidence indicates that cell wall synthesis continues
throughout, structurally supporting the cell and preventing cell
wall rupture.
It is important to note that turgor pressure is the central
biophysical parameter in this theory (qualitative theory of plant
cell growth). Turgor first decays as the wall is chemically


15
Figure 4 : Typical positive and negative stretch growth
responses. The negative stretch growth response
can be elicited by hanging a weight heavier than
0.5 mg from the sporangium of an inverted stage IVb
sporangiophore. The positive response can be
elicited by removing a weight heavier than 0.5 mg
(which has hung for 60 minutes) from an inverted
stage IVb sporangiophore.


16
loosened.lt then regulates cell water uptake and finally provides
the driving force for cell extension.
There are several mathematical models of plant cell growth,
stated in terms of turgor pressure, which have proven very useful.
Lockhart was the first to postulate that cell expansion is mechan-
ically driven by turgor pressure and that turgor is coupled to the
rate of water uptake (24). His original equations, which describe
steady-state cell wall expansion and steady-state cell water uptake,
have been reformulated and are referred to as the Growth Equations.
The steady-state Growth Equation for irreversible cell wall ex-
pansion is given by:
v = ^(P-Pc) (1.1)
where v is the cell's relative volumetric growth rate, is the cell
wall extensibility, P is the turgor pressure, and Pc is the yield
threshold or critical pressure. The steady-state Growth Equation
for cell water uptake, essentially a statement of the conservation
of mass, is given by:
v L(Ajt-P) (1.2)
where L is the cell's hydraulic conductance, and An- is the osmotic
pressure difference between the internal cell solution and the
external water source. During steady-state growth, equation (1.1)
equals equation (1.2).


17
Ortega (28) recently augmented equation (1.1) to take into
account reversible cell wall expansion. This Augmented Growth
Equation is given by:
v = *(P-PC) + i ^ (1.3)
where e is the cell's volumetric elastic modulus.
Green developed an equation which describes the tendency of
some plant cells to reapproach their basal growth rate following a
perturbation in a given biophysical parameter (36) This self-
stabilization equation, or as it will be referred to here, Genera-
lized Growth Equation, is given by:
3E A'Dv where D and A are constants. The term Dv is usually identified as a
growth deceleration or strain hardening function (36), while A is a
growth promoting or accelerating parameter.
SECTION 5
TURGOR PRESSURE MEASUREMENT
The last section demonstrated the importance of turgor
pressure in plant cell growth. Although plant physiologists have
long recognized its importance, they have had difficulty measuring
turgor due to the small size and frailness of most cells. Roelofsen


estimated the turgor pressure in Phycomyces in 1950 as the
externally applied pressure causing cessation of cell growth (3).
This so called iron lung technique is indirect, however, and
only gives a rough estimate of the true turgor pressure. In 1968,
Green (20,21) measured turgor pressure in Nitella using a gas filled
microcapillary which was inserted into the cell's vacuole. The
compression of a gas bubble within the microcapillary gave a direct
measurement of the turgor pressure. Although a great improvement
over the iron lung technique, this method cannot be used to directly
alter turgor, and in addition, cannot accurately detect dynamic
turgor changes.
Turgor pressure measurement improved dramatically with the
introduction of the pressure probe by Stuedle and Zimmerman in 1974
(35). With this instrument, essentially a microcapillary coupled to
a solid state pressure transducer, one can now continuously measure
not only steady-state turgor pressure, but also dynamic turgor
pressure changes. Additionally, the pressure probe allows direct
experimental control of turgor so that various biophysical parame-
ters can be estimated with relative ease (8,9,11,34,35,37,12,34).
SECTION 6
THESIS PREVIEW
This thesis reports and discusses the results of three
investigations. In the first study, stage IVb sporangiophores were
subjected to creep tests using a new technique to impose constant
increased turgor pressure. This method utilized the pressure probe


to step up turgor by injecting inert silicon oil into the cell
vacuole. It appears that this method is the most direct means
available to determine the in vivo creep response of plant cells.
It will be shown that Phycomyces exhibits two distinct
growth responses to turgor step-ups, each depending on the magnitude
of the pressure step-up.*, AP. Following AP's of less than
approximately 0.02 MPa, the growth rate increases within one minute
to a new higher steady rate. Conversely, following AP's greater
than 0.02 MPa, but less than approximately 0.1 MPa, the spor-
angiophore's growth rate decreases dramatically for approximately
five minutes and then gradually reapproaches the prestimulus rate
during the subsequent 20 to 60 minutes. Growth remains depressed,
by 50% or more, one hour after a AP larger than approximately 0.1
MPa.
It will be shown that Phycomyce's growth response to AP's of
less than 0.02 MPa can be modeled by either the steady-state Growth
Equation (1.1) or the Augmented Growth Equation (1.3). Since
sporangiophores respond to AP's of less than 0.02 MPa in a manner
that is consistent with the Growth Equations, (1.1) and (1.3), then
cell wall extensibility and cell critical turgor pressure, Pc,
within these equations can be estimated using creep data. It was
found that the average critical pressure in 7 tests was 0.262 MPa
while ^ was approximately 0.0209.MPa"1 min"1.
It will also be demonstrated that the cell's response to
pressure step-ups between 0.02 and 0.10 MPa can be modeled by an
adapted form of the Generalized Growth Equation (1.4). It will be


argued that the sporangiophore's growth response to AP's greater
than 0.02 MPa is the previously reported negative stretch growth
response.
In the second study, stage IVb sporangiophores were plucked
from their mycelia, placed in water, adapted, and then removed from
water. Turgor pressure and growth were continuously measured
throughout the adaptation period and the subsequent period of water
deprivation with the aim of determining the cell's turgor pressure
behavior during cell wall stress relaxation. In approximately half
of these experiments, it was found that the sporangiophore continued
growing while turgor remained essentially fixed, for two or more
hours out of water. This result supports the hypothesis that the
sporangiophore contains a significant extracellular, intrawall water
source which maintains cell water uptake following water removal
(12). In four experiments, however, pressure did decay (a result
that is consistent with the qualitative theory of plant cell
growth), to a constant magnitude of approximately 0.09 MPa. This
final constant turgor was identified as the ultimate critical
pressure (see Green, 21). Additionally, the characteristics of
these decays were consistent with the Augmented Growth Equation
model, in that pressure decayed nearly exponentially to a final
constant magnitude (9,28). The finding that Pc is approximately 0.10
MPa following stress relaxation, but approximately 0.26 MPa during
creep, suggests that Phycomyces has an adjustable critical pressure
which remains fairly close to turgor pressure during normal growth


but which adjusts downward during stress relaxation, behavior
exhibited by Nitella (21).
The last study that is reported in this thesis consists of
experiments which were designed to determine the turgor pressure
behavior in Phycomyces during the sporangiophore's positive and
negative light growth responses. As previously mentioned, a
knowledge of turgor's behavior during sensory stimulated growth
might indicate whether the period of accelerated growth results
solely from altered cell wall mechanical properties or whether
turgor also plays a role. It was found that turgor remains
essentially constant throughout these responses, proving that these
responses are effected solely by biochemical modification of the
cell wall.


CHAPTER II
IN VIVO CREEP GROWTH RESPONSES OF PHYCOMYCES
SECTION 1
INTRODUCTION
Many biological materials, including plant cell walls, have
viscoelastic properties. The two most common methods used to
characterize the mechanical properties of a viscoelastic material
are the creep test, in which the material is instantaneously
subjected to a constant stress, and the stress relaxation test, in
which the material is instantaneously subjected to a constant
strain. In either test, one of the two parameters, stress or
strain, is experimentally controlled while the other is measured as
a function of time. Theoretically, either procedure should yield
the same constitutive relationship between stress and strain.
It has proven difficult, however, to use either viscoelastic
test to develop constitutive relationships between the measurable
biological analogs of stress and strain: turgor pressure and cell
growth. Using an Instron machine to impose a constant longitudinal
strain, Ortega established the viscoelastic nature of the spor-
angiophore of Phycomyces (27). He found that an imposed
longitudinal stress relaxed nearly exponentially and that the
relaxation was similar to that of a linear Maxwell viscoelastic


23
material, i.e., a viscous dashpot connected in series to a spring.
Although the Instron technique is useful in characterizing the
material properties of cell walls (5), it is difficult to relate the
imposed cell wall stresses to those imposed by turgor pressure.
Several investigators'have inflated dead cell walls, with
mercury to study the wall's mechanical behavior during creep tests
(26). In many cases, a correlation has been found between the rate
of in vivo growth and the subsequent rate of creep. However, in
other cells, no such correlation could be established (36).
Additionally, while the mercury inflation technique approximates the
multiaxial stress states imposed by turgor pressure, this method
measures only the material properties of the dead cell wall. The
metabolic activity occurring during in vivo growth remains unknown.
Certainly, a correlation between turgor and growth cannot be
established using this technique.
In 1968, Green (20) developed an in vivo creep test using a
gas filled capillary inserted into a Nitella internode cell which
allowed experimental control and measurement of cell turgor pres-
sure. With this method, he was able to study the growth responses
of Nitella to large pressure changes (approximately 0.1 MPa). He
subsequently established a quantitative biophysical model of plant
cell growth in Nitella in terms of turgor pressure and growth rate.
Using the steady-state Growth Equations, and his turgor and growth
measurements, he was also able to estimate the cell wall's extensi-
bility and yield threshold (21). This pioneering work may have
suffered one perceptible weakness however, in that the method used


24
to adjust turgor, an external osmoticum, was indirect. The cell
wall's resistance to water transport may have prevented instan-
taneous pressure step-ups. Additionally, in cell walls containing
free solutes and/or free water, it is impossible to achieve a true
pressure step-up with this method due to slow osmotic equilibration.
The introduction of the pressure probe in 1974 allowed not
only direct measurement of turgor pressure, but also offered the
capability to directly control turgor. Cosgrove et al., have
exploited this capability in pressure clamp experiments in which
turgor is temporarily stepped up in order to determine a cell's
water transport properties (11). Investigators have also used the
pressure probe to determine turgor behavior during wall stress
relaxation (9). However, it appears, that until now, no one has used
the pressure probe to investigate the creep response of a plant cell
to long term turgor pressure step-ups.
This chapter reports the first such measurement. The in
vivo creep response of Phycomyces was investigated using a method in
which turgor was stepped up (via the pressure probe), by injecting
inert silicon oil into the cell vacuole.
There were two principal reasons for performing these
experiments. The first reason was to investigate the sporang-
iophore's growth response to increased turgor. This information is
fundamental if one wishes to gain some understanding of turgor's
role in cell expansion. The second reason for these experiments
arose from Ortega's earlier demonstration of the sporangiophore's


viscoelastic properties (27) This earlier result suggested that a
creep test might be used to either construct a biophysically based
constitutive relationship between cell growth and turgor pressure,
or to adapt an existing relationship, such as the Growth Equation
(1.1), to model sporangiophore growth.
SECTION 2
MATERIALS AND METHODS
A description of the method used to grow sporangiophores is
given in Appendix A as is a general outline of the experimental
apparatus used in all experiments. Since the pressure probe is the
essential piece of equipment, used in all of the experiments
reported in this thesis, then its construction and operation will
now be discussed in detail.
Pressure Probe
Turgor pressure was measured using a custom made pressure
probe, similar to the one described by Husken, Steudle, and
Zimmerman (23). The pressure probe is shown schematically in Figure
5. The pressure probe consists of a microcapillary tip which screws
into a plexiglass pressure chamber. The pressure chamber is a T-
shaped cylindrical channel which allows movement of a screw driven
plunger through its horizontal leg. A Kulite model XT-190-300A or
XT-190-300G pressure transducer screws into the vertical leg of the
channel. The pressure chamber and the microcapillary tip are filled


Pressure
/Transducer
PRESSURE PROBE
Figure 5 : Schamatic description of the pressure probe
which was used in all experiments.
ro
cr>


with Dow 200 fluid, a 1 centistoke viscosity incompressible silicon
oil.
The transducer converts pressure inputs into proportional
voltage outputs. The model XT-190-300A transducer measures absolute
pressure while the XT-190-300G measures gauge, or actual turgor
pressure. The rated output response of the absolute pressure
transducer was 43.365 mV/MPa while that of the gauge pressure
transducer was 22.408 mV/MPa. The input sensitivity of each
transducer was determined with a U-tube manometer. It was deter-
mined to be 0.0005 MPa in the absolute transducer and 0.0007MPa in
the gauge transducer.
Pressure Probe Insertion and Turgor Pressure Measurement
Pressure within the pressure probe is controlled by screwing
the plunger into or out of the probe's pressure chamber. Generally,
the pressure had to be kept just above atmospheric prior to insert-
ing the microcapillary tip into the cell. Higher pressure would pour
oil from the tip onto the sporangiophore, causing the tip to slide
and inhibiting insertion.
Successful probe insertion was signaled when pressurized
cell sap moved rapidly back into the microcapillary tip. The cell
sap-silicon oil interface within the tip formed a meniscus which was
visible under a stereomicroscope (see Appendix A) as a thin dark
line. The meniscus could be moved within the tip by either increas-
ing or decreasing the pressure within the probe. To measure turgor
pressure, one had to minimize the amount of cell sap within the
microcapillary tip. This was accomplished by moving the meniscus to


28
a point within the tip which was very close to the cell, usually 10
to 30 /im away from the vacuole. To ensure that the tip was not
clogged by cell sap, one generally had to move the meniscus
slightly, back and forth, by pulsing the probe's pressure up and
down continuously.
Creep Experimental Procedure
Stage IVb sporangiophores were adapted to room conditions
(overhead broadband light source, 21-22C, physiologically inert red
back illumination) for 30 minutes. Following adaptation, cell
elongation measurements were initiated and continued at approximate
1 to 2 minute intervals throughout each experiment. After 10 to 30
minutes of fairly steady growth was observed, the pressure probe was
inserted into the cell vacuole.
Turgor pressure was measured and recorded continuously on a
chart recorder throughout the remainder of each experiment. The
cell was allowed to adapt to the inserted pressure probe for another
10 to 30 minutes during which time elongation continued to be
measured.
Following this second adaptation period, turgor pressure was
stepped up by injecting a drop of silicon oil into the cell vacuole.
Drop sizes ranged from 0.2 to 1.5% of cell volume. The pressure was
kept constant manually for another 20 to 60 minutes while cell
elongation continued to be measured.
Note, throughout the remainder of this chapter, the terms
"small pressure step-up" and "large pressure step-up" will be used


to refer to AP's of magnitude less than 0.02 MPa and to AP's of
magnitude greater than 0.02 MPa, respectively.
SECTION 3
CREEP TEST RESULTS
In order to simplify analysis, the natural logarithm of
sporangiophore length was plotted versus time for every creep
experiment. Figures 6,7,8, and 9 show typical results.
In general, all of these curves were linear prior to
pressure probe insertion. However,in approximately 50 % of the
creep tests which were performed, the slope decreased immediately
following probe insertion. Slopes remained constant, before and
after probe insertion, in the remainder of the experiments (until
the pressure was stepped up at time tp).
Turgor step-ups of magnitude less than approximately 0.02
MPa caused a qualitatively similar response in nearly every such
experiment. As seen in Figures 6 and 7, the slope of the growth
curve increased within one minute to a new higher constant value,
and remained fixed during the next 20 to 40 minutes. This general
response was repeated in every experiment in which the slope of the
growth curve was unchanged by probe insertion.
Turgor step-ups between approximately 0.02 and 0.10 MPa also
caused qualitatively similar responses. As seen in Figures 8 and 9,
the slope of the growth curve decreased dramatically within the
first minute following a large pressure increase and then remained
relatively flat during the following 1 to 10 minutes. The slope
then gradually increased during the subsequent 3 to 60 minute


30
Figure 6 : Representative creep response to a pressure
step-up smaller than 0.02 MPa. Note that
, basal growth was not affected by probe
insertion and that the increase in slope
occured almost immediately following
application of AP.AP-0.015 MPa.


In L 0.79 r
0.77
0.75-
0.73 -
0.71 *
0.69
probe
inserted
it pressure
|stepped up
20
Time (min)
40
Turgor
(MPa)
0.4
0.2
Figure 7 : Representative creep response to a AP smaller
than 0.02 MPa. Growth was unaffected by
pressure probe insertion and the increase
in growth rate occured almost immediately
following the application of the pressure
step-up. AP-0.006 MPa. The post step-up growth
rate was 155% that of the prestep-up rate.


Turgor (MPa)
06
0.4
0.2
0
Figure 8 : Representative creep response to a AP
larger than 0.02 MPa. The basal growth
rate was not affected by insertion of the
pressure probe. The post step-up growth
rate reached the basal rate approximately
4 minutes following the pressure step-up.
AP-0.0023 MPa.


33
Turgor (MPa)
Figure 9 : Representative creep response to a AP
larger than 0.02 MPa. The basal growth
rate was essentially unaffected by probe
insertion. The growth rate at the end of
this experiment was approximately 45% of
the prestimulus rate. AP-0.023 MPa.


34
period, and in some cases reached a constant magnitude equal to the
prestep-up value.
The sporangiophore's growth response to AP's larger than
0.02 MPa was elicited over a range of pressure step-ups from 0.02 to
0.125 MPa. It did not occur every time AP was in this range,
however. Instead, the first response discussed above would be
elicited. For example, in one experiment, the slope of the growth
curve increased to a new constant value almost immediately following
a pressure increase of 0.046 MPa. The former response did occur in
every experiment in which AP was greater than 0.06 MPa, however.
The growth curves following AP's larger than 0.02 MPa
generally became flatter, i.e., the slope decrease was relatively
greater, as the magnitude of AP increased (see Figure 10). For
example, 60 minutes after a pressure step-up of 0.10 MPa, the slope
of the curve was only 50% that of the prestimulus slope, whereas 35
minutes after a AP of 0.03 MPa, the slope was equal to the pre-
stimulus value.
Creep Responses in Terms of Growth
The sporangiophore's relative rate of elongational growth,
2, where 2 = (1/1)(dl/dt)(1 is sporangiophore length at time t), can
be shown to be equal to the slope of the ln(l) vs t curve as
follows. First, recall that the derivative with respect to t, of
the function ln(l), where 1 = l(t), is given by (l/l)dl/dt, the
relative elongational growth rate. Now, replace the differentials
above by finite differences, so it is seen that


Figure 10 : This figure depicts the increasing response
size seen with increasing AP. Note the elastic
responses which occur immediately after the
application of the 0.036 and 0.127 MPa
pressure step-ups.


(2.1)
36
i
1 dl = dlnl
1 dt dt
Alnl
At
where the last quantity on the right is simply the slope of the
ln(l) versus t curve.
It is now apparent what the experimental ln(l) versus time
curves show how the sporangiophore's relative elongational growth
rate behaves before and after a pressure step-up. The experimental
results thus indicate that relative elongational growth in the stage
IVb sporangiophore of Phycomyces is altered by pressure step-ups in
two ways. Following a pressure step-up of less than approximately
0.02 MPa, the cell's relative rate of elongational growth increases
within a minute to a new higher constant rate (refer to Figures 6
and 7). This rate is then maintained for at least 20 to 60 minutes
following the pressure stimulus. Conversely, following a pressure
step-up greater than approximately 0.02 MPa, the sporangiophore's
relative elongational growth rate decreases within a minute to a
low, somewhat variable rate (refer to Figures 8 and 9). One to ten
minutes after the stimulus, growth begins to accelerate, so that 20
to 60 minutes after the stimulus, growth is anywhere from 50 to 100%
of the prestimulus rate. Additionally, as shown in Figure 10, the
length and magnitude of the growth depression following a large
pressure step-up appears to increase with the magnitude of the step-
up.
Creep Response in Experiments Exhibiting Altered
and Unaltered Growth Rate Following Probe Insertion
Growth, as previously mentioned, was found to decrease
following pressure probe insertion, in approximately 50% of the


creep tests which were performed. This occurred in 15 out of 24
experiments in which AP was less than 0.02 MPa, and in 3 out of 11
experiments in which AP was greater than 0.02 MPa.
In all 9 of the small pressure step-up experiments in which
the relative elongational growth rate remained constant following
probe insertion, the cell responded in a manner qualitatively
similar to that shown in Figures 6 and 7. In 9 of the 15 other
small AP experiments showing post-insertion growth loss, growth also
increased to a higher constant rate following the pressure step-up
stimulus. A typical result from such an experiment is shown in
Figure 11. Of the 6 remaining small AP experiments showing post-
insertion growth loss, growth decreased in 3 following a AP, while
no response at all could be detected in the other 3.
In all 8 of the large pressure step-up experiments in which
growth was unaffected by probe insertion, the cell responded in a
manner qualitatively similar to that shown in Figures 8, 9, and 10.
Conversely, no response was detected in the three large AP experi-
ments in which growth decreased following probe insertion.
Creep Control Experiments
Control experiments were performed in order to determine
whether the presence of silicon oil within the sporangiophore
altered cell growth. The procedure used in these experiments was
identical to that used in the creep experiments, except that,
instead of applying a pressure step-up at time tp, pressure was
pulsed up from, and then back down to the basal turgor. The 2 to 5
second pulse, 0.003 MPa in magnitude, served to inject a small oil


Turgor (MPa)
Figure 11 : This figure shows a typical creep response
to a AP smaller than 0.02 MPa in a cell
whose growth was affected by pressure probe
insertion. The depressed post-insertion/
pre-step-up growth rate was usually constant
and increased immediately following a AP to a
new, constant rate. AP-0.007 MPa.


drop into the cell vacuole. A representative result of 7
experiments is shown in Figure 12.
Growth decreased following probe insertion in 4 of the 7
control experiments which were performed. However, the elongational
growth rate remained constant following oil injection in all 3 of
the experiments showing no post-insertion growth loss. Conversely,
growth decreased following oil injection in all 4 of the experiments
showing post-insertion growth loss.
SECTION 4
ANALYSIS AND DISCUSSION
Data Selection Criteria
The loss of growth rate following pressure probe insertion
could reflect any of a number of altered cell properties. It could
be caused, for example, by loss of turgor pressure, lowered basal
metabolism, lowered water uptake, or any combination of these or
other factors. Since the principal interest lies in determining the
cell's normal in vivo response to increased turgor pressure, then
those experiments exhibiting growth loss following probe insertion
were not considered in the following data analysis. Only those
experiments in which the relative elongational growth rate remained
constant throughout the 10 to 30 minute period before and the 10 to
20 minute after pressure probe insertion were evaluated. This
reduced the data base by 52%.


Time (min)
Figure 12 : A representative creep control result. Note
that the basal growth rate did not change
following probe insertion nor following the
injection of the oil drop.


41
Creep Control Experiment
The results of the creep control experiments which were
discussed in the last section demonstrate that the presence of
silicon oil alone within the cell vacuole has no effect on the basal
growth rate. This result is qualitatively supported by earlier work
which showed that the growing zone of the stage IVb sporangiophore
is functionally autonomous (3). When metabolism is inhibited in all
but the apical 3.5 mm of the sporangiophore, a region that contains
the growing zone, normal growth and growth responses continue for 3
to 4 hours (3).
The control experiments demonstrate that the sporang-
iophore's growth responses to turgor pressure step-ups are effected
solely by increased pressure.
Phvcomvce's Growth Response to Pressure
Step-ups Smaller Than 0.02 MPa
The finding that sporangiophore growth rate increases
following a small AP qualitatively agrees with Dennison and Roth's
earlier finding that the growth rate increases after a 0.3 mg weight
is hung from a sporangiophore (16). Although the uniaxial stress
induced by such a longitudinal load only approximates the multiaxial
stress induced by a turgor step-up, both stimuli can cause
substantial growth rate changes in the longitudinal direction only.
This is evident, since the sporangiophore's radial extensibility is
very small, approximately 1/16 that of the longitudinal direction
(27). Thus both stimuli are functionally equivalent in Phycomyces.


42
A Qualitative Model of Sporangiophore Growth
The finding that a small turgor step-up causes an increase
in the elongational growth rate demonstrates for the first time that
the stage IVb sporangiophore qualitatively obeys the Growth Equa-
tions, (1.1) and (1.3):
v *(P-PC) , (1.1)
v - (P-Pc) + i g . (1.3)
This is apparent because these models make a simple prediction: the
relative volumetric growth rate will increase following a pressure
increase. To see this, first assume that <(> and Pc in these
equations are each constant. This assumption is valid since it is
desired to show that these models predict a sporangiophore's growth
response to a small pressure step-up. Next, replace the term v in
equations (1.1) and (1.3), with the approximate term (1/1)(dl/dt).
This approximation is valid in Phycomyces since the sporangiophore's
absolute rate of elongational growth is about 16 times larger than
its rate of radial expansion (27). Hence, elongational growth
represents essentially all volumetric expansion. Mathematically,
this approximation is derived as follows:
1 dV 1 d(lA') A' 1 dl 1 dl
V V dt 1A' dt A' 1 dt I dt
where V is the cell's volume at time t and A' is its cross-sectional
r _
area, which is assumed constant. Now, having established the
equivalence of v with (1/1) (dl/dt) (and assuming and^cto be con-
stant) it is apparent from (1.1) and (1.3) that an increase in P


43
from one constant magnitude to another will theoretically cause an
increase in the relative elongational growth rate of Phycomyces, as
was observed.
This.finding has many important implications. First, these
equations may now be used, in combination with experimental data, to
estimate various biophysical parameters, such as cell wall exten-
sibility, and critical pressure (see 21). Second, these equations
provide a coherent mathematical framework to characterize sporang-
iophore growth. For example, a possible functional relationship
between extensibility and turgor pressure might now be logically
determined. Or if desired, a relationship between relative elong-
ational growth and extensibility might be found. Third, the
biophysics underlying sporangiophore growth can be better understood
by using this model in combination with experimental results. For
example, Green used the Growth Equation model and experimental
pressure step-up results on Nitella to postulate that the critical
pressure in this cell adjusts with changing turgor pressure. He
hypothesized that the critical pressure was lowered by an unknown
metabolic process and was raised by mechanical strain hardening
(21).
Estimating Extensibility and Critical Pressure
Now that it has been established that Phycomyces qualit-
atively obeys the Growth Equations, (1.1) and (1.3), these equations
can be used in combination with experimental creep data to estimate
both cell wall extensibility and cell critical pressure, Pc.
Extensibility can be estimated from equation (1.1) (see Green, 21).


First assume that and Pc are constant, and then take the differen-
tial of both sides. The resulting equation:
dv = $dP
(2.3)
can then be rearranged to yield:
4, =, ^
9 dP
(2.4)
To obtain numerical values of from experimental data, the differ-
entials in the last equation must be replaced by finite differences,
so that finally
dv d fdlnl^
dP dP [ dt J
A(Alnl/At)
AP
(Alnl) fAlnll
l At l At J
AP
, (2.5)
where equation (2.2) was used and where the subscripts 1 and 2 refer
to measurements made before and after a pressure step-up from Px to
P2.
Critical pressures can now be estimated by inserting the
above determined values of into (1.1) and rearranging to get:
The equality of the second and third terms follows from the
definition of given in (2.5).
Table 1 shows the extensibilities and critical pressures
that were calculated from 7 small pressure step-up experiments.
(Recall that the small AP experiments were the only ones in which
growth increased following a AP. Hence, these are the only


45
Table 1
Extensibilities and Critical Pressures
Calculated From Creep Experiments
lx(min'1) 12(min*1) Pi(MPa) AP(MPa) (MPa'1min'1) Pc (MPa) (Pi-Pc) (MPa)
0.00120 0.00150 0.391 0.046 0.00652 0.207 0.184
0.00085 0.00100 0.406 0.015 0.00533 0.247 0.085
0.00185 0.00220 0.240 0.006 0.05833 0.208 0.032
0.00120 0.00135 0.226 0.008 0.01875 0.162 0.064
0.00145 0.00170 0.347 0.005 0.05000 0.318 0.029
0.00057 0.00060 0.430 0.009 0.00323 0.253 0.176
0.00060 0.00063 0.510 0.019 0.00135 0.440 0.066
4 0.02046 MPa"1min"1
Pc - 0.262 MPa
(P-Pc) 0.091 MPa


experimental results which obey the Growth Equations. As noted,
only those experiments in which cell growth was unaffected by probe
insertion are being considered in this analysis.)
As seen in Table 1, extensibilities ranged from 0.00135 to
0.058 MPa"1 min"1 and averaged 0.0205 MPa"1 min"1. Critical
pressures ranged from 0.029 to 0.184 MPa and averaged 0.262 MPa.
The critical pressures were close to the equilibrium turgor pres-
sures, the average difference between P and Pc being 0.0909 MPa.
The average extensibility of 0.0205 MPa"1 min"1 in Phyco-
myces is comparable to the 0.0167 MPa"1 min"1 value that Green est-
imated in Nitella using a similar experimental technique and anal-
ysis (21). The sporangiophore's average extensibility is an order
of magnitude larger than the 0.0013 MPa"1 min"1 value that Cosgrove
found in excised pea stems (9) using stress relaxation tests.
The average critical pressure of 0.262 MPa is nearly identi
cal to the 0.2 MPa value reported for Nitella (21). Additionally,
the average 0.0909 MPa difference between P and Pc is of the same
order of magnitude as the 0.02 MPa difference observed in Nitella
(21).
Comparison of Experimental and Theoretical Creep Responses
to Pressure Sten-uns Smaller Than 0.02 MPa
The extensibilities and critical pressures that were
calculated in the last subsection can now be used determine the
theoretical creep response predicted by the Augmented Growth
Equation (1.1). To accomplish this, first multiply both sides of
the Growth Equation by differential dt to get:


47
vdt = i dV = J(P-Pc)dt (2.7)
Next, note that pressure as a function of time can be represented
as:
P. (P2-P1)U(t-tp) + Px (2.8)
where Pj^ and P2 are the equilibrium pre and post step-up turgor
pressures, respectively, and where U(t tp ) is the unit step-
function. Replacing P in (2.7) by the right hand side of (2.8),
employing equation (2.2), and then integrating from time 0 (i.e.,
the beginning of the experiment) to some arbitrary time t finally
yields:
lnl lnlQ + 0(P1-Pc)t , t and
lnl = lnlQ + (P2-P(j) (t-tp) + ^(P1-Pc)tp t>tp (2.9b)
where 1 is the sporangiophore's length at time t, 1Q is its length
at time 0, and tp is the time when the pressure is stepped up from
Pi to P2.
Equation (2.9a) states that the growth rate prior tp a step-
up is simply the basal growth rate, ^(Pi-Pc) Conversely, equation
(2.9b), states that the growth rate following a small AP has


48
increased by a constant magnitude equal to ^(P2 Pi), which has
already been shown to be qualitatively true.
creep responses depicted in Figures 6 and 7 and the corresponding
theoretical creep response predicted by equations (2.9). The
maximum deviation between experimental and theoretical creep values
of ln(l) was found to be approximately 1.5% of the experimental
value in these particular experiments. The agreement between
experiment and theory is obviously better in experiments yielding
linear creep curves.
Modeling Soorangionhore Growth with the
Augmented Growth Equation
predicted by the steady-state Growth Equation is essentially that
predicted by the Augmented Growth Equation. This latter theoretical
response is given by:
Figures 13 and 14 show a comparison of the experimental
It is important to note that the theoretical creep response
lnl lnlQ + <^(P1-Pc)t
and
(2.10)
lnl lnlQ +*(P2-P1)(t-tp) + ^(P1-Pc)(t) + i (Pa-Pi)
t>tp
where e is the volumetric elastic modulus. Mathematically, this
equation differs from that derived from the steady-state equation by
the factor (l/e)(P2 -Pi). Since the magnitude of the volumetric


Turgor (MPa)
InL
1.60 r
1.58 H
1.561-
-experiment
o-eqn. 2.9
0.4
0.2
1.54-
1.52 L
0
probe
inserted
1
1
pressure
stepped up
'_____i_
20 40 60
0
Time (min)
Figure 13 : Comparison between an experimental creep response
to a small AP and the theoretical response
predicted by the Growth Equation (1.1). The
experimental curve is that shown in Figure 6.


50
Figure 14 : Comparison between an experimental creep response
to a small AP and the theoretical response
predicted by the Growth Equation (1.1). The
experimental curve is that shown in Figure 7.


elastic modulus is approximately 10 MPa while that of (P2 Px) is
approximately 0.01 MPa, it is apparent that this term will be
relatively small, so that either model could represent the sporang-
iophore's creep response to small pressure step-ups.
However, the Augmented Growth Equation predicts that at
time tp when pressure is stepped up, there will be an instantaneous
change in sporangiophore length from l(tp) to l(tp) + (1/e)(P2-Pt).
This instantaneous change in length results from elastic stretch
imposed by the higher turgor pressure. An elastic response was in
fact observed in a number of experiments, and was particularly
evident at larger AP's (see Figure 10), a result suggesting that the
Augmented Growth Equation may be a more realistic model of sporang-
iophore growth.
There are two additional pieces of evidence which support
this idea. First, it was found that this equation predicts the
creep response of the stage IVb sporangiophore to within 0.7%. As
shown in Figure 15, the agreement between the experimental creep
curve and theoretical creep curve predicted by the Augmented Growth
Equation is very close.
The second additional piece of evidence supporting the
hypothesis that the Augmented Growth Equation models sporangiophore
growth comes from Ortega's earlier uniaxial stress relaxation tests
(27). As mentioned, he observed that stress decays as though the
sporangiophore's cell wall were a Maxwell viscoelastic material.
Since a modified form of this constitutive relationship is actually
equivalent to the Augmented Growth Equation in Phycomyces (see


52
Figure 15 : Comparison between an experimental creep
response to a small AP and the theoretical
response predicted by the Augmented Growth
Equation(1.3). The experimental curve is
that shown in Figure 7.


Ortega, 28), then the applicability of the Augmented Growth Equation
as a model of sporangiophore growth is again suggested.
The question of whether sporangiophore growth can be modeled
by the Augmented Growth Equation is very difficult to answer.
Presently, it would be impossible to determine whether in vivo
growth is related to turgor pressure as in either the Augmented
Growth Equation or the steady-state Growth Equation. Instead, one
must be content to establish the general utility of either model in
predicting the cell's pressure or growth response to a given
pressure or growth stimulus. In this respect, either model appears
to satisfactorily predict Phycomyce's creep responses to small
pressure step-ups.
Phvcomvce's Growth Response to Pressure Sten-uos
Between 0.02 and 0.10 MPa and the Negative Stretch Response
The sporangiophore's growth response to large pressure
step-ups appears to correspond to the negative growth response
reported earlier (16). This response, as mentioned, occurs when a
weight heavier than 0.5 mg is hung from the sporangium of an
inverted stage IVb sporangiophore. It is characterized by a one
minute latency, 5 to 10 minutes of drastically reduced growth rate,
and a final 40 to 60 minute period of gradually accelerated growth.
The following observations support the idea that both
responses are actually the same response. First, the sporang-
iophore 's relative elongational growth rate is reduced by approx-
imately 50% within a minute after a large pressure step-up and
remains dramatically reduced for approximately 5 to 10 minutes


54
(refer to Figure 10). Subsequent to this, growth gradually acceler-
ates in most experiments toward the prestimulus rate. Second, the
observed increase in response size and duration with increasing AP
correlates with the larger negative response seen with heavier loads
(16).
If the negative stretch response and the creep response are
indeed the same response, then an interesting question arises as to
what event elicits the response. The minimum longitudinal load,
which elicits the negative stretch response equals 0.5 mg while the
minimum turgor pressure step-up required to elicit the response is
approximately 0.02 MPa. A simple calculation, in which the force
exerted by turgor at any horizontal cross-section of the
sporangiophore is set equal to the reaction force of the cell wall
(assuming a cell cross-sectional area of 1.77(108)m2 and a cell
wall cross-sectional area of 2.83(10'10)m2) shows that the average
longitudinal wall stress, a, increases by 0.026 MPa following a 0.5
mg load stimulus, but increases by 2.083 Mpa following a step-up of
0.02 Mpa, indicating that the response is not effected by a change
in a. Indeed, if the responses are the same, then it can now be
shown that the negative stretch response is not elicited by a change
in the average wall stress state. First, note that the change in
longitudinal stress following a load application may actually be
smaller than 0.026 MPa since turgor may drop as the sporangiophore
is plastically strained. Nonetheless, it.is apparent that the
change in the average longitudinal stress does not elicit the
negative stretch response. Likewise, average radial and tangential


stresses in the applied load case will either remain constant or
decrease, while both will increase following a pressure step-up.
Average shear stress changes could cause the response, but one would
expect that these are of the same order of magnitude as the
longitudinal, radial and tangential stress changes, so that, this
possibility seems unlikely.
This analysis supports Dennison's hypothesis that the
negative stretch response is elicited by a critical amount of
longitudinal strain, and is somewhat independent of the applied
stress (3).
Self-stabilizing Growth Following a Large Pressure Step-up
The sporangiophore's growth response following pressure
step-ups between 0.02 and 0.10 MPa can be modeled by the self-
stabilization, or Generalized Growth Equation, (1.4). This equa-
tion, which is given by:
dv
^ = A Dv . (1.4)
states that any dynamic change in the growth rate, v is caused by
two processes. The first process, encompassed in the parameter A,
is metabolically controlled and tends to accelerate growth (36).
Physically, this process could, for example, consist of enzymatic
action on cell wall cross-links, allowing faster growth. The second
process, described by the term Dv, tends to decelerate cell growth.
Taiz refers to this term as a strain hardening function, since the
parameter D generally remains rather fixed during hormone acceler-
ated growth (36).


In order to determine the theoretical creep response
predicted by the Generalized Growth Equation, assume that the
parameters A and D are constant. Then, divide both sides of
equation (1.4) by the term (A Dv) and multiply both sides by dt.
This gives the following differential equation:
dv
(A-dv)
- dt
(2.11)
which when integrated leads to:
- i ln(A-Dv) t + C
(2.12)
The constant of integration, C, can be determined by employing the
condition v vQ when pressure is stepped-up at time 0. The
resulting equation, given by:
dlnl
dt
(2.13)
(where equation (2.2) has been inserted) must be integrated once
more with respect to t. Performing this operation, and using the
initial condition 1(0) 1Q, finally gives the theoretical creep
response:
lnl lnlQ + £(t) + (gj- Jfi)(e-Dt-1) (2.14)
Noting that A/D Vs (from equation 1.4), where vs is the steady
prestimulus growth rate, this last equation can be rewritten as:
lnl lnl0 + vs(t) + (XslXfi)(e-Dt-l)
(2.15)


57
To determine the magnitude of the parameters A and D, refer
to equation (2.15) and note that this equation predicts that after a
sufficient time, the ln(l) versus t curve will have the same slope
as the prestimulus curve, i.e., vs, but that it will be offset by
(vs-v0)/D. In short, the graphically determined offset between the
steady prestimulus curve and the steady post-stimulus curve equals
(vs-v0)/D. Since (vs-vQ) is known, then D and A can be calculated.
Figures 16 and 17 show a comparison between the experimental
creep curves depicted in Figures 8 and 9 and theoretical creep
curves calculated using the procedure described above.
The maximum difference between experimental and theoretical
sporangiophore lengths in Figure 16 is approximately 5 pm, while it
is approximately 10 pm in Figure 17.
The agreement between theory and experiment decreases as the
size of the pressure step-up increases. Some of the deviation
between experiment and theory is attributable to difficulty in
estimating the offset,(vs-v0)/D. This difficulty is particularly
evident in the experiment in which pressure was stepped up by 0.127
MPa (see Figure 10). However, the deviation could also reflect the
inapplicability of the Generalized Growth Equation for modeling
Phycomyces' growth response to large pressure increases.
The strong agreement between this model and experiment at
AP's near 0.02 MPa does indicate that Phycomyces has the self-
stabilization property found in Nitella (21). Interestingly
however, Nitella's growth response to large pressure step-ups (on
the order of 0.1 MPa) is qualitatively opposite to that of


Turgor (MPa)
0.6
0.4
0.2
0
Figure 16 : Comparison between an experimental creep
response to a large AP and the theoretical
response predicted by the self-stabilization
Equation, (4). The experimental curve is that
shown in Figure 8.


59
In L
0.95
033
0.91
i
Figure 17 :
Turgor (MPa)


experiment o-eqn. 2.15 -
" 6 o.o

probe inserted L pressure stepped up i 1 1
10 20
Time (min)
0.4
02
30
Comparison between an experimental creep
response to a small AP and the theoretical
response predicted by the self-stabilization
equation(1.4). The experimental curve is
that shown in Figure 9.


Phycomyces. Following a pressure step-up, Nitella's growth rate
accelerates dramatically, and then gradually decelerates to the
prestimulus rate, all within an hour (21). Given the similarities
between these two cells (see 20,21,and 27), these differing growth
responses may reflect the fact that Nitella is diffusely growing
(i.e., growth occurs over the entire cell), while Phycomyces is tip-
growing .
SECTION 5
CONCLUSIONS
A new method to determine the creep response of living plant
cells was introduced in this chapter. This method borrows on
Green's gas capillary method (20), and the pressure clamp technique
(11). It appears to be the most direct method to step-up, control,
and measure turgor pressure during creep. Problems with slow
osmotic equilibration are overcome with this method, as are
difficulties with turgor control and measurement. Control experi-
ments show that silicon oil which is injected into the vacuole of
Phycomyces is physiologically inert.
Using this method, it was found that Phycomyces responds to
turgor step-ups smaller and larger than 0.02 MPa in two distinct
ways. Following pressure step-ups smaller than 0.02 MPa, sporang-
iophore growth increases within a minute to a new steady rate and is
maintained at that rate during the next 20 to 60 minutes. Con-
versely, following a step-up larger than 0.02 MPa, growth decreases


61
dramatically for 1 to 10 minutes and then gradually accelerates
toward the prestimulus rate during the subsequent 3 to 60 minutes.
The results of the small AP experiments indicate that the
stage IVb sporangiophore obeys the steady-state, and Augmented
Growth Equations. Hence, these equations can be used in combination
with experimental data to estimate cell wall extensibilities,
elastic moduli, and critical pressures (see 20,21,29). The cal-
culated values of range from 0.00135 to 0.058 MPa'1-min'1 and
average 0.0205 MPa'1-min'1. The calculated values of Pc range from
0.029 to 0.184 MPa and average 0.262 MPa.
These calculated extensibilities and critical pressures are
used to determine the theoretical creep response predicted by the
steady-state and the Augmented Growth Equations. It is argued that
the latter equation is a more accurate model of sporangiophore
growth since it takes into account observed post AP elastic strain,
and since its predicted creep response is slightly closer to
experiment. Additionally, earlier work (27) hints at a constitutive
relationship between pressure and growth similar to that encompassed
in the Augmented Growth Equation.
The creep responses following pressure step-ups larger than
0.02 Mpa appear to be the earlier reported negative stretch response
(16). Both responses have an approximate one minute latency,
followed by a 5 to 10 minute period of dramatically reduced growth
and a subsequent period of gradually accelerated growth. If these
responses are indeed the same response, then it can be shown that


62
the negative stretch response is not elicited by a change in average
wall stress.
Finally, it was found that the sporangiophore's growth
response to large pressure step-ups can be modeled by the General-
ized Growth Equation.


CHAPTER III
STRESS RELAXATION IN PHYCOMYCES
SECTION 1
INTRODUCTION
The predominant view of plant cell growth holds that
metabolically mediated stress relaxation in the cell wall causes
transient turgor decay (33). Lowered turgor in turn induces
incremental cell water uptake which irreversibly strains the
loosened cell wall. In a non-transpiring, ideal cell containing no
appoplastic water, water uptake is prevented when the cell is
removed from its source of water. Wall stress relaxation continues
however, causing continued turgor pressure decay. As pressure
decreases and wall loosening continues, wall stress relaxes until
the physical yield threshold of the cell is reached. At this point,
pressure no longer decays, but remains constant at the ultimate
critical pressure (9).
This theoretical picture of wall stress relaxation was
experimentally tested by Cosgrove et al., who used the pressure probe
to continuously measure turgor decay in excised pea stems removed
from water (9). Although the stems initially continued growing due
to extracellular water, pressure eventually underwent decay to a
constant magnitude following depletion of this water'source.


64
This chapter reports on similar stress relaxation tests
which were performed on stage IVb sporangiophores of Phycomyces.
There were three purposes for performing these tests. First, it was
desired to determine turgor's behavior during suppression of
external water uptake. This knowledge might prove useful in
assessing whether the cell has an apoplastic water source, for
example. The second purpose of these experiments was to test the
qualitative theory of wall stress relaxation discussed above, using
Phycomyces. This theory makes one simple prediction: turgor will
decay in a nontranspiring plant cell after it is removed from its
water supply. The last purpose of this study was to test some of
the predictions made by the'Augmented Growth Equation during stress
relaxation. The results of Chapter two suggest that this equation
can be used as a model of sporangiophore growth. Hence, these
experiments will test the validity of this hypothesis.
SECTION 2
MATERIALS AND METHODS
Sporangiophores were grown as described in Appendix A. The
supporting experimental apparatus, i.e., the pressure probe,
recording system, and observation equipment were those described in
the preceding Chapter and in Appendix A. A special environmental
chamber had to constructed for these experiments in order to
suppress cell transpiration and to allow control of external water
uptake (see Figure 18). As shown in this figure, the water level
within the box was raised and lowered with a syringer- Wet paper


65
z Sporangiophore
/'
ENVIRONMENTAL CHAMBER
Figure 18 : Schematic description of the environmental
chamber which was used in all stress
relaxation tests. Water deprivation was
initiated by lowering the water level below
the sporangiophore's basal tip with the
syringe.


66
towels lined most of the inner surfaces of the box in order to
saturate the chamber space with water vapor, which in turn, sup-
presses cell transpiration.
The first step in these experiments was to pluck healthy
looking stage IVb sporangiophores from their growth medium. Plucked
sporangiophores can grow in water for up to 20 hours, exhibiting
normal growth and growth responses throughout (3). Plucking
sporangiophores is accomplished by carefully pulling the sporang-
iopohore's basal tip from the mycelium using fine tipped tweezers.
Once plucked, a sporangiophore was quickly attached with vaseline to
the chamber's support rod (which was extended outside the box) and
then lowered into the box. The sporangiophore's basal tip was
generally immersed in less than 2mm of water, since it proved
difficult to lower the water by more than this amount at the
initiation of water deprivation.
After the sporangiophore's basal tip was immersed in water,
the pressure probe's microcapillary tip was inserted into the
chamber and the chamber sealed with vaseline. The cell was then
allowed to adapt in 100% humidity for at least 40 minutes. (It was
assumed that the relative humidity within the box was 100% when
condensation was visible on the observation windows.) Following the
adaptation period, cell elongation measurements were initiated and
continued at approximate one to two minute intervals. After 10 to
20 minutes of fairly steady growth was observed, the pressure probe
was inserted into the cell. Turgor pressure and cell elongation
were then measured throughout the remainder of each experiment.


67
Twenty to thirty minutes following probe insertion, the
water within the chamber was lowered below the sporangiophore's
basal end. Turgor and elongation were then simultaneously measured
for another 1 to 5 hours.
SECTION 3
RESULTS
Turgor pressure did not decay for an hour or more following
water deprivation in approximately 50% of the stress relaxation
experiments which were performed. Additionally, sporangiophores
usually continued growing at approximately 4 nm/min during these
periods.
To ensure that an undetected external water source was not
allowing continued water uptake, experiments were performed in which
sporangiophores were immersed (within the environmental chamber) in
paraffin oil. Oil immersion had no discernable affect, however,
since turgor remained fixed and slow cell elongation continued (for
an hour or more) as before. In one experiment, elongation continued
and turgor pressure remained constant for 5 hours following cell
immersion.
In contrast, pressure decayed in four experiments to a
constant magnitude of approximately 0.10 MPa. Two of these decays
were very slow, occurring over 2 hours as shown in Figure 19. Note
that cell growth continued throughout these prolonged decay periods
and that the pressure decay ceased as soon as growth stopped.
Decays were relatively rapid, occurring within approximately 20


10
5
0
Growth
Rate
(um/min)
Time (min)
Figure 19 : An experimental pressure decay which occured
during a stress relaxation test. Water
deprivation was initiated at time equals 2
minutes. Note that growth continued for
approximately 130 minutes afterward, and that
turgor pressure decayed continuously to a final
constant magnitude of 0.08 MPa.


minutes, in the other two experiments exhibiting decreasing press-
ure. Figure 20 shows the results from one of these experiments.
Note that the initiation of these rapid decays occurred almost
immediately following the cessation of growth. The final constant
turgor pressures in these four experiments ranged from 0.08. MPa to
0.10 MPa and were measured for approximately 10 to 20 minutes.
SECTION 4
DISCUSSION AND ANALYSIS
Theoretical Pressure Decay During Wall Stress Relaxation
It was shown in Chapter 2 that the Augmented Growth Equation
predicts the creep response of Phycomyces to small pressure
step-ups. This result shows that this equation is a valid bio-
physical constitutive relationship for Phycomyces. Since the cell
wall is a viscoelastic material (27), then theoretically this
equation can be used to predict the cell's pressure decay during
wall stress relaxation.
The theoretical pressure decay predicted by this equation
can be determined as follows. First, recall that the Augmented
Growth Equation, given by:
v = states that the relative rate of cell expansion on the right side of
(1.3) is identical to the relative rate of water uptake, v, on the
left side. Water uptake ceases, i.e., v = 0, in an ideal cell,


70
Figure 20 : A turgor pressure decay during a stress relaxation
experiment. The external water source was removed
at time equals 23 minutes. The sporangiophore
subsequently shrank (growth rate less than 0) and
rapid pressure decay ensued. The final, relatively
constant turgor pressure was approximately 0.10 MPa


71
(containing no apoplastic water) when it is removed from its water
source. Inserting this condition into (1.3) leads to:
0
*(P-PC>
1 dP
e dt
(3.1)
This equation in P can be rearranged and then integrated by assuming
that , Pc, and e are constant. Imposing the initial condition that
P(0) = Px where Pt is the initial equilibrium turgor pressure,
finally leads to an equation describing turgor pressure decay during
stress relaxation:
P (P1-Pc)ee^t + Pc . (3.2)
Equation predicts that P will decay exponentially to a
constant turgor pressure of Pc, the critical turgor pressure. The
half-time for this decay is given by:
t
ln2
1/2 e
(3.3)
In non-ideal cells containing significant apoplastic water,
the stress relaxation half-time is usually modified with a correc-
tion factor c ( see 9) so that:
*-\/z
ln2
c e
(3.4)
The corresponding stress relaxation equation for a non-ideal cell is
given by:
p (Pi-Pc)e-e^ct + Pc
(3.5)


72
Since c is less than 1 in a non-ideal cell, it is apparent from the
last two equations that stress relaxation is slower in such a cell
than in an equivalent ideal cell having the same material proper-
ties. However, the qualitative pressure behavior during relaxation
is similar for both cells, i.e., pressure decays exponentially to a
final constant turgor.
Comparison Between Theoretical and
Experimental Stress Relaxation
To calculate the theoretical pressure decay predicted by the
Augmented Growth Equation, one must first determine the decay half-
time from experimental results. By definition, the half-time is the
length of time required for pressure to decay to a magnitude half
way between the initial and final turgors. For example, in Figure
20, the initial and final turgor pressures are 0.275 and 0.090 MPa,
respectively. Hence, the turgor magnitude that is half the dif-
ference between these and in excess of the final turgor is 0.1875
MPa. The corresponding half-time is approximately 5 minutes. Once
the value of t1/2 is known, then the exponent in either equation
(3.2) or (3.5) can be calculated using equation (3.3) or (3.4),
respectively. Inserting the exponent into either decay equation
along with the experimentally measured value of Pc finally allows
calculation of the theoretical pressure decay.
Figure 21 compares the theoretical pressure decay determined
as above with the experimental decay shown in Figure 20. As
indicated in Figure 21, pressure decayed somewhat faster than
exponentially in this particular experiment.


Figure 21 : A comparison between the experimental turgor
pressure decay shown in Figure 20 and the decay
predicted by the Augmented Growth Equation.


The Augmented Growth Equation can also be used to calculate
the pressure decay in the two experiments exhibiting prolonged
decays concurrent with slow cell growth. To determine the theoret-
ical decay, use the same procedure described in the preceding
subsection, except assume that v is constant (i.e., v equals some
]
experimentally determined average growth rate) in equation (1.3).
Integrating and using the same initial condition, i.e., P(0) = Px,
leads to the following equation:
P (Px-Pc-jJe"6^ + (J + Pc) (3.6)
The magnitude of the exponent is found as described above,
and inserted into (3.6) along with the experimentally measured
values of P^, Pc, and v. The magnitude of can be estimated as the
average 0.0209 MPa-1 min'1 value determined from the creep tests
(discussed in Chapter 2).
Figure 22 shows a comparison between the theoretical decay
predicted by equation (3.6) and the experimental decay shown in
Figure 19.
Discussion of Stress Relaxation Results
The results of the four stress relaxation tests in which
pressure decayed to a final constant magnitude are consistent with
the qualitative theory of plant cell growth (see 33). As mentioned,
this theory makes the simple prediction that turgor pressure will
decrease in a non-transpiring cell after it is removed from its
water source. This result does not confirm this theory but does
indicate that a wall loosening process is involved in.growth. This


Growth
Rate

Time
Figure 22 : A comparison between the experimental turgor
pressure decay shown in Figure 19 and the decay
predicted by the Augmented Growth Equation.


76
i
is apparent from the two experiments exhibiting rapid pressure
decays following cessation of growth. When the cell no longer
grows, water uptake has stopped and the cell's mass remains constant
(no transpiration). The only way pressure can decay in this
constant volume system is via a wall loosening process.
As shown in Figures 21 and 22, pressure decays during stress
relaxation in a manner that is consistent with the Augmented Growth
Equation, i.e., pressure decays somewhat exponentially to a final
constant magnitude. Interestingly, this equation appears to model
pressure decay behavior in both non-growing and growing sporang-
iophores removed from water. This finding has several important
implications. First, this finding provides further support for the
hypothesis that the Augmented Growth Equation reliably models
sporangiophore growth. Since the sporangiophore's growth behavior
during creep and its turgor pressure behavior during wall stress
relaxation can be predicted by this equation, then this is certainly
a useful model of sporangiophore growth.
Second, this finding suggests that Phycomyces has an
adjustable critical turgor pressure. Apparently, Pc remains fairly
close to turgor during creep (the average difference between P and Pc
being 0.0909) but adjusts downward during pressure decay to the
ultimate critical pressure (see 9). An adjustable critical pressure
which approaches P during pressure step-ups but which adjusts
downward following pressure step-downs is thought to operate in
Nitella (21). Green postulated that Nitella's Pc is lowered
metabolically following a decrease in turgor and is raised following


an increase in growth rate. There is not sufficient data, however,
to evaluate whether similar processes control Pc in Phycomyces.
Third, this finding (specifically the result that pressure
decays to a.relatively fixed final magnitude) suggest that the cell
wall does indeed have a physical yield threshold.
The 0.09 MPa ultimate critical pressure in Phycomyces is
lower than the Pc of 0.2 and 0.3 MPa measured in Nitella and pea
stems (21,9), respectively.
Extracellular Water in Phvcomvces
The results of stress relaxation tests in which pressure
remained fixed while growth continued following water deprivation
support the hypothesis that the cell wall of Phycomyces contains an
extracellular water source. Such a source could maintain cell water
uptake and hence, turgor, following water removal. Cosgrove et al.
(21) first postulated that Phycomyces has an apoplastic water source
after observing anomalous turgor pressure behavior during pressure
clamp and water immersion experiments. They found that turgor did
not change appreciably after sporangiophores were immersed in water,
and observed that much smaller volumes of oil than expected were
required to step-up turgor in pressure clamp experiments. Both
results suggest that free water and solutes within the cell wall
buffer osmotic pressure changes within the cell.
Three additional observations lend support to the idea
that Phycomyces contains an extracellular water source. First,an
intrawall water source comprising only 0.3 to 0.8% of the wall's
volume could maintain the 2 to 5 hours of observed 4 ^m/min growth


following water removal. Second, the period of continued growth and
fixed turgor pressure following water removal has also been observed
in excised pea stems, which contain significant apoplastic water.
The third piece of evidence supporting this idea comes
from the stress relaxation half-times that were measured. Assuming
that and e are constant and equal to 0.0209 MPa'1 min'1 (see
Chapter 2) and 10 MPa (12), one finds that the stress relaxation
half-time predicted by (3.3) for an ideal cell is 2.77 minutes.
However the experimental t1/2*s of 5, 14, and 58 minutes are
approximately 2 to 20 times longer than this. Inserting the above
half-times into (3.4), one finds that the correction factor c ranges
in value from 0.06 to 0.66, indicating significant nonideality in
Phycomyces.
SECTION 5
CONCLUSIONS
Stress relaxation experiments show that turgor pressure
decays in non-transpiring cells of Phycomyces when they are removed
from water, a result that is consistent with the qualitative theory
of plant cell growth (33). In addition, the characteristics of the
decay, both in growing and non-growing cells, are consistent with
the Augmented Growth Equation model of plant cell growth. That is,
pressure decays (somewhat) exponentially to a final constant
magnitude.
The ultimate critical pressure was approximately 0.09 MPa in
four stress relaxation tests exhibiting pressure decay. Since the


79
Pc's determined from creep experiments are approximately 0.26 MPa,
then an adjustable Pc in Phycomyces is suggested.
Experiments in which growth continued under constant
pressure for an hour or more out of water or while immersed in
paraffin oil, indicate that the cell wall of Phycomyces contains a
significant appoplastic water source. A source comprising only 0.3
to 0.8% of cell wall volume could support the observed growth during
water deprivation.


CHAPTER IV
TURGOR PRESSURE BEHAVIOR DURING THE LIGHT GROWTH RESPONSE
SECTION 1
INTRODUCTION
Phycomyces responds to various sensory stimuli by altering
either its growth rate and/or its direction of growth. A symmetric
stimulus, as mentioned, induces a symmetric growth response (i.e.,
growth is altered uniformly on opposite flanks of the growing zone
wall), while an asymmetric stimulus elicits an asymmetric growth
response, (i.e., differential growth on opposing flanks of the
growing zone wall).
Many workers are keenly interested in the sensory physiology
of Phycomyces. They wish to elucidate, on the molecular level, the
events occurring between reception of a sensory stimulus and the
cell's corresponding growth response, in hopes of ultimately
understanding sensory transduction in higher organisms (13,14).
Although much of this work has concentrated on understanding the
light growth responses of Phycomyces (see 3,14), other studies have
investigated sensory transduction during the geotropic, wind,
avoidance, and stretch responses (3,16,28,7): A conclusive trans-
duction chain for any of these responses has yet to be constructed.


Indeed, a concrete understanding of the last steps in any response
is lacking.
Ortega, et al. (30), have demonstrated that cell wall
extensibility increases during the period of accelerated growth
induced by a step-up in light fluence rate (i.e.,the positive light
growth response). These investigators have also shown that extensi-
bility increases during the anemotropic (4) and avoidance (29)
responses. Although these results strongly suggest that biochemical
wall loosening represents the last event in these sensory responses,
it has not been known whether turgor pressure changes also play a
role in altering the growth rate.
The pressure probe, however, offers the capability to
measure turgor pressure during-these responses, and thus, possibly .
determine the final corresponding transduction event. This chapter
reports the first turgor pressure measurements ever taken during a
sensory stimulated growth response in Phycomyces. Specifically,
turgor pressure was measured continuously during the positive and
negative light growth responses.
SECTION 2
MATERIALS AND METHODS
Sporangiophores used in these experiments were grown as
described in Appendix A. Appendix A also describes the apparatus
employed in these experiments.
Stage IVb sporangiophores, 2 to 4 cm long, were first
adapted for 30 to 40 minutes, in room conditions (20 25C), to an


overhead broadband incandescent light bulb. The blue light fluence
rate of this source was 0.65 mW/cm Effective blue light fluence
rates were determined with Schott filters (BG5 and NG11) and a
photodiode (United Detector Technology, model 10DP/SB, NBS traceable
calibration) connected in series to a picoammeter. (The photodiode
was positioned below the light source and the filters, at a distance
from the light source that was equal to the distance between the
light source and the sporangiophore (45.7 cm).)
Following this initial adaptation period, cell elongation
measurements were initiated and continued at approximate 1 to 2
minute intervals throughout each experiment. The pressure probe was
inserted into the cell after 10 to 30 minutes of stable growth were
observed. The cell was allowed to adapt to probe insertion for
another 30 minutes, after which, the light fluence rate was either
stepped up or stepped down. Turgor pressure and cell elongation
were then measured for another 30 to 90 minutes.
Additional experiments, using the same procedure, were
performed using a fiber optic light source. The prestimulus blue
light fluence rate from this source was 0.89 mW/cm, while the step-
up and step-down blue light fluence rates were 3.60 mW/cm2 and 0.40
mW/cm2, respectively.
SECTION 3
RESULTS
It was found that turgor pressure remained essentially
constant throughout the 30 minute period before, and the 30 to 90


minute period after the application of a light step-up or step-down
stimulus to a stage IVb sporangiophore.
Figure 23 shows a representative result from one of 15 light
step-up experiments. The results from all of these tests had
similar characteristics: a latency between stimulus and response of
3 to 5 minutes, a subsequent 5 to 10 period of accelerated growth,
and finally, a gradual return to the prestimulus growth rate. In
each experiment, turgor pressure remained essentially fixed through-
out the entire response.
Figure 24 shows a representative result from one of seven
light step-down experiments. As in the positive light step-up
experiments, the results from the negative light step-down experi-
ments exhibited similar characteristics: a latency between stimulus
and response of approximately 5 minutes, a subsequent 5 to 10 minute
period of decelerated growth, and finally, the gradual resumption of
normal basal growth 10 to 15 minutes following the stimulus. In
each experiment, turgor pressure remained essentially constant
throughout the response.
SECTION 4
DISCUSSION
The results of these experiments demonstrate for the first
time that the transient alterations in growth rate which occur
during a symmetric light growth response result solely from altered
cell wall mechanical properties. Although a question arises as to
whether alterations in cell water uptake could play a role in these


84
Growth Turgor
Rate Pressure
(/wrn/min) (M Pa)
0.6
0.5
o.4
0.3
o.2
o.t
0
Figure 23 : Representative trugor pressure behavior during the
positive light growth response. Note that turgor
pressure remained essentially constant throughout
the entire response.


85
Figure 24 : Representative trugor pressure behavior during the
negative light growth response. Note that turgor
pressure remained essentially constant throughout
the entire response.


responses, this possibility seems unlikely, given the large dif-
ference between cell wall extensibility, ,{= 0.0209 MPa'1 min'1,
see Chapter 2) and cell hydraulic conductance, L (= 0.416 MPa'1
min'1, see 12). The relatively inextensible sporangiophore wall
would not yield proportionally, but instead would cause turgor to
change in response to any significant alterations in cell water
uptake.
The finding that the positive and negative light growth
responses are mediated solely by altered cell wall mechanical
properties demonstrates that this modification process represents
the penultimate event in these sensory responses. The biochemical
events which cause altered cell wall properties remains unknown,
however. With regards to the positive light growth response, Ortega
(30) hypothesized that an increase in enzymatic activity (perhaps
chitinase) could loosen the cell wall during the period of
accelerated growth. Since chitin synthesis increases during this
response, he postulated that the gradual resumption of basal growth
reflects increased wall synthesis.
It has been argued that most sensory stimulated growth
responses in Phycomyces are effected principally by altered cell
wall mechanical properties since the vacuole and mycelium are
non-septate (3). Any changes in turgor pressure would have to occur
throughout the entire mycelium. The results of this Chapter
certainly support this idea. These results also resolve the
question of turgor pressure's role in Phycomyces' adaptation to
symmetrically altered blue light fluence rates. Since turgor


remains essentially constant throughout the corresponding growth
responses, it apparently cannot be involved in any biomechanical
adaptation process, e.g., strain hardening.


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