Citation |

- Permanent Link:
- http://digital.auraria.edu/AA00002987/00001
## Material Information- Title:
- Elongation growth behavior of chara corallina the effect of a longitudinal force on growth and an analysis of the resulting stress distribution
- Creator:
- Araneta, Eric Craig
- Publication Date:
- 2004
- Language:
- English
- Physical Description:
- xi, 65 leaves : ; 28 cm
## Subjects- Subjects / Keywords:
- Chara corallina -- Growth ( lcsh )
Stress concentration ( lcsh ) - Genre:
- bibliography ( marcgt )
theses ( marcgt ) non-fiction ( marcgt )
## Notes- Bibliography:
- Includes bibliographical references (leaves 63-65).
- General Note:
- Department of Mechanical Engineering
- Statement of Responsibility:
- by Eric Craig Araneta.
## Record Information- Source Institution:
- |University of Colorado Denver
- Holding Location:
- Auraria Library
- Rights Management:
- All applicable rights reserved by the source institution and holding location.
- Resource Identifier:
- 57495108 ( OCLC )
ocm57495108 - Classification:
- LD1190.E55 2004m A72 ( lcc )
## Auraria Membership |

Full Text |

ELONGATION GROWTH BEHAVIOR OF CHARA CORALLINA: THE EFFECT
OF A LONGITUDINAL FORCE ON GROWTH AND AN ANALYSIS OF THE RESULTING STRESS DISTRIBUTION by Eric Craig Araneta B.S., University of Central Florida, 1988 A thesis submitted to the University of Colorado at Denver in partial fulfillment of the requirements for the degree of Master of Science Mechanical Engineering 2000 This thesis for the Master of Science degree by Eric Craig Araneta has been approved by Date Araneta, Eric (M.S., Mechanical Engineering) Elongation Growth Behavior of Chara corallina: The Effect of a Longitudinal Force on Growth and An Analysis of the Resulting Stress Distribution Thesis directed by Professor Joseph K.E. Ortega ABSTRACT The elongation growth rates of single intemode cells of Chara corallina were determined before and after they were subjected to uniaxial longitudinal forces of different magnitudes. An increase in growth rates (accelerated growth) was observed after the application of longitudinal forces. In general, the magnitude and duration of the accelerated growth depended on the magnitude of the longitudinal force. Following the accelerated growth, the growth rate returned to a steady value that was typically greater than the basal growth rate (i.e., before the application of the longitudinal force). Theoretical work was conducted that demonstrated how the ratio of transverse stress and longitudinal stress in the cell wall was altered after the application of longitudinal forces. Experiments were conducted in an attempt to determine the longitudinal elastic modulus of in vivo cell intemodes. The results of this study have implications on the common practice of hanging a weight on the end of an intemode cell in order to measure the growth rate using a variety of electronic displacement transducers. m This abstract accurately represents the content of the candidates thesis. I recommend its publication. Signed Joseph K.E. Ortega IV DEDICATION I would like to dedicate this thesis to my wife Erica, without whom this would not have been possible. ACKNOWLEDGEMENT I wish to give special thanks to my advisor, Ken Ortega, for his guidance, mentorship and patience in educating me in the fields of scientific investigation and mechanical engineering. I wish to thank Professor Samuel W. Welch for his input in the analysis portion of this thesis, for serving on my thesis committee and for all his help and guidance given to me during my education as a graduate student. I wish to thank Elena Ortega and Jessica Olsen for their input, suggestions and help with the experiments. I wish to thank Ted Proseus and John Boyer of the University of Delaware for supplying the initial Chara cuttings and for their instructions on the cultivation and care of Chara corallina. I wish to thank Professor Georgia Lesh-Laurie for her assistance with the experiments and for serving on my thesis committee. This work was supported by National Science Foundation grant IBN- 9603956 to J.K.E. Ortega. CONTENTS Figures.............................................................ix Tables..............................................................xi Chapter 1. General Introduction......................................... 1 1.1 Selection of Test Organism................................. 3 1.2 Statement of the Problem..................................... 5 1.3 Preview of Thesis Content.................................... 7 2. Materials and Methods........................................9 2.1 Plant Materials.............................................. 9 2.2 Longitudinal Force...........................................9 2.3 Longitudinal Elastic Modulus...................................11 3. Effect of a Longitudinal Force on the Longitudinal Growth Rate.................................................. 14 3.1 Growth Rate Acceleration.......................................14 3.2 Duration of Acceleration Period as a Result of Application of a Longitudinal Force.......................... 20 3.3 Resulting Steady Growth....................................... 23 3.4 Discussion.................................................... 26 4. Analysis of Cell Elongation................................... 29 vii 4.1 The Influence of Cell Wall Structure on Cell Elongation........... 29 4.2 Intemode Cell Wall Structure and Material Properties of Nitella.. 30 4.3 Theoretical Analysis of Cell Wall Stress Distribution..............32 4.4 Analysis of Cell Wall Stress Distribution for a Chara Intemode.... 42 4.5 Discussion........................................................ 49 5. Longitudinal Elastic Modulus...................................... 50 5.1 Discussion.........................................................58 Appendix A. Development of Chara Cultures......................................59 B. Construction of Experimental Apparatus.............................61 References...........................................................63 vm FIGURES Figure 1.2.1 Schematic Illustration of the Apparatus from Zhu and Boyer (1992) and Proseus et al. (1999), for the Measurement of Cell Elongation.......................6 2.3.1 Schematic Illustration of the Apparatus for Longitudinal Elastic Modulus Experiments................. 13 3.1.1 Length of a Chara Intemode as a Function of Time for an Applied Force of 8.51 g....................... 16 3.1.2 Length of a Chara Intemode as a Function of Time for an Applied Force of 3.56 g..........................18 3.1.3 Length of a Chara Intemode as a Function of Time for an Applied Force of 2.4 g............................19 3.2.1 Duration of Acceleration Period as a Function of Applied Force..............................................21 3.3.1 Ratio of Resulting Steady Growth Rate to B asal Growth Rate as a Function of the Applied Force...............24 4.3.1 Cylindrical Thin-Walled Pressure Vessel........................34 4.3.2 Free Body Diagram of a Segment of a Cylindrical Thin-Walled Pressure Vessel...................................36 4.3.3 Free Body Diagram of a Cylindrical Thin-Walled Pressure Vessel........................................................38 4.3.4 Free Body Diagram of a Cylindrical Thin-Walled Pressure Vessel with an Externally Applied Force..............41 IX 4.4.1 The Stress Ratio as a Function of Applied Force for Various Turgor Pressures.................................48 5.1 Stress vs. Strain for a Typical Experiment....................52 5.2 Mean Stress vs. Mean Strain for Each of the Applied Forces....54 5.3 Mean Stress vs. Mean Strain For Trial One and Trial Two...... 56 B. 1. Apparatus for Longitudinal Force Experiments..................61 B .2. Apparatus for Longitudinal Elastic Modulus Experiments........62 x TABLES Table 3.2.1 Applied Longitudinal Forces with Their Associated Acceleration Periods............................................22 3.3.1 Ratio of Resulting Steady Growth Rate to Basal Growth Rate as a Function of the Applied Force.........................25 4.4.1 Membrane Stress Distribution for a Pressurized Cylindrical Membrane with a Turgor Pressure of 0.5 MPa..........44 4.4.2 Membrane Stress Distribution for a Pressurized Cylindrical Membrane with a Turgor Pressure of 0.7 MPa..........45 4.4.3 Membrane Stress Distribution for a Pressurized Cylindrical Membrane with a Turgor Pressure of 1.0 MPa..........46 xi 1. General Introduction The mechanics of plant cell wall extension are studied by plant physiologists who want a better understanding of plant cell growth. Plant, algal and fungal cell growth depend on two simultaneous and interdependent physical processes: the net rate of water uptake and the net rate of cell wall extension (Ortega, 1985, 1990, 1994). The equation describing the net rate of water uptake was obtained by applying the conservation of water mass to the plant cell (Ortega et al., 1988). The conservation law states that the rate of change of water mass in the plant cell must be equal to the difference between the flow rate of water into and out of the cell. The application of this conservation law results in the mathematical expression known as the first Augmented Growth Equation (Equation 1.1) (Ortega et al., 1988; Ortega ,1990, 1994): v, = fdV' \ dt j /Vw = L(Ax- P)-T (1.1) where vw is the relative rate of change in volume of the cell contents (mostly water), Vw is the volume of the cell contents (mostly water), t is the time, L is relative hydraulic conductance, A# is the difference in osmotic pressure between the cell sap and the external medium, P is the turgor pressure (the pressure difference between the cell interior and the external medium), and T is the relative transpiration rate. 1 The term, L(Ax P), represents the relative rate of water uptake and the term, T, represents the relative rate at which water is lost from the cell by transpiration. For cells that do not transpire (such as an alga in an aqueous growth medium) the term, T, is zero. The equation that describes the rate of cell wall extension is the second Augmented Growth Equation (Ortega, 1985). The second Augmented Growth Equation relates the relative rate of change in volume of the cell wall chamber to the sum of the relative rate of irreversible (plastic) extension and the relative rate of reversible (elastic) extension. The second Augmented Growth Equation (Equation 1.2) is: f dV' = V dt j /Vc=
f dP}
is the critical turgor pressure (a value of turgor pressure below which growth does |