**Research Associate Professor of Plant Biology**

Ph.D. 1998, University of Vermont

**Email:** Chunfang.Wei@uvm.edu

**Phone:** 802-656-0701

**Office:** 334 Jeffords Hall

**Research Area:** Biophysics, Theoretical Physics

My work initially centered on testing the Cohesion-Tension theory and the validity of the Scholander pressure bomb technique. Then in cooperation with Professor Philip M. Lintilhac, my research activities have focused on *Loss of Stability* theory (mechanism for stress relaxation in the walls of living cells), cell elasticity, cell wall anisotropic modulus, ball tonometry, and other growth-related projects.

**1. Testing the Cohesion-Tension (CT) theory.**

The CT theory is fundamental to the understanding of water movement in plants. According to the theory, water is pulled upwards by high tensions (low negative pressures) created in the xylem vessels and tracheids of higher plants by the evaporation of water vapor from leaves. However, the validity of this theory had come under question in the 1990s mainly because of the work done by Professor Ulrich Zimmermann and his colleagues at the University of Wurzburg, Germany (Balling and Zimmermann 1990). The most serious challenge came from their pressure probe work which failed to confirm the presence of absolute negative xylem pressures consistent with the predictions of the CT theory. Hot debate on the validity of the CT theory had thus surfaced in the past decade (Tyree 1997).

Using the oil-filled pressure probe and pressurization techniques, my research demonstrates that significant absolute negative pressures do present in xylem vessels. Moreover, these negative pressures change rapidly and reversibly with changes in light intensity and root-bomb pressure, indicating that xylem pressure very much depends on transpiration rate (Wei et al. 1999a). Using the Scholander pressure bomb technique, my research also shows that the balancing pressures of the leaves coincide well with the probed xylem pressures, and therefore that the transpiration rate under different conditions can explain the changes in xylem pressure (Wei et al. 1999b).

To support the above experimental results, a computer program was also written to solve for the pressure drop across the network of resistors in our hydraulic architecture model of a maize plant. This computational model successfully predicted the observed dependence of xylem pressure on the evaporative flux density. In conclusion, my research demonstrates that xylem pressure changes do indeed follow the predictions of the CT theory. The findings have been published in Trends in Plant Science, Plant Physiology, Journal of Experimental Botany, and Plant, Cell and Environment.

Other related accomplishments associated with this study also include:

- This is the first time to successfully apply an oil-filled pressure probe in measuring true negative xylem pressures. Prior to my work this experimental approach was considered technically impossible.
- This study successfully measures absolute negative xylem pressures down to -1 MPa, the most negative xylem pressure ever recorded.

**2. The controversial 1:1 relationship over the pressure bomb technique**

Many efforts have been made to measure the water potential of plant tissue. The most important and widely accepted method is the Scholander pressure bomb technique. However, it has been suggested that this pressure bomb did not actually measure xylem water potential. A major experiment leading to this puzzle involved sealing fully hydrated (xylem pressure presumably zero) into a pressure bomb under conditions where the xylem pressure could be measured directly (using a pressure transducer) at the cut end. Balling and Zimmermann (1990) found that the response of the pressure transducer to increasing gas pressure was not 1:1. This outcome was considered to be in total contradiction to the underlying hypothesis of the Scholander pressure bomb technique and therefore had cast doubt on the validity of the technique as a whole.

To resolve the puzzle I carefully run the experiment, using *Tsuga canadensis* and *Nicotiana rustica*, and measured the water potential isotherms, the wood densities, and the diameter changes of the stems and petioles. The results concluded that the non 1:1 outcome was due to the compression of air bubbles in embolized xylem vessels, evaporation of water from the tissue, and the expansion of the sealed stem segment (or petiole) protruding beyond the seal of the pressure bomb. I also provided the mathematical analysis to predict the magnitude of the deviation from the 1:1 relationship. The predicted value coincided with the experimental data. This research confirms that the Scholander pressure bomb is capable of measuring the water potential of plant tissue, at least in the range of 0 to -10 bars. This work has been published in Journal of Experimental Botany (Wei et al. 2000). (In fact the non 1:1 relationship does not in any way invalidate the Scholander pressure bomb technique because in the pressure bomb measurement the xylem pressure never reaches positive values.)

**3. Ball tonometry.**

With the cooperation of Prof. Lintilhac, we have developed a new method for measuring cell turgor pressure in thin-walled plant cells which we have termed **Ball Tonometry**. The cell turgor pressure is determined by observing and measuring the area of the contact patch formed when a spherical glass probe is lowered onto the cell surface with a known force. The major merits of ball tonometry are its non-destructiveness, speed, and relatively easy handling. The limitation of this method lie in the fact that it is suitable only for superficial cells that are directly accessible to the probe and to cells that are relatively thin walled and not heavily decorated with surface features. It is also not suitable for measuring pressures in flaccid cells. This work has been published in the Journal of Plant Growth Regulation (Lintilhac et al. 2000).

**4. Quantitative analysis of cell elasticity and cell stiffness.**

My aim on this project was to study the elasticity and load bearing ability of plant tissue at the cellular level. Unlike previous studies, I considered the cell as a whole entity, and used Boussinesq's solution (a theory of elasticity for a semi-infinite elastic body) to derive the relevant equations that related the elastic parameters and cell deformation. The Young's modulus and Poisson's ratio of the cells were obtained by loading a tensile force on onion epidermal peels of different turgor pressures, and measuring the elongation and the lateral contraction of the peels. The effects of cell elasticity and turgor pressure on cell deformation were determined by ball tonometry. For cells with a turgor pressure of at least 0.34 MPa, the predicted contact area agreed well with the measured area. The equations could also predict cell turgor pressure with a deviation from the measured value of 0.01 MPa.

This study shows that the common method of measuring Young's modulus and Poisson's ratio and the application of a relevant theory of elasticity can provide a valid approach to the study of cell elasticity. This study also provides a method of measuring cell turgor pressure. In addition, this study has proposed a cell physiological concept, *cell stiffness*, and gives its mathematical description. This work has been published in Plant Physiology (Wei et al. 2001).

**5. Loss of stability (LOS), the mechanism of stress relaxation in plant cell walls.**

This study perhaps represents the most significant outcome of my collaboration with Professor Philip Lintilhac. I reexamined the physical basis of cell wall extension growth under turgor generated stress. Traditional understanding of the process interprets the stretching of primary plant cell walls as being due to viscoelastic behavior. I found that this viscoelastic model of cell wall relaxation, which dates from the work of Preston, Cleland, Lockhart, and others in the 1960s, has serious shortcomings because the prerequisite for viscoelastic does not conform to the realities of plant cell growth. In the meantime I found that the neglected work of the Russian physicist Panovko can be developed into a sound mechanism for the interpretation of cell wall extension growth.

Panovko showed that the theory of *Loss of Stability* (LOS) can be applied to materials in tension, leading to the conclusion that the relaxation of stresses in the walls of any pressure vessel is rigorously modeled using LOS (Panovko and Gubanova 1965). We have proposed that LOS also provides a more appropriate and versatile model of stress relaxation in growing plant cells. We show that when treated as a manifestation of LOS, the regulation of cell turgor has a rigorous and demonstrable basis in the geometrical and physical properties of the cell wall and the cell?s ability to import water. Thus plant cell growth can be regarded as an inherently self-limiting process, tunable by biochemical or structural means.

The significance of this work lies in the fact that it brings a fresh approach to the understanding of the physics of stress relaxation in plant cell walls, and that it is based on physical first principles. Moreover, our LOS theory has resolved several old standing difficulties associated with the traditional viscoelastic model. For instance, the previous model based on viscoelastic theory cannot predict a reasonable cell turgor value, nor can it explain why in living cells a reduction in turgor pressure of only 0.02 MPa can result in the immediate cessation of growth (Taiz 1984). With our LOS theory, however, the above puzzling observations can now be convincingly explained (Wei and Lintilhac 2003).

Our LOS theory, along with its different extensions, has resulted in several publications in the Journal of Theoretical Biology, Planta, and Plant Physiology. My personal contribution to this work has been both on the theoretical and the experimental side. I uncovered the relevant historical resources and developed the mathematical underpinnings to the point where they could be applied to plant materials. I also constructed the experimental protocols and guided the interpretation of the results.

**6. The anisotropic modulus and LOS behavior of Chara cell walls**

The anisotropic mechanical properties of plant cell walls have long been studied as a the principle determinant of cell shape and growth rate. Previous studies on wall anisotropy have focused on revealing longitudinal and transverse moduli only, but modulus values along other directions have not been worked out. My work in this area is aimed to fill this gap and also to provide analytic mathematical solutions to the problem.

To obtain the all-around anisotropic elasticity of *Chara* walls, I applied a tensile load on wall ribbons excised from the cell walls along twelve different azimuths. The resulting stress-strain relationships were then used to calculate the modulus values. To clarify the relative values of the wall moduli, the complete all-around anisotropic modulus is presented in polar coordinates, with the value of longitudinal modulus normalized to one unit. The equations describing the stress relationships, however, are expressed using the traditional coordinates, so that the compliance reflecting the walls? elastic anisotropy can take form of a "6 by 6" matrix. This facilitates discussions of the connection between the offset of the axes and the general relationship between transverse and longitudinal stresses in the walls of cylindrical cells.

The outcomes of this study provide the first detailed multi-azimuthal description of the anisotropic elastic modulus of the walls. Also, this study differs from previous studies in which mechanical loading of the wall materials was performed under creep conditions. I used ramp-loading conditions which meet the requirements for *Loss of Stability*. This is significant because the results show that whereas a linear relationship between wall extension and log time is typical for creep-based experiments, it is not seen under ramp-loading conditions. These findings have been published in Planta (Wei et al. 2006).

**7. Loss of Stability in cylindrical plant cells**

It has long been supposed that cell geometry and cell turgor is linked in growing cells. For instance, noting the reported discrepancy between multiaxial and uniaxial yield stress values in

Beginning with an analysis of the 3-Dimensional stress and strain of a cylindrical pressure vessel, and the corresponding matrix form of the stress-strain relationship, I demonstrate that *Loss of Stability* is an inevitable result of gradually increasing internal pressure in a cylindrical cell. In order to provide an initial validation of our calculations, I obtained wall dimensions, wall elastic moduli and turgor pressures of sequential internodal cells of intact *Chara corallina* plants by direct measurement. The results show that turgor pressure predictions based on *Loss of Stability* theory fall well within the expected physiological range of turgor pressures.

I also studied the effect of varying wall Poisson's ratio on extension growth in living cells, showing that while increasing elastic modulus has an understandably negative effect on wall expansion, increasing Poisson's ratio would be expected to accelerate wall expansion. This is the first time the role of Poisson's ratio in plant cell growth been verified. The manuscript reporting the outcomes of this work will be published in Plant Physiology (forthcoming).

**8. Ongoing study: Sporangial Development (mathematical and structural Analysis)**

This is the main goal of my current research activities. There are several general features of sporangial development which unify all multicellular sporangia and which can be taken as indicators of a common underlying mechanism at work in them all. For instance, sporangia are typically layered structures, possessing an ordered surface layer of thick-walled sterile sporangial wall cells, and an inner layer of more thin-walled cells which also highly ordered and usually dividing by means of repeated anticlinal divisions. Although there has been considerable work on the ultrastructure of the megagametophyte in plants, and on the associated topics of pollen tube growth and chemotaxis, there has been little work on understanding the nature of the triggering mechanism for the earliest event(s) in sporangial development.

On the experimental front of this project, we are currently working on an experimental model in which we can follow the development of sexual activity in a precise way by means of time-lapse photomicrography. My goal is to develop a new set of mathematical tools with which to study this early moment in the life history of multicellular plants. I believe that these same mathematical tools will also be available for the analysis of other similar situations and will open the way for an understanding of how physical and geometrical factors can be a developmental effectors in plants. This is a long term project; we expect to reach our aim within 2 years.

- Wei, C. and P. M. Lintilhac, (2008). Response to Schopfer letter.
*Plant Physiology 147*:935-938. - Wei, C. and P. M. Lintilhac, (2007). Loss of Stability: A new look at the physics of cell wall behavior during plant cell growth.
*Plant Physiology 145*:763-772. - Wei, C., L. S. Lintilhac, and P. M. Lintilhac. (2006). Loss of stability, pH, and the anisotropic extensibility of
*Chara*cell walls.*Planta. 223*:1058-1067. Download PDF - Loodts, J., E. Tijskens, C. Wei, E. Vanstreels, B. Nicola, and H. Ramon. (2006). Micromechanics: Simulating the elastic behavior of onion epidermis tissue.
*Journal of Texture Studies 37*:16-34. - Wei, C. and P. M. Lintilhac. (2003). Loss of Stability - A New Model for Stress Relaxation in Plant Cell Walls.
*Journal of Theoretical Biology 224*:305-312. Download PDF - Wei, C., P. M. Lintilhac, and J. J. Tanguay. (2001). An insight into cell elasticity and load bearing ability: measurement and theory.
*Plant Physiology 126*:1129-1138. - Wei, C., E. Steudle, M. T. Tyree, and P. M. Lintilhac. (2001). The essential of direct xylem pressure measurement.
*Plant Cell and Environment 24*(5):549-555. - Kuzeja, P. S., P. M. Lintilhac, and C. Wei. (2001). Root elongation against a constant force: experiment with a computerized feedback-controlled device.
*Journal of Plant Physiology 158*(5):673-676. - Wei, C., E. Steudle, and M. T. Tyree. (2000). Reply of water ascent in plants: the ongoing debate.
*Trends in Plant Sciences 5*(4):145-147. - Wei, C., M. T. Tyree, and J. P. Bennink. (2000). The transmission of gas pressure to xylem fluid pressure when plants are inside a pressure bomb.
*Journal of Experimental Botany 51*: 309-316. - Lintilhac, P. M., C. Wei, J. J. Tanguay, and J. O. Outwater. (2000). Ball Tonometry: a rapid, non-destructive method for measuring cell turgor pressure in thin-walled plant cells.
*Journal of Plant Growth Regulation 19*:90-97. - Wei, C., M. T. Tyree, and E. Steudle. (1999). Direct measurement of xylem pressure in leaves of intact maize plants. A test of the Cohesion-Tension theory taking hydraulic architecture into consideration.
*Plant Physiology121*:1191-1205. - Wei, C., E. Steudle, and M. T. Tyree. (1999). Water ascent in plants: do ongoing controversies have a sound basis?
*Trends in Plant Science 4*(9):372- 375. - Wei, C. (1990). Method of images for dielectric.
*University Physics (China) 102*:46-48. - Wei, C. (1989). Superconducting Super Collider.
*Guangxi Physics Journal (China) 10*(2):24-35. - Wei, C. (1988). The scattering of electromagnetic waves in turbulent atmosphere.
*Guangxi Natural Science (China) 8*:79-84. - Wei, C. (1987). The effect of fluctuating refraction index on electromagnetic waves.
*Guangxi Physics (China) 87*:12-18. - Wei, C. (1987).
*Electrodynamics*(textbook). Guangxi Nationality Institute Press (China). p. 362.