Joseph K. E. Ortega

Mechanics and modeling of plant cell growth

Cellular expansive growth is one of the foundations of morphogenesis. In plant and fungal cells, expansive growth is ultimately determined by manipulating the mechanics of the cell wall. Therefore, theoretical and biophysical descriptions of cellular growth processes focus on mathematical models of cell wall biomechanical responses to tensile stresses, produced by the turgor pressure. To capture and explain the biological processes they describe, mathematical models need quantitative information on relevant biophysical parameters, geometry and cellular structure. The increased use of mechanical modeling approaches in plant and fungal cell biology emphasizes the need for the concerted development of both disciplines and underlines the obligation of biologists to understand basic biophysical principles.

Plant cell growth in tissue

Cell walls are part of the apoplasm pathway that transports water, solutes, and nutrients to cells within plant tissue. Pressures within the apoplasm (cell walls and xylem) are often different from atmospheric pressure during expansive growth of plant cells in tissue. The previously established Augmented Growth Equations are modified to evaluate the turgor pressure, water uptake, and expansive growth of plant cells in tissue when pressures within the apoplasm are lower and higher than atmospheric pressure. Analyses indicate that a step-down and step-up in pressure within the apoplasm will cause an exponential decrease and increase in turgor pressure, respectively, and the rates of water uptake and expansive growth each undergo a rapid decrease and increase, respectively, followed by an exponential return to their initial magnitude. Other analyses indicate that pressure within the apoplasm decreases exponentially to a lower value after a step-down in turgor pressure, which simulates its behavior after an increase in expansive growth rate. Also, analyses indicate that the turgor pressure decays exponentially to a constant value that is the sum of the critical turgor pressure and pressure within the apoplasm during stress relaxation experiments in which pressures within the apoplasm are not atmospheric pressure. Additional analyses indicate that when the turgor pressure is constant (clamped), a decrease in pressure within the apoplasm elicits an increase in elastic expansion followed by an increase in irreversible expansion rate. Some analytical results are supported by prior experimental research, and other analytical results can be verified with existing experimental methods.

A New Pressure Probe Method to Determine the Average Volumetric Elastic Modulus of Cells in Plant Tissue.

A new in vivo method was used to determine an average volumetric elastic modulus ([epsilon]ave) for nongrowing cells in plant tissue. This method requires that both the relative transpiration rate, T, of the tissue and the average turgor pressure decay rate, (dP/dt)ave, of the cells are measured after the water source is removed from the plant tissue. Then [epsilon]ave is calculated from the equation [epsilon]ave = (-dP/dt)ave/T. This method was used to determine [epsilon]ave for cortical cells in stems of pea seedlings (Pisum sativum L.). The results demonstrate that [epsilon]ave increases from virtually zero at low P (approximately 0.01MPa) to approximately 10 MPa at high P (approximately 0.5 MPa). Analyses of the results indicate that the relationship between [epsilon]ave and P can be approximated by a linear function and more accurately approximated by a saturating exponential function: [epsilon]ave = [epsilon][infinity symbol][1 - exp {-k(P - Po)}], where Po is a plateau pressure (approximately 0.01 MPa), k is a rate constant (approximately 7 per MPa), and [epsilon][infinity symbol] (approximately 10 MPa) is the hypothetical maximum value of [epsilon]ave as P -> [infinity symbol]. Solutions for the turgor pressure decay (due to transpiration) as functions of time and symplasmic water mass (after the water source is removed) are derived.

Phycornyces: TURGOR PRESSURE BEHAVIOR DURING THE LIGHT AND AVOIDANCE GROWTH RESPONSES

Abstract— The turgor pressure of the stage 4b sporangiophore of Phycomyces blakesleeanus was continuously measured with a pressure probe before and during a period of increased elongational growth rate elicited by a step‐up in blue light fiuence rate (a positive light growth response) or by a double‐barrier stimulus (avoidance growth response). In these and other experiments it was found that a step‐up in turgor pressure between 0.02 and 0.05 MPa may elicit an increase in growth rate that is comparable to those of the light and avoidance growth responses. The results of the present work demonstrate that the turgor pressure does not increase during these growth responses, indicating that the increased growth rate is solely the result of altered cell wall mechanical properties. Furthermore, very small decreases in turgor pressure could be detected during the period of increased growth rate. This turgor pressure depression is predicted by the Growth Equations, and provides further support for the conclusion that the light and avoidance growth responses are solely the result of changes in cell wall mechanical properties.

A comparison of cell-wall-yielding properties for two developmental stages of Phycomyces sporangiophores : determination by in-vivo creep experiments

The yielding properties of the cell wall, irreversible wall extensibility (m) and yield threshold (Y), are determined for stage I sporangiophores of Phycomyces blakesleeanus from in-vivo creep experiments, and compared to the values of m and Y previously determined for stage IVb sporangiophores using the same pressureprobe method (Ortega et al., 1989, Biophys. J. 56, 465). In either stage the sporangiophore enlarges (grows) predominately in length, in a specific region termed the “growing zone”, but the growth rates of stage I (5–20 urn · min−1) are smaller than those of stage IVb (30–70 μm · min−1). The results demonstrate that this difference in growth rate is the consequence of a smaller magnitude of m for stage I sporangiophores; the obtained values of P (turgor pressure), Y, and P-Y (effective turgor for irreversible wall extension) for stage I sporangiophores are slightly larger than those of stage IVb sporangiophores. Also, it is shown that the magnitude of m for the stage I sporangiophore is regulated by altering the length of the growing zone, Lg. A relationship between m and Lg is obtained which can account for the difference between values of m determined for stage I and stage IVb sporangiophores. Finally, it is shown that similar changes in the magnitude of m and ϕ (which have been used interchangeably in the literature as a measure of irreversible wall extensibility) may not always represent the same changes in the cell-wall properties.

A Study of the Stationary Volumetric Elastic Modulus during Dehydration and Rehydration of Stems of Pea Seedlings

The relationship between cortical-cell turgor pressure (P) and tissue water mass (W) was determined for stem segments of pea (Pisum sativum L.) seedlings subjected to hydration and dehydration. This allowed a test for elastic hysteresis in the cortical cells. The P-W curves for dehydration and hydration were not coincident. In some experiments, the P-W curves exhibited a “roll-off” at high P, similar to the “plateau effect” sometimes observed in pressure-chamber studies. When hydration was followed by a 4-h dehydration, the tissue water mass (W0) at minimum turgor was reduced. This might reflect a reduction in apoplastic water mass and/or a contraction of the symplast during dehydration. Neglecting the decrease in W0 leads to underestimates of the stationary volumetric elastic modulus ([epsilon]stat). The result of an analysis that assumes W0 was constant during hydration suggests that there was no significant difference in [epsilon]stat between dehydration and hydration and, hence, no significant elastic hysteresis. However, a 16-h dehydration increased [epsilon]stat; this might be a response to water stress.

Stiff Mutant Genes of Phycomyces Affect Turgor Pressure and Wall Mechanical Properties to Regulate Elongation Growth Rate

Regulation of cell growth is paramount to all living organisms. In plants, algae and fungi, regulation of expansive growth of cells is required for development and morphogenesis. Also, many sensory responses of stage IVb sporangiophores of Phycomyces blakesleeanus are produced by regulating elongation growth rate (growth responses) and differential elongation growth rate (tropic responses). “Stiff” mutant sporangiophores exhibit diminished tropic responses and are found to be defective in at least five genes; madD, E, F, G, and J. Prior experimental research suggests that the defective genes affect growth regulation, but this was not verified. All the growth of the single-celled stalk of the stage IVb sporangiophore occurs in a short region termed the “growth zone.” Prior experimental and theoretical research indicates that elongation growth rate of the stage IVb sporangiophore can be regulated by controlling the cell wall mechanical properties within the growth zone and the magnitude of the turgor pressure. A quantitative biophysical model for elongation growth rate is required to elucidate the relationship between wall mechanical properties and turgor pressure during growth regulation. In this study, it is hypothesized that the mechanical properties of the wall within the growth zone of stiff mutant sporangiophores are different compared to wild type (WT). A biophysical equation for elongation growth rate is derived for fungal and plant cells with a growth zone. Two strains of stiff mutants are studied, C149 madD120 (−) and C216 geo- (−). Experimental results demonstrate that turgor pressure is larger but irreversible wall deformation rates within the growth zone and growth zone length are smaller for stiff mutant sporangiophores compared to WT. These findings can explain the diminished tropic responses of the stiff mutant sporangiophores. It is speculated that the defective genes affect the amount of wall-building material delivered to the inner cell wall.

Cell Wall Loosening in the Fungus, Phycomyces blakesleeanus

A considerable amount of research has been conducted to determine how cell walls are loosened to produce irreversible wall deformation and expansive growth in plant and algal cells. The same cannot be said about fungal cells. Almost nothing is known about how fungal cells loosen their walls to produce irreversible wall deformation and expansive growth. In this study, anoxia is used to chemically isolate the wall from the protoplasm of the sporangiophores of Phycomyces blakesleeanus. The experimental results provide direct evidence of the existence of chemistry within the fungal wall that is responsible for wall loosening, irreversible wall deformation and elongation growth. In addition, constant-tension extension experiments are conducted on frozen-thawed sporangiophore walls to obtain insight into the wall chemistry and wall loosening mechanism. It is found that a decrease in pH to 4.6 produces creep extension in the frozen-thawed sporangiophore wall that is similar, but not identical, to that found in frozen-thawed higher plant cell walls. Experimental results from frozen-thawed and boiled sporangiophore walls suggest that protein activity may be involved in the creep extension.

Helical growth of stage-IVb sporangiophores of Phycomyces blakesleeanus : the relationship between rotation and elongation growth rates

Abstract. An understanding of the relationship between the two components of helical growth (rotation rate and elongation rate) is fundamental to understanding the biophysical and molecular mechanism(s) of cell wall extension in algal cells, fungal cells, and plant stems and roots. Helical growth occurs throughout development of the sporangiophores of Phycomyces blakesleeanus. Previous studies within the growth zone of stage-IVb sporangiophores have reported conflicting conclusions. An implicit assumption in the previous studies [E.S. Castle (1937) J Cell Comp Physiol 9:477–489; R. Cohen and M. Delbruck (1958) J Cell Comp Physiol 52:361–388; J.K.E. Ortega et al. (1974) Plant Physiol 53:485–490] was that the relationship between rotation rate and elongation rate was independent of the magnitude of the elongation rate. In the present study, for stage-IVb sporangiophores growing at a steady rate, it is shown that the ratio of rotation rate and elongation rate decreases as the elongation rate increases. Previously proposed biophysical and molecular mechanisms cannot account for the observed behavior. The previously postulated fibril-reorientation mechanism [J.K.E. Ortega and R.I. Gamow (1974) J Theor Biol 47:317–332; J.K.E. Ortega et al. (1974) Plant Physiol 53:485–490] is modified to accommodate this new finding. Other experiments were conducted to determine how the ratio of rotation rate and elongation rate behaves during a pressure response (a transient decrease in elongation rate produced by a large step-up in turgor pressure using the pressure probe). Results of these experiments indicate that this ratio increases during the pressure response.

Dimensionless number is central to stress relaxation and expansive growth of the cell wall

Experiments demonstrate that both plastic and elastic deformation of the cell wall are necessary for wall stress relaxation and expansive growth of walled cells. A biophysical equation (Augmented Growth Equation) was previously shown to accurately model the experimentally observed wall stress relaxation and expansive growth rate. Here, dimensional analysis is used to obtain a dimensionless Augmented Growth Equation with dimensionless coefficients (groups of variables, or Π parameters). It is shown that a single Π parameter controls the wall stress relaxation rate. The Π parameter represents the ratio of plastic and elastic deformation rates, and provides an explicit relationship between expansive growth rate and the wall’s mechanical properties. Values for Π are calculated for plant, algal, and fungal cells from previously reported experimental results. It is found that the Π values for each cell species are large and very different from each other. Expansive growth rates are calculated using the calculated Π values and are compared to those measured for plant and fungal cells during different growth conditions, after treatment with IAA, and in different developmental stages. The comparison shows good agreement and supports the claim that the Π parameter is central to expansive growth rate of walled cells.