Biophysical properties of Saccharomyces cerevisiae and their relationship with HOG pathway activation

Parameterized models of biophysical and mechanical cell properties are important for predictive mathematical modeling of cellular processes. The concepts of turgor, cell wall elasticity, osmotically active volume, and intracellular osmolarity have been investigated for decades, but a consistent rigorous parameterization of these concepts is lacking. Here, we subjected several data sets of minimum volume measurements in yeast obtained after hyper-osmotic shock to a thermodynamic modeling framework. We estimated parameters for several relevant biophysical cell properties and tested alternative hypotheses about these concepts using a model discrimination approach. In accordance with previous reports, we estimated an average initial turgor of 0.6 ± 0.2 MPa and found that turgor becomes negligible at a relative volume of 93.3 ± 6.3% corresponding to an osmotic shock of 0.4 ± 0.2 Osm/l. At high stress levels (4 Osm/l), plasmolysis may occur. We found that the volumetric elastic modulus, a measure of cell wall elasticity, is 14.3 ± 10.4 MPa. Our model discrimination analysis suggests that other thermodynamic quantities affecting the intracellular water potential, for example the matrix potential, can be neglected under physiological conditions. The parameterized turgor models showed that activation of the osmosensing high osmolarity glycerol (HOG) signaling pathway correlates with turgor loss in a 1:1 relationship. This finding suggests that mechanical properties of the membrane trigger HOG pathway activation, which can be represented and quantitatively modeled by turgor.     

A Computational Framework for 3D Mechanical Modeling of Plant Morphogenesis with Cellular Resolution

The link between genetic regulation and the definition of form and size during morphogenesis remains largely an open question in both plant and animal biology. This is partially due to the complexity of the process, involving extensive molecular networks, multiple feedbacks between different scales of organization and physical forces operating at multiple levels. Here we present a conceptual and modeling framework aimed at generating an integrated understanding of morphogenesis in plants. This framework is based on the biophysical properties of plant cells, which are under high internal turgor pressure, and are prevented from bursting because of the presence of a rigid cell wall. To control cell growth, the underlying molecular networks must interfere locally with the elastic and/or plastic extensibility of this cell wall. We present a model in the form of a three dimensional (3D) virtual tissue, where growth depends on the local modulation of wall mechanical properties and turgor pressure. The model shows how forces generated by turgor-pressure can act both cell autonomously and non-cell autonomously to drive growth in different directions. We use simulations to explore lateral organ formation at the shoot apical meristem. Although different scenarios lead to similar shape changes, they are not equivalent and lead to different, testable predictions regarding the mechanical and geometrical properties of the growing lateral organs. Using flower development as an example, we further show how a limited number of gene activities can explain the complex shape changes that accompany organ outgrowth.     

A biophysical analysis of stem and root diameter variations in woody plants

A comprehensive model of stem and root diameter variation was developed. The stem (or root) was represented using two coaxial cylinders corresponding with the mature xylem and the extensible tissues. The extensible tissues were assumed to behave as a single cell separated from the mature xylem by a virtual membrane. The mature xylem and the extensible tissues are able to dilate with temperature and grow. Moreover, the extensible tissues are able to shrink and swell according to water flow intensity. The model is mainly based on the calculation of water volume flows in the "single cell" that are described using the principles of irreversible thermodynamics. The elastic response to storage volume and plastic extension accompanying growth are described. The model simulates diameter variation due to temperature, solute accumulation, and xylem, water potential. The model was applied to the peach (Prunus persica) stem and to the plum (Prunus domestica x Prunus spinosa) root. The simulation outputs corresponded well with the diameter variation observed. The model predicts that variations of turgor pressure and osmotic potential are smaller than the variations of xylem water potential. It also demonstrates correlations between the xylem water potential, the turgor pressure, the elastic modulus, and the osmotic potential. The relationship between the diameter and the xylem water potential exhibits a substantial hysteresis, as observed in field data. A sensitivity analysis using the model parameters showed that growth and shrinkage were highly sensitive to the initial values of the turgor pressure and to the reflection coefficient of solutes. Shrinkage and growth were sensitive to elastic modulus and wall-yielding threshold pressure, respectively. The model was not sensitive to changes in temperature.     

Analysis of the dynamic and steady-state responses of growth rate and turgor pressure to changes in cell parameters

The physical analysis of plant cell enlargment is extended to show the dependence of turgor pressure and growth rate under steady-state conditions on the parameters which govern cell wall extension and water transport in growing cells and tissues, and to show the dynamic responses of turgor and growth rate to instantaneous changes in one of these parameters. The analysis is based on the fact that growth requires simultaneous water uptake and irreversible wall expansion. It shows that when a growing cell is perturbed from its steady-state growth rate, it will approach the steady-state rate with exponential kinetics. The half-time of the transient adjustment depends on the biophysical parameters governing both water transport and irreversible wall expansion. When wall extensibility is small compared to hydraulic conductance, the growth rate is controlled by the yielding properties of the cell wall, while the half-time for changes in growth rate is controlled by the water transport parameters. The reverse situation occurs when hydraulic conductance is lower than wall extensibility. The analysis also shows explicitly that turgor pressure is tightly coupled with growth rate when growth is controlled by both water transport and wall yielding parameters.     

Experimental evidence for negative turgor pressure in small leaf cells of Robinia pseudoacacia L versus large cells of Metasequoia glyptostroboides Hu et W.C.Cheng. 1. Evidence from pressure‐volume curve analysis of dead tissue.

This paper provides a mini‐review of evidence for negative turgor pressure in leaf cells starting with experimental evidence in the late 1950s and ending with biomechanical models published in 2014. In the present study, biomechanical models were used to predict how negative turgor pressure might be manifested in dead tissue, and experiments were conducted to test the predictions. The main findings were as follows: (i) Tissues killed by heating to 60 or 80 °C or by freezing in liquid nitrogen all became equally leaky to cell sap solutes and all seemed to pass freely through the cell walls. (ii) Once cell sap solutes could freely pass the cell walls, the shape of pressure‐volume curves was dramatically altered between living and dead cells. (iii) Pressure‐volume curves of dead tissue seem to measure negative turgor defined as negative when inside minus outside pressure is negative. (iv) Robinia pseudoacacia leaves with small palisade cells had more negative turgor than Metasequoia glyptostroboides with large cells. (v) The absolute difference in negative turgor between R. pseudoacacia and M. glyptostroboides approached as much as 1.0 MPa in some cases. The differences in the manifestation of negative turgor in living versus dead tissue are discussed.     

Osmotic adjustment and the accumulation of organic solutes in whole cells and protoplasts of Saccharomyces cerevisiae

In the presence of a suitable carbon source, whole cells and protoplasts of Saccharomyces cerevisiae synthesized glycerol as a compatible organic solute in response to increased external osmotic pressure. Boyle-van't Hoff plots showed that protoplasts, and non-turgid cells, exhibited a linear relationship between volume and the external osmotic pressure (i.e. they behaved as near-ideal osmometers), and that both protoplasts and cells have a component which is not osmotically responsive--the non-osmotic volume (NOV). Glycerol levels in whole cells and protoplasts were elevated by increased external osmotic pressure over a similar time-scale to the period of exponential cell growth, reaching a maximum value at 6-12 h and declining thereafter. This suggests that the restoration of turgor pressure in whole cells was not the sole regulator of glycerol accumulation. Stationary phase whole cells had negligible levels of intracellular glycerol after growth in a medium of raised osmotic pressure. However, intracellular trehalose synthesis in these cells began earlier and reached a higher maximum level than in basal medium. Once exponential growth had stopped, cell turgor and internal osmotic pressure decreased somewhat. These new, lower values may be determined by the extent of trehalose accumulation in stationary phase cells.     

西鄂尔多斯地区强旱生小灌木的水分参数

应用PV技术研究了西鄂尔多斯地区绵刺、红沙、四合木和霸王柴4种超旱生灌木的水分关系参数膨压(ψ_P)、细胞弹性模量(ε)、细胞体积比(RCV)及其相互关系.结果表明：在4种荒漠旱生灌木中,红沙保持最大膨压的能力最强(a=2.4593).不同荒漠旱生灌木保持膨压的方式不同：绵刺通过弹性调节保持膨压(ε_max=8.4005 MPa);红沙通过渗透调节来保持膨压(ψ_π100=-3.1302 MPa;ψ₀=-3.5074 MPa);四合木通过渗透调节和弹性调节的协同作用来维持膨压;霸王柴通过渗透调节来保持膨压,而弹性调节能力较弱.绵刺具有柔软而高弹性的细胞壁,是构成其根茎系统快速吸收和传导水分能力的因素之一.四合木具有较柔软而高弹性的细胞壁且ψ_P的变化随RCV减小而趋于缓慢,说明四合木具有较强的持水能力和抗脱水能力.     

Structural mechanics of plant cells

The precise quantification of the structural behaviour of living plant cells presents many difficulties. In view of this, an approximate model has been developed by treating the cells as flexible shells having simple geometrical shapes, and subjected to internal pressure.The analysis assumes the cell walls to be made of long-chain polymeric substances whose stress-deformation behaviour can be characterised either by a Mooney-Rivlin or neo-Hookean material. The presence of microfibrils in plant cell walls has been simulated by treating the shells as being reinforced by thin inextensible, but flexible, cords. The established theories of large elastic deformations of such reinforced materials are used in the main analysis.The two main problems dealt with are the relationship of cell volume to turgor pressure and the time course of cell enlargement with influx of water. The analysis also allows for known external stress conditions on the outer periphery of the cells.The complicated closed equations derived are presented in the form of charts using non-dimensional parameters. These charts form the basis for the calculation of absolute values for a wide range of practical conditions obtaining in nature. The performance of the models is considered in relation to recent experimental data.     

Yeast osmosensor Sln1 and plant cytokinin receptor Cre1 respond to changes in turgor pressure

Very little is known about how cellular osmosensors monitor changes in osmolarity of the environment. Here, we report that in yeast, Sln1 osmosensor histidine kinase monitors changes in turgor pressures. Reductions in turgor caused by either hyperosmotic stress, nystatin, or removal of cell wall activate MAPK Hog1 specifically through the SLN1 branch, but not through the SHO1 branch of the high osmolarity glycerol pathway. The integrity of the periplasmic region of Sln1 was essential for its sensor function. We found that activity of the plant histidine kinase cytokinin response 1 (Cre1) is also regulated by changes in turgor pressure, in a manner identical to that of Sln1, in the presence of cytokinin. We propose that Sln1 and Cre1 are turgor sensors, and that similar turgor-sensing mechanisms might regulate hyperosmotic stress responses both in yeast and plants.     

Origins of Escherichia coli Growth Rate and Cell Shape Changes at High External Osmolality

In Escherichia coli, a sudden increase in external concentration causes a pressure drop across the cell envelope, followed by an active recovery. After recovery, and if the external osmolality remains high, cells have been shown to grow more slowly, smaller, and at reduced turgor pressure. Despite the fact that the active recovery is a key stress response, the nature of these changes and how they relate to each other is not understood. Here, we use fluorescence imaging of single cells during hyperosmotic shocks, combined with custom made microfluidic devices, to show that cells fully recover their volume to the initial, preshock value and continue to grow at a slower rate immediately after the recovery. We show that the cell envelope material properties do not change after hyperosmotic shock, and that cell shape recovers along with cell volume. Taken together, these observations indicate that the turgor pressure recovers to its initial value so that reduced turgor is not responsible for the reduced growth rate observed immediately after recovery. To determine the point at which the reduction in cell size and turgor pressure occurs after shock, we measured the volume of E. coli cells at different stages of growth in bulk cultures. We show that cell volume reaches the same maximal level irrespective of the osmolality of the media. Based on these measurements, we propose that turgor pressure is used as a feedback variable for osmoregulatory pumps instead of being directly responsible for the reduction in growth rates. Reestablishment of turgor to its initial value might ensure correct attachment of the inner membrane and cell wall needed for cell wall biosynthesis.     

Origins of Escherichia coli Growth Rate and Cell Shape Changes at High External Osmolality

In Escherichia coli, a sudden increase in external concentration causes a pressure drop across the cell envelope, followed by an active recovery. After recovery, and if the external osmolality remains high, cells have been shown to grow more slowly, smaller, and at reduced turgor pressure. Despite the fact that the active recovery is a key stress response, the nature of these changes and how they relate to each other is not understood. Here, we use fluorescence imaging of single cells during hyperosmotic shocks, combined with custom made microfluidic devices, to show that cells fully recover their volume to the initial, preshock value and continue to grow at a slower rate immediately after the recovery. We show that the cell envelope material properties do not change after hyperosmotic shock, and that cell shape recovers along with cell volume. Taken together, these observations indicate that the turgor pressure recovers to its initial value so that reduced turgor is not responsible for the reduced growth rate observed immediately after recovery. To determine the point at which the reduction in cell size and turgor pressure occurs after shock, we measured the volume of E. coli cells at different stages of growth in bulk cultures. We show that cell volume reaches the same maximal level irrespective of the osmolality of the media. Based on these measurements, we propose that turgor pressure is used as a feedback variable for osmoregulatory pumps instead of being directly responsible for the reduction in growth rates. Reestablishment of turgor to its initial value might ensure correct attachment of the inner membrane and cell wall needed for cell wall biosynthesis.     

An alternative method for analysing pressure-volume curves produced with the pressure chamber

Abstract. An equation is derived relating tissue water potential to relative water content. This equation may be used to lit a single curve to a set of data such as the standard pressure volume measurements made with a pressure chamber. From such a single curve fitting operation, estimates of the parameters involved may be found, and this allows calculation of such quantities as bulk modulus of elasticity, osmotic potential at full turgor and at the turgor loss point, pressure potential, and the weight of symplastic water. The method of analysis has several advantages, which are illustrated using pressure chamber data obtained from leaves of Lombardy poplar, Populus nigra L. 'italica'.     

Stomatal action directly feeds back on leaf turgor: new insights into the regulation of the plant water status from non‐invasive pressure probe measurements

Uptake of CO₂ by the leaf is associated with loss of water. Control of stomatal aperture by volume changes of guard cell pairs optimizes the efficiency of water use. Under water stress, the protein kinase OPEN STOMATA 1 (OST1) activates the guard‐cell anion release channel SLOW ANION CHANNEL‐ASSOCIATED 1 (SLAC1), and thereby triggers stomatal closure. Plants with mutated OST1 and SLAC1 are defective in guard‐cell turgor regulation. To study the effect of stomatal movement on leaf turgor using intact leaves of Arabidopsis, we used a new pressure probe to monitor transpiration and turgor pressure simultaneously and non‐invasively. This probe permits routine easy access to parameters related to water status and stomatal conductance under physiological conditions using the model plant Arabidopsis thaliana. Long‐term leaf turgor pressure recordings over several weeks showed a drop in turgor during the day and recovery at night. Thus pressure changes directly correlated with the degree of plant transpiration. Leaf turgor of wild‐type plants responded to CO₂, light, humidity, ozone and abscisic acid (ABA) in a guard cell‐specific manner. Pressure probe measurements of mutants lacking OST1 and SLAC1 function indicated impairment in stomatal responses to light and humidity. In contrast to wild‐type plants, leaves from well‐watered ost1 plants exposed to a dry atmosphere wilted after light‐induced stomatal opening. Experiments with open stomata mutants indicated that the hydraulic conductance of leaf stomata is higher than that of the root–shoot continuum. Thus leaf turgor appears to rely to a large extent on the anion channel activity of autonomously regulated stomatal guard cells.     

The effect of dimethylsulfoxide on the water transport response of rat hepatocytes during freezing.

Successful improvement of cryopreservation protocols for cells in suspension requires knowledge of how such cells respond to the biophysical stresses of freezing (intracellular ice formation, water transport) while in the presence of a cryoprotective agent (CPA). This work investigates the biophysical water transport response in a clinically important cell type--isolated hepatocytes--during freezing in the presence of dimethylsulfoxide (DMSO). Sprague-Dawley rat liver hepatocytes were frozen in Williams E media supplemented with 0, 1, and 2 M DMSO, at rates of 5, 10, and 50 degrees C/min. The water transport was measured by cell volumetric changes as assessed by cryomicroscopy and image analysis. Assuming that water is the only species transported under these conditions, a water transport model of the form dV/dT = f(Lpg([CPA]), ELp([CPA]), T(t)) was curve-fit to the experimental data to obtain the biophysical parameters of water transport--the reference hydraulic permeability (Lpg) and activation energy of water transport (ELp)--for each DMSO concentration. These parameters were estimated two ways: (1) by curve-fitting the model to the average volume of the pooled cell data, and (2) by curve-fitting individual cell volume data and averaging the resulting parameters. The experimental data showed that less dehydration occurs during freezing at a given rate in the presence of DMSO at temperatures between 0 and -10 degrees C. However, dehydration was able to continue at lower temperatures (< -10 degrees C) in the presence of DMSO. The values of Lpg and ELp obtained using the individual cell volume data both decreased from their non-CPA values--4.33 x 10(-13) m3/N-s (2.69 microns/min-atm) and 317 kJ/mol (75.9 kcal/mol), respectively--to 0.873 x 10(-13) m3/N-s (0.542 micron/min-atm) and 137 kJ/mol (32.8 kcal/mol), respectively, in 1 M DMSO and 0.715 x 10(-13) m3/N-s (0.444 micron/min-atm) and 107 kJ/mol (25.7 kcal/mol), respectively, in 2 M DMSO. The trends in the pooled volume values for Lpg and ELp were very similar, but the overall fit was considered worse than for the individual volume parameters. A unique way of presenting the curve-fitting results supports a clear trend of reduction of both biophysical parameters in the presence of DMSO, and no clear trend in cooling rate dependence of the biophysical parameters. In addition, these results suggest that close proximity of the experimental cell volume data to the equilibrium volume curve may significantly reduce the efficiency of the curve-fitting process.     

Turgor Pressure Regulation in Valonia utricularis: Effect of Cell Wall Elasticity and Auxin

The electrical membrane resistance rho(0) of the marine alga Valonia utricularis shows a marked maximum in dependence on the turgor pressure. The critical pressure, P(c), at which the maximum occurs, as well as its absolute value, rho(0) (max), are strongly volume-dependent. Both P(c) and rho(0) (max), increase with decreasing cell volume. It seems likely, that these relationships reflect the elastic properties of the cell wall, because the volumetric elastic modulus, epsilon, is also volume-dependent, increasing hyperbolically with cell volume. Both P(c) and rho(0) (max) can be affected by external application of indole-3-acetic acid at concentrations of 2.10(-7)m to 2 .10(-5)m. The critical pressure is shifted by 1.2 to 6 bars toward higher pressures and the maximum membrane resistance increased up to 5.6-fold. During the course of the experiments (up to 4 hours), however, IAA had no effect on the volumetric elastic modulus, epsilon.The maximum in membrane resistance is discussed in terms of a pressure-dependent change of potassium fluxes. The volume dependence of P(c) and rho(0) (max) suggests that not only turgor pressure but also epsilon must be considered as a regulating parameter during turgor pressure regulation. On this basis a hypothesis is presented for the transformation of both, a pressure signal and of changes in the elastic properties of the cell wall into alterations of ion fluxes. It is assumed that the combined effects of tension and compression of the membranes as well as the interaction between membrane and cell wall opposingly change the number of transport sites for K(+) providing a turgor-sensing mechanism that regulates ion fluxes. The IAA effects demonstrated are consistent with this view, suggesting that the basic mechanisms for turgor pressure regulation and growth regulation are similar.Any relation connecting growth rate with turgor pressure should be governed by two parameters, i.e. by a yielding pressure, at which cell growth starts, and by the critical pressure, at which it ceases again.     

Turgor pressure and water transport properties of suspension-cultured cells of Chenopodium rubrum L.

The turgor pressure and water relation parameters were determined in single photoautotrophically grown suspension cells and in individual cells of intact leaves of Chenopodium rubrum using the miniaturized pressure probe. The stationary turgor pressure in suspension-cultured cells was in the range of betwen 3 and 5 bar. From the turgor pressure relaxation process, induced either hydrostatically (by means of the pressure probe) or osmotically, the halftime of water exchange was estimated to be 20±10 s. No polarity was observed for both ex- and endosmotic water flow. The volumetric elastic modulus, , determined from measurements of turgor pressure changes, and the corresponding changes in the fractional cell volume was determined to be in the range of between 20 and 50 bar. increases with increasing turgor pressure as observed for other higher plant and algal cells. The hydraulic conductivity, Lp, is calculated to be about 0,5–2·10^–6 cm s^–1 bar^–1. Similar results were obtained for individual leaf cells of Ch. rubrum. Suspension cells immobilized in a cross-linked matrix of alginate (6 to 8% w/w) revealed the same values for the half-time of water exchange and for the hydraulic conductivity, Lp, provided that the turgor pressure relaxation process was generated hydrostatically by means of the pressure probe. Thus, it can be concluded that the unstirred layer from the immobilized matrix has no effect on the calculation of Lp from the turgor pressure relaxation process, using the water transport equation derived for a single cell surrounded by a large external volume. By analogy, this also holds true for Lp-values derived from turgor pressure changes generated by the pressure probe in a single cell within the leaf tissue. The fair similarity between the Lp-values measured in mesophyll cells in situ and mesophyll-like suspension cells suggests that the water transport relations of a cell within a leaf are not fundamentally different from those measured in a single cell.     

Theoretical and experimental exclusion of errors in the determination of the elasticity and water transport parameters of plant cells by the pressure probe technique

The volumetric elastic modulus of the cell wall and the hydraulic conductivity of the cell membranes were measured on ligatured compartments of different sizes of Chara corallina internodes using the pressure probe technique. The ratio between intact cell surface area and the area of puncture in the cell wall and membrane introduced by the microcapillary of the pressure probe was varied over a large range by inserting microcapillaries of widely varying diameters in different sized compartments. The relationship of the elastic modulus and the hydraulic conductivity to turgor pressure was independent of the ratio of intact cell surface area to the area of injury. The increase in the hydraulic conductivity below 2 bar turgor pressure and the volume dependence of the elastic modulus were shown to be the same as those observed in intact nonligatured cells. Theoretical considerations of the possible influence of injury of the cell wall and cell membrane around the inserted microcapillary on the measurement of the water transport and cell wall parameters do not explain the experimental findings. Thus, mechanical artifacts, if at all present, are too small to account for the observed dependence of the hydraulic conductivity and the elastic modulus on turgor pressure. The pressure probe technique thus represents an accurate method for measuring water transport parameters in both giant algal cells and in tissue cells of higher plants.     

Pressure probe technique for measuring water relations of cells in higher plants

A new method is described for continuously measuring cell turgor pressure (P), hydraulic conductivity (L_p), and volumetric elastic modulus (ε) in higher plant cells, using a pressure probe. This technique permits volume changes, ΔV, and turgor pressure changes, ΔP, to be determined with an accuracy of 10⁻⁵ to 10⁻⁶ μl and 3 to 5·10⁻² bar, respectively.

The main principle of the new method is the same as the pressure probe developed by Zimmermann and Steudle in which pressure is transmitted to a pressure transducer by means of an oil-filled capillary introduced into the cell. In order to use the pressure probe for small tissue cells, the effective compressible volume of the apparatus has to be sufficiently small in comparison to the volume of the cell itself. This is achieved by accurately fixing the oil/cell sap boundary in the very tip of the microcapillary by means of an electronic feedback mechanism, so that the effective volume of the apparatus is reduced to about 2 to 10% of the cell volume. In this way also, errors arising from compressibility of the apparatus and temperature fluctuations can be excluded.

Measurements on tissues cells of Capsicum annuum fruits yield ε values of 2 to 25 bar. Furthermore, ε can be shown to be a function of both cell turgor pressure and cell volume; ε increases with increasing turgor pressure and is higher in larger cells.