Amicus Plato, sed magis amica veritas: plots must obey the laws they refer to and models shall describe biophysical reality!

In the companion paper, we discussed in details proper linearization, calculation of the inactive osmotic volume, and analysis of the results on the Boyle-vant’ Hoff plots. In this Letter, we briefly address some common errors and misconceptions in osmotic modeling and propose some approaches, namely: (1) inapplicability of the Kedem–Katchalsky formalism model in regards to the cryobiophysical reality, (2) calculation of the membrane hydraulic conductivity L_p in the presence of permeable solutes, (3) proper linearization of the Arrhenius plots for the solute membrane permeability, (4) erroneous use of the term “toxicity” for the cryoprotective agents, and (5) advantages of the relativistic permeability approach (RP) developed by us vs. traditional (“classic”) 2-parameter model.     

Hydraulic Conductivity (Lp) and Its Activation Energy (Ea), Cryoprotectant Agent Permeability (Ps) and ItsEa, and Reflection Coefficients (?) for Golden Hamster Individual Pancreatic Islet Cell Membranes

Long-term cryopreservation of islets of Langerhans would be advantageous to a clinical islet transplantation program. Fundamental cryobiology utilizes knowledge of basic biophysical characteristics to increase the understanding of the preservation process and possibly increase survival rate. In this study several of these previously unreported characteristics have been determined for individual islet cells isolated from Golden hamster islets. Using an electronic particle counting device and a temperature control apparatus, dynamic volumetric response of individual islet cells to anisosmotic challenges of 1.5 M dimethyl sulfoxide (DMSO) and 1.5 M ethylene glycol (EG) were recorded at four temperatures (8, 22, 28, and 37°C). The resulting curves were fitted using Kedem and Katchalsky equations which describe water flux and cryoprotectant agent (CPA) flux based on hydraulic conductivity (L_p), CPA permeability (P_s), and reflection coefficient (?) for the membrane. For Golden hamster islet cells,L_p,P_s, and ? for DMSO at 22°C were found to be 0.23 ± 0.06 μm/min/atm, 0.79 ± 0.32 × 10⁻³cm/min, and 0.55 ± 0.37 (n= 11) (mean ± SD), respectively. For EG at 22°C,L_pequaled 0.23 ± 0.06 μm/min/atm,P_sequaled 0.63 ± 0.20 × 10⁻³cm/min, and ? was 0.75 ± 0.17 (n= 9). Arrhenius plots (lnL_por lnP_sversus 1/temperature (K)) were created by adding the data from the other three temperatures and the resulting linear regression yielded correlation coefficients (r) of 0.99 for all four plots (L_pandP_sfor both CPAs). Activation energies (E_a) ofL_pandP_swere calculated from the slopes of the regressions. The values for DMSO were found to be 12.43 and 18.34 kcal/mol forL_pandP_s(four temperatures, totaln= 52), respectively. For EG,E_aofL_pwas 11.69 kcal/mol andE_aofP_swas 20.35 kcal/mol (four temperatures, totaln= 58).     

The calcium‐dependent protein kinase CPK7 acts on root hydraulic conductivity

The hydraulic conductivity of plant roots (Lp_r) is determined in large part by the activity of aquaporins. Mechanisms occurring at the post‐translational level, in particular phosphorylation of aquaporins of the plasma membrane intrinsic protein 2 (PIP2) subfamily, are thought to be of critical importance for regulating root water transport. However, knowledge of protein kinases and phosphatases acting on aquaporin function is still scarce. In the present work, we investigated the Lp_r of knockout Arabidopsis plants for four Ca²⁺‐dependent protein kinases. cpk7 plants showed a 30% increase in Lp_r because of a higher aquaporin activity. A quantitative proteomic analysis of wild‐type and cpk7 plants revealed that PIP gene expression and PIP protein quantity were not correlated and that CPK7 has no effect on PIP2 phosphorylation. In contrast, CPK7 exerts a negative control on the cellular abundance of PIP1s, which likely accounts for the higher Lp_r of cpk7. In addition, this study revealed that the cellular amount of a few additional proteins including membrane transporters is controlled by CPK7. The overall work provides evidence for CPK7‐dependent stability of specific membrane proteins.     

The determination of membrane transport parameters with the cell pressure probe: theory suggests that unstirred layers have significant impact

A simulation model was written to compute the time-kinetics of turgor pressure, P, change in Chara corallina during cell pressure probe experiments. The model allowed for the contribution of a membrane plus zero, one, or two unstirred layers of any desired thickness. The hypothesis that a cell with an unstirred layer is a composite membrane that will follow the same kind of kinetics with or without unstirred layers was tested. Typical ‘osmotic pulse’ experiments yield biphasic curves with minimum or maximum pressures, P_min(max), at time t_min(max) and a solute exponential decay with halftime . These observed data were then used to compute composite membrane properties, namely the parameters L_p = the hydraulic conductance, σ = reflection coefficient and P_s = solute permeability using theoretical equations. Using the simulation model, it was possible to fit an experimental data set to the same values of P_min(max), t_min(max) and incorporating different, likely values of unstirred layer thickness, where each thickness requires a unique set of plasmalemma membrane values of L_p, σ and P_s. We conclude that it is not possible to compute plasmalemma membrane properties from cell pressure probe experiments without independent knowledge of the unstirred layer thickness.     

Membrane Transport Generated by the Osmotic and Hydrostatic Pressure. Correlation Relation for Parameters L p, σ, and ω

Standard approach to membrane transport generated by osmotic andhydrostatic pressures, developed by Kedem and Katchalsky, is based onprinciples of thermodynamics of irreversible processes. In this paper wepropose an alternative technique. We derive transport equations from fewfairly natural assumptions and a mechanistic interpretation of the flows.In particular we postulate that a sieve-type membrane permeability isdetermined by the pore sizes and these are random within certain range.Assuming that an individual pore is either permeable or impermeable tosolute molecules, the membrane reflection coefficient depends on the ratioof permeable and impermeable pores. Considering flows through permeableand impermeable pores separately, we derive equations for the total volumeflux, solute flux and the solvent flux across the membrane. Comparing themechanistic equations to the Kedem-Katchalsky equations we find the formereasier to interpret physically. Based on the mechanistic equations we alsoderive a correlation relation for the membrane transport parameters L _p,, and . This relation eliminates the need for experimentaldetermination of all three phenomenological parameters, which in somecases met with considerable difficulties.     

An artificial osmotic cell: a model system for simulating osmotic processes and for studying phenomena of negative pressure in plants

Abstract An artificial osmotic cell has been constructed using reverse osmosis membranes. The cell consisted of a thin film of an osmotic solution (thickness: 100 to 200 μm) containing a non-permeating solute and was bounded between the membrane and the front plate of a pressure transducer which continuously recorded cell turgor. The membrane was supported by metal grids to withstand positive and negative pressures (P). At maximum, negative pressures of up to –0.7 MPa (absolute) could be created within the film on short-term and pressures of up to –0.3 MPa could be maintained without cavitation for several hours. As with living plant cells, the application of osmotic solutions of a non-permeating solute resulted in monophasic relaxations of turgor pressure from which the hydraulic conductivity of the membrane (Lp) and the elastic modulus of the cell (?) could be estimated. The application of solutions with permeating solutes resulted in biphasic pressure relaxation curves (as for living cells) from which the permeability (P_s) and reflection (σ_s) coefficients could be evaluated for the given membrane. Lp, P_s, and σ_s were independent of P and did not change upon transition from the positive to the negative range of pressure. It is concluded that the artificial cell could be used to simulate certain transport properties of living cells and to study phenomena of negative pressure as they occur in the xylem and, perhaps, also in living cells of higher plants.     

Oxidative gating of water channels (aquaporins) in Chara by hydroxyl radicals

Hydroxyl radicals (*OH) as produced in the Fenton reaction (Fe²⁺ + H₂O₂ = Fe³⁺ + OH^– + *OH) have been used to reversibly inhibit aquaporins in the plasma membrane of internodes of Chara corallina. Compared to conventional agents such as HgCl₂, *OH proved to be more effective in blocking water channels and was less toxic to the cell. When internodes were treated for 30 min, cell hydraulic conductivity (Lp) decreased by 90% or even more. This effect was reversed within a few minutes after removing the radicals from the medium. In contrast to HgCl₂, radical treatment reduced membrane permeability of small lipophilic organic solutes (ethanol, acetone, 1‐propanol, and 2‐propanol) by only 24 to 52%, indicating some continued limited movement of these solutes across aquaporins. The biggest effect of *OH treatment on solute permeability was found for isotopic water (HDO), which largely used water channels to cross the membrane. Inhibition of aquaporins reduced the diffusional water permeability (P_d) by about 70%. For the organic test solutes, which mainly use the bilayer to cross the membrane, channel closure caused anomalous (negative) osmosis; that is, cells had negative reflection coefficients (σ_s) and were transiently swelling in a hypertonic medium. From the ratio of bulk (Lp or osmotic permeability coefficient, P_f) to diffusional (P_d) permeability of water, the number (N) of water molecules that align in water channels was estimated to be N = P_f/P_d = 46 (on average). Radical treatment decreased N from 46 to 11, a value still larger than unity, which would be expected for a membrane lacking pores. The gating of aquaporins by *OH radicals is discussed in terms of a direct action of the radicals when passing the pores or by an indirect action via the bilayer. The rapid recovery of inhibited channels may indicate an easy access of cytoplasmic antioxidants to closed water channels. As hydrogen peroxide is a major signalling substance during different biotic and abiotic stresses, the reversible closure of water channels by *OH (as produced from H₂O₂ in the apoplast in the presence of transition metals such as Fe²⁺ or Cu⁺) may be downstream of the H₂O₂ signalling. This may provide appropriate adjustments in water relations (hydraulic conductivity), and a common response to different kinds of stresses.     

The arbuscular mycorrhizal symbiosis regulates aquaporins activity and improves root cell water permeability in maize plants subjected to water stress

Studies have suggested that increased root hydraulic conductivity in mycorrhizal roots could be the result of increased cell‐to‐cell water flux via aquaporins. This study aimed to elucidate if the key effect of the regulation of maize aquaporins by the arbuscular mycorrhizal (AM) symbiosis is the enhancement of root cell water transport capacity. Thus, water permeability coefficient (P_f) and cell hydraulic conductivity (L_pc) were measured in root protoplast and intact cortex cells of AM and non‐AM plants subjected or not to water stress. Results showed that cells from droughted‐AM roots maintained P_f and L_pc values of nonstressed plants, whereas in non‐AM roots, these values declined drastically as a consequence of water deficit. Interestingly, the phosphorylation status of PIP2 aquaporins increased in AM plants subjected to water deficit, and P_f values higher than 12 μm s^?1 were found only in protoplasts from AM roots, revealing the higher water permeability of AM root cells. In parallel, the AM symbiosis increased stomatal conductance, net photosynthesis, and related parameters, showing a higher photosynthetic capacity in these plants. This study demonstrates a better performance of AM root cells in water transport under water deficit, which is connected to the shoot physiological performance in terms of photosynthetic capacity.     

Involvement of a glucosinolate (sinigrin) in the regulation of water transport in Brassica oleracea grown under salt stress

Members of the Brassicaceae are known for their contents of nutrients and health‐promoting phytochemicals, including glucosinolates. The concentrations of these chemopreventive compounds (glucosinolate‐degradation products, the bioactive isothiocyanates) may be modified under salinity. In this work, the effect of the aliphatic glucosinolate sinigrin (2‐propenyl‐glucosinolate) on plant water balance, involving aquaporins, was explored under salt stress. For this purpose, water uptake and its transport through the plasma membrane were determined in plants after NaCl addition, when sinigrin was also supplied. We found higher hydraulic conductance (L₀) and water permeability (P_f) and increased abundance of PIP2 aquaporins after the direct administration of sinigrin, showing the ability of the roots to promote cellular water transport across the plasma membrane in spite of the stress conditions imposed. The higher content of the allyl‐isothiocyanate and the absence of sinigrin in the plant tissues suggest that the isothiocyanate is related to water balance; in fact, a direct effect of this nitro‐sulphate compound on water uptake is proposed. This work provides the first evidence that the addition of a glucosinolate can regulate aquaporins and water transport: this effect and the mechanism(s) involved merit further investigation.     

On the derivation of the Kargol's mechanistic transport equations from the Kedem-Katchalsky phenomenological equations

In the present article, it was demonstrated that--by starting from the so-called adjusted Kedem-Katchalsky (KK) phenomenological equations (Suchanek et al. 2004), i.e. the equations: Jv=LpDeltaP-LpDDeltaPi. JD=-LDpDeltaP+LDDeltaPi it is possible to derive practical transport equations (for the volume flow and the solute flow) in the form of the Kargol s mechanistic transport equations (Kargol and Kargol 2000, 2001, 2003a,b,c, 2004; Kargol 2002). On this basis, it has been found that the KK thermodynamic formalism for membrane transport (practical equations) is in general identical with the mechanistic equations for membrane transport.     

A model for the blood–brain barrier permeability to water and small solutes

The blood–brain barrier (BBB) has unique structures in order to protect the central nervous system. In addition to the tight junction of the microvessel endothelium, there is a uniform and narrow matrix-like basement membrane (BM) sandwiched between the vessel wall and the astrocyte foot processes ensheathing the cerebral microvessel. To understand the mechanism by which these structural components modulate permeability of the BBB, we developed a mathematical model for water and solute transport across the BBB. The fluid flow in the cleft regions of the BBB were approximated by the Poiseuille flow while those in the endothelial surface glycocalyx layer (SGL) and BM were approximated by the Darcy and Brinkman flows, respectively. Diffusion equations in each region were solved for the solute transport. The anatomical parameters were obtained from electron microscopy studies in the literature. Our model predicts that compared to the peripheral microvessels with endothelium only, the BM and the wrapping astrocytes can reduce hydraulic conductivity (L_p) of the BBB and the permeability to sodium fluorescein (P^NaF) by up to 6-fold when the fiber density in the BM is the same as that in the SGL. Even when the SGL and the tight junctions of the endothelium are compromised, the BM and astrocyte foot processes can still maintain the low L_p and P^NaF of the BBB. Our model predictions indicate that the BM and astrocytes of the BBB provide a great protection to the CNS under both physiological and pathological conditions.     

Investigations into biophysical regulation mechanisms of physiological water exchange of the Nitella translucens cells with the surroundings

In the present paper, we have presented a theoretical discussion of specific biophysical mechanisms pertaining to the regulation (by means of internal factors) of physiological water exchange with the water medium by the cells of the Nitella translucens. The investigation has demonstrated that these cells have a capacity for water exchange regulation through changes in the values of transport parameters of the cell membrane (i.e. the filtration coefficient L_p and the reflection coefficient σ), as well as changes in the concentration C_si (inside the cells) of the osmotically active solute.     

Variable effects of arbuscular mycorrhizal fungal inoculation on physiological and molecular measures of root and stomatal conductance of diverse Medicago truncatula accessions

Association with arbuscular mycorrhizal fungi (AMF) can impact on plant water relations; mycorrhizal plants can exhibit increased stomatal conductance (g_s) and root hydraulic conductance (normalized to root dry weight, L_o), and altered expression of aquaporins (AQP). Many factors regulate such responses; however, plant intraspecific diversity effects have yet to be explored. Twenty geographically diverse accessions of Medicago truncatula were inoculated with the AMF Funneliformis mosseae or mock‐inoculated, and grown under well‐watered conditions. Biomass, g_s, shoot nutrient concentrations and mycorrhizal colonization were measured in all accessions, and L_o and gene expression in five accessions. The diverse accessions varied in physiology and gene expression; some accessions were also larger or had higher g_s when colonized by F. mosseae. In the five accessions, L_o was higher in two accessions when colonized by AMF and also maintained within a much smaller range than the mock‐inoculated plants. Expression of MtPIP1 correlated with both g_s and L_o, and when plants were more than 3% colonized, mycorrhizal colonization correlated with L_o. Accession and AMF treatments had profound effects on M. truncatula, including several measures of plant water relations. Correlations between response variables, especially between molecular and physiological variables, across genotypes, highlight the findings of this study.     

OZONE-INDUCED MEMBRANE PERMEABILITY CHANGES

The effect of 0.5 ppm ozone for 0.5-1 hr on plant cell membrane permeability was ascertained. Permeabilities to both water and solutes were estimated by measuring leaf disc weight changes and following tritiated water and ⁸⁶Rb fluxes. Measurements were made immediately after ozone exposure and 24 hr after exposure. The reflection coefficient, σ, an index of solute permeability, decreased in ozone-treated primary leaves of pinto bean (Phaseolus vulgaris). The latter indicates an increase in membrane solute permeability or internal solute leakage. Water and THO flux estimates both indicated a decrease in membrane permeability to water; both the hydraulic conductivity (L_p) and the water diffusional coefficient (L_D) apparently decreased, an anomaly which is discussed. These data indicate that ozone has a direct effect on membrane function by altering permeability characteristics. We assume from these data that cell membranes are primary target sites for ozone injury.     

Osmotic water permeability of isolated vacuoles

We measured the osmotic water permeability (P _os) of vacuoles isolated from onion (Allium cepa L.), rape (Brassica napus L.), petunia (Petunia hybrida Hook.) and red beet (Beta vulgaris L.). For all the vacuolar types investigated, P _os values were in the range 200–1000 μm s⁻¹. The change in membrane surface area induced by an osmotic gradient was smaller than 2–6%. The vacuolar P _os values for red beet and onion were reduced by 1 mM HgCl₂, to 14% and 30% of the control values, respectively, but were partially restored to 51% and 76% by 5 mM β-mercaptoethanol. These results suggest that aquaporins were present in all the vacuoles tested. In HgCl₂-treated onion vacuoles, the reduced P _os (56 μm s⁻¹) had a low activation energy (approx. 6 kJ mol⁻¹), indicating that water permeation was still occurring mainly via aquaporins, and that the water permeability of the lipid part of the vacuolar membrane is probably very low. Received: 18 February 1999 / Accepted: 21 June 1999     

Water channel does not limit evaporation of water from plant cells

Evaporation of water from the cell surface of the internode ofChara corallina was not affected by HgCl₂ which is known to inhibit water channels. This makes a sharp contrast to the fact that most of osmotically driven water transport is inhibited by HgCl₂. Also in radish hypocotyls whose epidermis had been peeled off, evaporation of water was not inhibited by HgCl₂, while osmotic water transport was significantly inhibited. The cell wall tube was prepared by squeezing out the content of theChara internode. The rate of evaporation from the cell wall tube filled with 150 mM KCl was almost equal to that from the living cell. The apparent hydraulic conductivity of the cell calculated from evaporation rate was found to be 1–2×10⁻³ pm s⁻¹ Pa⁻¹ which is about 1/1000 times the hydraulic conductivity of the plasma membrane (L_p) and 1/40 times the L_p under maximal inhibition with HgCl₂. It is concluded that under the relative humidity of 53–70% the rate of evaporation of water from the cell surface is limited by the rate of evaporation from the cell wall which is so low that the loss of water can be supplemented without delay from the cell interior across the plasma membrane even when water channels are completely closed.     

Rapid shoot‐to‐root signalling regulates root hydraulic conductance via aquaporins

We investigated how root hydraulic conductance (normalized to root dry weight, L_o) is regulated by the shoot. Shoot topping (about 30% reduction in leaf area) reduced L_o of grapevine (Vitis vinifera L.), soybean (Glycine max L.) and maize (Zea mays L.) by 50 to 60%. More detailed investigations with soybean and grapevine showed that the reduction in L_o was not correlated with the reduction in leaf area, and shading or cutting single leaves had a similar effect. Percentage reduction in L_o was largest when initial L_o was high in soybean. Inhibition of L_o by weak acid (low pH) was smaller after shoot damage or leaf shading. The half time of reduction in L_o was approximately 5 min after total shoot decapitation. These characteristics indicate involvement of aquaporins. We excluded phloem‐borne signals and auxin‐mediated signals. Xylem‐mediated hydraulic signals are possible since turgor rapidly decreased within root cortex cells after shoot topping. There was a significant reduction in the expression of several aquaporins in the plasma membrane intrinsic protein (PIP) family of both grapevine and soybean. In soybean, there was a five‐ to 10‐fold reduction in GmPIP1;6 expression over 0.5–1 h which was sustained over the period of reduced L_o.