The absence of AQP4/TRPV4 complex substantially reduces acute cytotoxic edema following ischemic injury.

Introduction: Astrocytic Aquaporin 4 (AQP4) and Transient receptor potential vanilloid 4 (TRPV4) channels form a functional complex that likely influences cell volume regulation, the development of brain edema, and the severity of the ischemic injury. However, it remains to be fully elucidated whether blocking these channels can serve as a therapeutic approach to alleviate the consequences of having a stroke. Methods and results: In this study, we used in vivo magnetic resonance imaging (MRI) to quantify the extent of brain lesions one day (D1) and seven days (D7) after permanent middle cerebral artery occlusion (pMCAO) in AQP4 or TRPV4 knockouts and mice with simultaneous deletion of both channels. Our results showed that deletion of AQP4 or TRPV4 channels alone leads to a significant worsening of ischemic brain injury at both time points, whereas their simultaneous deletion results in a smaller brain lesion at D1 but equal tissue damage at D7 when compared with controls. Immunohistochemical analysis 7 days after pMCAO confirmed the MRI data, as the brain lesion was significantly greater in AQP4 or TRPV4 knockouts than in controls and double knockouts. For a closer inspection of the TRPV4 and AQP4 channel complex in the development of brain edema, we applied a real-time iontophoretic method in situ to determine ECS diffusion parameters, namely volume fraction (α) and tortuosity (λ). Changes in these parameters reflect alterations in cell volume, and tissue structure during exposure of acute brain slices to models of ischemic conditions in situ, such as oxygen-glucose deprivation (OGD), hypoosmotic stress, or hyperkalemia. The decrease in α was comparable in double knockouts and controls when exposed to hypoosmotic stress or hyperkalemia. However, during OGD, there was no decrease in α in the double knockouts as observed in the controls, which suggests less swelling of the cellular components of the brain. Conclusion: Although simultaneous deletion of AQP4 and TRPV4 did not improve the overall outcome of ischemic brain injury, our data indicate that the interplay between AQP4 and TRPV4 channels plays a critical role during neuronal and non-neuronal swelling in the acute phase of ischemic injury.

Chronic alcohol consumption alters extracellular space geometry and transmitter diffusion in the brain.

Already moderate alcohol consumption has detrimental long-term effects on brain function. However, how alcohol produces its potent addictive effects despite being a weak reinforcer is a poorly understood conundrum that likely hampers the development of successful interventions to limit heavy drinking. In this translational study, we demonstrate widespread increased mean diffusivity in the brain gray matter of chronically drinking humans and rats. These alterations appear soon after drinking initiation in rats, persist into early abstinence in both species, and are associated with a robust decrease in extracellular space tortuosity explained by a microglial reaction. Mathematical modeling of the diffusivity changes unveils an increased spatial reach of extrasynaptically released transmitters like dopamine that may contribute to alcohol's progressively enhanced addictive potency.

High potassium exposure reveals the altered ability of astrocytes to regulate their volume in the aged hippocampus of GFAP/EGFP mice.

In this study, we focused on age-related changes in astrocyte functioning, predominantly on the ability of astrocytes to regulate their volume in response to a pathological stimulus, namely extracellular 50 mM K+ concentration. The aim of our project was to identify changes in the expression and function of transport proteins in the astrocytic membrane and properties of the extracellular space, triggered by aging. We used three-dimensional confocal morphometry, gene expression profiling, immunohistochemical analysis, and diffusion measurement in the hippocampal slices from 3-, 9-, 12-, and 18-month-old mice, in which astrocytes are visualized by enhanced green fluorescent protein under the control of the promoter for human glial fibrillary acidic protein. Combining a pharmacological approach and the quantification of astrocyte volume changes evoked by hyperkalemia, we found that marked diversity in the extent of astrocyte swelling in the hippocampus during aging is due to the gradually declining participation of Na+-K+-Cl- transporters, glutamate transporters (glutamate aspartate transporter and glutamate transporter 1), and volume-regulated anion channels. Interestingly, there was a redistribution of Na+-K+-Cl- cotransporter and glutamate transporters from astrocytic soma to processes. In addition, immunohistochemical analysis confirmed an age-dependent decrease in the content of Na+-K+-Cl- cotransporter in astrocytes. The overall extracellular volume changes revealed a similar age-dependent diversity during hyperkalemia as observed in astrocytes. In addition, the recovery of the extracellular space was markedly impaired in aged animals.

The role of aquaporin-4 and transient receptor potential vaniloid isoform 4 channels in the development of cytotoxic edema and associated extracellular diffusion parameter changes.

The proper function of the nervous system is dependent on the balance of ions and water between the intracellular and extracellular space (ECS). It has been suggested that the interaction of aquaporin-4 (AQP4) and the transient receptor potential vaniloid isoform 4 (TRPV4) channels play a role in water balance and cell volume regulation, and indirectly, of the ECS volume. Using the real-time iontophoretic method, we studied the changes of the ECS diffusion parameters: ECS volume fraction α (α = ECS volume fraction/total tissue volume) and tortuosity λ (λ2  = free/apparent diffusion coefficient) in mice with a genetic deficiency of AQP4 or TRPV4 channels, and in control animals. The used models of cytotoxic edema included: mild and severe hypotonic stress or oxygen-glucose deprivation (OGD) in situ and terminal ischemia/anoxia in vivo. This study shows that an AQP4 or TRPV4 deficit slows down the ECS volume shrinkage during severe ischemia in vivo. We further demonstrate that a TRPV4 deficit slows down the velocity and attenuates an extent of the ECS volume decrease during OGD treatment in situ. However, in any of the cytotoxic edema models in situ (OGD, mild or severe hypotonic stress), we did not detect any alterations in the cell swelling or volume regulation caused by AQP4 deficiency. Overall, our results indicate that the AQP4 and TRPV4 channels may play a crucial role in severe pathological states associated with their overexpression and enhanced cell swelling. However, detailed interplay between AQP4 and TRPV4 channels requires further studies and additional research.

A deficiency of the link protein Bral2 affects the size of the extracellular space in the thalamus of aged mice.

Bral2 is a link protein stabilizing the binding between lecticans and hyaluronan in perineuronal nets and axonal coats (ACs) in specific brain regions. Using the real-time iontophoretic method and diffusion-weighted magnetic resonance, we determined the extracellular space (ECS) volume fraction (α), tortuosity (λ), and apparent diffusion coefficient of water (ADCW ) in the thalamic ventral posteromedial nucleus (VPM) and sensorimotor cortex of young adult (3-6 months) and aged (14-20 months) Bral2-deficient (Bral2-/- ) mice and age-matched wild-type (wt) controls. The results were correlated with an analysis of extracellular matrix composition. In the cortex, no changes between wt and Bral2-/- were detected, either in the young or aged mice. In the VPM of aged but not in young Bral2-/- mice, we observed a significant decrease in α and ADCW in comparison with age-matched controls. Bral2 deficiency led to a reduction of both aggrecan- and brevican-associated perineuronal nets and a complete disruption of brevican-based ACs in young as well as aged VPM. Our data suggest that aging is a critical point that reveals the effect of Bral2 deficiency on VPM diffusion. This effect is probably mediated through the enhanced age-related damage of neurons lacking protective ACs, or the exhausting of compensatory mechanisms maintaining unchanged diffusion parameters in young Bral2-/- animals. A decreased ECS volume in aged Bral2-/- mice may influence the diffusion of neuroactive substances, and thus extrasynaptic and also indirectly synaptic transmission in this important nucleus of the somatosensory pathway.

Transplantation of Mesenchymal Stromal Cells in Patients With Amyotrophic Lateral Sclerosis: Results of Phase I/IIa Clinical Trial.

Amyotrophic lateral sclerosis (ALS) is a progressive untreatable neurodegenerative disorder, leading to the death of the cortical and spinal motoneurons (MNs). Bone marrow-derived mesenchymal stem/stromal cells (BM-MSCs) may represent a new approach to slowing down the progression of ALS by providing neurotrophic support to host MNs and by having an anti-inflammatory effect. We have designed a prospective, nonrandomized, open-label clinical trial (phase I/IIa, EudraCT No. 2011-000362-35) to assess the safety and efficacy of autologous multipotent BM-MSCs in ALS treatment. Autologous BM-MSCs were isolated and expanded under GMP conditions. Patients received 15 ± 4.5 × 106 of BM-MSCs via lumbar puncture into the cerebrospinal fluid. Patients were monitored for 6 months before treatment and then for an 18-month follow-up period. Potential adverse reactions were assessed, and the clinical outcome was evaluated by the ALS functional rating scale (ALSFRS), forced vital capacity (FVC), and weakness scales (WSs) to assess muscle strength on the lower and upper extremities. In total, 26 patients were enrolled in the study and were assessed for safety; 23 patients were suitable for efficacy evaluation. After intrathecal BM-MSC application, about 30% of the patients experienced a mild to moderate headache, resembling the headaches after a standard lumbar puncture. No suspected serious adverse reactions (SUSAR) were observed. We found a reduction in ALSFRS decline at 3 months after application (p < 0.02) that, in some cases, persisted for 6 months ( p < 0.05). In about 80% of the patients, FVC values remained stable or above 70% for a time period of 9 months. Values of WS were stable in 75% of patients at 3 months after application. Our results demonstrate that the intrathecal application of BM-MSCs in ALS patients is a safe procedure and that it can slow down progression of the disease.

Brain Diffusivity and Structural Changes in the R6/2 Mouse Model of Huntington Disease.

Diffusion-weighted magnetic resonance (DW-MR) is an important diagnostic tool in Huntington disease (HD), a fatal hereditary neurodegenerative disorder. To clarify the nature of diffusivity changes in HD, we compared the apparent diffusion coefficient of water (ADCW ) acquired by DW-MR with extracellular space volume fraction α and tortuosity λ, measured by the iontophoretic method in the R6/2 mouse model of HD and in wild-type controls (WT). In anisotropic globus pallidus (GP), diffusion measurements were performed in the mediolateral (x), rostrocaudal (y), and ventrodorsal (z) axes. In HD animals, we detected an increase in ADCW in all axes and larger α than in WT mice. No significant difference between WT and HD mice was found in the values of tortuosity (λx , λy , λz ). Despite structural changes in GP, diffusion anisotropy was unaffected in HD mice. Immunohistochemical analysis revealed in HD mice weaker expression of extracellular matrix and a decrease in neuron numbers compared with WT mice. Glial fibrillary acidic protein staining detected astrogliosis-like changes in the morphology of astrocytic processes in HD GP. In the somatosensory cortex, no significant differences in the studied parameters were found. We conclude that in the R6/2 model of HD, a decrease in the number of neurons in the GP results in increased ADCW and α values. Values of λ were not significantly changed as the increase of diffusion obstacles formed by reactive astrocytes was compensated for by the extracellular matrix reduction. © 2016 Wiley Periodicals, Inc.

Correlation between relaxometry and diffusion tensor imaging in the globus pallidus of Huntington's disease patients.

Huntington's disease (HD) is an inherited neurodegenerative disorder with progressive impairment of motor, behavioral and cognitive functions. The clinical features of HD are closely related to the degeneration of the basal ganglia, predominantly the striatum. The main striatal output structure, the globus pallidus, strongly accumulates metalloprotein-bound iron, which was recently shown to influence the diffusion tensor scalar values. To test the hypothesis that this effect dominates in the iron-rich basal ganglia of HD patients, we examined the globus pallidus using DTI and T2 relaxometry sequences. Quantitative magnetic resonance (MR), clinical and genetic data (number of CAG repeats) were obtained from 14 HD patients. MR parameters such as the T2 relaxation rate (RR), fractional anisotropy (FA) and mean diffusivity (MD) were analysed. A positive correlation was found between RR and FA (R2=0.84), between CAG and RR (R2=0.59) and between CAG and FA (R2=0.44). A negative correlation was observed between RR and MD (R2=0.66). A trend towards correlation between CAG and MD was noted. No correlation between MR and clinical parameters was found. Our results indicate that especially magnetic resonance FA measurements in the globus pallidus of HD patients may be strongly affected by metalloprotein-bound iron accumulation.

The impact of alpha-syntrophin deletion on the changes in tissue structure and extracellular diffusion associated with cell swelling under physiological and pathological conditions.

Aquaporin-4 (AQP4) is the primary cellular water channel in the brain and is abundantly expressed by astrocytes along the blood-brain barrier and brain-cerebrospinal fluid interfaces. Water transport via AQP4 contributes to the activity-dependent volume changes of the extracellular space (ECS), which affect extracellular solute concentrations and neuronal excitability. AQP4 is anchored by α-syntrophin (α-syn), the deletion of which leads to reduced AQP4 levels in perivascular and subpial membranes. We used the real-time iontophoretic method and/or diffusion-weighted magnetic resonance imaging to clarify the impact of α-syn deletion on astrocyte morphology and changes in extracellular diffusion associated with cell swelling in vitro and in vivo. In mice lacking α-syn, we found higher resting values of the apparent diffusion coefficient of water (ADCW) and the extracellular volume fraction (α). No significant differences in tortuosity (λ) or non-specific uptake (k'), were found between α-syn-negative (α-syn -/-) and α-syn-positive (α-syn +/+) mice. The deletion of α-syn resulted in a significantly smaller relative decrease in α observed during elevated K(+) (10 mM) and severe hypotonic stress (-100 mOsmol/l), but not during mild hypotonic stress (-50 mOsmol/l). After the induction of terminal ischemia/anoxia, the final values of ADCW as well as of the ECS volume fraction α indicate milder cell swelling in α-syn -/- in comparison with α-syn +/+ mice. Shortly after terminal ischemia/anoxia induction, the onset of a steep rise in the extracellular potassium concentration and an increase in λ was faster in α-syn -/- mice, but the final values did not differ between α-syn -/- and α-syn +/+ mice. This study reveals that water transport through AQP4 channels enhances and accelerates astrocyte swelling. The substantially altered ECS diffusion parameters will likely affect the movement of neuroactive substances and/or trophic factors, which in turn may modulate the extent of tissue damage and/or drug distribution.

Cell death/proliferation and alterations in glial morphology contribute to changes in diffusivity in the rat hippocampus after hypoxia-ischemia.

To understand the structural alterations that underlie early and late changes in hippocampal diffusivity after hypoxia/ischemia (H/I), the changes in apparent diffusion coefficient of water (ADC(W)) were studied in 8-week-old rats after H/I using diffusion-weighted magnetic resonance imaging (DW-MRI). In the hippocampal CA1 region, ADC(W) analyses were performed during 6 months of reperfusion and compared with alterations in cell number/cell-type composition, glial morphology, and extracellular space (ECS) diffusion parameters obtained by the real-time iontophoretic method. In the early phases of reperfusion (1 to 3 days) neuronal cell death, glial proliferation, and developing gliosis were accompanied by an ADC(W) decrease and tortuosity increase. Interestingly, ECS volume fraction was decreased only first day after H/I. In the late phases of reperfusion (starting 1 month after H/I), when the CA1 region consisted mainly of microglia, astrocytes, and NG2-glia with markedly altered morphology, ADC(W), ECS volume fraction and tortuosity were increased. Three-dimensional confocal morphometry revealed enlarged astrocytes and shrunken NG2-glia, and in both the contribution of cell soma/processes to total cell volume was markedly increased/decreased. In summary, the ADC(W) increase in the CA1 region underlain by altered cellular composition and glial morphology suggests that considerable changes in extracellular signal transmission might occur in the late phases of reperfusion after H/I.

Bral1: its role in diffusion barrier formation and conduction velocity in the CNS.

At the nodes of Ranvier, excitable axon membranes are exposed directly to the extracellular fluid. Cations are accumulated and depleted in the local extracellular nodal region during action potential propagation, but the impact of the extranodal micromilieu on signal propagation still remains unclear. Brain-specific hyaluronan-binding link protein, Bral1, colocalizes and forms complexes with negatively charged extracellular matrix (ECM) proteins, such as versican V2 and brevican, at the nodes of Ranvier in the myelinated white matter. The link protein family, including Bral1, appears to be the linchpin of these hyaluronan-bound ECM complexes. Here we report that the hyaluronan-associated ECM no longer shows a nodal pattern and that CNS nerve conduction is markedly decreased in Bral1-deficient mice even though there were no differences between wild-type and mutant mice in the clustering or transition of ion channels at the nodes or in the tissue morphology around the nodes of Ranvier. However, changes in the extracellular space diffusion parameters, measured by the real-time iontophoretic method and diffusion-weighted magnetic resonance imaging (MRI), suggest a reduction in the diffusion hindrances in the white matter of mutant mice. These findings provide a better understanding of the mechanisms underlying the accumulation of cations due to diffusion barriers around the nodes during saltatory conduction, which further implies the importance of the Bral1-based extramilieu for neuronal conductivity.

Extracellular diffusion parameters in the rat somatosensory cortex during recovery from transient global ischemia/hypoxia.

Changes in the extracellular space diffusion parameters during ischemia are well known, but information about changes during the postischemic period is lacking. Extracellular volume fraction (alpha) and tortuosity (lambda) were determined in the rat somatosensory cortex using the real-time iontophoretic method; diffusion-weighted magnetic resonance imaging was used to determine the apparent diffusion coefficient of water. Transient ischemia was induced by bilateral common carotid artery clamping for 10 or 15 mins and concomitant ventilation with 6% O(2) in N(2). In both ischemia groups, a negative DC shift accompanied by increased potassium levels occurred after 1 to 2 mins of ischemia and recovered to preischemic values within 3 to 5 mins of reperfusion. During ischemia of 10 mins duration, alpha typically decreased to 0.07+/-0.01, whereas lambda increased to 1.80+/-0.02. In this group, normal values of alpha=0.20+/-0.01 and lambda=1.55+/-0.01 were registered within 5 to 10 mins of reperfusion. After 15 mins of ischemia, alpha increased within 40 to 50 mins of reperfusion to 0.29+/-0.03 and remained at this level. Tortuosity (lambda) increased to 1.81+/-0.02 during ischemia, recovered within 5 to 10 mins of reperfusion, and was increased to 1.62+/-0.01 at the end of the experiment. The observed changes can affect the diffusion of ions, neurotransmitters, metabolic substances, and drugs in the nervous system.

Brain metabolism and diffusion in the rat cerebral cortex during pilocarpine-induced status epilepticus.

The real-time iontophoretic method using tetramethylammonium-selective microelectrodes and diffusion-weighted magnetic resonance imaging were used to measure the extracellular space volume fraction alpha, tortuosity lambda and apparent diffusion coefficient of water (ADC(W)) 240 min after the administration of pilocarpine in urethane-anaesthetized rats. The obtained data were correlated with extracellular lactate, glucose, and glutamate concentrations and the lactate/pyruvate-ratio, determined by intracerebral microdialysis. The control values of alpha and lambda were 0.19+/-0.004 and 1.58+/-0.01, respectively. Following pilocarpine application, alpha decreased to 0.134+/-0.012 100 min later. Thereafter alpha increased, reaching 0.176+/-0.009 140 min later. No significant changes in lambda were observed during the entire time course of the experiment. ADC(W) was significantly decreased 100 min after pilocarpine application (549+/-8 microm(2) s(-1)) compared to controls (603+/-11 microm(2) s(-1)); by the end of the experiments, ADC(W) had returned to control values. The basal cortical levels of lactate, the lactate/pyruvate ratio, glucose and glutamate were 0.61+/-0.05 mmol/l, 33.16+/-4.26, 2.42+/-0.13 mmol/l and 6.55+/-1.31 micromol/l. Pilocarpine application led to a rise in lactate, the lactate/pyruvate ratio and glutamate levels, reaching 2.92+/-0.60 mmol/l, 84.80+/-11.72 and 22.39+/-5.85 micromol/l within about 100 min, with a subsequent decrease to control values 140 min later. The time course of changes in glucose levels was different, with maximal levels of 3.49+/-0.24 mmol/l reached 40 min after pilocarpine injection and a subsequent decrease to 1.25+/-0.40 mmol/l observed 200 min later. Pathologically increased neuronal activity induced by pilocarpine causes cell swelling followed by a reduction in the ECS volume fraction, which can contribute to the accumulation of toxic metabolites and lead to the start of epileptic discharges.

Reduced extracellular space in the brain of tenascin-R- and HNK-1-sulphotransferase deficient mice.

Tenascin-R (TN-R), a large extracellular glycoprotein, is an important component of the adult brain's extracellular matrix (ECM); tenascin-C (TN-C) is expressed mainly during early development, while human natural killer 1 (HNK-1) is a sulphated carbohydrate epitope that attaches to these molecules, modifying their adhesive properties. To assess their influence on extracellular space (ECS) volume and geometry, we used the real-time iontophoretic method to measure ECS volume fraction alpha and tortuosity lambda, and diffusion-weighted magnetic resonance imaging (MRI) to measure the apparent diffusion coefficient of water (ADC(W)). Measurements were performed in vivo in the cortex and CA1 hippocampal region of TN-R-, TN-C- and HNK-1 sulphotransferase (ST)-deficient adult mice and their wild-type littermate controls. In both cortex and hippocampus, the lack of TN-R or HNK-1 sulphotransferase resulted in a significant decrease in alpha and lambda. Compared with controls, alpha in TN-R-/- and ST-/- mice decreased by 22-26% and 9-15%, respectively. MRI measurements revealed a decreased ADC(W) in the cortex, hippocampus and thalamus. ADC(W) reflected the changes in alpha; the decrease in lambda indicated fewer diffusion obstacles in the ECS, presumably due to a decreased macromolecular content. No significant changes were found in TN-C-/- animals. We conclude that in TN-R-/- and ST-/- mice, which show morphological, electrophysiological and behavioural abnormalities, the ECS is reduced and its geometry altered. TN-R, as an important component of the ECM, appears to maintain an optimal distance between cells. The altered diffusion of neuroactive substances in the brain will inevitably affect extrasynaptic transmission, neuron-glia interactions and synaptic efficacy.

Changes in extracellular space size and geometry in APP23 transgenic mice: a model of Alzheimer's disease.

Diffusion parameters of the extracellular space (ECS) are changed in many brain pathologies, disturbing synaptic as well as extrasynaptic "volume" transmission, which is based on the diffusion of neuroactive substances in the ECS. Amyloid deposition, neuronal loss, and disturbed synaptic transmission are considered to be the main causes of Alzheimer's disease dementia. We studied diffusion parameters in the cerebral cortex of transgenic APP23 mice, which develop a pathology similar to Alzheimer's disease. The real-time tetramethylammonium (TMA) method and diffusion-weighted MRI were used to measure the ECS volume fraction (alpha = ECS volume/total tissue volume) and the apparent diffusion coefficients (ADCs) of TMA (ADC(TMA)), diffusing exclusively in the ECS and of water (ADC(W)). Measurements were performed in vivo in 6-, 8-, and 17- to 25-month-old hemizygous APP23 male and female mice and age-matched controls. In all 6- to 8-month-old APP23 mice, the mean ECS volume fraction, ADC(TMA), and ADC(W) were not significantly different from age-matched controls (alpha = 0.20 +/- 0.01; ADC(TMA), 580 +/- 16 microm(2).s(-1); ADC(W), 618 +/- 19 microm(2).s(-1)). Aging in 17- to 25-month-old controls was accompanied by a decrease in ECS volume fraction and ADC(W), significantly greater in females than in males, but no changes in ADC(TMA). ECS volume fraction increased (0.22 +/- 0.01) and ADC(TMA) decreased (560 +/- 7 microm(2).s(-1)) in aged APP23 mice. The impaired navigation observed in these animals in the Morris water maze correlated with their plaque load, which was twice as high in females (20%) as in males (10%) and may, together with changed ECS diffusion properties, account for the impaired extrasynaptic transmission and spatial cognition observed in old transgenic females.

Independence of extracellular tortuosity and volume fraction during osmotic challenge in rat neocortex.

The structural properties of brain extracellular space (ECS) are summarised by the tortuosity (lambda) and the volume fraction (alpha). To determine if these two parameters were independent, we varied the size of the ECS by changing the NaCl content to alter osmolality of bathing media for rat cortical slices. Values of lambda and alpha were extracted from diffusion measurements using the real-time ionophoretic method with tetramethylammonium (TMA+). In normal medium (305 mosmol kg(-1)), the average value of lambda was 1.69 and of alpha was 0.24. Reducing osmolality to 150 mosmol kg(-1), increased lambda to 1.86 and decreased alpha to 0.12. Increasing osmolality to 350 mosmol kg(-1), reduced lambda to about 1.67 where it remained unchanged even when osmolality increased further to 500 mosmol kg(-1). In contrast, alpha increased steadily to 0.42 as osmolality increased. Comparison with previously published experiments employing 3000 M(r) dextran to measure lambda, showed the same behaviour as for TMA+, including the same constant lambda in hypertonic media but with a steeper slope in the hypotonic solutions. These data show that lambda and alpha behave differently as the ECS geometry varies. When alpha decreases, lambda increases but when alpha increases, lambda rapidly attains a constant value. A previous model allowing cellular shape to alter during osmotic challenge can account qualitatively for the plateau behaviour of lambda.