Computation of coupled diffusion of oxygen, glucose and lactic acid in an intervertebral disc

The present numerical study aims to investigate the disc nutrition and factors affecting it by evaluating the concentrations of oxygen, glucose and lactic acid in the disc while accounting for the coupling between these species via the pH level in the tissue and the nonlinear concentration-consumption (for glucose and oxygen) and concentration-production (for lactate) relations. The effects of changes in the endplate exchange area (EA) adjacent to the nucleus or the inner annulus for the transport of nutrients and in the disc geometry as well as tissue diffusivities under static compression loading on species concentrations are also studied. Moreover, alterations in solute diffusion following a central endplate fracture are investigated. An axisymmetric geometry with four distinct regions is considered. Supply sources are assumed at the outer annulus periphery and disc endplates. Coupling between different solutes, pH level, endplate disruptions (calcifications and fractures) and mechanical loads substantially influenced the distribution of nutrients throughout the disc as well as the magnitude and location of critical concentrations; maximum for the lactic acid and minimum for oxygen and glucose. In cases with loss of endplate permeability and/or disruptions therein, as well as changes in geometry and fall in diffusivity associated with fluid expression, the nutrient concentrations could fall to levels inadequate to maintain cellular activity or viability, thus initiating or accelerating disc degeneration.     

Nutrient distribution and metabolism in the intervertebral disc in the unloaded state: A parametric study

A 2-D finite element model for the intervertebral disc in which quadriphasic theory is coupled to the transport of solutes involved in cellular nutrition was developed for investigating the main factors contributing to disc degeneration. Degeneration is generally considered to result from chronic disc cell nutrition insufficiency, which prevents the cells from renewing the extracellular matrix and thus leads to the loss of proteoglycans. Hence, the osmotic power of the disc is decreased, causing osmomechanical impairments. Cellular metabolism depends strongly on the oxygen, lactate and glucose concentrations and on pH in the disc. To study the diffusion of these solutes in a mechanically or osmotically loaded disc, the osmomechanical and diffusive effects have to be coupled. The intervertebral disc is modeled here using a plane strain formulation at the equilibrium state under physiological conditions after a long rest period (called unloaded state). The correlations between solute distribution and various properties of healthy and degenerated discs are investigated. The numerical simulation shows that solute distribution in the disc depends very little on the elastic modulus or the proteoglycan concentration but greatly on the porosity, diffusion coefficient and endplate diffusion area. This coupled model therefore opens new perspectives for investigating intervertebral disc degeneration mechanisms.     

The effect of sustained compression on oxygen metabolic transport in the intervertebral disc decreases with degenerative changes

Intervertebral disc metabolic transport is essential to the functional spine and provides the cells with the nutrients necessary to tissue maintenance. Disc degenerative changes alter the tissue mechanics, but interactions between mechanical loading and disc transport are still an open issue. A poromechanical finite element model of the human disc was coupled with oxygen and lactate transport models. Deformations and fluid flow were linked to transport predictions by including strain-dependent diffusion and advection. The two solute transport models were also coupled to account for cell metabolism. With this approach, the relevance of metabolic and mechano-transport couplings were assessed in the healthy disc under loading-recovery daily compression. Disc height, cell density and material degenerative changes were parametrically simulated to study their influence on the calculated solute concentrations. The effects of load frequency and amplitude were also studied in the healthy disc by considering short periods of cyclic compression. Results indicate that external loads influence the oxygen and lactate regional distributions within the disc when large volume changes modify diffusion distances and diffusivities, especially when healthy disc properties are simulated. Advection was negligible under both sustained and cyclic compression. Simulating degeneration, mechanical changes inhibited the mechanical effect on transport while disc height, fluid content, nucleus pressure and overall cell density reductions affected significantly transport predictions. For the healthy disc, nutrient concentration patterns depended mostly on the time of sustained compression and recovery. The relevant effect of cell density on the metabolic transport indicates the disturbance of cell number as a possible onset for disc degeneration via alteration of the metabolic balance. Results also suggest that healthy disc properties have a positive effect of loading on metabolic transport. Such relation, relevant to the maintenance of the tissue functional composition, would therefore link disc function with disc nutrition.     

Effect of endplate calcification and mechanical deformation on the distribution of glucose in intervertebral disc: a 3D finite element study

The intervertebral disc (IVD) is avascular, receiving nutrition from surrounding vasculature. Theoretical modelling can supplement experimental results to understand nutrition to IVD more clearly. A new, 3D finite element model of the IVD was developed to investigate effects of endplate calcification and mechanical deformation on glucose distributions in IVD. The model included anatomical disc geometry, non-linear coupling of cellular metabolism with pH and oxygen concentration and strain-dependent properties of the extracellular matrix. Calcification was simulated by reducing endplate permeability (～79%). Mechanical loading was applied based on in vivo disc deformation during the transition from supine to standing positions. Three static strain conditions were considered: supine, standing and weight-bearing standing. Minimum glucose concentrations decreased 45% with endplate calcification, whereas disc deformation led to a 4.8-63% decrease, depending on the endplate condition (i.e. normal vs. calcified). Furthermore, calcification more strongly affected glucose concentrations in the nucleus compared to the annulus fibrous region. This study provides important insight into nutrient distributions in IVD under mechanical deformation.     

Analysis of cell viability in intervertebral disc: Effect of endplate permeability on cell population

Responsible for making and maintaining the extracellular matrix, the cells of intervertebral discs are supplied with essential nutrients by diffusion from the blood supply through mainly the cartilaginous endplates (CEPs) and disc tissue. Decrease in transport rate and increase in cellular activity may adversely disturb the intricate supply–demand balance leading ultimately to cell death and disc degeneration. The present numerical study aimed to introduce for the first time cell viability criteria into nonlinear coupled nutrition transport equations thereby evaluating the dynamic nutritional processes governing viable cell population and concentrations of oxygen, glucose and lactic acid in the disc as CEP exchange area dropped from a fully permeable condition to an almost impermeable one. A uniaxial model of an in vitro cell culture analogue of the disc is first employed to examine and validate cell viability criteria. An axisymmetric model of the disc with four distinct regions was subsequently used to investigate the survival of cells at different CEP exchange areas.In agreement with measurements, predictions of the diffusion chamber model demonstrated substantial cell death as essential nutrient concentrations fell to levels too low to support cells. Cells died away from the nutrient supply and at higher cell densities. In the disc model, the nucleus region being farthest away from supply sources was most affected; cell death initiated first as CEP exchange area dropped below ～40% and continued exponentially thereafter to depletion as CEP calcified further. In cases with loss of endplate permeability and/or disruptions therein, as well as changes in geometry and fall in diffusivity associated with fluid outflow, the nutrient concentrations could fall to levels inadequate to maintain cellular activity or viability, resulting in cell death and disc degeneration.     

Effect of Cartilage Endplate on Cell Based Disc Regeneration: A Finite Element Analysis

This study examines the effects of cartilage endplate (CEP) calcification and the injection of intervertebral disc (IVD) cells on the nutrition distributions inside the human IVD under physiological loading conditions using multiphasic finite element modeling. The human disc was modeled as an inhomogeneous mixture consisting of a charged elastic solid, water, ions (Na⁺ and Cl⁻), and nutrient solute(oxygen,glucose and lactate) phases. The effect of the endplate calcification was simulated by a reduction of the tissue porosity (i.e., water volume faction) from 0.60 to 0.48. The effect of cell injection was simulated by increasing the cell density in the nucleus pulposus (NP) region by 50%, 100%, and 150%. Strain-dependent transport properties(e.g., hydraulic permeability and solute diffusivities) were considered to couple the solute transport and the mechanical loading. The simulation results showed that nutrient solute distribution inside the discis maintained at a stable state during the day and night. The physiological diurnal cyclic loading does not change the nutrient environment in the human IVD. The cartilage endplate plays a significant role in the nutrient supply to human IVD. Calcification of the cartilage endplate significantly reduces the nutrient levels in human IVD. Therefore, in cell based therapy for IVD regeneration, theincreased nutrient demand as a result of cell injection needs to be addressed. Excessive numbers of injected cells may cause further deterioration of the nutrient environment in the degenerated disc. This study is important for understanding the pathology of IVD degeneration and providing new insights into cell based therapies for low back pain.     

3D finite element analysis of nutrient distributions and cell viability in the intervertebral disc: effects of deformation and degeneration

The intervertebral disc (IVD) receives important nutrients, such as glucose, from surrounding blood vessels. Poor nutritional supply is believed to play a key role in disc degeneration. Several investigators have presented finite element models of the IVD to investigate disc nutrition; however, none has predicted nutrient levels and cell viability in the disc with a realistic 3D geometry and tissue properties coupled to mechanical deformation. Understanding how degeneration and loading affect nutrition and cell viability is necessary for elucidating the mechanisms of disc degeneration and low back pain. The objective of this study was to analyze the effects of disc degeneration and static deformation on glucose distributions and cell viability in the IVD using finite element analysis. A realistic 3D finite element model of the IVD was developed based on mechano-electrochemical mixture theory. In the model, the cellular metabolic activities and viability were related to nutrient concentrations, and transport properties of nutrients were dependent on tissue deformation. The effects of disc degeneration and mechanical compression on glucose concentrations and cell density distributions in the IVD were investigated. To examine effects of disc degeneration, tissue properties were altered to reflect those of degenerated tissue, including reduced water content, fixed charge density, height, and endplate permeability. Two mechanical loading conditions were also investigated: a reference (undeformed) case and a 10% static deformation case. In general, nutrient levels decreased moving away from the nutritional supply at the disc periphery. Minimum glucose levels were at the interface between the nucleus and annulus regions of the disc. Deformation caused a 6.2% decrease in the minimum glucose concentration in the normal IVD, while degeneration resulted in an 80% decrease. Although cell density was not affected in the undeformed normal disc, there was a decrease in cell viability in the degenerated case, in which averaged cell density fell 11% compared with the normal case. This effect was further exacerbated by deformation of the degenerated IVD. Both deformation and disc degeneration altered the glucose distribution in the IVD. For the degenerated case, glucose levels fell below levels necessary for maintaining cell viability, and cell density decreased. This study provides important insight into nutrition-related mechanisms of disc degeneration. Moreover, our model may serve as a powerful tool in the development of new treatments for low back pain.     

Effects of mechanical compression on metabolism and distribution of oxygen and lactate in intervertebral disc

The objective of this study was to examine the effects of mechanical compression on metabolism and distributions of oxygen and lactate in the intervertebral disc (IVD) using a new formulation of the triphasic theory. In this study, the cellular metabolic rates of oxygen and lactate were incorporated into the newly developed formulation of the mechano-electrochemical mixture model [Huang, C.-Y., Gu, W.Y., 2007. Effect of tension-compression nonlinearity on solute transport in charged hydrated fibrosus tissues under dynamic unconfined compression. Journal of Biomechanical Engineering 129, 423-429]. The model was used to numerically analyze metabolism and transport of oxygen and lactate in the IVD under static or dynamic compression. The theoretical analyses demonstrated that compressive loading could affect transport and metabolism of nutrients. Dynamic compression increased oxygen concentration, reduced lactate accumulation, and promoted oxygen consumption and lactate production (i.e., energy conversion) within the IVD. Such effects of dynamic loading were dependent on strain level and loading frequency, and more pronounced in the IVD with less permeable endplate. In contrast, static compression exhibited inverse effects on transport and metabolism of oxygen and lactate. The theoretical predictions in this study are in good agreement with those in the literature. This study established a new theoretical model for analyzing cellular metabolism of nutrients in hydrated, fibrous soft tissues under mechanical compression.     

The effect of degenerative morphological changes of the intervertebral disc on the lumbar spine biomechanics: a poroelastic finite element investigation

Intervertebral disc degeneration involves changes in the spinal anatomical structures. The mechanical relevance of the following changes was investigated: disc height, endplate sclerosis, disc water content, permeability and depressurisation. A poroelastic nonlinear finite element model of the L4-L5 human spine segments was employed. Loads represented a daily cycle (500 N compression combined with flexion-extension motion for 16 h followed by 200 N compression for 8 h). In non-degenerative conditions, the model predicted a diurnal axial displacement of 1.32 mm and a peak intradiscal pressure of 0.47 MPa. Axial displacement, facet force and range of motion in flexion-extension are decreased by decreasing disc height. By decreasing the initial water content, axial displacement, facet force and fluid loss were all reduced. Endplate sclerosis did not have a significant influence on the calculated results. Depressurisation determined an increase of the disc effective stress, possibly inducing failure. Degenerative instability was not calculated in any simulations.     

The effect of degenerative morphological changes of the intervertebral disc on the lumbar spine biomechanics: a poroelastic finite element investigation

Intervertebral disc degeneration involves changes in the spinal anatomical structures. The mechanical relevance of the following changes was investigated: disc height, endplate sclerosis, disc water content, permeability and depressurisation. A poroelastic nonlinear finite element model of the L4–L5 human spine segments was employed. Loads represented a daily cycle (500 N compression combined with flexion–extension motion for 16 h followed by 200 N compression for 8 h). In non-degenerative conditions, the model predicted a diurnal axial displacement of 1.32 mm and a peak intradiscal pressure of 0.47 MPa. Axial displacement, facet force and range of motion in flexion–extension are decreased by decreasing disc height. By decreasing the initial water content, axial displacement, facet force and fluid loss were all reduced. Endplate sclerosis did not have a significant influence on the calculated results. Depressurisation determined an increase of the disc effective stress, possibly inducing failure. Degenerative instability was not calculated in any simulations.     

Dynamic cultivation of human mesenchymal stem cells in a rotating bed bioreactor system based on the Z®RP platform

Because the regeneration of large bone defects is limited by quantitative restrictions and risks of infections, the development of bioartificial bone substitutes is of great importance. To obtain a three‐dimensional functional tissue‐like graft, static cultivation is inexpedient due to limitations in cell density, nutrition and oxygen support. Dynamic cultivation in a bioreactor system can overcome these restrictions and furthermore provide the possibility to control the environment with regard to pH, oxygen content, and temperature. In this study, a three‐dimensional bone construct was engineered by the use of dynamic bioreactor technology. Human adipose tissue derived mesenchymal stem cells were cultivated on a macroporous zirconium dioxide based ceramic disc called Sponceram®. Furthermore, hydroxyapatite coated Sponceram® was used. The cells were cultivated under dynamic conditions and compared with statically cultivated cells. The differentiation into osteoblasts was initiated by osteogenic supplements. Cellular proliferation during static and dynamic cultivation was compared measuring glucose and lactate concentration. The differentiation process was analysed determining AP‐expression and using different specific staining methods. Our results demonstrate much higher proliferation rates during dynamic conditions in the bioreactor system compared to static cultivation measured by glucose consumption and lactate production. Cell densities on the scaffolds indicated higher proliferation on native Sponceram® compared to hydroxyapatite coated Sponceram®. With this study, we present an excellent method to enhance cellular proliferation and bone lineage specific growth of tissue like structures comprising fibrous (collagen) and globular (mineral) extracellular components. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009     

Is post-contrast MRI a valuable method for the study of the nutrition of the intervertebral disc?

Decreased nutrition has been proposed as a potential mechanism leading to intervertebral disc degeneration. A method to investigate it in vivo is the MRI evaluation of the transport of a paramagnetic contrast agent, which is assumed to diffuse through the endplate to the disc using the same mechanisms as the cell nutrients. However, previous numerical studies questioned the value of this method as a model to investigate disc nutrition. To assess its validity, a parametric osmoporoelastic finite element model of a lumbar intervertebral disc incorporating diffusion and convection of a solute (representing the contrast agent) was developed. A Taguchi sensitivity analysis was performed in order to assess the relevance of various parameters which influence the solute transport. Subsequently, a full-factorial sensitivity analysis was used to investigate specifically the diffusion coefficients of the contrast agent. The most important parameters in determining the results were the disc height, the diffusion coefficients and the pharmacokinetic of the contrast agent. However, diffusion coefficients values as measured in in vitro studies would lead to insubstantial enhancement of the MRI signal. Thus, transport mechanisms other than pure diffusion should be active in in vivo transport of the contrast agent. In conclusion, the study showed that post-contrast MRI may not be suited for a quantitative analysis, but only for a qualitative examination aimed for example to detect endplate lesions. Open questions remain on the use of post-contrast MRI for the investigation of the relevance of reduced nutrition as a trigger to disc degeneration.     

Analysis of nonlinear coupled diffusion of oxygen and lactic acid in intervertebral discs

The transport of oxygen and lactate (i.e., lactic acid) in the human intervertebral disc was investigated accounting for the measured coupling between species via the pH level in the tissue. Uncoupled cases were also analyzed to identify the extent of the effect of such coupling on the solute gradients across the disc. Moreover, nonlinear lactic production rate versus lactic concentration and oxygen consumption rate versus oxygen concentration were considered. The nonlinear coupled diffusion equations were solved using an in-house finite element program and an axisymmetric model of the disc with distinct nucleus and anulus regions. A pseudotransient approach with a backward integration scheme was employed to improve convergence. Coupled simulations influenced the oxygen concentration and lactic acid concentration throughout the disc, in particular the gradient of concentrations along the disc mid-height to the nucleus-anulus boundary where the solutes reached their most critical values; minimum for the oxygen tension and maximum for the lactate. Results suggest that for realistic estimates of nutrient and metabolite gradients across the disc, it could be important to take into account the coupling between the rates of synthesis and overall local metabolite/nutrient concentration.     

Nutrient utilization by bovine articular chondrocytes: a combined experimental and theoretical approach

A combined experimental-numerical approach was adopted to characterize glucose and oxygen uptake and lactate production by bovine articular chondrocytes in a model system. For a wide range of cell concentrations, cells in agarose were supplemented with either low or high glucose medium. During an initial culture phase of 48 h, oxygen was monitored noninvasively using a biosensor system. Glucose and lactate were determined by medium sampling. In order to quantify glucose and oxygen uptake, a finite element approach was adopted to describe diffusion and uptake in the experimental model. Numerical predictions of lactate, based on simple relations for cell metabolism, were found to agree well for low glucose, but not for high glucose medium. Oxygen did not play a role in either case. Given the close association between chondrocyte energy metabolism and matrix synthesis, a quantifiable prediction of utilization can present a valuable contribution in the optimization of tissue engineering conditions.     

Metabolic activities of Listeria monocytogenes in the presence of sodium propionate, acetate, lactate and citrate

The effects of sodium propionate, acetate, lactate and citrate on cell proliferation, glucose and oxygen consumption, and ATP production in Listeria monocytogenes were investigated in growing and resting cells. Media pH was 6.7-6.8. Growth inhibition increased while glucose consumption continued in the presence of ≥ 1% propionate, ≥ 3% acetate and ≥ 5% lactate in broth during incubation at 35°C, indicating that glucose consumption was uncoupled from cell proliferation. Acetate and propionate were the most effective antilisterials, whereas citrate (5%) was only slightly inhibitory. Of the four salts, only lactate supported growth, oxygen consumption and ATP production. While concentrations of 1 and 5% propionate, acetate and citrate did not have an effect on oxygen consumption, they inhibited ATP production. ATP production in the presence of the four salts was consistently lower at pH 6.0 than at neutral pH. Lactate served as an alternative energy source for L. monocytogenes in the absence of glucose but became toxic to the organism in the presence of the carbohydrate.     

Quantitative analysis of exogenous IGF-1 administration of intervertebral disc through intradiscal injection

Exogenous administration of IGF-1 has been proposed as a therapy for disc degeneration. The objectives of this study were to develop a numerical model for quantitatively analysing exogenous administration of IGF-1 into the intervertebral disc (IVD) via intradiscal injection and to investigate the effects of IGF-1 administration on distribution of glucose and oxygen in the IVD. In this study, the reversible binding reaction between IGF-1 and IGF binding proteins was incorporated into the mechano-electrochemical mixture model. The model was used to numerically analyse transport of IGF-1, glucose, oxygen and lactate in the IVD after IGF-1 administration. The enhancement of IGF-1 on lactate production was also taken into account in the theoretical model. The numerical analyses using finite element method demonstrated that the binding reactions significantly affect the time-dependent distribution of IGF-1 in the IVD. It was found that the region affected by IGF-1 was smaller and the duration of the therapeutic IGF-1 level was longer in the degenerated disc with a higher concentration of IGF binding proteins. It was also found that the IGF-1 injection can reduce glucose concentration and increase lactate accumulation (i.e., lower pH) in the IVD and these influences were regulated by the IGF-1 binding reactions. This study indicated the complexity of intradiscal administration of growth factors, which needs to be fully analysed in order to achieve a successful outcome. The new theoretical model developed in this study can serve as a powerful tool in analysing and designing the optimal treatments of growth factors for disc degeneration.     

The mechanical behaviour of bony endplate and annulus in prolapsed disc configuration

The mechanical response of intervertebral joints is deeply influenced by disc degeneration. The phenomenon is expressed in terms of variations in the biomechanical properties of the material, whose compressibility characteristics change because of the liquid content loss in the tissue and, what is even more important, to prolapse. In this work, the problem is investigated by means of a computational mechanics approach; a coupled material and geometric non-linear model is developed, representing vertebra, annulus and nucleus submitted to an axial load. A transversely isotropic law is assumed for cortical bone in the vertebral body and an isotropic law for the cancellous portion; a hyperelastic formulation is assumed for the disc, allowing effective interpretation of the mechanical characteristics of degeneration. The results obtained are reported with regard to bony endplate and annulus behaviour; interaction phenomena between bony endplate and nucleus are emphasized.     

Acetate accumulation and regulation by process parameters control in Chinese hamster ovary cell culture

Chinese hamster ovary (CHO) cells represent a group of predominantly used mammalian hosts for producing recombinant therapeutic proteins. Known for their rapid proliferation rates, CHO cells undergo aerobic glycolysis that is characterized by fast glucose consumption, that ultimately gives rise to a group of small-molecule organic acids. However, only the function of lactate has been extensively studied in CHO cell culture. In this study, we observed the accumulation of acetate from the late exponential phase to harvest day, potentially contributing to the pH decline in late culture stage regardless of lactate consumption. In addition, we evaluated the acidification of the fresh media and the cell culture suspension, and the data revealed that acetate presented a lower acidification capacity compared to lactate and exhibited limited inhibitory effect on cells with less than 20 mM supplemented in the media. This study also explored the ways to control acetate accumulation in CHO cell culture by manipulating the process parameters such as temperature, glucose, and pH control. The positive correlation between the specific glucose consumption rate and acetate generation rate provides evidence of the endogenous acetate generation from overflow metabolism. Reducing these parameters (temperature, glucose consumption) and HCl-controlled low pH ultimately suppress acetate build-up. In addition, the specific acetate generation rate and relevant glucose consumption rate are found to be a metabolic trait associated with specific cell lines. Taken together, the results presented in these experiments provide a means to advance industrial CHO cell culture process control and development.     

Numerical exploration of the combined effect of nutrient supply,tissue condition and deformation in the intervertebral disc

Novel strategies to heal discogenic low back pain could highly benefit from comprehensive biophysical studies that consider both mechanical and biological factors involved in intervertebral disc degeneration. A decrease in nutrient availability at the bone–disc interface has been indicated as a relevant risk factor and as a possible initiator of cell death processes. Mechanical behaviour of both healthy and degenerated discs could highly interact with cell death in these compromised situations. In the present study, a mechano-transport finite element model was used to investigate the nature of mechanical effects on cell death processes via load-induced metabolic transport variations. Cycles of static sustained compression were chosen to simulate daily human activity. Healthy and degenerated cases were simulated as well as a reduced supply of solutes and an increase in solute exchange area at the bone–disc interface. Results showed that a reduction in metabolite concentrations at the bone–disc boundaries induced cell death, even when the increased exchange area was simulated. Slight local mechanical enhancements of glucose in the disc centre were capable of decelerating cell death but occurred only with healthy mechanical properties. However, mechanical deformations were responsible for a worsening in terms of cell death in the inner annulus, a disadvantaged zone far from the boundary supply with both an increased cell demand and a strain-dependent decrease of diffusivity. Such adverse mechanical effects were more accentuated when degenerative properties were simulated. Overall, this study paves the way for the use of biophysical models for a more integrated understanding of intervertebral disc pathophysiology.     

Respiratory metabolism of L-929 cells at different water contents and volumes

Oxygen consumption was measured in mouse L-929 cells whose volumes and water contents were reduced by adding sorbitol to the medium. The volume of water lost due to a given sorbitol supplement exceeded the loss in apparent cell volume. An explanation is given for this discrepancy. The rate of oxygen uptake in the absence of exogenous respiratory substrate was essentially the same in cells whose total volume was reduced by 45%, amounting to a loss of about 70% of the total cell water, compared to controls at 'physiological' volume and water content. Cells under these same conditions responded to added substrates (pyruvate, glucose, and glutamine) and inhibitors (iodoacetate and 2-deoxyglucose) in nearly the same way as control cells. These observations are in accord with and add to previous work showing that very large fluctuations in cell volume and water content have only modest effects on the rates and directions of a variety of metabolic processes. The results are interpreted in terms of current views on the composition and organization of the aqueous compartments of eucaryotic cells.