A Theoretical Analysis of Water Transport Through Chondrocytes

Because of the avascular nature of adult cartilage, nutrients and waste products are transported to and from the chondrocytes by diffusion and convection through the extracellular matrix. The convective interstitial fluid flow within and around chondrocytes is poorly understood. This theoretical study demonstrates that the incorporation of a semi-permeable membrane when modeling the chondrocyte leads to the following findings: under mechanical loading of an isolated chondrocyte the intracellular fluid pressure is on the order of tens of Pascals and the transmembrane fluid outflow, on the order of picometers per second, takes several days to subside; consequently, the chondrocyte behaves practically as an incompressible solid whenever the loading duration is on the order of minutes or hours. When embedded in its extracellular matrix (ECM), the chondrocyte response is substantially different. Mechanical loading of the tissue leads to a fluid pressure difference between intracellular and extracellular compartments on the order of tens of kilopascals and the transmembrane outflow, on the order of a nanometer per second, subsides in about 1 h. The volume of the chondrocyte decreases concomitantly with that of the ECM. The interstitial fluid flow in the extracellular matrix is directed around the cell, with peak values on the order of tens of nanometers per second. The viscous fluid shear stress acting on the cell surface is several orders of magnitude smaller than the solid matrix shear stresses resulting from the ECM deformation. These results provide new insight toward our understanding of water transport in chondrocytes.     

A driving force for change: interstitial flow as a morphoregulator

Dynamic stresses that are present in all living tissues drive small fluid flows, called interstitial flows, through the extracellular matrix. Interstitial flow not only helps to transport nutrients throughout the tissue, but also has important roles in tissue maintenance and pathobiology that have been, until recently, largely overlooked. Here, we present evidence for the various effects of interstitial flow on cell biology, including its roles in embryonic development, tissue morphogenesis and remodeling, inflammation and lymphedema, tumor biology and immune cell trafficking. We also discuss possible mechanisms by which interstitial flow can induce morphoregulation, including direct shear stress, matrix-cell transduction (as has been proposed in the endothelial glycocalyx) and the newly emerging concept of autologous gradient formation.     

Change in properties of the glycocalyx affects the shear rate and stress distribution on endothelial cells

The endothelial glycocalyx mediates interactions between the blood flow and the endothelium. This study aims to evaluate, quantitatively, effects of structural change of the glycocalyx on stress distribution and shear rate on endothelial cells. In the study, the endothelial glycocalyx is modeled as a surface layer of fiber matrix and when exposed to laminar shear flow, the matrix deforms. Fluid velocity and stress distribution inside the matrix and on cell membranes are studied based on a binary mixture theory. Parameters, such as the height and porosity of the matrix and the drag coefficient between fluid and matrix fibrils, are based on available data and estimation from experiments. Simple theoretical solutions are achieved for fluid velocity and stress distribution in the surface matrix. Degradation of the matrix, e.g., by enzyme digestion, is represented by reductions in the volume fraction of fibrils, height, and drag coefficient. From a force balance, total stress on endothelial surface remains constant regardless of structural alteration of the glycocalyx. However, the stress that is transmitted to endothelial cells by direct "pulling" of fiber branches of the glycocalyx is reduced significantly. Fluid shear rate at the cell membrane, on the other hand, increases. The study gives quantitative insight into the effect of the structural change of the glycocalyx on the shear rate and pulling stress on the endothelium. Results can be used to interpret experiments on effects of the glycocalyx in shear induced endothelial responses.     

Cells in 3D matrices under interstitial flow: Effects of extracellular matrix alignment on cell shear stress and drag forces

Interstitial flow is an important regulator of various cell behaviors both in vitro and in vivo, yet the forces that fluid flow imposes on cells embedded in a 3D extracellular matrix (ECM), and the effects of matrix architecture on those forces, are not well understood. Here, we demonstrate how fiber alignment can affect the shear and pressure forces on the cell and ECM. Using computational fluid dynamics simulations, we show that while the solutions of the Brinkman equation accurately estimate the average fluid shear stress and the drag forces on a cell within a 3D fibrous medium, the distribution of shear stress on the cellular surface as well as the peak shear stresses remain intimately related to the pericellular fiber architecture and cannot be estimated using bulk-averaged properties. We demonstrate that perpendicular fiber alignment of the ECM yields lower shear stress and pressure forces on the cells and higher stresses on the ECM, leading to decreased permeability, while parallel fiber alignment leads to higher stresses on cells and increased permeability, as compared to a cubic lattice arrangement. The Spielman–Goren permeability relationships for fibrous media agreed well with CFD simulations of flow with explicitly considered fibers. These results suggest that the experimentally observed active remodeling of ECM fibers by fibroblasts under interstitial flow to a perpendicular alignment could serve to decrease the shear and drag forces on the cell.     

Effects of extracellular fiber architecture on cell membrane shear stress in a 3D fibrous matrix

Interstitial fluid flow has been shown to affect the organization and behavior of cells in 3D environments in vivo and in vitro, yet the forces driving such responses are not clear. Due to the complex architecture of the extracellular matrix (ECM) and the difficulty of measuring fluid flow near cells embedded in it, the levels of shear stress experienced by cells in this environment are typically estimated using bulk-averaged matrix parameters such as hydraulic permeability. While this is useful for estimating average stresses, it cannot yield insight into how local matrix fiber architecture-which is cell-controlled in the immediate pericellular environment-affects the local stresses imposed on the cell surface. To address this, we used computational fluid dynamics to study flow through an idealized mesh constructed of a cubic lattice of fibers simulating a typical in vitro collagen gel. We found that, in such high porosity matrices, the fibers strongly affect the flow fields near the cell, with peak shear stresses up to five times higher than those predicted by the Brinkman equation. We also found that minor remodeling of the fibers near the cell surface had major effects on the shear stress profile on the cell. These findings demonstrate the importance of fiber architecture to the fluid forces on a cell embedded in a 3D matrix, and also show how small modifications in the local ECM can lead to large changes in the mechanical environment of the cell.     

Fibroblast alignment under interstitial fluid flow using a novel 3-D tissue culture model

Interstitial flow is an important component of the microcirculation and interstitial environment, yet its effects on cell organization and tissue architecture are poorly understood, in part due to the lack of in vitro models. To examine the effects of interstitial flow on cell morphology and matrix remodeling, we developed a tissue culture model that physically supports soft tissue cultures and allows microscopic visualization of cells within the three-dimensional matrix. In addition, pressure-flow relationships can be continuously monitored to evaluate the bulk hydraulic resistance as an indicator of changes in the overall matrix integrity. We observed that cells such as human dermal fibroblasts aligned perpendicular to the direction of interstitial flow. In contrast, fibroblasts in static three-dimensional controls remained randomly oriented, whereas cells subjected to fluid shear as a two-dimensional monolayer regressed. Also, the dynamic measurements of hydraulic conductivity suggest reorganization toward a steady state. These primary findings help establish the importance of interstitial flow on the biology of tissue organization and interstitial fluid balance.     

Modeling Tissue Polarity in Context

Polarity is critical for development and tissue-specific function. However, the acquisition and maintenance of tissue polarity is context dependent. Thus, cell and tissue polarity depend on cell adhesion which is regulated by the cytoskeleton and influenced by the biochemical composition of the extracellular microenvironment and modified by biomechanical cues within the tissue. These biomechanical cues include fluid flow induced shear stresses, cell-density and confinement-mediated compression, and cellular actomyosin tension intrinsic to the tissue or induced in response to morphogens or extracellular matrix stiffness. Here, we discuss how extracellular matrix stiffness and fluid flow influence cell–cell and cell–extracellular matrix adhesion and alter cytoskeletal organization to modulate cell and tissue polarity. We describe model systems that when combined with state of the art molecular screens and high-resolution imaging can be used to investigate how force modulates cell and tissue polarity.     

Shear stress-induced redistribution of the glycocalyx on endothelial cells in vitro

The glycocalyx is the inner most layer of the endothelium that is in direct contact with the circulating blood. Shear stress affects its synthesis and reorganization. This study focuses on changes in the spatial distribution of the glycocalyx caused by shear stimulation and its recovery following the removal of the shear stress. Sialic acid components of the glycocalyx on human umbilical vain endothelial cells are observed using confocal microscopy. The percentage area of the cell membrane covered by the glycocalyx, as well as the average fluorescence intensity ratio between the apical and edge areas of the cell is used to assess the spatial distribution of the glycocalyx on the cell membrane. Our results show that following 24 h shear stimulation, the glycocalyx relocates near the edge of endothelial cells (i.e., cell–cell junction regions). Following the removal of the shear stress, the glycocalyx redistributes and gradually appears in the apical region of the cell membrane. This redistribution is faster in the early hours ( $<$ 4 h) after shear stimulation than that in the later stage (e.g., between 8 and 24 h). We further investigate the recovery of the glycocalyx after its enzyme degradation under either static or shear flow conditions. Our results show that following 24 h recovery under shear flow, the glycocalyx reappears predominantly near the edge of endothelial cells. Static and shear flow conditions result in notable changes in the spatial recovery of the glycocalyx, but the difference is not statistically significant. We hypothesize that newly synthesized glycocalyx is not structurally well developed. Its weak interaction with flow results in less than significant redistribution, contrary to what has been observed for a well-developed glycocalyx layer.     

Cell morphological response to low shear stress in a two-dimensional culture microsystem with magnitudes comparable to interstitial shear stress

Slow interstitial flow can lead to large changes in cell morphology. Since conventional biological assays are adapted to two-dimensional culture protocols, there is a need to develop a microfluidic system that can generate physiological levels of interstitial flow. Here we developed a system that uses a passive osmotic pumping mechanism to generate sustained and steady interstitial flows for two-dimensional cultures. Two different cell types, fibroblasts and mesenchymal stem cells, were selected because they are generally exposed to interstitial flow. To quantify the cellular response to interstitial shear flow in terms of proliferation and alignment, 4 rates of flow were applied. We found that the proliferation rate of fibroblasts varied linearly with wall shear stress. In addition, alignment of fibroblast cells depended linearly on the magnitude of the shear stress, whereas mesenchymal stem cells were aligned regardless of the magnitude of shear stress. This suggested that mesenchymal stem cells are very sensitive to shear stresses, even at levels generated by interstitial flow. The results presented here emphasize the need to consider the mechanosensitivity and the natural role of different cell types when evaluating their responses to fluid flow.     

Glycocalyx modulates the motility and proliferative response of vascular endothelium to fluid shear stress

Flow-induced mechanotransduction in vascular endothelial cells has been studied over the years with a major focus on putative connections between disturbed flow and atherosclerosis. Recent studies have brought in a new perspective that the glycocalyx, a structure decorating the luminal surface of vascular endothelium, may play an important role in the mechanotransduction. This study reports that modifying the amount of the glycocalyx affects both short-term and long-term shear responses significantly. It is well established that after 24 h of laminar flow, endothelial cells align in the direction of flow and their proliferation is suppressed. We report here that by removing the glycocalyx by using the specific enzyme heparinase III, endothelial cells no longer align under flow after 24 h and they proliferate as if there were no flow present. In addition, confluent endothelial cells respond rapidly to flow by decreasing their migration speed by 40% and increasing the amount of vascular endothelial cadherin in the cell-cell junctions. These responses are not observed in the cells treated with heparinase III. Heparan sulfate proteoglycans (a major component of the glycocalyx) redistribute after 24 h of flow application from a uniform surface profile to a distinct peripheral pattern with most molecules detected above cell-cell junctions. We conclude that the presence of the glycocalyx is necessary for the endothelial cells to respond to fluid shear, and the glycocalyx itself is modulated by the flow. The redistribution of the glycocalyx also appears to serve as a cell-adaptive mechanism by reducing the shear gradients that the cell surface experiences.     

Insights into interstitial flow,shear stress,and mass transport effects on ECM heterogeneity in bioreactor-cultivated engineered cartilage hydrogels

Interstitial flow in articular cartilage is secondary to compressive and shear deformations during joint motion and has been linked with the well-characterized heterogeneity in structure and composition of its extracellular matrix. In this study, we investigated the effects of introducing gradients of interstitial flow on the evolution of compositional heterogeneity in engineered cartilage. Using a parallel-plate bioreactor, we observed that Poiseuille flow stimulation of chondrocyte-seeded agarose hydrogels led to an increase in glycosaminoglycan and type II collagen deposition in the surface region of the hydrogel exposed to flow. Experimental measurements of the interstitial flow fields based on the fluorescence recovery after photobleaching technique suggested that the observed heterogeneity in composition is associated with gradients in interstitial flow in a boundary layer at the hydrogel surface. Interestingly, the interstitial flow velocity profiles were nonlinearly influenced by flow rate, which upon closer examination led us to the original observation that the apparent hydrogel permeability decreased exponentially with increased interfacial shear stress. We also observed that interstitial flow enhances convective mass transport irrespective of molecular size within the boundary layer near the hydrogel surface and that the convective contribution to transport diminishes with depth in association with interstitial flow gradients. The implications of the nonlinearly inverse relationship between the interfacial shear stress and the interstitial flux and permeability and its consequences for convective transport are important for tissue engineering, since porous scaffolds comprise networks of Poiseuille channels (pores) through which interstitial flow must navigate under mechanical stimulation or direct perfusion.     

The effects of spatial inhomogeneities on flow through the endothelial surface layer

Flow through the endothelial surface layer (the glycocalyx and adsorbed plasma proteins) plays an important but poorly understood role in cell signaling through a process known as mechanotransduction. Characterizing the flow rates and shear stresses throughout this layer is critical for understanding how flow-induced ionic currents, deformations of transmembrane proteins, and the convection of extracellular molecules signal biochemical events within the cell, including cytoskeletal rearrangements, gene activation, and the release of vasodilators. Previous mathematical models of flow through the endothelial surface layer are based upon the assumptions that the layer is of constant hydraulic permeability and constant height. These models also assume that the layer is continuous across the endothelium and that the layer extends into only a small portion of the vessel lumen. Results of these models predict that fluid shear stress is dissipated through the surface layer and is thus negligible near endothelial cell membranes. In this paper, such assumptions are removed, and the resultant flow rates and shear stresses through the layer are described. The endothelial surface layer is modeled as clumps of a Brinkman medium immersed in a Newtonian fluid. The width and spacing of each clump, hydraulic permeability, and fraction of the vessel lumen occupied by the layer are varied. The two-dimensional Navier-Stokes equations with an additional Brinkman resistance term are solved using a projection method. Several fluid shear stress transitions in which the stress at the membrane shifts from low to high values are described. These transitions could be significant to cell signaling since the endothelial surface layer is likely dynamic in its composition, density, and height.     

Pseudopod projection and cell spreading of passive leukocytes in response to fluid shear stress

Recent evidence suggests that circulating leukocytes respond to physiological levels of fluid shear stress. This study was designed to examine the shear stress response of individual leukocytes adhering passively to a glass surface. Human leukocytes were exposed to a step fluid shear stress with amplitude between 0.2 and 4 dyn/cm(2) and duration between 1 and 20 min. The response of the cells was determined in the form of projected cell area measurements by high-resolution observation before, during, and after fluid shear application. All cells selected initially had a round morphology. After application of fluid shear many cells projected pseudopodia and spread on the glass surface. The number of leukocytes responding with pseudopod projection and the extent of cell spreading increased with increasing amplitude and duration of fluid shear stress. Pseudopod projection after exposure to a step fluid shear occurs following a delay that is insensitive to the shear stress amplitude and duration. Leukocytes that did not project pseudopodia and spread in response to low shear stress could be shown to respond to a second shear step of higher amplitude. The spreading response requires an intact actin network and activated myosin molecules. Depleting the cell glycocalyx with protease treatment enhances the spreading response in sheared leukocytes. These results indicate that passive leukocytes respond to fluid shear stress with active pseudopod projection and cell spreading. This behavior may contribute to cell spreading on endothelium and other cells as well as to transendothelial migration of leukocytes in the microcirculation.     

Effect of glycocalyx on shear-dependent albumin uptake in endothelial cells

The glycocalyx layer on the surface of an endothelial cell is an interface barrier for uptake of macromolecules, such as low-density lipoprotein and albumin, in the cell. The shear-dependent uptake of macromolecules thus might govern the function of the glycocalyx layer. We therefore studied the effect of glycocalyx on the shear-dependent uptake of macromolecules into endothelial cells. Bovine aorta endothelial cells were exposed to shear stress stimulus ranging from 0.5 to 3.0 Pa for 48 h. The albumin uptake into the cells was then measured using confocal laser scanning microscopy, and the microstructure of glycocalyx was observed using electron microscopy. Compared with the uptake into endothelial cells under static conditions (no shear stress stimulus), the albumin uptake at a shear stress of 1.0 Pa increased by 16% and at 3.0 Pa decreased by 27%. Compared with static conditions, the thickness of the glycocalyx layer increased by 70% and the glycocalyx charge increased by 80% at a shear stress of 3.0 Pa. The albumin uptake at a shear stress of 3.0 Pa for cells with a neutralized (no charge) glycocalyx layer was almost twice that of cells with charged layer. These findings indicate that glycocalyx influences the albumin uptake at higher shear stress and that glycocalyx properties (thickness and charge level) are involved with the shear-dependent albumin uptake process.     

Fluid shear stress stimulates incorporation of hyaluronan into endothelial cell glycocalyx

Vascular endothelial cells are shielded from direct exposure to flowing blood by the endothelial glycocalyx, a highly hydrated mesh of glycoproteins, sulfated proteoglycans, and associated glycosaminoglycans (GAGs). Recent data indicate that the incorporation of the unsulfated GAG hyaluronan into the endothelial glycocalyx is essential to maintain its permeability barrier properties, and we hypothesized that fluid shear stress is an important stimulus for endothelial hyaluronan synthesis. To evaluate the effect of shear stress on glycocalyx synthesis and the shedding of its GAGs into the supernatant, cultured human umbilical vein endothelial cells (i.e., the stable cell line EC-RF24) were exposed to 10 dyn/cm2 nonpulsatile shear stress for 24 h, and the incorporation of [3H]glucosamine and Na2[35S]O4 into GAGs was determined. Furthermore, the amount of hyaluronan in the glycocalyx and in the supernatant was determined by ELISA. Shear stress did not affect the incorporation of 35S but significantly increased the amount of glucosamine-containing GAGs incorporated in the endothelial glycocalyx [168 (SD 17)% of static levels, P < 0.01] and shedded into the supernatant [231 (SD 41)% of static levels, P < 0.01]. Correspondingly with this finding, shear stress increased the amount of hyaluronan in the glycocalyx [from 26 (SD 24) x 10(-4) to 46 (SD 29) x 10(-4) ng/cell, static vs. shear stress, P < 0.05] and in the supernatant [from 28 (SD 11) x 10(-4) to 55 (SD 16) x 10(-4) ng x cell(-1) x h(-1), static vs. shear stress, P < 0.05]. The increase in the amount of hyaluronan incorporated in the glycocalyx was confirmed by a threefold higher level of hyaluronan binding protein within the glycocalyx of shear stress-stimulated endothelial cells. In conclusion, fluid shear stress stimulates incorporation of hyaluronan in the glycocalyx, which may contribute to its vasculoprotective effects against proinflammatory and pro-atherosclerotic stimuli.     

Heparan sulfate proteoglycans mediate interstitial flow mechanotransduction regulating MMP-13 expression and cell motility via FAK-ERK in 3D collagen

Background

Interstitial flow directly affects cells that reside in tissues and regulates tissue physiology and pathology by modulating important cellular processes including proliferation, differentiation, and migration. However, the structures that cells utilize to sense interstitial flow in a 3-dimensional (3D) environment have not yet been elucidated. Previously, we have shown that interstitial flow upregulates matrix metalloproteinase (MMP) expression in rat vascular smooth muscle cells (SMCs) and fibroblasts/myofibroblasts via activation of an ERK1/2-c-Jun pathway, which in turn promotes cell migration in collagen. Herein, we focused on uncovering the flow-induced mechanotransduction mechanism in 3D.

Methodology/Principal Findings

Cleavage of rat vascular SMC surface glycocalyx heparan sulfate (HS) chains from proteoglycan (PG) core proteins by heparinase or disruption of HS biosynthesis by silencing N-deacetylase/N-sulfotransferase 1 (NDST1) suppressed interstitial flow-induced ERK1/2 activation, interstitial collagenase (MMP-13) expression, and SMC motility in 3D collagen. Inhibition or knockdown of focal adhesion kinase (FAK) also attenuated or blocked flow-induced ERK1/2 activation, MMP-13 expression, and cell motility. Interstitial flow induced FAK phosphorylation at Tyr925, and this activation was blocked when heparan sulfate proteoglycans (HSPGs) were disrupted. These data suggest that HSPGs mediate interstitial flow-induced mechanotransduction through FAK-ERK. In addition, we show that integrins are crucial for mechanotransduction through HSPGs as they mediate cell spreading and maintain cytoskeletal rigidity.

Conclusions/Significance

We propose a conceptual mechanotransduction model wherein cell surface glycocalyx HSPGs, in the presence of integrin-mediated cell-matrix adhesions and cytoskeleton organization, sense interstitial flow and activate the FAK-ERK signaling axis, leading to upregulation of MMP expression and cell motility in 3D. This is the first study to describe a flow-induced mechanotransduction mechanism via HSPG-mediated FAK activation in 3D. This study will be of interest in understanding the flow-related mechanobiology in vascular lesion formation, tissue morphogenesis, cancer cell metastasis, and stem cell differentiation in 3D, and also has implications in tissue engineering.     

Flow rates in perfusion bioreactors to maximise mineralisation in bone tissue engineering in vitro

In bone tissue engineering experiments, fluid-induced shear stress is able to stimulate cells to produce mineralised extracellular matrix (ECM). The application of shear stress on seeded cells can for example be achieved through bioreactors that perfuse medium through porous scaffolds. The generated mechanical environment (i.e. wall shear stress: WSS) within the scaffolds is complex due to the complexity of scaffold geometry. This complexity has so far prevented setting an optimal loading (i.e. flow rate) of the bioreactor to achieve an optimal distribution of WSS for stimulating cells to produce mineralised ECM. In this study, we demonstrate an approach combining computational fluid dynamics (CFD) and mechano-regulation theory to optimise flow rates of a perfusion bioreactor and various scaffold geometries (i.e. pore shape, porosity and pore diameter) in order to maximise shear stress induced mineralisation. The optimal flow rates, under which the highest fraction of scaffold surface area is subjected to a wall shear stress that induces mineralisation, are mainly dependent on the scaffold geometries. Nevertheless, the variation range of such optimal flow rates are within 0.5–5 mL/min (or in terms of fluid velocity: 0.166–1.66 mm/s), among different scaffolds. This approach can facilitate the determination of scaffold-dependent flow rates for bone tissue engineering experiments in vitro, avoiding performing a series of trial and error experiments.     

Fluid shear stress regulates the invasive potential of glioma cells via modulation of migratory activity and matrix metalloproteinase expression

Background

Glioma cells are exposed to elevated interstitial fluid flow during the onset of angiogenesis, at the tumor periphery while invading normal parenchyma, within white matter tracts, and during vascular normalization therapy. Glioma cell lines that have been exposed to fluid flow forces in vivo have much lower invasive potentials than in vitro cell motility assays without flow would indicate.

Methodology/Principal Findings

A 3D Modified Boyden chamber (Darcy flow through collagen/cell suspension) model was designed to mimic the fluid dynamic microenvironment to study the effects of fluid shear stress on the migratory activity of glioma cells. Novel methods for gel compaction and isolation of chemotactic migration from flow stimulation were utilized for three glioma cell lines: U87, CNS-1, and U251. All physiologic levels of fluid shear stress suppressed the migratory activity of U87 and CNS-1 cell lines. U251 motility remained unaltered within the 3D interstitial flow model. Matrix Metalloproteinase (MMP) inhibition experiments and assays demonstrated that the glioma cells depended on MMP activity to invade, and suppression in motility correlated with downregulation of MMP-1 and MMP-2 levels. This was confirmed by RT-PCR and with the aid of MMP-1 and MMP-2 shRNA constructs.

Conclusions/Significance

Fluid shear stress in the tumor microenvironment may explain reduced glioma invasion through modulation of cell motility and MMP levels. The flow-induced migration trends were consistent with reported invasive potentials of implanted gliomas. The models developed for this study imply that flow-modulated motility involves mechanotransduction of fluid shear stress affecting MMP activation and expression. These models should be useful for the continued study of interstitial flow effects on processes that affect tumor progression.     

Mechanisms for biopolymer accumulation in immobilized Acinetobacter calcoaceticus system

The gram-positive bacteria, Acinetobacter calcoaceticus, is capable of accumulating biopolymer in the carrier matrix of an immobilized cell system. Several possible mechanisms for the biopolymer accumulation are evaluated. It appears that direct solid surface polymer adsorption and polymer diffusion limitation within the pore space are minor factors in biopolymer accumulation. Calculations demonstrate that the cell bound polymer to dry cell weight ratio is much higher for immobilized cells than for free cells. The higher cell-bound polymer to dry-cell-weight ratio for immobilized cells as well as the accumulation of the immobilized cells in the Celite matrix are believed to be the main factors for biopolymer accumulation in the Carrier matrix. Further studies reveal that the cell-bound polymer to dry-cell-weight ratio is strongly affected by shear forces. At zero shear stress, such as would be present in the carrier matrix, cell bound polymer to dry cell weight ratio can be as high as 1.6. As the shear stress increases, this ratio decreases. When shear stress increases above 5 dyn/cm(2), a level equivalent to the shear experienced by free cells in a stirred tank fermentation, cell-bound polymer decreases to less than 20% of dry cell weight. A macroscopic model is developed to describe the effect of shear stress on the cell-bound polymer to dry-cell-weight ratio.