Transport of major solutes and the relationship between solute concentrations and discharge in the Apure River,Venezuela

The Apure River is a major white-water tributary of the Orinoco River in Venezuela. The Apure is rich in solutes; its contribution to dissolved inorganic solids in the Orinoco (24%) is proportionately much greater than its contribution to discharge (6%). About 40% of the calcium and bicarbonate at the mouth of the Orinoco originate in the Apure drainage. The relationship between discharge and the concentrations of major solutes in the Apure was characterized with a two-compartment hyperbolic mixing model. Previous applications of the two-compartment model have been based on separate determinations of the model parameter , which is a constant describing watershed hydrology, for each solute from data on concentrations. The use of a weighted mean for all solutes is proposed as a means of assessing the importance of processes other than mixing. The model, when used on the Apure data, shows that a strong dilution effect prevails for sodium, calcium, magnesium, sulfate, and bicarbonate, and that a strong purging effect (increase of concentration with increasing discharge) is characteristic of soluble silicon. Biological immobilization of soluble silicon by diatoms during the season of low discharge is sufficiently large to account for the positive relationship between discharge and the concentration of soluble silicon. Specific transport rates of solutes from the basin are generally higher than global averages. In contrast, specific transport of chloride is low. Atmospheric sources control chloride transport in the Apure watershed; the low transport rates of chloride are probably explained by the great distance between the Apure watershed and the oceanic sources of atmospheric chloride.     

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.     

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.     

Effects of dynamic loading on solute transport through the human cartilage endplate

Nutrient and metabolite transport through the cartilage endplate (CEP) is important for maintaining proper disc nutrition, but the mechanisms of solute transport remain unclear. One unresolved issue is the role of dynamic loading. In comparison to static loading, dynamic loading is thought to enhance transport by increasing convection. However, the CEP has a high resistance to fluid flow, which could limit solute convection. Here we measure solute transport through site-matched cadaveric human lumbar CEP tissues under static vs. dynamic loading, and we determine how the degree of transport enhancement from dynamic loading depends on CEP porosity and solute size. We found that dynamic loading significantly increased small and large solute transport through the CEP: on average, dynamic loading increased the transport of sodium fluorescein (376 Da) by a factor of 1.85 ± 0.64 and the transport of a large dextran (4000 Da) by a factor of 4.97 ± 3.05. Importantly, CEP porosity (0.65 ± 0.07; range: 0.47–0.76) strongly influenced the degree of transport enhancement. Specifically, for both solutes, transport enhancement was greater for CEPs with low porosity than for CEPs with high porosity. This is because the CEPs with low porosity were susceptible to larger improvements in fluid flow under dynamic loading. The CEP becomes less porous and less hydrated with aging and as disc degeneration progresses. Together, these findings suggest that as those changes occur, dynamic loading has a greater effect on solute transport through the CEP compared to static loading, and thus may play a larger role in disc nutrition.     

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.     

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.     

Three-dimensional inhomogeneous triphasic finite-element analysis of physical signals and solute transport in human intervertebral disc under axial compression

A 3D inhomogeneous finite-element model for charged hydrated soft tissues containing charged/uncharged solutes was developed and applied to analyze the mechanical, chemical, and electrical signals within the human intervertebral disc during an axial unconfined compression. The effects of tissue properties and boundary conditions on the physical signals and the transport of fluid and solute were investigated. The numerical simulation showed that, during disc compression, the fluid pressurization and the effective (von Misses) solid stress were more pronounced in the annulus fibrosus (AF) region near the interface between AF and nucleus pulposus (NP). In NP, the distributions of the fluid pressure, effective stress, and electrical potential were more uniform than those in AF. The electrical signals were very sensitive to fixed charge density. Changes in material properties of NP (water content, fixed charge density, and modulus) affected fluid pressure, electrical potential, effective stress, and solute transport in the disc. This study is important for understanding disc biomechanics, disc nutrition, and disc mechanobiology.     

In planta function of compatible solute transporters of the AtProT family

The three proline transporters of Arabidopsis thaliana (AtProTs) transport the compatible solutes proline and glycine betaine and the stress-induced compound γ-aminobutyric acid when expressed in heterologous systems. The aim of the present study was to show transport and physiological relevance of these three AtProTs in planta. Using single, double, and triple knockout mutants and AtProT-overexpressing lines, proline content, growth on proline, transport of radiolabelled betaine, and expression of AtProT genes and enzymes of proline metabolism were analysed. AtProT2 was shown to facilitate uptake of L- and D-proline as well as [(14)C]glycine betaine in planta, indicating a role in the import of compatible solutes into the root. Toxic concentrations of L- and D-proline resulted in a drastic growth retardation of AtProT-overexpressing plants, demonstrating the need for a precise regulation of proline uptake and/or distribution. Furthermore evidence is provided that AtProT genes are highly expressed in tissues with elevated proline content--that is, pollen and leaf epidermis.     

Fluid flow and convective transport of solutes within the intervertebral disc

Previous experimental and analytical studies of solute transport in the intervertebral disc have demonstrated that for small molecules diffusive transport alone fulfils the nutritional needs of disc cells. It has been often suggested that fluid flow into and within the disc may enhance the transport of larger molecules. The goal of the study was to predict the influence of load-induced interstitial fluid flow on mass transport in the intervertebral disc.An iterative procedure was used to predict the convective transport of physiologically relevant molecules within the disc. An axisymmetric, poroelastic finite-element structural model of the disc was developed. The diurnal loading was divided into discrete time steps. At each time step, the fluid flow within the disc due to compression or swelling was calculated. A sequentially coupled diffusion/convection model was then employed to calculate solute transport, with a constant concentration of solute being provided at the vascularised endplates and outer annulus. Loading was simulated for a complete diurnal cycle, and the relative convective and diffusive transport was compared for solutes with molecular weights ranging from 400 Da to 40 kDa.Consistent with previous studies, fluid flow did not enhance the transport of low-weight solutes. During swelling, interstitial fluid flow increased the unidirectional penetration of large solutes by approximately 100%. Due to the bi-directional temporal nature of disc loading, however, the net effect of convective transport over a full diurnal cycle was more limited (30% increase). Further study is required to determine the significance of large solutes and the timing of their delivery for disc physiology.     

Validation of theoretical framework explaining active solute uptake in dynamically loaded porous media

Solute transport in biological tissues is a fundamental process necessary for cell metabolism. In connective soft tissues, such as articular cartilage, cells are embedded within a dense extracellular matrix that hinders the transport of solutes. However, according to a recent theoretical study (Mauck et al., 2003, J. Biomech. Eng. 125, 602–614), the convective motion of a dynamically loaded porous solid matrix can also impart momentum to solutes, pumping them into the tissue and giving rise to concentrations which exceed those achived under passive diffusion alone. In this study, the theoretical predictions of this model are verified against experimental measurements. The mechanical and transport properties of an agarose–dextran model system were characterized from independent measurements and substituted into the theory to predict solute uptake or desorption under dynamic mechanical loading for various agarose concentrations and dextran molecular weights, as well as different boundary and initial conditions. In every tested case, agreement was observed between experiments and theoretical predictions as assessed by coefficients of determination ranging from R²=0.61 to 0.95. These results provide strong support for the hypothesis that dynamic loading of a deformable porous tissue can produce active transport of solutes via a pumping mechanisms mediated by momentum exchange between the solute and solid matrix.     

Production of oestrone and oestradiol-17 beta by different regions of the filamentous pig blastocyst

Pig blastocysts aged 14, 16 and 18 days were divided into 15 cm segments representing tissue adjacent to the embryonic disc, an intermediate section and the tip region. Whenever total blastocyst length allowed, the intermediate segment was divided into proximal and distal portions for separate culture. All were rinsed with buffer and incubated with dehydroepiandrosterone for 3 h. Rinsing buffer and incubation medium were subsequently assayed for concentrations of oestrone and oestradiol-17 beta. The highest production of oestrogen was found in the embryonic disc region. The intermediate regions had the lowest synthetic ability, while the tip region produced more oestrogens than the intermediate regions but less than the disc region. The production of oestrone was higher (P less than 0.05) in 18-day-old blastocysts than in younger ones while oestradiol-17 beta production was lower (P less than 0.05) on Day 16. The proportional role of the embryonic disc region as oestrogen-producing tissue increased over time. On Day 14, each intermediate region produced over 70% as much oestrogen as the disc region. These proportions declined on Days 16 and 18 to about 50 and 30% respectively. The regional variation in the ability of blastocysts to produce oestrogens may have some influence on the ability of the blastocyst to create an adequate microenvironment within the uterus which permits successful differentiation and placentation.     

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.     

Disruption of the thrombospondin-2 gene alters the lamellar morphology but does not permit vascularization of the adult mouse lumbar disc

Introduction

The biological basis for the avascular state of the intervertebral disc is not well understood. Previous work has suggested that the presence of thrombospondin-1 (TSP-1), a matricellular protein, in the outer annulus reflects a role for this protein in conferring an avascular status to the disc. In the present study we have examined thrombospondin-2 (TSP-2), a matricellular protein with recognized anti-angiogenic activity in vivo and in vitro.

Methods

We examined both the location and expression of TSP-2 in the human disc, and its location in the disc and bordering soft tissues of 5-month-old normal wild-type (WT) mice and of mice with a targeted disruption of the TSP-2 gene. Immunohistochemistry and quantitative histology were utilized in this study.

Results

TSP-2 was found to be present in some, but not all, annulus cells of the human annulus and the mouse annulus. Although there was no difference in the number of disc cells in the annulus of TSP-2-null mice compared with that of WT animals, polarized light microscopy revealed a more irregular lamellar collagen structure in null mouse discs compared with WT mouse discs. Additionally, vascular beds at the margins of discs of TSP-2-null mice were substantially more irregular than those of WT animals. Counts of platelet endothelial cell adhesion molecule-1-positive blood vessels in the tissue margin bordering the ventral annulus showed a significantly larger vascular bed in the tissue bordering the disc of TSP-2-null mice compared with that of WT mice (P = 0.0002). There was, however, no vascular ingrowth into discs of the TSP-2-null mice.

Conclusion

These data confirm a role for TSP-2 in the morphology of the disc and suggest the presence of other inhibitors of angiogenesis in the disc. We have shown that although an increase in vasculature was present in the TSP-2-null tissue in the margin of the disc, vascular ingrowth into the body of the disc did not occur. Our results point to the need for future research to understand the transition from the well-vascularized status of the fetal and young discs to the avascular state of the adult human disc or the small mammalian disc.     

Static compression of articular cartilage can reduce solute diffusivity and partitioning: implications for the chondrocyte biological response.

Chondrocytes depend upon solute transport within the avascular extracellular matrix of adult articular cartilage for many of their biological activities. Alterations to bioactive solute transport may, therefore, represent a mechanism by which cartilage compression is transduced into cellular metabolic responses. We investigated the effects of cartilage static compression on diffusivity and partitioning of a range of model solutes including dextrans of molecular weights 3 and 40 kDa, and tetramethylrhodamine (a 430 Da fluorophore). New fluorescence methods were developed for real-time visualization and measurement of transport within compressed cartilage explants. Experimental design allowed for multiple measurements on individual explants at different compression levels in order to minimize confounding influences of compositional variations. Results demonstrate that physiological levels of static compression may significantly decrease solute diffusivity and partitioning in cartilage. Effects of compression were most dramatic for the relatively high molecular weight solutes. For 40 kDa dextran, diffusivity decreased significantly (p<0.01) between 8% and 23% compression, while partitioning of 3 and 40 kDa dextran decreased significantly (p<0.01) between free-swelling conditions and 8% compression. Since diffusivity and partitioning can influence pericellular concentrations of bioactive solutes, these observations support a role for perturbations to solute transport in mediating the cartilage biological response to compression.     

Effects of elevated solute concentrations on the fermentation of lactose by Kluyveromyces marxianus Y-113

Summary The effect of increased solute concentrations on the fermentation of lactose to ethanol by Kluyveromyces marxianus Y-113 was investigated in batch culture. Elevated concentrations of lactose, maltose, NaCl or ethanol all inhibited the fermentation but to varying extents. Maltose was the least inhibitory of the solutes added while ethanol, and in particular the combination of high ethanol and high lactose concentrations, had the greatest inhibitory action. A maximum concentration of 45–52 g/l ethanol was achieved before growth and ethanol production ceased.     

Physical signals and solute transport in human intervertebral disc during compressive stress relaxation: 3D finite element analysis

A 3D finite element model for charged hydrated soft tissues containing charged/uncharged solutes was developed based on the multi-phasic mechano-electrochemical mixture theory (Lai et al., J. Biomech. Eng. 113 (1991), 245-258; Gu et al., J. Biomech. Eng. 120 (1998), 169-180). This model was applied to analyze the mechanical, chemical and electrical signals within the human intervertebral disc during an unconfined compressive stress relaxation test. The effects of tissue composition [e.g., water content and fixed charge density (FCD)] on the physical signals and the transport rate of fluid, ions and nutrients were investigated. The numerical simulation showed that, during disc compression, the fluid pressurization was more pronounced at the center (nucleus) region of the disc while the effective (von Mises) stress was higher at the outer (annulus) region. Parametric analyses revealed that the decrease in initial tissue water content (0.7-0.8) increased the peak stress and relaxation time due to the reduction of permeability, causing greater fluid pressurization effect. The electrical signals within the disc were more sensitive to FCD than tissue porosity, and mechanical loading affected the large solute (e.g., growth factor) transport significantly, but not for small solute (e.g., glucose). Moreover, this study confirmed that the interstitial fluid pressurization plays an important role in the load support mechanism of IVD by sharing more than 40% of the total load during disc compression. This study is important for understanding disc biomechanics, disc nutrition and disc mechanobiology.     

Effect of cutting on solute uptake by plasma membrane vesicles from sugar beet (Beta vulgaris L.) leaves.

The uptake of sucrose, 3-O-methylglucose (3-O-MeG), and valine were studied in discs and in purified plasma membrane vesicles (PMV) prepared from sugar beet (Beta vulgaris L.) exporting leaves. The uptake capacities of freshly excised leaf discs were compared with the uptake in discs that had been floated for 12 h on a simple medium (aging) and with discs excised from leaves that had been cut from the plant 12 h before the experiments (cutting). After cutting, sucrose uptake amounted to twice the uptake measured in fresh discs, whereas the uptake of 3-O-MeG and valine remained unaffected. In aged leaf discs, there was a general stimulation of uptake, which represented 400, 300, and 400% of the uptake measured in fresh discs for sucrose, 3-O-MeG, and valine, respectively. Sucrose uptake in fresh discs was sensitive to N-ethylmaleimide (NEM), to p-chloromercuribenzenesulfonic acid (PCMBS), and to mersalyl acid (MA). Although cutting induced the appearance of a sucrose uptake system that is poorly sensitive to NEM but sensitive to PCMBS and MA, aging induced the development of an uptake system that is sensitive to NEM but poorly sensitive to PCMBS and MA. Autoradiographs of discs fed with [14C]sucrose show that cutting resulted in an increase of vein labeling with little effect in the mesophyll, whereas aging induced an increase of labeling located mainly in the mesophyll. The data show that cutting is sufficient to induce dramatic and selective changes in the uptake properties of leaf tissues and that the effects of cutting and aging on the uptake of organic solutes are clearly different. Parallel experiments were run with purified PMV prepared from fresh and cut leaves. The uptake of sugars and amino acids was studied after imposition of an artificial proton motive force (pmf). Comparison of the uptake properties of PMV and of leaf tissues indicate that the recovery of the sucrose uptake system in PMV is better than the recovery of the hexose and of the valine uptake systems. As observed with the leaf discs, cutting induced a 2-fold increase of the initial rate of sucrose uptake in PMV but did not affect the uptake of valine and 3-O-MeG. Cutting induced an increase of both Vmax and Km of the sucrose transport system in PMV. Measurements of the pmf imposed on the vesicles indicated that the increase of sucrose uptake induced by cutting was not due to a better integrity of the vesicles. Hexoses did not compete with sucrose for uptake in PMV from fresh and cut leaves, and maltose was a stronger inhibitor of sucrose uptake in PMV from cut leaves than in PMV from fresh leaves. The sensitivity of sucrose uptake to NEM, PCMBS, and MA in PMV from fresh and cut leaves paralleled that described above for the corresponding leaf discs. These data show that (a) the changes induced by cutting on sucrose uptake by leaf discs are due to membrane phenomena and not to the metabolism of sucrose; (b) the study of sucrose uptake with PMB gives a good account of the physiological situation; and (c) the specific effects induced by cutting on the sucrose uptake system are not lost during the preparation of the PMV.     

The effect of cyclic deformation and solute binding on solute transport in cartilage

Diffusive transport must play an important role in transporting nutrients into cartilage due to its avascular nature. Recent theoretical studies generally support the idea that cyclic loading enhances large molecule transport through advection. However, to date, reactive transport, i.e. the effects of solute binding, has not yet been taken into consideration in cyclically deformed cartilage. In the present study, we develop a reactive transport model to describe the potential role of binding of solute within cyclically deformed cartilage. Our results show that binding does have a significant effect on transport, particularly for the low IGF-I concentrations typical of synovial fluid. A dynamic loading regime of high strain magnitudes (up to 10%) in combination with high frequencies (e.g. 1 Hz) was seen to produce the most dramatic results with enhanced total uptake ratio as high as 25% averaged over the first 5h of cyclic loading.