Analysis of the dynamic permeation experiment with implication to cartilaginous tissue engineering

In the present study, a I-D dynamic permeation of a monovalent electrolyte solution through a negatively charged-hydrated cartilaginous tissue is analyzed using the mechano-electrochemical theory developed by Lai et al. (1991) as the constitutive model for the tissue. The spatial distributions of stress, strain, fluid pressure, ion concentrations, electrical potential, ion and fluid fluxes within and across the tissue have been calculated. The dependencies of these mechanical, electrical and physicochemical responses on the tissue fixed charge density, with specified modulus, permeability, diffusion coefficients, and frequency and magnitude of pressure differential are determined. The results demonstrate that these mechanical, electrical and physicochemical fields within the tissue are intrinsically and nonlinearly coupled, and they all vary with time and depth within the tissue.     

Electrical signals for chondrocytes in cartilage

An important step toward understanding signal transduction mechanisms modulating cellular activities is the accurate predictions of the mechanical and electro-chemical environment of the cells in well-defined experimental configurations. Although electro-kinetic phenomena in cartilage are well known, few studies have focused on the electric field inside the tissue. In this paper, we present some of our recent calculations of the electric field inside a layer of cartilage (with and without cells) in an open circuit one-dimensional (1D) stress relaxation experiment. The electric field inside the tissue derives from the streaming effects (streaming potential) and the diffusion effect (diffusion potential). Our results show that, for realistic cartilage material parameters, due to deformation-induced inhomogeneity of the fixed charge density, the two potentials compete against each other. For softer tissue, the diffusion potential may dominate over the streaming potential and vice versa for stiffer tissue. These results demonstrate that for proper interpretation of the mechano-electrochemical signal transduction mechanisms, one must not ignore the diffusion potential.     

On the electric potentials inside a charged soft hydrated biological tissue: streaming potential versus diffusion potential

The main objective of this study is to determine the nature of electric fields inside articular cartilage while accounting for the effects of both streaming potential and diffusion potential. Specifically, we solve two tissue mechano-electrochemical problems using the triphasic theories developed by Lai et al. (1991, ASME J. Biomech Eng., 113, pp. 245-258) and Gu et al. (1998, ASME J. Biomech. Eng., 120, pp. 169-180) (1) the steady one-dimensional permeation problem; and (2) the transient one-dimensional ramped-displacement, confined-compression, stress-relaxation problem (both in an open circuit condition) so as to be able to calculate the compressive strain, the electric potential, and the fixed charged density (FCD) inside cartilage. Our calculations show that in these two technically important problems, the diffusion potential effects compete against the flow-induced kinetic effects (streaming potential) for dominance of the electric potential inside the tissue. For softer tissues of similar FCD (i.e., lower aggregate modulus), the diffusion potential effects are enhanced when the tissue is being compressed (i.e., increasing its FCD in a nonuniform manner) either by direct compression or by drag-induced compaction; indeed, the diffusion potential effect may dominate over the streaming potential effect. The polarity of the electric potential field is in the same direction of interstitial fluid flow when streaming potential dominates, and in the opposite direction of fluid flow when diffusion potential dominates. For physiologically realistic articular cartilage material parameters, the polarity of electric potential across the tissue on the outside (surface to surface) may be opposite to the polarity across the tissue on the inside (surface to surface). Since the electromechanical signals that chondrocytes perceive in situ are the stresses, strains, pressures and the electric field generated inside the extracellular matrix when the tissue is deformed, the results from this study offer new challenges for the understanding of possible mechanisms that control chondrocyte biosyntheses.     

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.     

Water transport in plants: Role of the apoplast

The present state of modelling of water transport across plant tissue is reviewed. A mathematical model is presented which incorporates the cell-to-cell (protoplastic) and the parallel apoplastic path. It is shown that hydraulic and osmotic properties of the apoplast may contribute substantially to the overall hydraulic conductivity of tissues (Lp_r) and reflection coefficients (67-1). The model shows how water and solutes interact with each other during their passage across tissues which are considered as a network of hydraulic resistors and capacitances (composite transport model). Emphasis is on the fact that hydraulic properties of tissues depend on the nature of the driving force. Osmotic gradients cause a much smaller tissue Lp_r than hydrostatic. Depending on the conditions, this results in variable hydraulic resistances of tissues and plant organs. For the root, the model readily explains the well-known phenomenon of variable hydraulic resistance for the uptake of water and non-linear force/flow relations. Along the cell-to-cell (protoplastic) path, water flow may be regulated by the opening and closing of selective water channels (aquaporins) which have been shown to be affected by different environmental factors. H Lambers Section editor     

Fixed Electrical Charges and Mobile Ions Affect the Measurable Mechano-Electrochemical Properties of Charged-Hydrated Biological Tissues: The Articular Cartilage Paradigm

The triphasic constitutive law [Lai, Hou and Mow (1991)] has been shown in some special 1D cases to successfully model the deformational and transport behaviors of charged-hydrated, porous-permeable, soft biological tissues, as typified by articular cartilage. Due to nonlinearities and other mathematical complexities of these equations, few problems for the deformation of such materials have ever been solved analytically. Using a perturbation procedure, we have linearized the triphasic equations with respect to a small imposed axial compressive strain, and obtained an equilibrium solution, as well as a short-time boundary layer solution for the mechano- electrochemical (MEC) fields for such a material under a 2D unconfined compression test. The present results show that the key physical parameter determining the deformational behaviors is the ratio of the perturbation of osmotic pressure to elastic stress, which leads to changes of the measurable elastic coefficients. From the short-time boundary layer solution, both the lateral expansion and the applied load are found to decrease with the square root of time. The predicted deformations, flow fields and stresses are consistent with the analysis of the short time and equilibrium biphasic (i.e., the solid matrix has no attached electric charges) [Armstrong, Lai and Mow (1984)]. These results provide a better understanding of the manner in which fixed electric charges and mobile ions within the tissue contribute to the observed material responses.     

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.     

A linearized formulation of triphasic mixture theory for articular cartilage,and its application to indentation analysis

The negative charges on proteoglycans significantly affect the mechanical behaviors of articular cartilage. Mixture theories, such as the triphasic theory, can describe quantitatively how this charged nature contributes to the mechano-electrochemical behaviors of such tissue. However, the mathematical complexity of the theory has hindered its application to complicated loading profiles, e.g., indentation or other multi-dimensional configurations. In this study, the governing equations of triphasic mixture theory for soft tissue were linearized and dramatically simplified by using a regular perturbation method and the use of two potential functions. We showed that this new formulation can be used for any axisymmetric problem, such as confined or unconfined compressions, hydraulic perfusion, and indentation. A finite difference numerical program was further developed to calculate the deformational, electrical, and flow behaviors inside the articular cartilage under indentation. The calculated tissue response was highly consistent with the data from indentation experiments (our own and those reported in the literature). It was found that the charged nature of proteoglycans can increase the apparent stiffness of the solid matrix and lessen the viscous effect introduced by fluid flow. The effects of geometric and physical properties of indenter tip, cartilage thickness, and that of the electro-chemical properties of cartilage on the resulting deformation and fluid pressure fields across the tissue were also investigated and presented. These results have implications for studying chondrocyte mechanotransduction in different cartilage zones and for tissue engineering designs or in vivo cartilage repair.     

Relationship between streaming potential and compressive stress in bovine intervertebral tissue

The intervertebral disc is formed by the nucleus pulposus (NP) and annulus fibrosus (AF), and intervertebral tissue contains a large amount of negatively charged proteoglycan. When this tissue becomes deformed, a streaming potential is induced by liquid flow with positive ions. The anisotropic property of the AF tissue is caused by the structural anisotropy of the solid phase and the liquid phase flowing into the tissue with the streaming potential. This study investigated the relationship between the streaming potential and applied stress in bovine intervertebral tissue while focusing on the anisotropy and loading location. Column-shaped specimens, 5.5 mm in diameter and 3 mm thick, were prepared from the tissue of the AF, NP and the annulus–nucleus transition region (AN). The loading direction of each specimen was oriented in the spinal axial direction, as well as in the circumferential and radial directions of the spine considering the anisotropic properties of the AF tissue. The streaming potential changed linearly with stress in all specimens. The linear coefficients k_e of the relationship between stress and streaming potential depended on the extracted positions. These coefficients were not affected by the anisotropy of the AF tissue. In addition, these coefficients were lower in AF than in NP specimens. Except in the NP specimen, the k_e values were higher under faster compression rate conditions. In cyclic compression loading the streaming potential changed linearly with compressive stress, regardless of differences in the tissue and load frequency.     

A mechano-electrochemical model of radial deformation of the capillary glycocalyx

A mechano-electrochemical theory of the surface glycocalyx on capillary endothelial cells is presented that models the structure as a mixture of electrostatically charged macromolecules hydrated in an electrolytic fluid. Disturbances arising from mechanical deformation are introduced as perturbations away from a nearly electroneutral equilibrium environment. Under mechanical compression of the layer, such as might occur on the passing of stiff leukocytes through capillaries, the model predicts that gradients in the electrochemical potential of the compressed layer cause a redistribution of mobile ions within the glycocalyx and a rehydration and restoration of the layer to its equilibrium dimensions. Because of the large deformations of the glycocalyx arising from passing leukocytes, nonlinear kinematics associated with finite deformations of the layer are accounted for in the theory. A pseudo-equilibrium approximation is invoked for the transport of the mobile ions that reduces the system of coupled nonlinear integro-differential equations to a single nonlinear partial differential equation that is solved numerically for the compression and recovery of the glycocalyx using a finite difference method on a fixed grid. A linearized model for small strains is also obtained as verification of the finite difference solution. Results of the asymptotic analysis agree well with the nonlinear solution in the limit of small deformations of the layer. Using existing experimental and theoretical estimates of glycocalyx properties, the glycocalyx fixed-charge density is estimated from the analysis to be approximately 1 mEq/l, i.e., we estimate that there exists approximately one fixed charge on the glycocalyx for every 100 ions in blood. Such a charge density would result in a voltage differential between the undeformed glycocalyx and the capillary lumen of approximately 0.1 mV. In addition to providing insight into the mechano-electrochemical dynamics of the layer under deformation, the model suggests several methods for obtaining improved estimates of the glycocalyx fixed-charge density and permeability in vivo.     

A comparison between mechano-electrochemical and biphasic swelling theories for soft hydrated tissues

Biological tissues like intervertebral discs and articular cartilage primarily consist of interstitial fluid, collagen fibrils and negatively charged proteoglycans. Due to the fixed charges of the proteoglycans, the total ion concentration inside the tissue is higher than in the surrounding synovial fluid (cation concentration is higher and the anion concentration is lower). This excess of ion particles leads to an osmotic pressure difference, which causes swelling of the tissue. In the last decade several mechano-electrochemical models, which include this mechanism, have been developed. As these models are complex and computationally expensive, it is only possible to analyze geometrically relatively small problems. Furthermore, there is still no commercial finite element tool that includes such a mechano-electrochemical theory. Lanir (Biorheology, 24, pp. 173-187, 1987) hypothesized that electrolyte flux in articular cartilage can be neglected in mechanical studies. Lanir's hypothesis implies that the swelling behavior of cartilage is only determined by deformation of the solid and by fluid flow. Hence, the response could be described by adding a deformation-dependent pressure term to the standard biphasic equations. Based on this theory we developed a biphasic swelling model. The goal of the study was to test Lanir's hypothesis for a range of material properties. We compared the deformation behavior predicted by the biphasic swelling model and a full mechano-electrochemical model for confined compression and 1D swelling. It was shown that, depending on the material properties, the biphasic swelling model behaves largely the same as the mechano-electrochemical model, with regard to stresses and strains in the tissue following either mechanical or chemical perturbations. Hence, the biphasic swelling model could be an alternative for the more complex mechano-electrochemical model, in those cases where the ion flux itself is not the subject of the study. We propose thumbrules to estimate the correlation between the two models for specific problems.     

Streaming potential of human lumbar anulus fibrosus is anisotropic and affected by disc degeneration.

The streaming potential responses of non-degenerate and degenerate human anulus fibrosus were measured in a one-dimensional permeation configuration under static and dynamic loading conditions. The goal of this study was to investigate the influence of the changes in tissue structure and composition on the electrokinetic behavior of intervertebral disc tissues. It was found that the static streaming potential of the anulus fibrosus depended on the degenerative grade of the discs (p = 0.0001) and on the specimen orientation in which the fluid flows (p = 0.0001). For a statically applied pressure of 0.07 MPa, the ratio of streaming potential to applied pressure ranged from 5.3 to 6.9 mV/MPa and was largest for Grade I tissue with axial orientation and lowest for Grade III tissue with circumferential orientation. The dynamic streaming potential responses of anulus fibrosus were sensitive to the degeneration of the disc: the total harmonic distortion factor increased by 108%, from 3.92 +/- 0.66% (mean +/- SD) for Grade I specimens to 8.15 +/- 3.05% for Grades II and III specimens. The alteration of streaming potential reflects the changes in tissue composition and structure with degeneration. To our knowledge, this is the first reported data for the streaming potential of human intervertebral disc tissues. Knowledge of the streaming potential response of the intervertebral disc provides an understanding of potentially important signal transduction mechanisms in the disc and of the etiology of intervertebral disc degeneration.     

Effects of tension-compression nonlinearity on solute transport in charged hydrated fibrous tissues under dynamic unconfined compression

Cartilage is a charged hydrated fibrous tissue exhibiting a high degree of tension-compression nonlinearity (i.e., tissue anisotropy). The effect of tension-compression nonlinearity on solute transport has not been investigated in cartilaginous tissue under dynamic loading conditions. In this study, a new model was developed based on the mechano-electrochemical mixture model [Yao and Gu, 2007, J. Biomech. Model Mechanobiol., 6, pp. 63-72, Lai et al., 1991, J. Biomech. Eng., 113, pp. 245-258], and conewise linear elasticity model [Soltz and Ateshian, 2000, J. Biomech. Eng., 122, pp. 576-586; Curnier et al., 1995, J. Elasticity, 37, pp. 1-38]. The solute desorption in cartilage under unconfined dynamic compression was investigated numerically using this new model. Analyses and results demonstrated that a high degree of tissue tension-compression nonlinearity could enhance the transport of large solutes considerably in the cartilage sample under dynamic unconfined compression, whereas it had little effect on the transport of small solutes (at 5% dynamic strain level). The loading-induced convection is an important mechanism for enhancing the transport of large solutes in the cartilage sample with tension-compression nonlinearity. The dynamic compression also promoted diffusion of large solutes in both tissues with and without tension-compression nonlinearity. These findings provide a new insight into the mechanisms of solute transport in hydrated, fibrous soft tissues.     

Cartilage electromechanics--II. A continuum model of cartilage electrokinetics and correlation with experiments

We have formulated a continuum model for linear electrokinetic transduction in cartilage. Expressions are derived for the streaming potential and streaming current induced by oscillatory, uniaxial confined compression of the tissue, as well as the mechanical stress generated by a current density or potential difference applied to the tissue. The experimentally observed streaming potential and current-generated stress response, measured on the same specimens, are compared with the predictions of the theory over a wide frequency range. The theory compares well with the data for reasonable values of cartilage intrinsic mechanical parameters and electrokinetic coupling coefficients. Experiments also show a linear relationship between the stimulus amplitude and the transduction response amplitude, within the range of stimulus amplitudes of interest. This observation is shown to be consistent with the predictions of the linear theory.     

Apoplasmic and Protoplasmic Water Transport through the Parenchyma of the Potato Storage Organ

Stationary volume fluxes through living and denatured parenchyma slices of the potato (Solanum tuberosum L.) storage organ were studied to estimate the hydraulic conductivity of the cell wall and to evaluate the significance of water transport through protoplasts, cell walls, and intercellular spaces. Slices were placed between liquid compartments, steady-state fluxes induced by pressure or concentration gradients of low- and high-molecular-mass osmotica were measured, and water transport pathways were distinguished on the basis of their difference in limiting pore size. The protoplasts were the dominating route for osmotically driven water transport through living slices, even in the case of a polymer osmoticum that is excluded from cell walls. The specific hydraulic conductivity of the cell wall matrix is too small to allow a significant contribution of the narrow cell wall bypass to water flow through the living tissue. This conclusion is based on (a) ultrafilter coefficients of denatured parenchyma slices, (b) the absence of a significant difference between ultrafilter coefficients of the living tissue slices for osmotica with low and high cell wall reflection coefficients, and (c) the absence of a significant interaction (solvent drag) between apoplasmic permeation of mannitol and the water flux caused by a concentration difference of excluded polyethylene glycol. Liquid-filled intercellular spaces were the dominating pathways for pressure-driven volume fluxes through the parenchyma tissue.     

The influence of the fixed negative charges on mechanical and electrical behaviors of articular cartilage under unconfined compression

Unconfined compression test has been frequently used to study the mechanical behaviors of articular cartilage, both theoretically and experimentally. It has also been used in explant and gel-cell-complex studies in tissue engineering. In biphasic and poroelastic theories, the effect of charges fixed on the proteoglycan macromolecules in articular cartilage is embodied in the apparent compressive Young's modulus and the apparent Poisson's ratio of the tissue, and the fluid pressure is considered to be the portion above the osmotic pressure. In order to understand how proteoglycan fixed charges might affect the mechanical behaviors of articular cartilage, and in order to predict the osmotic pressure and electric fields inside the tissue in this experimental configuration, it is necessary to use a model that explicitly takes into account the charged nature of the tissue and the flow of ions within its porous interstices. In this paper, we used a finite element model based on the triphasic theory to study how fixed charges in the porous-permeable soft tissue can modulate its mechanical and electrochemical responses under a step displacement in unconfined compression. The results from finite element calculations showed that: 1) A charged tissue always supports a larger load than an uncharged tissue of the same intrinsic elastic moduli. 2) The apparent Young's modulus (the ratio of the equilibrium axial stress to the axial strain) is always greater than the intrinsic Young's modulus of an uncharged tissue. 3) The apparent Poisson's ratio (the negative ratio of the lateral strain to the axial strain) is always larger than the intrinsic Poisson's ratio of an uncharged tissue. 4) Load support derives from three sources: intrinsic matrix stiffness, hydraulic pressure and osmotic pressure. Under the unconfined compression, the Donnan osmotic pressure can constitute between 13%-22% of the total load support at equilibrium. 5) During the stress-relaxation process following the initial instant of loading, the diffusion potential (due to the gradient of the fixed charge density and the associated gradient of ion concentrations) and the streaming potential (due to fluid convection) compete against each other. Within the physiological range of material parameters, the polarity of the electric potential depends on both the mechanical properties and the fixed charge density (FCD) of the tissue. For softer tissues, the diffusion effects dominate the electromechanical response, while for stiffer tissues, the streaming potential dominates this response. 6) Fixed charges do not affect the instantaneous strain field relative to the initial equilibrium state. However, there is a sudden increase in the fluid pressure above the initial equilibrium osmotic pressure. These new findings are relevant and necessary for the understanding of cartilage mechanics, cartilage biosynthesis, electromechanical signal transduction by chondrocytes, and tissue engineering.     

Water transport across plant tissue: Role of water channels

The contribution of water-filled, selective membrane pores (water channels) is integrated into a general concept of water transport in plant tissue. The concept is based on the composite anatomical structure of tissues which results in a composite transport pattern. Three main pathways of water flow have been distinguished, ie the apoplastic, symplastic and transcellular (vacuolar) paths. Since the symplastic and transcellular components can not be distinguished experimentally, these components are summarized as a cell-to-cell component. Water channel activity may control the overall water flow across tissues provided that the contribution of the apoplastic component is relatively low. The composite transport model has been applied to roots where most of the data are available. Comparison of the hydraulic conductivity at the root cell and organ levels shows that, depending on the species, there may be a dominating cell-to-cell or apoplastic water flow. Most remarkably, there are differences in the hydraulic conductivity of roots which depend on the nature of the force used to drive water flows (osmotic or hydrostatic pressure gradients). This is predicted by the model. The composite transport model explains low reflection coefficients of roots, the variability in root hydraulic resistance and differences between herbaceous and woody species. It is demonstrated that there is also a composite transport of water at the membrane level (water channel arrays vs bilayer arrays). This results in low reflection coefficients of plasma membranes for certain test solutes as derived for isolated internodes of Chara. The titration of water channel activity in this alga with mercurials and its dependence on changes in temperature or external concentration show that water channels do not exclusively transport water. Rather, they are permeable to relatively big uncharged organic solutes. The result indicates that, at least for Chara, the concept of an exclusive transport of water across water channels has to be questioned.     

Application of the Na+ recirculation theory to ion coupled water transport in low- and high resistance osmoregulatory epithelia

The theory of Na+ recirculation for isosmotic fluid absorption follows logically from Hertz's convection-diffusion equation applied to the exit of water and solutes from the lateral intercellular space. Experimental evidence is discussed indicating Na+ recirculation based upon the following approaches: (i) An isotope tracer method in small intestine. Simultaneous measurement of water flow and ion transport in toad skin epithelium demonstrating, (ii) occasional hyposmotic absorbates, and (iii) reduced fluid absorption in the presence of serosal bumetanide. (iv) Studies of the metabolic cost of net Na+ absorption demonstrating an efficiency that is lower than the 18 Na+ per O2 consumed given by the stoichiometry of the Na+/K+-pump. Mathematical modeling predicts a significant range of observations such as isosmotic transport, hyposmotic transport, solvent drag, anomalous solvent drag, the residual hydraulic permeability in proximal tubule of AQP1(-/-) mice, the adverse relationship between hydraulic permeability and the concentration difference needed to reverse transepithelial water flow, and in a non-contradictory way the wide range of metabolic efficiencies from above to below 18 Na+/O2. Certain types of observations are poorly or not at all reproduced by the model. It is discussed that such lack of agreement between model and experiment is due to cellular regulations of ion permeabilities that are not incorporated in the modeling. Clarification of these problems requires further experimental studies.     

Mitochondrial Ca2+ transport in lean and genetically obese (ob/ob) mice.

Isolated mitochondria from liver or brown adipose tissue of obese ob/ob mice demonstrated increased rates of Ca2+ uptake and release compared with those of lean mice. This enhanced transport activity was not found in mitochondria from kidney or skeletal muscle. Respiration-induced membrane potential was the same in mitochondria from lean and ob/ob mice. It is therefore concluded that the increased Ca2+ uptake rates reflect an activation of the Ca2+ uniporter rather than a change in the electrophoretic driving force. As mitochondria from pre-obese ob/ob mice did not show elevated rates of Ca2+ transport, the activated transport in the obese animals was thus a consequence of the state of obesity rather than being a direct effect of the ob/ob genotype. It is suggested that the enhanced activity of the Ca2+-transport pathways in liver and brown adipose tissue may alter metabolic functions in these tissues by modifying cytoplasmic or intramitochondrial Ca2+ concentrations.     

Interconversion of components of the bacterial proton motive force by electrogenic potassium transport.

The influence of K+ ions on the components of the transmembrane proton motive force (delta mu H+) in intact bacteria was investigated. In K+-depleted cells of the glycolytic bacterium STreptococcus faecalis the addition of K+ ions caused a depolarization of the membrane by about 60 mV. However, since the depolarization was compensated for by an increase in the transmembrane pH gradient (delta pH), the total proton motive force remained almost constant at about 120 mV. Half-maximal changes in the potential were observed at K+ concentrations at which the cells accumulated K+ ions extensively. In EDTA-treated, K+-depleted cells of Escherichia coli K-12, the addition of K+ ions to the medium caused similar, although smaller changes in the components of delta mu H+. Experiments with various E. coli K-12 K+ transport mutants showed that for the observed potential changes the cells required either a functional TrkA or Kdp K+ transport system. These data are interpreted to mean that the inward movement of K+ ions via each of these bacterial transport systems is electrogenic. Consequently, it leads to a depolarization of the membrane, which in its turn allows the cell to pump more protons into the medium.