Stability properties of elementary dynamic models of membrane transport

Living cells are characterized by their capacity to maintain a stable steady state. For instance, cells are able to conserve their volume, internal ionic composition and electrical potential difference across the plasma membrane within values compatible with the overall cell functions. The dynamics of these cellular variables is described by complex integrated models of membrane transport. Some clues for the understanding of the processes involved in global cellular homeostasis may be obtained by the study of the local stability properties of some partial cellular processes. As an example of this approach, I perform, in this study, the neighborhood stability analysis of some elementary integrated models of membrane transport. In essence, the models describe the rate of change of the intracellular concentration of a ligand subject to active and passive transport across the plasma membrane of an ideal cell. The ligand can be ionic or nonionic, and it can affect the cell volume or the plasma membrane potential. The fundamental finding of this study is that, within the physiological range, the steady states are asymptotically stable. This basic property is a necessary consequence of the general forms of the expressions employed to describe the active and passive fluxes of the transported ligand.     

Plant membrane transport.

Recent developments in plant membrane transport, particularly concerning the vacuolar and plasma membranes, have increased our understanding of molecular aspects of primary pumps, carrier systems and ion channels.     

Discrimination criteria for apparent two-site transport models.

The medical beliefs of a people have in the past been studied principally by cultural anthropologists. The focus of these studies is usually on intrasocietal dynamics and cultural relativism—a striking orientation. However, beliefs about disease are integral to the way groups have and continue to adapt, and are thus important to both social and biological scientists. In order to study the role of medical beliefs in the adaptation of the group, a comparative approach is needed. This requires viewing these beliefs more generically, comparing their symbolic properties, and analyzing how they are used in explaining and dealing with actual occurrences of disease. The concept of a taxonomy of disease is introduced, as well as the notion of different semantic regions in the taxonomy. In the attempt to clarify the biological significance of a group's taxonomy of disease, and of its mode of operation, the ideas of uncertainty and information are employed. The significance and fruitfulness of this approach is discussed.     

Two-carrier models for mediated transport. I. Theoretical analysis of several two-carrier models.

Several possible models of two sequential and two simultaneous carriers of different affinities are theoretically analysed. Following the analysis we suggest for each model an experimental procedure capable of testing and rejecting the model.     

Two-carrier models for mediated transport I. Theoretical analysis of several two-carrier models

Several possible models of two sequential and two simultaneous carriers of different affinities are theoretically analysed. Following the analysis we suggest for each model an experimental procedure capable of testing and rejecting the model.     

Kinetic model for membrane transport. 1. Effects of membrane volume and partitioning kinetics

Equations for the transport of solutes through a membrane are derived, taking into account both the membrane volume and the partitioning kinetics, and have been found to involve two rate constants for solute transport, namely, those corresponding to solute transport from the solution to the membrane (k1) and from the membrane to the solution (k2). The time course followed before partitioning equilibrium has been attained, which is usually ignored, is shown to depend strongly on the relative magnitudes of k1 and k2.     

Methodology for predicting oxygen transport on an intravenous membrane oxygenator combining computational and analytical models

A computational methodology for accurately predicting flow and oxygen-transport characteristics and performance of an intravenous membrane oxygenator (IMO) device is developed, tested, and validated. This methodology uses extensive numerical simulations of three-dimensional computational models to determine flow-mixing characteristics and oxygen-transfer performance, and analytical models to indirectly validate numerical predictions with experimental data, using both blood and water as working fluids. Direct numerical simulations for IMO stationary and pulsating balloons predict flow field and oxygen transport performance in response to changes in the device length, number of and balloon pulsation frequency. Multifiber models are used to investigate interfiber interference and length effects for a stationary balloon whereas a single fiber model is used to analyze the effect of balloon pulsations on velocity and oxygen concentration fields and to evaluate oxygen transfer rates. An analytical lumped model is developed and validated by comparing its numerical predictions with experimental data. Numerical results demonstrate that oxygen transfer rates for a stationary balloon regime decrease with increasing number of fibers, independent of the fluid type. The oxygen transfer rate ratio obtained with blood and water is approximately two. Balloon pulsations show an effective and enhanced flow mixing, with time-dependent recirculating flows around the fibers regions which induce higher oxygen transfer rates. The mass transfer rates increase approximately 100% and 80%, with water and blood, respectively, compared with stationary balloon operation. Calculations with combinations of frequency, number of fibers, fiber length and diameter, and inlet volumetric flow rates, agree well with the reported experimental results, and provide a solid comparative base for analysis, predictions, and comparisons with numerical and experimental data.     

Regulation of intracellular membrane transport.

A number of proteins that are necessary for membrane transport have been identified using cell-free assays and yeast genetics. Although our knowledge of transport mechanisms remains limited, common themes are clearly emerging. In particular, specific GTP-binding proteins appear to be involved, not only at all steps of membrane traffic but also at more than one check-point within each step. The ordered sequence of events occurring during vesicle formation, targeting and fusion may be regulated in a stepwise manner by specific GTP-dependent switches, which act as modular elements of the transport mechanism.     

Anion transport and membrane morphology.

Freeze-fracture electronmicroscopy has been used to examine the membrane ultrastructure of human red blood cells in the presence of inhibitors of chloride exchange. The extent of inhibition was correlated with a decrease of intramembrane particle density on the B-fracture face. Dimethylsulfoxide (DMSO) and glycerol, which markedly and reversibly reduced the intramembrane particle density, were shown to drastically and reversibly inhibit chloride self-exchange. DMSO was shown to be a noncompetitive inhibitor of chloride flux.     

Kinetic model for membrane transport. 2. Time lag and overshoot

A lag time during the period of variation in solute concentration in the receiver phase and overshoot in that in the membrane phase have been predicted to occur with a kinetic model for membrane transport which takes into account both the membrane volume and the partitioning kinetics (Makino et al., Biophys. Chem. 35 (1990) 85). The duration of the lag time becomes longest when the donor and receiver phases have the same volume. This maximum grows in length with increase in the partition coefficient, tending to be proportional to the volume fraction of the receiver phase. Moreover, it displays an increase in length with decreasing membrane volume fraction. Overshoot occurs only when the volume fraction of the receiver phase is greater than that of the donor. Overshoot is observed during the earlier stages of membrane transport when the partition coefficient is smaller or the volume fraction of the receiver phase is larger.     

Biosensors based on membrane transport proteins.

We propose a novel class of biosensors based on membrane bound receptors or transport proteins as the sensing element. The protein is incorporated in a planar lipid bilayer which covers the transducer. The transducer may detect an electric current, a voltage, or a change in fluorescence. A prototype lactose sensor is presented which consists of a quartz slide covered by a lipid membrane containing the protein lactose permease from Escherichia coli. This protein is a lactose/H+ cotransporter, hence lactose in the external medium initiates lactose/H+ cotransport across the lipid membrane. This leads to a rise in proton concentration in the small volume between the lipid membrane and the quartz surface which can be detected by a pH-sensitive fluorescence dye.     

Proton transport by gastric membrane vesicles.

A highly purified membrane fraction was derived from hog gastric mucosa by a combination of differential and density gradient centrifugation and free flow electrophoresis. This final fraction was 35-fold enriched with respect to cation activated ouabain-insensitive ATPase. Antibody against this fraction was shown to be bound to the luminal surface of the gastric glands. The addition of ATP to this fraction or the density gradient fraction resulted in H+ uptake into an osmotically sensitive space. The apparent Km for ATP was 1.7-10(-4) M in the absence of a K+ gradient similar to that found for ATPase activity. The reaction is specific for ATP and requires cation in the sequence K+ greater than Rb+ greater than Cs+ greater than Na+ greater than Li+ and inhibited by ATPase inhibitors such as N,N'-dicylclohexyl-carbodiimide. Maximal H+ uptake occurs with an outward K+ gradient but the minimal apparent KA is found in the absence of a K+ gradient. The pH optimum for H+ uptake is between 5.8 and 6.2 which corresponds to the pH range for phosphroylation of the enzyme, but is considerably less than the pH maximum of the K+ dependent dephosphorylation. In the presence of an inward K+ gradient, protonophores such as tetrachlorsalicylanilide only partially abolish the H+ gradient but valinomycin dissipates 75% of the gradient, and nigericin abolishes the gradient. The vesicles therefore have a low K+ conductance but a measurable H+ conductance, hence a K+ gradient can produce an H+ gradient in the presence of valinomycin. The uptake and spontaneous leak of H+ are temperature sensitive with a similar transition temperature. Ultraviolet irradiation inactivates ATPase and proton transport at the same rate, approximately at twice the rate of p-nitrophenylphosphatase inactivation. It is concluded that H+ uptake by these vesicles is probably due to a dimeric (H+ + K+)-ATPase and is probably non-electrogenic.     

Impossibility of multiple steady states in a family of active membrane transport models

To study the dynamical behavior of active membrane transport models, Vieira and Bisch proposed a complex chemical network (model 3) with two cycles. One cycle involves monomers as pump units while the other cycle uses dimers. In their work, the stoichiometric network analysis was used to study the stability of steady states and the bifurcation analysis was done through numerical methods. They concluded that the possibility of multiple steady states in the model 3 could not be discarded. Here, a zero eigenvalue analysis is applied to prove the impossibility of multiple positive steady states in the model 3. (A positive steady state is one for which all species have positive concentrations.) Moreover, the result is generalized to its family networks. Received: 6 April 1998 / Revised version: 16 October 1998 / Accepted: 28 October 1998     

Testing models for transport systems dependent on periplasmic binding proteins.

A carrier model in which transport across the cytoplasmic membrane is mediated by a periplasmic binding protein (Krupka, R.M. (1992) Biochim. Biophys. Acta 1110, 1-10) is shown to account for many of the properties of these systems: (i) Michaelis-Menten kinetics; (ii) seemingly irreversible uptake; (iii) the absence of exchange transport and counter-transport; (iv) substrate half-saturation constants that in different systems may be lower or higher than the dissociation constant of the binding protein; (v) the high concentration of the binding protein in the periplasm and its weak association with the membrane component. The binding protein appears to function as a valve or rectifier that permits the substrate to enter the cell, but blocks exit in both the energized and de-energized states. The asymmetry depends on both the abruptness and the extent of the conformational change in the binding protein. Characteristically, these systems build up steep gradients across the membrane, circumstances in which such a valve might be important. In agreement with the mechanism, (a) the binding protein is missing in members of the same family of transporters that function in export of the substrate rather than import; and (b) in Gram-positive organisms, which have no periplasmic space, binding proteins function while anchored to the cytoplasmic membrane.     

Single-particle tracking: models of directed transport.

Single-particle tracking techniques make it possible to measure motion of individual particles on the cell surface. In these experiments, individual trajectories are observed, so the data analysis must take into account the randomness of individual random walks. Methods of data analysis are discussed for models combining diffusion and directed motion. In the uniform flow model, a tracer simultaneously diffuses and undergoes directed motion. In the conveyor belt model, a tracer binds and unbinds to a uniform conveyor belt moving with constant velocity. If a tracer is bound, it moves at the velocity of the conveyor belt; if it is unbound, it diffuses freely. Trajectories are analyzed using parameters that measure the extent and asymmetry of the trajectory. A method of assessing the usefulness of such parameters is presented, and pitfalls in data analysis are discussed. Joint probability distributions of pairs of extent and asymmetry parameters are obtained for a pure random walk. These distributions can be used to show that a trajectory is not likely to have resulted from a pure random walk.