A mathematical model for membrane transport of amino acid and Na+ in vesicles

Summary A model with a carrier having sites for both amino acid and Na⁺ can account for AIB (-aminoisobutyric acid) transport kinetics observed in membrane vesicles from SV3T3 (simian virus 40-tranformed Balb/c3T3 cells) and 3T3 (the parent cell line). The main feature of this cotransport model is that Na⁺ binding to carrier decreases the effectiveK _m for AIB transport, Na⁺ transport kinetics observed in both vesicle systems can be described by passive (possibly facilitated) diffusion. The lag of Na⁺ transport across the membrane compared to that for AIB, coupled to the Na⁺-dependent decrease in theK _m for AIB, accounts for the overshoot in intravesicular AIB observed for SV3T3 in the presence of an initial Na⁺ gradient. Extra-vesicular Na⁺ maintains a derease in theK _m for AIB influx before intra-vesicular Na⁺ has accumulated to balance it with a comparable decrease in theK _m for AIB efflux. 3T3 vesicles display little overshoot, and this finding can be explained mostly by a lower carrier affinity for Na⁺.     

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.     

Active transport membrane concentration amplifiers

Three different active transport membrane configurations are suggested for achieving concentration amplification in a circulating substrate solution. The steady-state characteristics of the structures are investigated on the basis of a linear approximation of the rate of active transport. An analysis of the effects of system parameters and geometry on the concentration gradient along the flow path is presented. It is seen that the concentration gradient may be synthesized by appropriate choice of membrane arrangement, flow and physico-chemical transport parameters.     

A mathematical model for neutrophil gradient sensing and polarization

Directed cell migration in response to chemical cues, also known as chemotaxis, is an important physiological process involved in wound healing, foraging, and the immune response. Cell migration requires the simultaneous formation of actin polymers at the leading edge and actomyosin complexes at the sides and back of the cell. An unresolved question in eukaryotic chemotaxis is how the same chemoattractant signal determines both the cell's front and back. Recent experimental studies have begun to reveal the biochemical mechanisms necessary for this polarized cellular response. We propose a mathematical model of neutrophil gradient sensing and polarization based on experimentally characterized biochemical mechanisms. The model demonstrates that the known dynamics for Rho GTPase and phosphatidylinositol-3-kinase (PI3K) activation are sufficient for both gradient sensing and polarization. In particular, the model demonstrates that these mechanisms can correctly localize the “front” and “rear” pathways in response to both uniform concentrations and gradients of chemical attractants, including in actin-inhibited cells. Furthermore, the model predictions are robust to the values of many parameters. A key result of the model is the proposed coincidence circuit involving PI3K and Ras that obviates the need for the “global inhibitors” proposed, though never experimentally verified, in many previous mathematical models of eukaryotic chemotaxis. Finally, experiments are proposed to (in)validate this model and further our understanding of neutrophil chemotaxis.     

Peristaltic transport of multilayered power-law fluids with distinct viscosities: a mathematical model for intestinal flows

This paper is concerned with the theoretical study of two-dimensional peristaltic flow of power-law fluids in three layers with different viscosities. The analysis is carried out under low Reynolds number and long wavelength approximations. The shapes of the interfaces are described by a system of non-linear algebraic equations which are solved numerically as streamlines. It is found that the non-uniformity in the intermediate and peripheral layers diminishes when the viscosity of the intermediate layer is increased and that of the outermost layer is kept unaltered for both the pseudo-plastic and dilatant fluids. Similar are the observations when the viscosity of the outermost layer is increased and that of the intermediate layer is kept fixed. The flow rate increases with the viscosities of the peripheral and the intermediate layers but the viscosity of the outermost layer is more effective. However, the knowledge of the effect of the viscosity of the intermediate layer facilitates us to achieve the required flow rate without disturbing the outermost layer. An increase in the flow behaviour index too favours larger flow rates. The trapping limits increase with the viscosity of the intermediate layer but decrease with the viscosity of the outermost layer and the flow behaviour index. Thus, a medicinal intervention that creates a more viscous intermediate layer and reduces pseudo plasticity may reduce constipation.     

Ion transport, membrane traffic and cellular volume control

Throughout their development, plants balance cell surface area and volume with ion transport and turgor. This balance lies at the core of cellular homeostatic networks and is central to the capacity to withstand abiotic as well as biotic stress. Remarkably, very little is known of its mechanics, notably how membrane traffic is coupled with osmotic solute transport and its control. Here we outline recent developments in the understanding of so-called SNARE proteins that form part of the machinery for membrane vesicle traffic in all eukaryotes. We focus on SNAREs active at the plasma membrane and the evidence for specialisation in enhanced, homeostatic and stress-related traffic. Recent studies have placed a canonical SNARE complex associated with the plasma membrane in pathogen defense, and the discovery of the first SNARE as a binding partner with ion channels has demonstrated a fundamental link to inorganic osmotic solute uptake. Work localising the channel binding site has now identified a new and previously uncharacterised motif, yielding important clues to a plausible mechanism coupling traffic and transport. We examine the evidence that this physical interaction serves to balance enhanced osmotic solute uptake with membrane expansion through mutual control of the two processes. We calculate that even during rapid cell expansion only a minute fraction of SNAREs present at the membrane need be engaged in vesicle traffic at any one time, a number surprisingly close to the known density of ion channels at the plant plasma membrane. Finally, we suggest a framework of alternative models coupling transport and traffic, and approachable through direct, experimental testing.     

A reduced-dimensional model for near-wall transport in cardiovascular flows

Near-wall mass transport plays an important role in many cardiovascular processes, including the initiation of atherosclerosis, endothelial cell vasoregulation, and thrombogenesis. These problems are characterized by large Péclet and Schmidt numbers as well as a wide range of spatial and temporal scales, all of which impose computational difficulties. In this work, we develop an analytical relationship between the flow field and near-wall mass transport for high-Schmidt-number flows. This allows for the development of a wall-shear-stress-driven transport equation that lies on a codimension-one vessel-wall surface, significantly reducing computational cost in solving the transport problem. Separate versions of this equation are developed for the reaction-rate-limited and transport-limited cases, and numerical results in an idealized abdominal aortic aneurysm are compared to those obtained by solving the full transport equations over the entire domain. The reaction-rate-limited model matches the expected results well. The transport-limited model is accurate in the developed flow regions, but overpredicts wall flux at entry regions and reattachment points in the flow.     

Analysis of a mathematical model for transport of I-albumin

The hypotheses and results given are motivated by the study of the distribution of albumin in man which represents a class of delay-differential systems. The approach used is to study the behavior of the solutions of nonlinear delay-differential systems with variable coefficients under the assumptions of continuity and boundedness of coefficients. The criterions are conditions on the roots of a certain “quasi-polynomial”, i.e., a polynomial in a variable and exponential of that variable. These criterions bear a resemblance to the ones in the case of constant coefficients and retardations and are applicable to this case also. The method is based on Lyapunov type functional with appropriate properties.     

The feasibility of utilizing a mathematical model in studying nonlinear transport processes in living systems

On the basis of proportionality between flow and its conjugated force a mathematical model for volume, current and osmotic flows was designed and a method for the experimental measurement of flows, the transbarrier (trans-segmental) potential and the rate of flow was devised. The results obtained experimentally as well as using the mathematical model indicate that the plant root is differentiated not only according to localization, but also according to the conductivity, permeability and selectivity of these tissues.     

The role of mechanical pressure difference in the generation of membrane voltage under conditions of concentration polarization

The mechanical pressure difference across the bacterial cellulose membrane located in a horizontal plane causes asymmetry of voltage measured between electrodes immersed in KCl solutions symmetrically on both sides of the membrane. For all measurements, KCl solution with lower concentration was above the membrane. In configuration of the analyzed membrane system, the concentration boundary layers (CBLs) are created only by molecular diffusion. The voltages measured in the membrane system in concentration polarization conditions were compared with suitable voltages obtained from the model of diffusion through CBLs and ion transport through the membrane. An increase of difference of mechanical pressure across the membrane directed as a difference of osmotic pressure always causes a decrease of voltage between the electrodes in the membrane system. In turn, for mechanical pressure difference across the membrane directed in an opposite direction to the difference of osmotic pressure, a peak in the voltage as a function of mechanical pressure difference is observed. An increase of osmotic pressure difference across the membrane at the initial moment causes an increase of the maximal value of the observed peak and a shift of this peak position in the direction of higher values of the mechanical pressure differences across the membrane.     

The role of selective transport in neuronal polarization

Neurons are functionally and morphologically polarized and possess two distinct types of neurites: axons and dendrites. Key molecules for axon formation are transported along microtubules and accumulated at the distal end of the nascent axons. In this review, we summarize recent advances in the understanding of the mechanisms involved in selective transport in neurons. In addition, we focus on motor proteins, cargo, cargo adaptors, and the loading and unloading of cargo.     

Placental blood flows and oxygen transfer during uterine contractions: A mathematical model

Theoretical calculations have been performed on the effects of changes in intrauterine pressure on maternal and fetal placental blood flows and pressures and transplacental O₂ exchange. Initial conditions and contraction profiles may be “assumed normal” or abnormal. The model predicts that the fetal O₂ deficit is most sensitive to the maximum intensity of the contraction and maternal mean arterial blood pressure, less sensitive to the duration of the contraction and far less sensitive to the value of maternal arterial PO₂. The umbilical venous PO₂ falls to a minimum at the peak of a contraction. Its level is most sensitive to contraction intensity and maternal blood pressure; while the value of maternal arterial PO₂ has less effect and the duration of contraction has essentially no effect. There is interaction between factors so that the effect of simultaneous changes is not necessarily in proportion to the effects of individual changes.     

A mathematical model for the transport of PAH analogues in the kidney

A single nephron model for the transport of p-aminohippurate (PAH) and its analogues through the kidney is investigated. One of the new features of the model is that it incorporates the epithelial cells surrounding the proximal tubules. These cells are the main anatomical sites of transport of PAH. The kinetics of PAH transport is described by a set of linear conservation equations. A stable numerical scheme which is backward Euler's in both space and time coordinates is used to analyze the mathematical problem. Our results are compatible with those of previously published models. An advantage of the present model is that we could study renal isotope images in terms of transport coefficients, flow rates, etc., of the isotope in the kidney and thus could evaluate the renal function in a more meaningful manner.     

A mathematical model of transmural transport of oxygen to the retina

A mathematical model of transmural transport of oxygen to a metabolizing retina is presented based on the equations of fluid dynamics. The equations of oxygen transfer are derived and then solved subject to the condition that the capillaries begin to transport oxygen at an initial time. The resulting transient analysis gives us insight into how diffusive and filtrative processes lead to the oxygen distributions both inside and outside capillaries. On the other hand, the steady state solution allows us to predict the cutoff intraocular pressure above which no oxygen is transferred to retinal tissue. It also gives quantitative relationships which allow us to postulate how intracapillary hypertension counterbalances elevated intraocular pressures and how low pressure glaucoma may arise from ineffective diffusive and filtrative processes of oxygen transport.