Analysis of the Components of Ionic Flux across a Membrane

The unidirectional flux of an ionic species may occur because of several mechanisms such as active transport, passive diffusion, exchange diffusion, etc. The contribution of such mechanisms to the total unidirectional flux across a membrane cannot be determined by only measuring that flux. It is shown that if the pertinent experimental data (the opposite unidirectional fluxes and the composite phenomenological resistance coefficient of the ionic species for a given electrochemical potential difference) obey a certain inequality, then the parameters of a model consisting of parallel, independent, active transport, and passive processes may be determined. Although the existence of "additional" processes including exchange diffusion, single-file pore diffusion, isotope interaction, etc. is not disproved, their existence is unnecessary if the inequality is satisfied. Two types of violations of the inequality may occur: (a) if the upper limit is disobeyed the presence of another substance contributing to the measured resistance and/or a constant affinity of the active transport process may be indicated; (b) if the lower limit is disobeyed it is necessary to postulate the existence of an additional process. For the latter type of violation, exchange diffusion is chosen as an example. Methods are given for determining the contribution of exchange diffusion, active transport, and passive diffusion to the unidirectional flux for some special cases.     

An automated system for continuous measurements of trace gas fluxes through snow: an evaluation of the gas diffusion method at a subalpine forest site,Niwot Ridge,Colorado

An experimental system for sampling trace gas fluxes through seasonal snowpack was deployed at a subalpine site near treeline at Niwot Ridge, Colorado. The sampling manifold was in place throughout the entire snow-covered season for continuous air sampling with minimal disturbance to the snowpack. A series of gases (carbon dioxide, water vapor, nitrous oxide, nitric oxide, ozone, volatile organic compounds) was determined in interstitial air withdrawn at eight heights in and above the snowpack at ~hourly intervals. In this paper, carbon dioxide data from 2007 were used for evaluation of this technique. Ancillary data recorded inlcuded snow physical properties, i.e., temperature, pressure, and density. Various vertical concentration gradients were determined from the multiple height measurements, which allowed calculation of vertical gas fluxes through the snowpack using Fick’s 1st law of diffusion. Comparison of flux results obtained from different height inlet combinations show that under most conditions fluxes derived from individual gradient intervals agree with the overall median of all data within a factor of 1.5. Winds were found to significantly influence gas concentration and gradients in the snowpack. Under the highest observed wind conditions, concentration gradients and calculated fluxes dropped to as low as 13% of non-wind conditions. Measured differential pressure amplitude exhibited a linear relationship with wind speed. This suggests that wind speed is a sound proxy for assessing advection transport in the snow. Neglecting the wind-pumping effect resulted in considerable underestimation of gas fluxes. An analysis of dependency of fluxes on wind speeds during a 3-week period in mid-winter determined that over this period actual gas fluxes were most likely 57% higher than fluxes calculated by the diffusion method, which omits the wind pumping dependency. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Nonsteady-State Three Compartment Tracer Kinetics: I. Theory

A set of differential equations is derived which describes the four unidirectional fluxes of a substance across the boundaries of the central compartment of a serially arranged three compartment system, and the amount of this substance present in the central compartment. An analytic solution is obtained which yields all of these quantities as functions of time. The analysis is associated with a defined set of repetitive experiments from which the necessary data are obtained and during which the two outer compartments must be subject to experimental control. The solution is applicable to both the initial steady state and a transient, time-dependent state created by making a step change in the initial conditions. It describes the fluxes and compartment size without assuming that constant kinetic coefficients relate the fluxes to compartmental quantities but is limited by the requirement that the response of the system be repeatable in time.     

A Numerical Study of the Hydrodynamic Stable Concentration Boundary Layers in a Membrane System Under Microgravitational Conditions

On the basis of the classic formula of the concentration Rayleigh number and the Kedem–Katchalsky equation for diffusive membrane transport, we derived the equations of sixteenth order which show the dependence of the thicknesses of the concentration boundary layers on the difference of the solution concentrations, the concentration Rayleigh number, the solute permeability coefficient of the membrane and the diffusion coefficients in the solution, the kinematic viscosity of the solution, the density of solutions, the temperature and gravitational acceleration. The obtained equation has numerical solutions in the first, third and fourth quadrant of a co-ordinate system. However, only two solutions from the first quadrant of the co-ordinate system have physical meaning. Confining ourselves to the set of solutions with physical meaning only, the thicknesses of concentration boundary layers for different parameters occurring in the obtained equation were calculated numerically.     

The release of active substances from selected carbohydrate biopolymer membranes

As a biopolymer application to control release systems is increasing at present, flat matrices (transdermal systems) should be highlighted. They constitute one of the most friendly form of drug administration to the patient. The present results concern investigations on the active substance release (ibuprofen and salicylic acid) from film matrices made from biopolymers: polylactid acid (PLA), dibutyrylchitin (DBC) and chitosan (CH). The amount of released active substance was examined with UV-VIS spectrophotometer. The release process was conducted in the medium of pH = 5.6 as the transdermal systems are applied to human skin surface of pH value approximating 5.6. Swelling of polymer samples was confirmed in the buffer of pH = 5.6 as well.The paper comprises the analysis of obtained release results according to the proposed two stage complex diffusion model.     

Tracer Diffusion and Unidirectional Fluxes

Available experimental data have been utilized to examine the effects of cross-coefficients on tracer diffusion and on the estimation of unidirectional fluxes from observations on tracer flow. In free solution or in a nonselective membrane, the interaction between the flows of tracer and the unlabelled substance are small at concentrations of biological interest for the nonelectrolytes urea, alanine, and β-alanine, and for sodium and chloride ions. Under these conditions, measurement of tracer flow can be used to predict flow of the bulk substance to an accuracy of a few per cent.     

Molecular study of the diffusional process of DMSO in double lipid bilayers

As a way to quantify the diffusion process of molecular compounds through biological membranes, we investigated in this study the dynamics of DMSO through an 1,2-Dipalmitoyl-sn-Glycero-3-Phosphocholine (DPPC) bilayer system. To properly account for the diffusion of DMSO due to a concentration gradient, a double DPPC bilayer was setup for our simulations. In such configuration, the aqueous phases can be explicitly associated with the extra and intracellular domains of the membrane, which is seldom the case in studies of single lipid bilayer due to the periodicity imposed by the simulations. DMSO molecules were initially contained in one of the aqueous phases (extracellular region) at a concentration of 5 wt.%. Molecular dynamics simulation was performed in this system for 95 ns at 350 K and 1 bar. The simulations showed that although many DMSO molecules penetrated the lipid bilayer, only about 10% of them crossed the bilayer to reach the other aqueous phase corresponding to the intracellular region of the membrane. The simulation time considered was insufficient to reach equilibrium of the DMSO concentration between the aqueous phases. However, the simulations provided sufficient information to estimate parameters to apply Fick's Law to model the diffusion process of the system. Using this model, we predicted that for the time considered in our simulation, the concentration of DMSO in the intracellular domain should have been about half of the actual value obtained. The model also predicted that equilibrium of the DMSO concentration in the system would be reached after about 2000 ns, approximately 20 times longer than the performed simulation.     

Laser interferometric investigation of solute transport through membrane-concentration boundary layer system

We investigate diffusive transport in a membrane system with a horizontally mounted membrane under concentration polarization conditions performed by a laser interferometry method. The data obtained from two different theoretical models are compared to the experimental results of the substance flux. In the first model, the membrane is considered as infinitely thin, while in the second one as a wall of finite thickness. The theoretical calculations show sufficient correspondence with the experimental results. On the basis of interferometric measurements, the relative permeability coefficient (ζ_s) for the system, consisting of the membrane and concentration boundary layers, was also obtained. This coefficient reflects the concentration polarization of the membrane system. The obtained results indicate that the coefficient ζ_s of the membrane-concentration boundary layer system decreases in time and seems to be independent of the initial concentration of the solute.     

Determination of Brain Interstitial Concentrations by Microdialysis

Microdialysis is an extensively used technique for the study of solutes in brain interstitial space. The method is based on collection of substances by diffusion across a dialysis membrane positioned in the brain. The outflow concentration reflects the interstitial concentration of the substance of interest, but the relationship between these two entities is at present unclear. So far, most evaluations have been based solely on calibrations in saline. This procedure is misleading, because the ease by which molecules in saline diffuse into the probe is different from that of tissue. We describe here a mathematical analysis of mass transport into the dialysis probe in tissue based on diffusion equations in complex media. The main finding is that diffusion characteristics of a given substance have to be included in the formula. These include the tortuosity factor (lambda) and the extracellular volume fraction (alpha). We have substantiated this by studies in a well-defined complex medium (red blood cell suspensions) as well as in brain. We conclude that the traditional calculation procedure results in interstitial concentrations that are too low by a factor of lambda 2/alpha for a given compound.     

Access permeability of ionic channels. Dependence on aqueous jump distance

The access diffusion permeability of pores with diameters comparable to the aqueous jump distance is characterized using a rate theory analysis for the aqueous diffusion process. It is found that this process gives rise to two permeability terms, one associated with bulk diffusion and the other a jump from the aqueous solution into a position where it has access to the channel. The latter term dominates for small channel diameters and vice versa for large channel diameters. The properties of access diffusion with respect to concentration polarization is shown to be different in the two limits of large and small values of the channel radius. A necessary criterion for bulk access diffusion to be rate limiting is given in terms of measured channel conductance G, aqueous jump distance lambda and aqueous resistivity rho, G greater than pi lambda/rho, which does not require a knowledge of channel geometry.     

Modeling of basolateral ATP release induced by hypotonic treatment in A6 cells

ATP is released from the basolateral membrane of A6 epithelia in response to hypotonic treatment. This study addresses the problem of ATP diffusion through the permeable supports used to culture the cells. A theoretical analysis of a recently introduced experimental protocol is presented and a model of ATP diffusion through the compartments of the measuring system is proposed. The model provides the ATP profiles near the cell layer and in the measurement chamber. Comparison of results from computer simulations and experimental data showed that the permeable support introduces a marked delay for ATP diffusion, supporting the correlation of apparently time-separated events: the mobilization of Ca²⁺ from internal stores and release of ATP from the cell. The model is consistent with experimental data obtained with the luciferin–luciferase pulse protocol and provides an indirect proof of related processes like the closure and opening of the lateral interspace that occur after imposing the hyposmotic shock. The influence of the pore structure of the permeable support in modulating the measured release rates revealed by computer simulation is experimentally validated for two types of Anopore filters.     

Threonine diffusion and threonine transport in Corynebacterium glutamicum and their role in threonine production

Transmembrane threonine fluxes (i.e., uptake, diffusion, and carrier-mediated excretion) all contribut-ing to threonine production by a recombinant strain of Corynebacterium glutamicum, were analyzed and quantitated. A threonine-uptake carrier that transports threonine in symport with sodium ions was identified. Under production conditions (i.e., when internal threonine is high), this uptake system catalyzed predominantly threonine/threonine exchange. Threonine export via the uptake system was excluded. Threonine efflux from the cells was shown to comprise both carrier-mediated excretion and passive diffusion. The latter process was analyzed after inhibition of all carrier-mediated fluxes. Threonine diffusion was found to proceed with a first-order rate constant of 0.003 min^–1 or 0.004 μl min^–1 (mg dry wt.)^–1, which corresponds to a permeability of 8 × 10^–10 cm s^–1. According to this permeability, less than 10% of the efflux observed under optimal conditions takes place via diffusion, and more than 90% must result from the activity of the excretion carrier. In addition, the excretion carrier was identified by (1) inhibition of its activity by amino acid modifying reagents and (2) its dependence on metabolic energy in the form of the membrane potential. Activity of the excretion system depended on the membrane potential, but not on the presence of sodium ions. Threonine export in antiport against protons is proposed. Received: 25 August 1995 / Accepted: 18 October 1995     

The application of compound bi-directional flow diffusion chemostats to the study of microbial interactions

Abstract A multi-stage bi-directional chemostat system has been developed in which solutes but not cells are allowed to diffuse between the individual growth chambers which are separated by 0.2 micron pore size polyvinyledene difluoride membranes. The experimental system enables the generation of physico-chemical gradients which, together with the spatial separation of the individual microbial processes, provides a useful laboratory model to study microbial interactions. This paper describes the construction of a multi-stage diffusion chemostat and its application in studying carbon flow in anaerobic estuarine sediments. Populations of Clostridium butyricum, Desulfovibrio desulfuricans and Chromatium vinosum were grown in the compound diffusion chemostat at a dilution rate of 0.03 h⁻¹ at 25°C, and the effects of inorganic nitrogen source and availability on carbon flow and individual cell populations were determined. C. butyricum and D. desulfuricans both used NO⁻₃ as an e⁻ acceptor with an increase in cell numbers. Under these growth conditions, free S²⁻ concentrations were lower, resulting in more stable cell populations than in comparable cultures grown on NH⁺₄ as nitrogen source.     

扩散对污染斑块上Smith种群生存的影响

通过建立两斑块的单种群扩散系统,主要研究扩散对其中受污染的斑块上种群生存的影响．文中所考虑的是污染斑块上外界毒素的输入量存在极限值的情形,得到如下结论：无扩散时,若此极限值超过某一定值,则污染斑块上的种群趋于灭绝;扩散存在且两斑块上种群的扩散系数满足一定的条件时,则可使该系统的种群永久生存或灭绝．     

On the role of diffusible binding partners in modulating the transport and concentration of proteins in tissues

Here a reactive-diffusion transport model is used to demonstrate two previously undescribed functional roles for diffusible binding partners in the transport of molecules into tissues. The uptake of the insulin-like growth (IGF) and its binding partner the IGF binding protein (IGFBP3) into cartilage is used a specific tissue example to demonstrate a general principal. First, we show that reversible binding between free protein (IGF) and its diffusible binding partner (free IGFBPs) increases the rate of protein uptake into the tissue. Second, selective degradation of the binding partner can increase the transient and steady state free protein in tissues, well above the concentration at the source boundary, with the maximum free concentration occurring distant from the source boundary, deep within the tissue. This finding is very much at odds with expectations based on a traditional diffusion analysis. In cartilage, using realistic parameters, these new mechanisms raise the free IGF concentration by an order of magnitude deep within the tissue. As the increase in free protein is ‘tunable’ by cells, our analyses are postulated to demonstrate a general regulatory principle that may operate in any tissues throughout the body.     

Easy Measurement of Diffusion Coefficients of EGFP-tagged Plasma Membrane Proteins Using k-Space Image Correlation Spectroscopy

Lateral diffusion and compartmentalization of plasma membrane proteins are tightly regulated in cells and thus, studying these processes will reveal new insights to plasma membrane protein function and regulation. Recently, k-Space Image Correlation Spectroscopy (kICS)¹ was developed to enable routine measurements of diffusion coefficients directly from images of fluorescently tagged plasma membrane proteins, that avoided systematic biases introduced by probe photophysics. Although the theoretical basis for the analysis is complex, the method can be implemented by nonexperts using a freely available code to measure diffusion coefficients of proteins. kICS calculates a time correlation function from a fluorescence microscopy image stack after Fourier transformation of each image to reciprocal (k-) space. Subsequently, circular averaging, natural logarithm transform and linear fits to the correlation function yields the diffusion coefficient. This paper provides a step-by-step guide to the image analysis and measurement of diffusion coefficients via kICS.First, a high frame rate image sequence of a fluorescently labeled plasma membrane protein is acquired using a fluorescence microscope. Then, a region of interest (ROI) avoiding intracellular organelles, moving vesicles or protruding membrane regions is selected. The ROI stack is imported into a freely available code and several defined parameters (see Method section) are set for kICS analysis. The program then generates a "slope of slopes" plot from the k-space time correlation functions, and the diffusion coefficient is calculated from the slope of the plot. Below is a step-by-step kICS procedure to measure the diffusion coefficient of a membrane protein using the renal water channel aquaporin-3 tagged with EGFP as a canonical example.     

Gravitational Effects in a Passive Transmembrane Transport: The Flux Graviosmotic and Gravidiffusive Effects in Non-Electrolytes

In this paper the classification ofthe gravitational effects in a passive transmembranetransport is presented. Among these effects there arethe flux and force gravitational effects (fluxgraviosmotic effect, osmotic pressure graviosmoticeffect, flux gravidiffusive effect, osmotic pressuregravidiffusive effect, voltage gravielectric effectand current gravielectric effect). The volume fluxgraviosmotic and solute flux gravidiffusive effectsmodel equations for a single-membrane system areelaborated. These models for binary and ternarynon-electrolyte solutions have been verified using anexperimental data volume and solute fluxes forosmotic-diffusion cell with horizontally mountedmembrane. In the experimental set-up, water was placedon one side of the membrane. The opposite side of themembrane was exposed to binary or ternary solutions ofdensities greater than that of water (aqueous glucoseor glucose-0.2 mole/l aqueous ethanol) and binary andternary solutions of densities larger than that ofwater (aqueous ethanol or ethanol-0.05 mole/l aqueousglucose). These experimental results are interpretedin terms of the convective instability that increasesthe diffusive permeability coefficient of junction:boundary layer/membrane/boundary layer.     

Lateral Membrane Diffusion Modulated by a Minimal Actin Cortex

Diffusion of lipids and proteins within the cell membrane is essential for numerous membrane-dependent processes including signaling and molecular interactions. It is assumed that the membrane-associated cytoskeleton modulates lateral diffusion. Here, we use a minimal actin cortex to directly study proposed effects of an actin meshwork on the diffusion in a well-defined system. The lateral diffusion of a lipid and a protein probe at varying densities of membrane-bound actin was characterized by fluorescence correlation spectroscopy (FCS). A clear correlation of actin density and reduction in mobility was observed for both the lipid and the protein probe. At high actin densities, the effect on the protein probe was ∼3.5-fold stronger compared to the lipid. Moreover, addition of myosin filaments, which contract the actin mesh, allowed switching between fast and slow diffusion in the minimal system. Spot variation FCS was in accordance with a model of fast microscopic diffusion and slower macroscopic diffusion. Complementing Monte Carlo simulations support the analysis of the experimental FCS data. Our results suggest a stronger interaction of the actin mesh with the larger protein probe compared to the lipid. This might point toward a mechanism where cortical actin controls membrane diffusion in a strong size-dependent manner.     

An Ion Displacement Membrane Model

The usual assumption in treating the diffusion of ions in an electric field has been that the movement of each ion is independent of the movement of the others. The resulting equation for diffusion by a succession of spontaneous jumps has been well stated by Parlin and Eyring. This paper will consider one simple case in which a different assumption is reasonable. Diffusion of monovalent positive ions is considered as a series of jumps from one fixed negative site to another. The sites are assumed to be full (electrical neutrality). Interaction occurs by the displacement of one ion by another. An ion leaves a site if and only if another ion, not necessarily of the same species, attempts to occupy the same site. Flux ratios and net fluxes are given as functions of the electrical potential, concentration ratios, and number of sites encountered in crossing the membrane. Quantitative comparisons with observations of Hodgkin and Keynes are presented.     

Influence of spatial structure on effective nutrient diffusion in bacterial biofilms

The main contribution of this paper is to use homogenization techniques to compute diffusion coefficients from experimental images of microbial biofilms. Our approach requires the analysis of several experimental spatial structures of biofilms in order to derive from them a Representative Volume Element (RVE). Then, we apply a suitable numerical procedure to the RVE to derive the diffusion coefficients. We show that diffusion coefficients significantly vary with the biofilm structure. These results suggest that microbial biofilm structures can favour nutrient access in some cases.