On the derivation of the Kargol's mechanistic transport equations from the Kedem-Katchalsky phenomenological equations

In the present article, it was demonstrated that--by starting from the so-called adjusted Kedem-Katchalsky (KK) phenomenological equations (Suchanek et al. 2004), i.e. the equations: Jv=LpDeltaP-LpDDeltaPi. JD=-LDpDeltaP+LDDeltaPi it is possible to derive practical transport equations (for the volume flow and the solute flow) in the form of the Kargol s mechanistic transport equations (Kargol and Kargol 2000, 2001, 2003a,b,c, 2004; Kargol 2002). On this basis, it has been found that the KK thermodynamic formalism for membrane transport (practical equations) is in general identical with the mechanistic equations for membrane transport.     

Some remarks on the Kedem-Katchalsky equations for non-electrolytes

The Kedem-Katchalsky equation for the flow of a non-electrolyte through a homogeneous membrane is shown to be a first order expansion of an exact integral of the Spiegler-Bearman-Kirkwood frictional equations under the assumption that the partial frictional coefficients, ζ _ij , are concentration independent. The equations are solved in terms of volume flow; there are no water-to-volume flow correction terms for the permeability, ω, or the reflection coefficient, σ. The precision of the expansion depends upon the magnitude of the water flow. The frictional coefficientsf _sm andf _sw are given as functions of the experimentally determined parameters ω and σ; the frictions, are shown to be independent ofL _p .     

Flow limits of Kedem-Katchalsky equations for fluid flux

The Kedem-Katchalsky equations for fluid flux across membranes may not be adequate for large solvent flows. In particular, for an example of two membranes in series, it is argued that they would predict physically unreasonable behavior. An alternate equation for solute flow is proposed for a simple sieving membrane. For the same example, this equation predicts more physically reasonable results.     

Mechanistic formalism for membrane transport generated by osmotic and mechanical pressure

Since the physical interpretation of practical Kedem-Katchalsky (KK) equations is not clear, we consider an alternative, mechanistic approach to membrane transport generated by osmotic and hydraulic pressure. We study a porous membrane with randomly distributed pore sizes (radii). We postulate that reflection coefficient (sigma p) of a single pore may equal 1 or 0. From this postulate we derive new (mechanistic) transport equations. Their advantage is in clear physical interpretation and since we show they are equivalent to the KK equations, the interpretation of the latter became clearer as well. Henceforth the equations allow clearer and more detailed interpretation of results concerning membrane mass transport. This is especially important from the point of view of biophysical studies on permeation processes across biological membranes, cell membranes including.     

Temperature dependence of Kedem-Katchalsky membrane transport coefficients for mature mouse oocytes in the presence of ethylene glycol.

Ethylene glycol (EG) is the emerging cryoprotectant of choice for preservation of mammalian embryos but has not been widely used for oocyte preservation. Techniques for oocyte cryopreservation need to be improved before they can be incorporated into routine clinical practice. Hence the permeability characteristics of oocytes in the presence of EG have been determined in order to facilitate the design of cryopreservation protocols using this cryoprotectant. Individual mouse oocytes were held using negative pressure applied to the zona pellucida by means of a micropipet. Each oocyte was perfused with 1 ml 1.5 mol L(-1) EG at 30, 19, or 10 degrees C, a total of 10 oocytes being perfused at each temperature. The osmotic response of each oocyte before, during and after perfusion was recorded on videotape. Measurements of mean cell diameter across three axes were used to calculate oocyte volume, assuming them to be spherical, and, using mathematical modeling, values for hydraulic conductivity (L(p)) were found to be 0.91 +/- 0.05, 0.51 +/- 0.02, and 0.18 +/- 0.01 microm min(-1) atm(-1); cryoprotectant permeability (P(EG)) was 0.24 +/- 0.01, 0.09 +/- 0.005, and 0.03 +/- 0.004 microm s(-1); and reflection coefficient (sigma) was 0.98 +/- 0.005, 0.96 +/- 0.01, and 0.97 +/- 0.01 at 30, 19, and 10 degrees C, respectively. The activation energy (E(a)) of L(p) was 14. 0 kCal mol(-1) and of P(EG) was 16.4 kCal mol(-1).     

Mechanistic approach to membrane mass transport processes (mini review)

Since the physical interpretation of practical Kedem-Katchalsky equations is not clear, we consider an alternative, mechanistic approach to membrane transport generated by osmotic and hydraulic pressure. We study a porous membrane with randomly distributed pore sizes (radii). We postulate that the reflection coefficient (sigma(p)) of a single pore may equal 1 or 0 only. From this postulate we derive new (mechanistic) transport equations. Their advantage is in clear physical interpretation.     

Discontinuous membrane helices in transport proteins and their correlation with function

Alpha-helical bundles and beta-barrel proteins represent the two basic types of architecture known for integral membrane proteins. Irregular structural motifs have been revealed with the growing number of structures determined. "Discontinuous" helices are present in membrane proteins that actively transport ions. In the Ca(2+)-ATPase, a primary active transporter, and in the secondary transporters NhaA, LeuT(Aa), ClC H(+)/Cl(-) exchanger and Glt(Ph), the helical structure of two membrane segments is interrupted and the interjacent polypeptide chain forms an extended peptide. The discontinuous helices are integrated in the membrane either as transmembrane-spanning or hairpin-type segments. In addition, the secondary transporters have inverted internal duplication domains, which are only weakly correlated with their amino acid sequence. The symmetry comprises either parts of or the complete molecule, but always includes the discontinuous helices. The helix-peptide-helix motif is correlated with the ion translocation function. The extended peptides with their backbone atoms, the helix termini and the polar/charged amino acid residues in close vicinity provide the basis for ion recognition, binding and translocation.     

Mechanistic insight into heterogeneity of trans-plasma membrane electron transport in cancer cell types

Trans-plasma membrane electron transfer (tMPET) is a process by which reducing equivalents, either electrons or reductants like ascorbic acid, are exported to the extracellular environment by the cell. TPMET is involved in a number of physiological process and has been hypothesised to play a role in the redox regulation of cancer metabolism. Here, we use a new electrochemical assay to elucidate the ‘preference’ of cancer cells for different trans tPMET systems. This aids in proving a biochemical framework for the understanding of tPMET role, and for the development of novel tPMET-targeting therapeutics. We have delineated the mechanism of tPMET in 3 lung cancer cell models to show that the external electron transfer is orchestrated by ascorbate mediated shuttling via tPMET. In addition, the cells employ a different, non-shuttling-based mechanism based on direct electron transfer via Dcytb. Results from our investigations indicate that tPMETs are used differently, depending on the cell type. The data generated indicates that tPMETs may play a fundamental role in facilitation of energy reprogramming in malignant cells, whereby tPMETs are utilised to supply the necessary energy requirement when mitochondrial stress occurs. Our findings instruct a deeper understanding of tPMET systems, and show how different cancer cells may preferentially use distinguishable tPMET systems for cellular electron transfer processes.     

Degradation of substance P by the neuroblastoma cells and their membrane

Cells of the N-18 line of mouse neuroblastoma and their membrane degrade substance P added exogenously. The degradation by the cells and their membrane, examined by high-performance liquid chromatography, is strongly inhibited by EDTA but scarcely inhibited by captopril and phosphoramidon. Gly-Leu-Met-NH2 is the major cleavage product among C-terminal fragments of substance P in both cases. Thus, the degradation of substance P by the neuroblastoma cells and their membrane seems to take place mainly through the hydrolysis between Phe8-Gly9 by EDTA-sensitive protease(s).     

Kinetic analysis of active membrane transport systems: equations for net velocity and isotope exchange.

Equations for the initial net velocity and for isotope exchange velocities in active membrane transport systems are presented. The equations are expressed entirely in terms of kinetic constants which are experimentally determinable from appropriate reciprocal plots, and replots of slope and intercept (for net velocity) or 1/Δslope and 1/Δintercept (for isotope exchange). The equations and plots are equally applicable to a soluble iso uni uni enzyme system.The effect of pH on sulfate transport by an ATP-sulfurylase negative mutant of Penicillium notatum was analyzed assuming that ³⁵SO₄²⁻ and H⁺ are cosubstrates of the transport system. The kinetics are consistent with an ordered addition to the carrier of one H⁺ ion followed by ³⁵SO₄²⁻, with H⁺ in equilibrium with the carrier and the carrier-H⁺ complex.     

Irreversible thermodynamic model equations of the transport across a horizontally mounted membrane

The Kedem-Katchalsky-Zelman model equations for transmembrane transport in multicomponent, non-ionic and heterogeneous solutions have been modified. The validity of this model for binary and ternary solutions was verified, using a cell with a horizontally mounted membrane. In the cell, volume and solute fluxes were measured as a function of gravitational configuration. In the experimental set-up, water was placed on one side of the membrane. The opposite side of the membrane was exposed to aqueous solutions of densities greater than that of water, aqueous ethanol (less dense than water) or glucose/ethanol/water solutions. The experimental results presented herein illustrate pseudo-phase transitions which occur from a non-convectional to convectional state or in the reverse direction.     

Energy-barrier models for membrane transport.

Energy-barrier models are analyzed to find hidden assumptions and establish ranges of validity. The analysis proceeds by comparison with integrated results for model continuum membranes. The main conclusions are that a simple energy-barrier model has a wide range of validity, is remarkably accurate even when its conditions of validity are not strictly met, and is almost always superior to the analogous equations of irreversible thermodynamics. Its major limitations are a possible nonphysical divergence at high electric fields or volume flows caused by breakdown of the transition-state approximation, and the inability to treat multicomponent mixtures except in a pseudobinary (Nernst-Planck) approximation.     

Time course equations of the amount of substance in a linear compartmental system and their computerized derivation

In this contribution, we present the symbolic time course equations corresponding to a general model of a linear compartmental system, closed or open, with or without traps and with zero input. The steady state equations are obtained easily from the transient phase equations by setting the time --> infinity. Special attention has been given to the open systems, for which an exhaustive kinetic analysis has been developed to obtain important properties. Besides, the results have been particularized to open systems without traps and an alternative expression for the distribution function of exit times has been provided. We have implemented a versatile computer program, that is easy to use and with a user-friendly format of the input of data and the output of results. This computer program allows the user to obtain all the information necessary to derive the symbolic time course equations for closed or open systems as well as for the derivation of the distribution function of exit times.     

Organelle identity and the organization of membrane traffic

Generating and maintaining features that distinguish one organelle from another is essential for accurate membrane traffic. Recent work has revealed that organelles express 'identity' by the local generation of activated GTP-binding proteins and lipid species. These recruiting determinants are then recognized by cytosolic proteins that facilitate the formation and delivery of vesicles at the correct compartment.     

Anion transport and membrane morphology

Summary 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.