Mechanistic equations for membrane substance transport and their identity with Kedem-Katchalsky equations

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. Hence the equations allow clearer and more detailed interpretation of results concerning membrane substances transport.     

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.     

Membrane Transport Generated by the Osmotic and Hydrostatic Pressure. Correlation Relation for Parameters L p, σ, and ω

Standard approach to membrane transport generated by osmotic andhydrostatic pressures, developed by Kedem and Katchalsky, is based onprinciples of thermodynamics of irreversible processes. In this paper wepropose an alternative technique. We derive transport equations from fewfairly natural assumptions and a mechanistic interpretation of the flows.In particular we postulate that a sieve-type membrane permeability isdetermined by the pore sizes and these are random within certain range.Assuming that an individual pore is either permeable or impermeable tosolute molecules, the membrane reflection coefficient depends on the ratioof permeable and impermeable pores. Considering flows through permeableand impermeable pores separately, we derive equations for the total volumeflux, solute flux and the solvent flux across the membrane. Comparing themechanistic equations to the Kedem-Katchalsky equations we find the formereasier to interpret physically. Based on the mechanistic equations we alsoderive a correlation relation for the membrane transport parameters L _p,, and . This relation eliminates the need for experimentaldetermination of all three phenomenological parameters, which in somecases met with considerable difficulties.     

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.     

Thermodynamic calculations for biochemical transport and reaction processes in metabolic networks

Thermodynamic analysis of metabolic networks has recently generated increasing interest for its ability to add constraints on metabolic network operation, and to combine metabolic fluxes and metabolite measurements in a mechanistic manner. Concepts for the calculation of the change in Gibbs energy of biochemical reactions have long been established. However, a concept for incorporation of cross-membrane transport in these calculations is still missing, although the theory for calculating thermodynamic properties of transport processes is long known. Here, we have developed two equivalent equations to calculate the change in Gibbs energy of combined transport and reaction processes based on two different ways of treating biochemical thermodynamics. We illustrate the need for these equations by showing that in some cases there is a significant difference between the proposed correct calculation and using an approximative method. With the developed equations, thermodynamic analysis of metabolic networks spanning over multiple physical compartments can now be correctly described.     

Membrane translocation of folded proteins

An ever-increasing number of proteins have been shown to translocate across various membranes of bacterial as well as eukaryotic cells in their folded states as a part of physiological and/or pathophysiological processes. Herein, we provide an overview of the systems/processes that are established or likely to involve the membrane translocation of folded proteins, such as protein export by the twin-arginine translocation system in bacteria and chloroplasts, unconventional protein secretion and protein import into the peroxisome in eukaryotes, and the cytosolic entry of proteins (e.g., bacterial toxins) and viruses into eukaryotes. We also discuss the various mechanistic models that have previously been proposed for the membrane translocation of folded proteins including pore/channel formation, local membrane disruption, membrane thinning, and transport by membrane vesicles. Finally, we introduce a newly discovered vesicular transport mechanism, vesicle budding and collapse, and present evidence that vesicle budding and collapse may represent a unifying mechanism that drives some (and potentially all) of folded protein translocation processes.     

Equations for membrane transport. Experimental and theoretical tests of the frictional model.

Frictional models for membrane transport are tested experimentally and theoretically for the simple case of a solution consisting of a mixture of two perfect gases and a membrane consisting of a porous graphite septum. Serious disagreement is found, which is traced to a missing viscous term. Kinetic theory is then used as a guide in formulating a corrected set of transport equations, and in giving a physical interpretation to the frictional coefficients. Sieving effects are found to be attributable to entrance effects rather than to true frictional effects within the body of the membrane. The results are shown to be compatible with nonequilibrium thermodynamics. Some correlations and predictions are made of the behavior of various transport coefficients for general solutions.     

Lumenal interactions in nuclear pore complex assembly and stability

Nuclear pore complexes (NPCs) provide a gateway for the selective transport of macromolecules across the nuclear envelope (NE). Although we have a solid understanding of NPC composition and structure, we do not have a clear grasp of the mechanism of NPC assembly. Here, we demonstrate specific defects in nucleoporin distribution in strains lacking Heh1p and Heh2p-two conserved members of the LEM (Lap2, emerin, MAN1) family of integral inner nuclear membrane proteins. These effects on nucleoporin localization are likely of functional importance as we have defined specific genetic interaction networks between HEH1 and HEH2, and genes encoding nucleoporins in the membrane, inner, and outer ring complexes of the NPC. Interestingly, expression of a domain of Heh1p that resides in the NE lumen is sufficient to suppress both the nucleoporin mislocalization and growth defects in heh1Δpom34Δ strains. We further demonstrate a specific physical interaction between the Heh1p lumenal domain and the massive cadherin-like lumenal domain of the membrane nucleoporin Pom152p. These findings support a role for Heh1p in the assembly or stability of the NPC, potentially through the formation of a lumenal bridge with Pom152p.     

A Physical Interpretation of the Phenomenological Coefficients of Membrane Permeability

A "translation" of the phenomenological permeability coefficients into friction and distribution coefficients amenable to physical interpretation is presented. Expressions are obtained for the solute permeability coefficient ω and the reflection coefficient σ for both non-electrolytic and electrolytic permeants. An analysis of the coefficients is given for loose membranes as well as for dense natural membranes where transport may go through capillaries or by solution in the lipoid parts of the membrane. Water diffusion and filtration and the relation between these and capillary pore radius of the membrane are discussed. For the permeation of ions through the charged membranes equations are developed for the case of zero electrical current in the membrane. The correlation of σ with ω and L_p for electrolytes resembles that for non-electrolytes. In this case ω and σ depend markedly on ion concentration and on the charge density of the membrane. The reflection coefficient may assume negative values indicating anomalous osmosis. An analysis of the phenomena of anomalous osmosis was carried out for the model of Teorell and Meyer and Sievers and the results agree with the experimental data of Loeb and of Grim and Sollner. A set of equations and reference curves are presented for the evaluation of ω and σ in the transport of polyvalent ions through charged membranes.     

Membrane hydrophobicity determines the activation free energy of passive lipid transport

The collective behavior of lipids with diverse chemical and physical features determines a membrane’s thermodynamic properties. Yet, the influence of lipid physicochemical properties on lipid dynamics, in particular interbilayer transport, remains underexplored. Here, we systematically investigate how the activation free energy of passive lipid transport depends on lipid chemistry and membrane phase. Through all-atom molecular dynamics simulations of 11 chemically distinct glycerophospholipids, we determine how lipid acyl chain length, unsaturation, and headgroup influence the free energy barriers for two elementary steps of lipid transport: lipid desorption, which is rate limiting, and lipid insertion into a membrane. Consistent with previous experimental measurements, we find that lipids with longer, saturated acyl chains have increased activation free energies compared to lipids with shorter, unsaturated chains. Lipids with different headgroups exhibit a range of activation free energies; however, no clear trend based solely on chemical structure can be identified, mirroring difficulties in the interpretation of previous experimental results. Compared to liquid-crystalline phase membranes, gel phase membranes exhibit substantially increased free energy barriers. Overall, we find that the activation free energy depends on a lipid’s local hydrophobic environment in a membrane and that the free energy barrier for lipid insertion depends on a membrane’s interfacial hydrophobicity. Both of these properties can be altered through changes in lipid acyl chain length, lipid headgroup, and membrane phase. Thus, the rate of lipid transport can be tuned through subtle changes in local membrane composition and order, suggesting an unappreciated role for nanoscale membrane domains in regulating cellular lipid dynamics.     

pH-Dependent Interactions Guide the Folding and Gate the Transmembrane Pore of the β-Barrel Membrane Protein OmpG

The physical interactions that switch the functional state of membrane proteins are poorly understood. Previously, the pH-gating conformations of the β-barrel forming outer membrane protein G (OmpG) from Escherichia coli have been solved. When the pH changes from neutral to acidic the flexible extracellular loop L6 folds into and closes the OmpG pore. Here, we used single-molecule force spectroscopy to structurally localize and quantify the interactions that are associated with the pH-dependent closure. At acidic pH, we detected a pH-dependent interaction at loop L6. This interaction changed the (un)folding of loop L6 and of β-strands 11 and 12, which connect loop L6. All other interactions detected within OmpG were unaffected by changes in pH. These results provide a quantitative and mechanistic explanation of how pH-dependent interactions change the folding of a peptide loop to gate the transmembrane pore. They further demonstrate how the stability of OmpG is optimized so that pH changes modify only those interactions necessary to gate the transmembrane pore.     

Managing Free-energy Barriers in Nuclear Pore Transport

The Nuclear Pore Complexes (NPC) facilitate highly selective gateways for transport of macromolecules across the Nuclear Envelope (NE). Based on the current accumulated knowledge of the architecture of NPC we have established a minimal physical model of the pore and the transport mechanism. The barrier properties of the NPC model are analyzed by the recently established Wang–Landau Monte Carlo computer simulation technique and the transport properties are extracted by employing Kramers’ theory of reaction rates. We show that our physical model can account for a range of characteristics observed for nuclear pore transport.     

Polyol permeability of the human red cell. Interpretation of glucose transport in terms of a pore

The kinetic equations describing transport through a pore that has a binding site and that undergoes a conformational change are identical to those of a carrier model. Therefore, in order to distinguish between the two models it is necessary to test specific predictions based on detailed mechanistic models. A pore model is described in which the substrate (glucose) is able to reach the single binding site only from the outside when the pore is in conformation I and only from the inside when it is conformation II. On the basis of this model it is predicted that solutes which do not have any specific affinity for the binding site should still have a finite permeability via the glucose transport system if they are the same size or smaller than glucose. This permeability should be proportional to the volume of distribution of the solute in the pore and should therefore decrease with increasing molecular size. A geometric pore volume can be estimated from this size dependence. In order to test these predictions, the glucose-dependent permeability of a series of 4-carbon (erythritol), 5-carbon (d-arabitol, l-arabitol and xylitol) and 6-carbon (d-mannitol, d-sorbitol and $\text{myo-}\text{inositol}$) polyols was measured. The permeability of all the polyols is decreased by the presence of glucose and the $\text{K}{}_{\mathrm{<mtext>I</mtext>}}$ of this “inhibitable” component is similar to that of d-sorbose, suggesting that this component is associated with the glucose transport system. Since these observations could be explained entirely in terms of a specific affinity for a carrier binding site, they do not exclude a carrier mechanism. However, as predicted for the pore model, this “inhibitable” permeability decreased with increasing molecular size and the calculated geometric pore volume was of a size that would be expected for a cell membrane pore.     

Life Cycle of an Electropore: Field-Dependent and Field-Independent Steps in Pore Creation and Annihilation

Electropermeabilization, an electric field-induced modification of the barrier functions of the cell membrane, is widely used in laboratories and increasingly in the clinic; but the mechanisms and physical structures associated with the electromanipulation of membrane permeability have not been definitively characterized. Indirect experimental observations of electrical conductance and small molecule transport as well as molecular dynamics simulations have led to models in which hydrophilic pores form in phospholipid bilayers with increased probability in the presence of an electric field. Presently available methods do not permit the direct, nanoscale examination of electroporated membranes that would confirm the existence of these structures. To facilitate the reconciliation of poration models with the observed properties of electropermeabilized lipid bilayers and cell membranes, we propose a scheme for characterizing the stages of electropore formation and resealing. This electropore life cycle, based on molecular dynamics simulations of phospholipid bilayers, defines a sequence of discrete steps in the electric field-driven restructuring of the membrane that leads to the formation of a head group-lined, aqueous pore and then, after the field is removed, to the dismantling of the pore and reassembly of the intact bilayer. Utilizing this scheme we can systematically analyze the interactions between the electric field and the bilayer components involved in pore initiation, construction and resealing. We find that the pore creation time depends strongly on the electric field gradient across the membrane interface and that the pore annihilation time is at least weakly dependent on the magnitude of the pore-initiating electric field and, in general, much longer than the pore creation time.     

A model for sieving of macromolecules by the glomerular membrane of the kidney.

The transport of water and of macromolecules across the glomerular membrane of the kidney depends on the membrane parameters (radius, length and number of pores) as well as on the hydrostatic and oncotic pressures on either side of the membrane. The filtration pressure decreases along the capillary loops from afferent to efferent end. Water and solute flows are thus given by a system of two differential equations. The sieving coefficient of the macromolecules is the ratio of solute to water flow. In the program described the differential equations are solved by the Runge-Kutta method (fourth order). Rosenbrock's method of minimization is used to adjust the theoretical to the experimental sieving coefficients. The pore radius, total pore area per unit of path length and conductance of the membrane, as well as the intracapillary hydrostatic pressure and its gradient can thus be determined.     

Nuclear Pore Complex Protein Sequences Determine Overall Copolymer Brush Structure and Function

The transport of cargo across the nuclear membrane is highly selective and accomplished by a poorly understood mechanism involving hundreds of nucleoporins lining the inside of the nuclear pore complex (NPC). Currently, there is no clear picture of the overall structure formed by this collection of proteins within the pore, primarily due to their disordered nature. We perform coarse-grained simulations of both individual nucleoporins and grafted rings of nups mimicking the in vivo geometry of the NPC and supplement this with polymer brush modeling. Our results indicate that different regions or blocks of an individual NPC protein can have distinctly different forms of disorder and that this property appears to be a conserved functional feature. Furthermore, this block structure at the individual protein level is critical to the formation of a unique higher-order polymer brush architecture that can exist in distinct morphologies depending on the effective interaction energy between the phenylalanine glycine (FG) domains of different nups. Because the interactions between FG domains may be modulated by certain forms of transport factors, our results indicate that transitions between brush morphologies could play an important role in regulating transport across the NPC, suggesting novel forms of gated transport across membrane pores with wide biomimetic applicability.     

Nuclear Pore Complex Protein Sequences Determine Overall Copolymer Brush Structure and Function

The transport of cargo across the nuclear membrane is highly selective and accomplished by a poorly understood mechanism involving hundreds of nucleoporins lining the inside of the nuclear pore complex (NPC). Currently, there is no clear picture of the overall structure formed by this collection of proteins within the pore, primarily due to their disordered nature. We perform coarse-grained simulations of both individual nucleoporins and grafted rings of nups mimicking the in vivo geometry of the NPC and supplement this with polymer brush modeling. Our results indicate that different regions or blocks of an individual NPC protein can have distinctly different forms of disorder and that this property appears to be a conserved functional feature. Furthermore, this block structure at the individual protein level is critical to the formation of a unique higher-order polymer brush architecture that can exist in distinct morphologies depending on the effective interaction energy between the phenylalanine glycine (FG) domains of different nups. Because the interactions between FG domains may be modulated by certain forms of transport factors, our results indicate that transitions between brush morphologies could play an important role in regulating transport across the NPC, suggesting novel forms of gated transport across membrane pores with wide biomimetic applicability.     

Ion transport through pores: transient phenomena

A theoretical analysis of non-stationary states in membrane pores is given in this paper, which is based on the rate-theory treatment of transport processes. The principal aim of this study is to give a basis for the interpretation of relaxation experiments in which an external parameter, such as the voltage across the membrane, is suddenly displaced. From the time course of the membrane current information about the microscopic properties of the pore may be obtained. The pore is considered as a sequence of binding sites, separated by energy barriers over which the ion has to jump. It is found that under certain conditions damped oscillations occur after the initial perturbations of the membrane. In all other cases the approach towards the steady state may be described by a discrete spectrum of n relaxation times, where n is the number of binding sites within the pore. In the case of a pore with regular energy profile (internal barriers of identical height) the relaxation times may be obtained as the roots of Tchebycheff polynomials for arbitrary n. It is shown that the present treatment becomes identical with the continuum analysis of transport processes in the limit of large n.     

蛋白质入核转运的机制和研究进展

细胞核膜是由外膜和内膜组成的磷脂双分子层结构,同时镶嵌一些核孔复合体（NPC）.核孔复合体是胞浆和胞核之间主动和被动转运的生理屏障.核内功能蛋白在胞浆内合成后通过核孔复合体进入胞核,这个过程除了需要NPC上核孔蛋白、胞浆内核转运受体和RanGTP等蛋白的参与外, 货物蛋白本身的结构特征在其入核转运过程中亦发挥重要作用.本文着重就蛋白入核转运的机制及近年来取得的相关进展进行综述.