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 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.     

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.     

The Balance of Fluid and Osmotic Pressures across Active Biological Membranes with Application to the Corneal Endothelium

The movement of fluid and solutes across biological membranes facilitates the transport of nutrients for living organisms and maintains the fluid and osmotic pressures in biological systems. Understanding the pressure balances across membranes is crucial for studying fluid and electrolyte homeostasis in living systems, and is an area of active research. In this study, a set of enhanced Kedem-Katchalsky (KK) equations is proposed to describe fluxes of water and solutes across biological membranes, and is applied to analyze the relationship between fluid and osmotic pressures, accounting for active transport mechanisms that propel substances against their concentration gradients and for fixed charges that alter ionic distributions in separated environments. The equilibrium analysis demonstrates that the proposed theory recovers the Donnan osmotic pressure and can predict the correct fluid pressure difference across membranes, a result which cannot be achieved by existing KK theories due to the neglect of fixed charges. The steady-state analysis on active membranes suggests a new pressure mechanism which balances the fluid pressure together with the osmotic pressure. The source of this pressure arises from active ionic fluxes and from interactions between solvent and solutes in membrane transport. We apply the proposed theory to study the transendothelial fluid pressure in the in vivo cornea, which is a crucial factor maintaining the hydration and transparency of the tissue. The results show the importance of the proposed pressure mechanism in mediating stromal fluid pressure and provide a new interpretation of the pressure modulation mechanism in the in vivo cornea.     

Single Water Channels of Aquaporin-1 Do not Obey the Kedem-Katchalsky Equations

The Kedem-Katchalsky (KK) equations are often used to obtain information about the osmotic properties and conductance of channels to water. Using human red cell membranes, in which the osmotic flow is dominated by Aquaporin-1, we show here that compared to NaCl the reflexion coefficient of the channel for methylurea, when corrected for solute volume exchange and for the water permeability of the lipid membrane, is 0.54. The channels are impermeable to these two solutes which would seem to rule out flow interaction and require a reflexion coefficient close to 1.0 for both. Thus, two solutes can give very different osmotic flow rates through a semi-permeable pore, a result at variance with both classical theory and the KK formulation. The use of KK equations to analyze osmotic volume changes, which results in a single hybrid reflexion coefficient for each solute, may explain the discrepancy in the literature between such results and those where the equations have not been employed. Osmotic reflexion coefficients substantially different from 1.0 cannot be ascribed to the participation of other 'hidden' parallel aqueous channels consistently with known properties of the membrane. Furthermore, we show that this difference cannot be due to second-order effects, such as a solute-specific interaction with water in only part of the channel, because the osmosis is linear with driving force down to zero solute concentration, a finding which also rules out the involvement of unstirred-layer effects. Reflexion coefficients smaller than 1.0 do not necessitate water-solute flow interaction in permeable aqueous channels; rather, the osmotic behaviour of impermeable molecular-sized pores can be explained by differences in the fundamental nature of water flow in regions either accessible or inaccessible to solute, created by a varying cross-section of the channel.     

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.     

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.     

Protein translocation across membranes.

Cellular membranes act as semipermeable barriers to ions and macromolecules. Specialized mechanisms of transport of proteins across membranes have been developed during evolution. There are common mechanistic themes among protein translocation systems in bacteria and in eukaryotic cells. Here we review current understanding of mechanisms of protein transport across the bacterial plasma membrane as well as across several organelle membranes of yeast and mammalian cells. We consider a variety of organelles including the endoplasmic reticulum, outer and inner membranes of mitochondria, outer, inner, and thylakoid membranes of chloroplasts, peroxisomes, and lysosomes. Several common principles are evident: (a) multiple pathways of protein translocation across membranes exist, (b) molecular chaperones are required in the cytosol, inside the organelle, and often within the organelle membrane, (c) ATP and/or GTP hydrolysis is required, (d) a proton-motive force across the membrane is often required, and (e) protein translocation occurs through gated, aqueous channels. There are exceptions to each of these common principles indicating that our knowledge of how proteins translocate across membranes is not yet complete.     

Membrane Permeability Modeling: Kedem–Katchalsky vs a Two-Parameter Formalism

The analysis of experiments for the purpose of determining cell membrane permeability parameters is often done using the Kedem–Katchalsky (KK) formalism (1958). In this formalism, three parameters, the hydraulic conductivity (L_p), the solute permeability (P_s), and a reflection coefficient (ς), are used to characterize the membrane. Sigma was introduced to characterize flux interactions when water and solute (cryoprotectant) cross the membrane through a common channel. However, the recent discovery and characterization of water channels (aquaporins) in biological membranes reveals that aquaporins are highly selective for water and do not typically cotransport cryoprotectants. In this circumstance, sigma is a superfluous parameter, as pointed out by Kedem and Katchalsky. When sigma is unneeded, a two-parameter model (2P) utilizing onlyL_pandP_sis sufficient, simpler to implement, and less prone to spurious results. In this paper we demonstrate that the 2P and KK formalism yield essentially the same result (L_pandP_s) when cotransporting channels are absent. This demonstration is accomplished using simulation techniques to compare the transport response of a model cell using a KK or 2P formalism. Sigma is often misunderstood, even when its use is appropriate. It is discussed extensively here and several simulations are used to illustrate and clarify its meaning. We also discuss the phenomenological nature of transport parameters in many experiments, especially when both bilayer and channel transport are present.     

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.     

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.     

Saccharomyces cerevisiae porin pore forms complexes with mitochondrial outer membrane proteins Om14p and Om45p

Numerous transport processes occur between the two mitochondrial (mt) membranes due to the diverse functions and metabolic processes of the mt organelle. The metabolite and ion transport through the mt outer membrane (OM) is widely assumed to be mediated by the porin pore, whereas in the mt inner membrane (IM) specific carriers are responsible for transport processes. Here, we provide evidence by means of Blue Native (BN)-PAGE analysis, co-immunoprecipitation, and tandem affinity purification that the two mt OM proteins Om14p and Om45p associate with the porin pore. Porin molecules seem to assemble independently to build the core unit. A subpopulation of these core units interacts with Om14p and Om45p. With preparative tandem affinity purification followed by MS analysis, we could identify interaction partners of this OM complex, which are mainly localized within the mt IM and function as carriers for diverse molecules. We propose a model for the role of the two OM proteins in addressing the porin pore to bind to specific channels in the mt IM to facilitate transport of metabolites.     

Two-chamber AFM: probing membrane proteins separating two aqueous compartments

Biological membranes compartmentalize and define physical borders of cells. They are crowded with membrane proteins that fulfill diverse crucial functions. About one-third of all genes in organisms code for, and the majority of drugs target, membrane proteins. To combine structure and function analysis of membrane proteins, we designed a two-chamber atomic force microscopy (AFM) setup that allows investigation of membranes spanned over nanowells, therefore separating two aqueous chambers. We imaged nonsupported surface layers (S layers) of Corynebacterium glutamicum at sufficient resolution to delineate a 15 A-wide protein pore. We probed the elastic and yield moduli of nonsupported membranes, giving access to the lateral interaction energy between proteins. We combined AFM and fluorescence microscopy to demonstrate the functionality of proteins in the setup by documenting proton pumping by Halobacterium salinarium purple membranes.     

Effect of protein adsorption on the transport characteristics of asymmetric ultrafiltration membranes.

The effects of bovine serum albumin adsorption on the transport characteristics of asymmetric poly(ether sulfone) ultrafiltration membranes were determined using polydisperse dextrans with gel permeation chromatography. Actual dextran sieving coefficients were evaluated from observed sieving data for both the clean and preadsorbed membranes using a stagnant film model. The flux dependence of the actual dextran sieving coefficients was used to evaluate the intrinsic membrane hindrance factors for convective (i.e., sieving) and diffusive transport for the different molecular weight dextrans using classical membrane transport theory. Protein adsorption caused a reduction in both dextran sieving and diffusion, with the magnitude of the reduction a function of the dextran molecular weight and pore size. The effects of adsorption on the specific pore area and the membrane porosity were then determined using a recent model for solute transport through asymmetric ultrafiltration membranes. The data indicate that protein adsorption occurs preferentially in the larger membrane pores, causing a greater reduction in solute sieving compared to the membrane hydraulic permeability and porosity than would be predicted on the basis of either a simple pore blockage or pore constriction model.     

High porosity with tiny pore constrictions and unbending pathways characterize the 3D structure of intervessel pit membranes in angiosperm xylem

Pit membranes between xylem vessels play a major role in angiosperm water transport. Yet, their three-dimensional (3D) structure as fibrous porous media remains unknown, largely due to technical challenges and sample preparation artefacts. Here, we applied a modelling approach based on thickness measurements of fresh and fully shrunken pit membranes of seven species. Pore constrictions were also investigated visually by perfusing fresh material with colloidal gold particles of known sizes. Based on a shrinkage model, fresh pit membranes showed tiny pore constrictions of ca. 20 nm, but a very high porosity (i.e. pore volume fraction) of on average 0.81. Perfusion experiments showed similar pore constrictions in fresh samples, well below 50 nm based on transmission electron microscopy. Drying caused a 50% shrinkage of pit membranes, resulting in much smaller pore constrictions. These findings suggest that pit membranes represent a mesoporous medium, with the pore space characterized by multiple constrictions. Constrictions are much smaller than previously assumed, but the pore volume is large and highly interconnected. Pores do not form highly tortuous, bent, or zigzagging pathways. These insights provide a novel view on pit membranes, which is essential to develop a mechanistic, 3D understanding of air-seeding through this porous medium.     

pH-control of the miscibility properties of a binary lipid alloy and its influence on the ion transport by gramicidin.

We studied the coupling of a membrane function (the transport of ions by the pore forming polypeptide gramicidin) to chemically driven phase changes in black membranes of binary lipid mixtures. In particular, we investigated the influence of the aqueous pH value on the fluid-fluid demixing effect of Ca2+ to phosphatidylcholine/phosphatidylglycerol bilayers. It is found that one can switch, under certain conditions, between a homogeneously mixed and a phase separated membrane by changing the pH. We interpret this as being caused by the change in the degree of dissociation of one of the lipid components.     

Physical Damage on Giant Vesicles Membrane as a Result of Methylene Blue Photoirradiation

In this study we pursue a closer analysis of the photodamage promoted on giant unilamellar vesicles membranes made of dioleoyl-sn-glycero-3-phosphocholine (DOPC) or 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), by irradiating methylene blue present in the giant unilamellar vesicles solution. By means of optical microscopy and electro-deformation experiments, the physical damage on the vesicle membrane was followed and the phospholipids oxidation was evaluated in terms of changes in the membrane surface area and permeability. As expected, oxidation modifies structural characteristics of the phospholipids that lead to remarkable membrane alterations. By comparing DOPC- with POPC-made membranes, we observed that the rate of pore formation and vesicle degradation as a function of methylene blue concentration follows a diffusion law in the case of DOPC and a linear variation in the case of POPC. We attributed this scenario to the nucleation process of oxidized species following a diffusion-limited growth regime for DOPC and in the case of POPC a homogeneous nucleation process. On the basis of these premises, we constructed models based on reaction-diffusion equations that fit well with the experimental data. This information shows that the outcome of the photosensitization reactions is critically dependent on the type of lipid present in the membrane.