Flux Ratio and Driving Forces in a Model of Active Transport

In order to analyze the energetics of active transport, a hypothetical carrier model is considered in which the active transport process is reduced to a minimal number of elementary steps. The relation between the following three quantities is examined: The affinity of the reaction driving the active transport, the ratio of isotope fluxes between identical solutions (“short-circuit”), and the maximal chemical potential difference which the active transport system can maintain. The interdependence of isotopeinteraction and the degree of coupling between transport and chemical reaction is shown explicitly: when the transport and chemical reaction are completely coupled, there is marked isotope interaction. In general, the logarithm of the short-circuit flux ratio (multiplied by RT) and the maximal chemical potential are not equal. The two quantities are approximately equal, when coupling between metabolism and transport is very loose, or when the reaction step is much faster than the transfer of the adsorbed solute across the barrier. Without prior knowledge of the kinetic parameters of the carrier, the maximal potential and the dependence of the metabolic reaction on solute flow have to be measured in order to derive the affinity of the driving reaction. Measurement of the flux ratio in the same system will then yield independent information on the carrier mechanism.     

Surface Charge Movements of Purple Membrane During Light-Dark Adaptation

The difference in the surface charge distribution between light-adapted and dark-adapted purple membranes was investigated with electric dichroism measurements from approximately pH 5 to pH 11. Purple membrane sheets in solution are oriented in a weak electric field by their permanent dipole moment, which is due to the charge distribution of the membrane surfaces and/or within the membrane. The degree of orientation of purple membrane sheets was obtained from the measurement of “electrical anisotropy” of retinal chromophore in the membranes. At about pH 7, there was no difference in the “electric anisotropy” between light- and dark-adapted purple membranes. At about pH 9, the electric anisotropy of dark-adapted purple membrane was larger than that of light-adapted purple membrane. But at around pH 6 the difference was opposite. Linear dichroism experiments did not show any change of retinal tilt angle with respect to the membrane normal between the two forms from approximately pH 5 to pH 10. This result indicates that the changes in the “electric anisotropy” are not due to the change of retinal tilt angle, but due to the change in the permanent dipole moment of the membrane. To estimate the change in surface charges from the permanent dipole moment, we investigated the difference of the permanent dipole moment between the native purple membrane and papain-treated purple membrane in which negative charges in the cytoplasmic-terminal part are removed. This estimation suggests that this light-dark difference at around pH 9 can be accounted for by a change of ~0.5 electric charge per bacteriorhodopsin (bR) molecule at either of the two surfaces of the membrane. We also found from pH electrode measurements that at about pH 8 or 9 light adaptation was accompanied by an uptake of ~0.1 protons per bR. A possible movement of protons during light-dark adaptation is discussed. The direction of the permanent dipole moment does not change with papain treatment. The permanent dipole moment in papain-treated purple membrane is estimated to be 27 ±2 debye/bR.     

Direct effects on the membrane potential due to "pumps" that transfer no net charge

The effects of active ionic transport are included in the derivation of a general expression for the zero current membrane potential. It is demonstrated that an active transport system that transfers no net charge (nonrheogenic) may, nevertheless, directly alter the membrane potential. This effect depends upon the exchange of matter within the membrane between the active and passive diffusion regimes. Furthermore, in the presence of such exchange, the transmembrane active fluxes measured by the usual techniques and the local pumped fluxes are not identical. Several common uses of the term “electrogenic pump” are thus shown to be inconsistent with each other. These inconsistencies persist when the derivation is extended to produce a Goldman equation modified to account for active transport; however, that equation is shown to be limited by less narrow constraints on membrane heterogeneity and internal electric field than those previously required. In particular, it is applicable to idealized mosaic membranes limited by these requirements.     

The Non-Steady-State Membrane Potential of Ion Exchangers with Fixed Sites

A system of equations, based upon the assumption that the only force acting on each ionic species is due to the gradient of its electrochemical potential, is used to deduce, in the non-steady state for zero net current, the expression of the difference of electric potential between two solutions separated by an ion exchange membrane with fixed monovalent sites. The membrane is assumed to be solely permeable to cations or anions, depending on whether the charge of the sites is -1 or +1, and not to permit any flow of solvent. Under the assumptions that the difference of standard chemical potentials of any pair of permeant monovalent species and the ratio of their mobilities are constant throughout the membrane, even when the spacing of sites is variable, explicit expressions are derived for the diffusion potential and total membrane potential as functions of time and of solution activities. The expressions are valid for any number of permeant monovalent species having ideal behavior and for two permeant monovalent species having “n-type” non-ideal behavior. The results show that for a step change in solution composition the observable potential across a membrane having fixed, but not necessarily uniformly spaced, sites becomes independent of time once equilibria are established at the boundaries of the membrane and attains its steady-state value even while the ionic concentration profiles and the electric potential profile within the membrane are changing with time.     

The Need for a Kinetics for Biological Transport

The traditional theory of transport across capillary membranes via a laminar Poiseuille flow is shown to be invalid. It is demonstrated that the random, diffusive nature of the molecular flow and interactions with the “pore” walls play an important role in the transport process. Neither the continuum Navier-Stokes theory nor the equivalent theory of irreversible thermodynamics is adequate to treat the problem. Combination of near-continuum hydrodynamic theory, noncontinuum kinetic theory, and the theory of fluctuations provides a first step toward modeling both liquid processes in general and membrane transport processes as a specific application.     

A Test of the Theory of the Steady-State Properties of an Ion Exchange Membrane with Mobile Sites and Dissociated Counterions

An experimental model system, formally equivalent to a liquid ion exchange membrane having completely dissociated sites and counterions, has been devised in order to test the steady-state properties recently deduced theoretically for such a membrane by Conti and Eisenman, (1966). In this system we have obtained quantitative experimental confirmation of the following theoretical expectations. (a) The current-voltage relationship is nonlinear and exhibits finite limiting currents with strong applied fields. (b) The mobile sites rearrange within the “membrane” under applied electric field to give a linear concentration profile and a logarithmic electric potential profile in the steady state. We have also extended the theory to consider the instantaneous conductance in the steady state. Theory and experiment indicate that in a mobile site membrane the instantaneous conductance in the steady state is not given by the chord conductance of the steady-state current-voltage relationship, in contrast to the situation in a fixed site membrane. This finding suggests a way of testing whether ions permeate across an unknown membrane by a fixed site or a dissociated mobile site mechanism.     

A quantitative analysis of the voltage-current relationships of fixed charge membranes and the associated property of "punch-through"

A theoretical analysis of the voltage-current relationship is carried out in a membrane consisting of two fixed charge regions, of opposite sign, in contact. This is achieved by applying the diffusion equations to this system in conjunction with the Poisson-Boltzmann equation. The latter has been successfully applied by Mauro to determine the profiles of the electrostatic potential in his treatment of the capacitative property of such a system. It is shown that the system displays the property of rectification and is very similar in many respects to a solid state P-N junction diode. It is also shown that for the case of reverse bias, an electrical breakdown phenomena can occur. This is referred to as the “punch-through” effect. “Punch-through” was observed in experiments on the electrical characteristics of the membranes of Chara australis and Nitella sp. The experimental results are discussed in relation to the theoretical analysis.     

Characterizing the Composition of Molecular Motors on Moving Axonal Cargo Using "Cargo Mapping" Analysis

Understanding the mechanisms by which molecular motors coordinate their activities to transport vesicular cargoes within neurons requires the quantitative analysis of motor/cargo associations at the single vesicle level. The goal of this protocol is to use quantitative fluorescence microscopy to correlate (“map”) the position and directionality of movement of live cargo to the composition and relative amounts of motors associated with the same cargo. “Cargo mapping” consists of live imaging of fluorescently labeled cargoes moving in axons cultured on microfluidic devices, followed by chemical fixation during recording of live movement, and subsequent immunofluorescence (IF) staining of the exact same axonal regions with antibodies against motors. Colocalization between cargoes and their associated motors is assessed by assigning sub-pixel position coordinates to motor and cargo channels, by fitting Gaussian functions to the diffraction-limited point spread functions representing individual fluorescent point sources. Fixed cargo and motor images are subsequently superimposed to plots of cargo movement, to “map” them to their tracked trajectories. The strength of this protocol is the combination of live and IF data to record both the transport of vesicular cargoes in live cells and to determine the motors associated to these exact same vesicles. This technique overcomes previous challenges that use biochemical methods to determine the average motor composition of purified heterogeneous bulk vesicle populations, as these methods do not reveal compositions on single moving cargoes. Furthermore, this protocol can be adapted for the analysis of other transport and/or trafficking pathways in other cell types to correlate the movement of individual intracellular structures with their protein composition. Limitations of this protocol are the relatively low throughput due to low transfection efficiencies of cultured primary neurons and a limited field of view available for high-resolution imaging. Future applications could include methods to increase the number of neurons expressing fluorescently labeled cargoes.     

Carrier Model for Active Transport of Ions across a Mosaic Membrane

The central purpose of this paper is to elucidate in a well defined system the meaning of certain phenomena and concepts associated with the active transport of ions. To this end a specific model for a carrier system which actively transports a single ionic species is analyzed and discussed in detail. It is assumed in this model that the carrier-mediated ionic transport occurs in regions of the membrane physically separate from those regions in which free ionic movement takes place,—coupling between the active and passive regions of the membrane occurring through local current flows. The model is seen to display the following characteristics: (a) Starting from identical solutions on the two sides of the membrane, there is produced a redistribution of ions; (b) with identical solutions on the two sides of the membrane there exists a potential difference across the membrane, i.e., the “pump” is electrogenic; (c) the “short circuit” current for symmetrical solutions is equal to the flux of the neutral ion carrier complex; (d) the rate of active transport (and hence of metabolism) is dependent on the ionic concentrations in the surrounding solutions. Throughout the paper comparison is made between features of the model and properties displayed by biological active transport systems, but there is no claim of an identity between the two.     

Exploiting Nanotechnologies and TRPV1 Channels to Investigate the Putative Anandamide Membrane Transporter

Background

Considerable efforts have been made to characterize the pathways regulating the extracellular levels of the endocannabinoid anandamide. However, none of such pathways has been so argued as the existence of a carrier-mediated transport of anandamide across the membrane. Apart from the lack of molecular evidence for such a carrier, the main reasons of this controversy lie in the methodologies currently used to study anandamide cellular uptake. Furthermore, the main evidence in favor of the existence of an “anandamide transporter” relies on synthetic inhibitors of this process, the selectivity of which has been questioned.

Methodology/Principal Findings

We used the cytosolic binding site for anandamide on TRPV1 channels as a biosensor to detect anandamide entry into cells, and exploited nanotechnologies to study anandamide membrane transport into intact TRPV1-overexpressing HEK-293 cells. Both fluorescence and digital holographic (DH) quantitative phase microscopy were used to study TRPV1 activation. Poly-ε-caprolactone nanoparticles (PCL-NPs) were used to incorporate anandamide, which could thus enter the cell and activate TRPV1 channels bypassing any possible specific protein(s) involved in the uptake process. We reasoned that in the absence of such protein(s), pharmacological tools previously shown to inhibit the “anandamide transporter” would affect in the same way the uptake of anandamide and PCL-NP-anandamide, and hence the activation of TRPV1. However, when masked into PCL-NPs, anandamide cellular uptake became much less sensitive to these agents, although it maintained the same pharmacokinetics and pharmacodynamics as that of “free” anandamide.

Conclusions

We found here that several agents previously reported to inhibit anandamide cellular uptake lose their efficacy when anandamide is prevented from interacting directly with plasma membrane proteins, thus arguing in favor of the specificity of such agents for the putative “anandamide transporter”, and of the existence of such mechanism.     

Structural transition produced by electric fields in aqueous sodium deoxyribonucleate

It was found that the birefringence of aqueous solutions of sodium DNA is anomalous when electric fields of high intensity (≥10⁴ v/cm) are applied. The magnitude of the birefringence first rose upon application of the orienting pulse, then fell as the field was sustained above a critical value. The occurrence of the effect depended upon macromolecular and electrolyte concentrations. Upon removal of the field, the birefringence was rapidly restored and then it decayed with an increase of the reorientational relaxation times, relative to those observed below the critical field. It is proposed that the electric field may cause aggregation of the macromolecules and then produce a structural transition concomitant with the electric field orientation effect. This transition may correspond to the “B” “A” structures identified in x-ray studies, or to a “B” “V” structure change, where “V” is a postulated new helical form stabilized by cooperative interactions of base and dipoles in the electric field. Field induced transitions of this type would be of interest in connection with molecular mechanisms of transport through membranes, nerve impulse transmission, or information storage.     

Shootin1–cortactin interaction mediates signal–force transduction for axon outgrowth

Motile cells transduce environmental chemical signals into mechanical forces to achieve properly controlled migration. This signal–force transduction is thought to require regulated mechanical coupling between actin filaments (F-actins), which undergo retrograde flow at the cellular leading edge, and cell adhesions via linker “clutch” molecules. However, the molecular machinery mediating this regulatory coupling remains unclear. Here we show that the F-actin binding molecule cortactin directly interacts with a clutch molecule, shootin1, in axonal growth cones, thereby mediating the linkage between F-actin retrograde flow and cell adhesions through L1-CAM. Shootin1–cortactin interaction was enhanced by shootin1 phosphorylation by Pak1, which is activated by the axonal chemoattractant netrin-1. We provide evidence that shootin1–cortactin interaction participates in netrin-1–induced F-actin adhesion coupling and in the promotion of traction forces for axon outgrowth. Under cell signaling, this regulatory F-actin adhesion coupling in growth cones cooperates with actin polymerization for efficient cellular motility.     

The Validity of the Ussing Flux Ratio Equation in a Three-Dimensionally Inhomogeneous Membrane

Derivations of the Ussing flux ratio equation have, until now, required the membrane to be both bounded by parallel planes and homogeneous, except in the transmembrane direction. These constraints have been necessary for the theoretical demonstration that the equation is independent of membrane parameters in the absence of carriers, coupling, solvent drag, or “single-file” diffusion. In a new derivation, the flux ratio equation is shown to be valid in this kind of diffusion regime without regard to the three-dimensional structure of the membrane. Thus the constraints on both membrane homogeneity and membrane geometry are shown to be unnecessary. The general use of this equation to differentiate between simple, uncoupled diffusion and other membrane transport phenomena is thus placed on a firmer base. However, as in earlier derivations, it is necessary that isopotential, isobaric, constant concentration surfaces exist sufficiently close to the membrane on both of its sides.     

A Continuum Mechanical Approach to the Flow Equations for Membrane Transport: I. Water Flow

A concept is presented for modeling flows through membranes using continuum mechanics. Viscous interactions (due to velocity gradients) are explicitly incorporated and position-dependent local water-membrane interactions are taken into account before obtaining slab averages. This is in distinction to other treatments where strictly one-dimensional force balance equations are written using slab average friction coefficients which are really composite functions of local interactions. It is shown that the viscous and other frictional interactions do not simply form linear combinations in the solutions to the equations of motion. Flow profiles for pressure-driven flows ranging from Poiseuille's flow to “diffusion” flow are obtained depending on the strength and extent of the water-membrane interaction. The model is also applied to self-diffusion flows and the measurement of “equivalent pore size.” It is shown that for a fixed pore size the ratio of filtration flow to self-diffusion flow for equal driving forces is able to vary over a wide range depending on the water-membrane interaction.     

RETROLENTAL FIBROPLASIA—Blindness in Infants of Low Weight at Birth

Retrolental fibroplasia is today the principal cause of blindness in children of preschool age, exceeding all other causes combined. The disease occurs in infants of low weight at birth, commonly those born prematurely. The incidence of the disease is rising at an alarming rate. Vitamin E deficiency, corticotropin (ACTH) deficiency, the use of cow''s milk in place of mother''s milk, and improper oxygenation have been suggested as etiologic factors but the cause remains a mystery. Often the incidence is high in institutions in which maximal care is given premature infants.Clinically, the disease advances through an “active” phase during which regression is possible, and a “subsiding” or “cicatricial” phase which terminates with the formation of a disorganized opaque mass behind the lens. The earliest manifestations are noted in the fundi. Hemorrhages, neovascularization, transudation commencing in the periphery, and retinal separation contribute to the formation of the characteristic retrolental membrane. The diagnosis may be made when the retrolental membrane is observed in the eye of an infant whose weight at birth was low. Differential diagnosis is required occasionally.Thus far, no form of therapy has prevented or reversed the pathologic changes successfully. Use of vitamin E, corticotropin and mother''s milk has not influenced the incidence of the disease. Avoidance of premature delivery if possible is indicated.     

Molecular insights into the primary nucleation of polymorphic amyloid β dimers in DOPC lipid bilayer membrane

Alzheimer''s disease (AD) pathology is characterized by loss of memory cognitive and behavioral deterioration. One of the hallmarks of AD is amyloid β (Aβ) plaques in the brain that consists of Aβ oligomers and fibrils. It is accepted that oligomers, particularly dimers, are toxic species that are produced extracellularly and intracellularly in membranes. It is believed that the disruption of membranes by polymorphic Aβ oligomers is the key for the pathology of AD. This is a first study that investigate the effect of polymorphic “α‐helix/random coil” and “fibril‐like” Aβ dimers on 1,2‐dioleoyl‐sn‐glycero‐3‐phosphocholine (DOPC) membrane. It has been found that the DOPC membrane promotes Aβ_1–42 “fibril‐like” dimers and impedes Aβ_1–42 “α‐helix/random coil” dimers. The N‐termini domains within Aβ_1–42 dimers play a role in Aβ aggregation in membrane milieus. In addition, the aromatic π–π interactions (involving residues F19 and F20 in Aβ_1–42) are the driving forces for the hydrophobic interactions that initiate the primary nucleation of polymorphic Aβ_1–42 dimers within DOPC membrane. Finally, the DOPC bilayer membrane thickness is locally decreased, and it is disrupted by an embedded distinct Aβ_1–42 dimer, due to relatively large contacts between Aβ_1–42 monomers and the DOPC membrane. This study reveals insights into the molecular mechanisms by which polymorphic early‐stage Aβ_1–42 dimers have distinct impacts on DOPC membrane.     

Kinetics of Diffusion and Convection in 3.2-Å Pores: Exact Solution by Computer Simulation

The kinetics of transport in pores the size postulated for cell membranes has been investigated by direct computer simulation (molecular dynamics). The simulated pore is 11 Å long and 3.2 Å in radius, and the water molecules are modeled by hard, smooth spheres, 1 Å in radius. The balls are given an initial set of positions and velocities (with an average temperature of 313° K) and the computer then calculates their exact paths through the pore. Two different conditions were used at the ends of the pore. In one, the ends are closed and the balls are completely isolated. In the other, the ball density in each end region is fixed so that a pressure difference can be established and a net convective flow produced. The following values were directly measured in the simulated experiments: net and diffusive (oneway) flux; pressure, temperature, and diffusion coefficients in the pore; area available for diffusion; probability distribution of ball positions in the pore; and the interaction between diffusion and convection. The density, viscosity, and diffusion coefficients in the bulk fluid were determined from the theory of hard sphere dense gases. From these values, the “equivalent” pore radius (determined by the same procedure that is used for cell membranes) was computed and compared with the physical pore radius of the simulated pore.     

Evaluation of Spontaneous Reports of Adverse Reactions to Drugs

An adverse drug-reaction monitoring system based on spontaneous reporting to a central register of adverse reactions has been in operation for eight years. As a test of the validity of the reports and of the probability of causal relationship between drug and reaction a random sample of 82 cases were followed up in detail. The sample included 17 deaths, 26 serious reactions, and 39 reactions of moderate or only minor severity. Altogether 78% of the reactions were considered to be “probably” drug related and 13% “possibly” drug related. It is concluded that the reports are of value in the detection and evaluation of drug safety.     

Resolving the Negative Potential Side (n-side) Water-accessible Proton Pathway of F-type ATP Synthase by Molecular Dynamics Simulations

The rotation of F₁F_o-ATP synthase is powered by the proton motive force across the energy-transducing membrane. The protein complex functions like a turbine; the proton flow drives the rotation of the c-ring of the transmembrane F_o domain, which is coupled to the ATP-producing F₁ domain. The hairpin-structured c-protomers transport the protons by reversible protonation/deprotonation of a conserved Asp/Glu at the outer transmembrane helix (TMH). An open question is the proton transfer pathway through the membrane at atomic resolution. The protons are thought to be transferred via two half-channels to and from the conserved cAsp/Glu in the middle of the membrane. By molecular dynamics simulations of c-ring structures in a lipid bilayer, we mapped a water channel as one of the half-channels. We also analyzed the suppressor mutant cP24D/E61G in which the functional carboxylate is shifted to the inner TMH of the c-protomers. Current models concentrating on the “locked” and “open” conformations of the conserved carboxylate side chain are unable to explain the molecular function of this mutant. Our molecular dynamics simulations revealed an extended water channel with additional water molecules bridging the distance of the outer to the inner TMH. We suggest that the geometry of the water channel is an important feature for the molecular function of the membrane part of F₁F_o-ATP synthase. The inclination of the proton pathway isolates the two half-channels and may contribute to a favorable clockwise rotation in ATP synthesis mode.