A channel mechanism for electrogenic ion pumps

Nonequilibrium voltage fluctuations in biological membranes. II. Voltage and current noise generated by ion carriers, channels and electrogenic pumps

As applications of the general theoretical framework of charge transport in biological membranes and related voltage and current noise, a number of model calculations are presented for ion carriers, rigid channels, channels with conformational substates and electrogenic pumps. The results are discussed with special reference to the problem of threshold values for sensory transduction processes and their limitations by voltage fluctuations. Furthermore, starting from the special results of model calculations, an attempt is made to determine more general aspects of electric fluctuations generated by charge-transport processes in biological membranes: different frequency dependences of voltage and current noise, and dependence of noise intensities with increasing distance from the equilibrium state.

Redox-linked proton translocation in cytochrome oxidase: the importance of gating electron flow. The effects of slip in a model transducer

In at least one component of the mitochondrial respiratory chain, cytochrome c oxidase, exothermic electron transfer reactions are used to drive vectorial proton transport against an electrochemical hydrogen ion gradient across the mitochondrial inner membrane. The role of the gating of electrons (the regulation of the rates of electron transfer into and out of the proton transport site) in this coupling between electron transfer and proton pumping has been explored. The approach involves the solution of the steady-state rate equations pertinent to proton pump models which include, to various degrees, the uncoupled (i.e., not linked to proton pumping) electron transfer processes which are likely to occur in any real electron transfer-driven proton pump. This analysis furnishes a quantitative framework for examining the effects of variations in proton binding site pKas and metal center reduction potentials, the relationship between energy conservation efficiency and turnover rate, the conditions for maximum power output or minimum heat production, and required efficiency of the gating of electrons. Some novel conclusions emerge from the analysis, including: An efficient electron transfer-driven proton pump need not exhibit a pH-dependent reduction potential; Very efficient gating of electrons is required for efficient electron transfer driven proton pumping, especially when a reasonable correlation of electron transfer rate and electron transfer exoergonicity is assumed; and A consideration of the importance and possible mechanisms of the gating of electrons suggests that efficient proton pumping by CuA in cytochrome oxidase could, in principle, take place with structural changes confined to the immediate vicinity of the copper ion, while proton pumping by Fea would probably require conformational coupling between the iron and more remote structures in the enzyme. The conclusions are discussed with reference to proton pumping by cytochrome c oxidase, and some possible implications for oxidative phosphorylation are noted.

A chemically explicit model for the molecular mechanism of the F1F0 H+-ATPase/ATP synthases

A general hypothesis for the molecular mechanism of membrane transport based on current knowledge of protein structure and the nature of ligand-induced protein conformational changes has recently been proposed [Scarborough, G. A. (1985) Microbiol. Rev. 49, 214-231]. According to this hypothesis, the essential reaction undergone by all proteinaceous transport catalysts is a ligand-induced hinge-bending-type conformational change that results in the transposition of binding-site residues from access on one side of the membrane to access on the other side. Subsequent release and/or alteration of the ligand or ligands that induce the conformational change facilitates the converse conformational change, which returns the binding-site residues to their original position. With this simple cyclic ligand-dependent gating process as a central feature, biochemically orthodox mechanisms for virtually all known transporters are readily conceived. In this article, a chemically explicit model for the molecular mechanism of the F1F0 H+-ATPase/ATP synthases of mitochondria, bacteria, and chloroplasts, formulated within the guidelines of this general transport paradigm, is presented. At least three points of potential interest arise from this exercise. First, with the aid of the model, it is possible to visualize how energy transduction catalyzed by these enzymes might proceed, with no major events left unspecified. Second, explicit possibilities as to the molecular nature of electric field effects on the transport process are raised. And finally, it is shown that enzyme conformational changes, energy-dependent binding-affinity changes, and several other related phenomena as well, need not be taken as evidence of "action at a distance" or indirect energy coupling mechanisms, as is sometimes assumed, because such events are also integral features of the mechanism presented, even though all of the key reactions proposed for both ATP-driven proton translocation and proton translocation-driven ATP synthesis occur at the enzyme active site.

Interpretation of steady-state current-voltage curves: consequences and implications of current subtraction in transport studies

A problem often confronted in analyses of charge-carrying transport processes in vivo lies in identifying porter-specific component currents and their dependence on membrane potential. Frequently, current-voltage (I-V)--or more precisely, difference-current-voltage (dI-V)--relations, both for primary and for secondary transport processes, have been extracted from the overall membrane current-voltage profiles by subtracting currents measured before and after experimental manipulations expected to alter the porter characteristics only. This paper examines the consequences of current subtraction within the context of a generalized kinetic carrier model for Class I transport mechanisms (U.-P. Hansen, D. Gradmann, D. Sanders and C.L. Slayman, 1981, J. Membrane Biol. 63:165-190). Attention is focused primarily on dI-V profiles associated with ion-driven secondary transport for which external solute concentrations usually serve as the experimental variable, but precisely analogous results and the same conclusions are indicated in relation to studies of primary electrogenesis. The model comprises a single transport loop linking n (3 or more) discrete states of a carrier 'molecule.' State transitions include one membrane charge-transport step and one solute-binding step. Fundamental properties of dI-V relations are derived analytically for all n-state formulations by analogy to common experimental designs. Additional features are revealed through analysis of a "reduced" 2-state empirical form, and numerical examples, computed using this and a "minimum" 4-state formulation, illustrate dI-V curves under principle limiting conditions. Class I models generate a wide range of dI-V profiles which can accommodate essentially all of the data now extant for primary and secondary transport systems, including difference current relations showing regions of negative slope conductance. The particular features exhibited by the curves depend on the relative magnitudes and orderings of reaction rate constants within the transport loop. Two distinct classes of dI-V curves result which reflect the relative rates of membrane charge transit and carrier recycling steps. Also evident in difference current relations are contributions from 'hidden' carrier states not directly associated with charge translocation in circumstances which can give rise to observations of counterflow or exchange diffusion. Conductance-voltage relations provide a semi-quantitative means to obtaining pairs of empirical rate parameters.(ABSTRACT TRUNCATED AT 400 WORDS)

Flow-force relationships for a six-state proton pump model: intrinsic uncoupling, kinetic equivalence of input and output forces, and domain of approximate linearity

General flow-force relations have been determined, by the Hill diagram method, for a six-state proton pump model with and without intrinsic uncoupling (molecular slipping). A computer-aided analysis of the resulting sigmoidal flow-force curves has been performed by using a set of physically meaningful rate constants. It is shown that gating effects and apparent irreversibility can arise from sigmoidicity. The regions of approximate linearity in the vicinity of inflection points, which may be far from equilibrium, have been examined with a view to characterization in terms of linear phenomenological equations, with due regard to the problems of kinetic equivalence of the forces and symmetry. The determination of thermodynamic parameters such as the degree of coupling, the phenomenological stoichiometry, and the efficiency in these regions is discussed, and their meaning is analyzed in relation to the parameters characterizing the Onsager domain close to equilibrium. The application of the phenomenological equations of near-equilibrium nonequilibrium thermodynamics to such regions is at best a simplification to be treated with great caution. A knowledge of the distance from equilibrium of the flow-controlling ranges of the forces (i.e., the ranges of approximate linearity) turns out to be crucial for the interpretation of thermodynamic parameters determined by manipulating one of the forces while the other remains constant, as well as for the interpretation of measurements of force ratios at static head. The latter approaches can give good estimates of the magnitude of the mechanistic stoichiometry and of the constant force if the pumps are highly coupled and are operating not far from equilibrium. The force-flow relationships are shown to be modified by intrinsic uncoupling, reflecting the regulatory influence of the forces on the extent and nature of the slip. Thus reaction slip increases, for example, as the force against which the proton pump operates increases. The possible physiological significance of regulated intrinsic uncoupling is discussed.

Complex membrane transport systems. A non-Markovian approach

This paper suggests a method of how to deal with complex membrane transport systems such as ion channels or ion pumps formed by proteins. The complexity of these systems results from the fact that proteins may undergo an internal dynamics of conformational changes and may thereby affect the transmembrane transport. Usually, complex transport systems are mapped into multi-state graphs and couched in terms of Markovian master equations. It is shown in this paper how the dimensionality of such multi-state systems can be reduced. The resulting description may be expressed in the form of a generalized master equation with a memory function as integral kernel. The memory function reflects the protein's own dynamics and its overall effect on the transport. This formalism, non-Markovian in nature, is applied to describe the time-dependent action of ion pumps. A general model is constructed on the basis of the rate theory which contains all the essential parts of ion pumps such as a catalytic unit and a channel-like conduit for ion translocation and which is still analytically tractable. The short-time behaviour of the pumping process turns out to be of particular interest, since it reveals the dynamics of the catalytic unit itself. A strong correlation of the particle's motion over times less than a certain correlation time has been found. This result is compared with experimental findings on the proton pump of Halobacterium halobium. It is concluded that such a perfect short-time memory could be a generic property of active transport systems.

Simple model can explain self-inhibition of red cell anion exchange

Ion translocation in red cell anion exchange is assumed to occur by means of an alternating access mechanism, in which a critical binding site for the transported ion alternates between two conformational states, each accessible from only one side of the membrane. If this alternating site is located within the transport protein at some distance from one or both surfaces of the membrane, an access channel is required to connect the alternating site to the adjacent bulk solution. This automatically leads to inhibition of transport at high concentrations of the transported ion because release of the ion from the alternating site can occur only via unoccupied channel sites.

Supramolecular organization of lysophosphatidylcholine-packaged Gramicidin A

Heat derived gramicidin A'/L-alpha-lysophosphatidylcholine complexes were separated on a sucrose gradient to form two fractions: Fraction A which had an approximately constant Gramicidin A' to phospholipid ratio of 8 to 10 lipid molecules per Gramicidin A' molecule and Fraction B which had a larger but variable ratio. Fluorescence and circular dichroism studies confirmed Fraction A to be a lipid-incorporated channel state. Electron microscopic studies, using uranyl acetate negative staining, showed fraction A to be a membranous state with the formation of bilayer vesicles, that is, the interaction of peptide and phospholipid micelles causes the lipid to reorganize into a bilayer structure. Freeze-fracture replicas of the channel incorporated state demonstrated the presence of a supramolecular organization of particles exhibiting a tendency to form rows with a 50-60 A periodicity along the row and with 70-80 A distance between rows. An idealized working model for the incorporated state is presented.

Energy coupling to ATP synthesis by the proton-translocating ATPase

This review summarizes recent work on energy coupling to ATP synthesis by the reversible, proton-translocating ATPase to mitochondria, chloroplasts, and bacteria. In the first sections, this enzyme is distinguished from other ATP-linked ion transport systems, and progress in the biochemical analysis is discussed. There is at present a reasonably consistent idea of the overall structure of the enzyme, and one can begin to assign specific functional roles to individual subunits of the complex. The latter half of the review deals with mechanisms of energy coupling, about which there is clear divergence of opinion. An "indirect coupling" model would allow for the possibility that H+ translocation transmits energy for ATP synthesis by driving the enzyme through a sequence of conformational states, so that H+ translocated need not take part in the chemistry of ATP synthesis. By contrast, a "direct coupling" mechanism would specify that H+ translocated must participate in the chemical reaction by combining with oxygen must participate in the chemical reaction by combining with oxygen from phosphate during the synthetic step. Such discussion is preceded by an outlined of the "proton well," since this idea forms the basis of one direct coupling model. In addition, it is suggested that the idea of a proton (ion) well may be of more general significance to the analysis of ion-coupled transport, because it includes the postulate that mechanistically significant ion binding can occur within the profile of the electric field. A proton (ion) well can be derived from both kinetic and equilibrium treatments, and from mechanistic considerations in fields as distinct as biochemistry and neurophysiology. As a result, it illustrates how further advances in formulating mechanisms of energy coupling might profit by a merger of technique and perspective from areas that have as a common goal an understanding of how large proteins catalyze movements of small molecules across a membrane.

Electrogenic proton transport in epithelial membranes

Certain polar epithelial cells have strong transport capacities for protons and can be examined in vitro as part of an intact epithelial preparation. Recent studies in the isolated turtle bladder and other tight urinary epithelial indicate that the apical membranes of the carbonic anhydrase-containing cell population of these tissues contain an electrogenic proton pump which has the characteristics of a proton-translocating ATPase. The translocation of protons is tightly coupled to the energy of ATP hydrolysis. Since the pump translocates protons without coupling to the movement of other ions, it may be regarded as an "ideal" electrogenic pump. The apparent simplicity of the functional properties has led to extensive studies of the characteristics of this pump and of the cellular organization of the secondary acid-base flows in the turtle bladder. Over a rather wide range of electrochemical potential gradients, for protons (delta approximately microH) across the epithelium, the rate of H+ transport is nearly linear with delta approximately microH. The formalisms of equivalent circuit analysis and nonequilibrium thermodynamics have been useful in describing the behavior of the pump, but these approaches have obvious limitations. We have attempted to overcome some of these limitations by developing a more detailed set of assumptions about each of the transport step across the pump complex and to formulate a working model for proton transport in the turtle bladder than can account for several otherwise unexplained experimental results. The model suggests that the real pump is neither a simple electromotive force nor a constant current source. Depending on the conditions, it may behave as one or the other.

The transport of cations in mitochondria

The present paper has reviewed several factors related to ion transport and examined the properties of cation transport in mitochondria. The analysis suggests that: (1) The concept that a metabolically dependent electrical potential across the mitochondrial membrane plays a role in determining ion fluxes and steady-state concentrations is not justified and the data indicate that such exchanges are generally electroneutral. (2) Generally, the influx and efflux of an ion proceed by the same mechanism with at least one exception. (3) There are indications that some of the steps in transport are common to several cations. (4) The idea that carrier or ionophoric molecules are involved in cation transport has been examined in some detail together with the possible involvement of some known mitochondrial components. In particular, a model has been introduced in which local charge imbalances produced by H+ fluxes serve as the driving force of transport. The molecules of the complex are arranged in series in a tripartite arrangement including a filter or gate, a nonselective channel and an H+-transferring portion linked to either electron transport or the ATPase. Parts of this model have been introduced by other investigators. Models in which different portions of channels have differing functions have been proposed previously for other transport systems.

Interpretation of current-voltage relationships for "active" ion transport systems: I. Steady-state reaction-kinetic analysis of class-I mechanisms

This paper develops a simple reaction-kinetic model to describe electrogenic pumping and co- (or counter-) transport of ions. It uses the standard steady-state approach for cyclic enzyme- or carrier-mediated transport, but does not assume rate-limitation by any particular reaction step. Voltage-dependence is introduced, after the suggestion of Läuger and Stark (Biochim. Biophys. Acta 211:458-466, 1970), via a symmetric Eyring barrier, in which the charge-transit reaction constants are written as k12 = ko12 exp(zF delta psi/2RT) and k21 = ko21 exp(-zF delta psi/2RT). For interpretation of current-voltage relationships, all voltage-independent reaction steps are lumped together, so the model in its simplest form can be described as a pseudo-2-state model. It is characterized by the two voltage-dependent reaction constants, two lumped voltage-independent reaction constants (k12, k21), and two reserve factors (ri, ro) which formally take account of carrier states that are indistinguishable in the current-voltage (I-V) analysis. The model generates a wide range of I-V relationships, depending on the relative magnitudes of the four reaction constants, sufficient to describe essentially all I-V datas now available on "active" ion-transport systems. Algebraic and numerical analysis of the reserve factors, by means of expanded pseudo-3-, 4-, and 5-state models, shows them to be bounded and not large for most combinations of reaction constants in the lumped pathway. The most important exception to this rule occurs when carrier decharging immediately follows charge transit of the membrane and is very fast relative to other constituent voltage-independent reactions. Such a circumstance generates kinetic equivalence of chemical and electrical gradients, thus providing a consistent definition of ion-motive forces (e.g., proton-motive force, PMF). With appropriate restrictions, it also yields both linear and log-linear relationships between net transport velocity and either membrane potential or PMF. The model thus accommodates many known properties of proton-transport systems, particularly as observed in "chemiosmotic" or energy-coupling membranes.

Fast stages of photoelectric processes in biological membranes. I. Bacteriorhodopsin

Bacteriorhodopsin-containing fragments of Halobacterium halobium membrane (bacteriorhodopsin sheets) were incorporated into a lecithin-impregnated collodion film, and fast stages of flash-induced electrogenesis were measured by two electrodes separated by this film. It is found that a single turnover of bacteriorhodopsin results in an electrogenic response composed of three main stages of the following tau: the first less than 200 ns, the second 15 - 70 microseconds and the third 10 ms. The second and third phases are of the same direction as an electric response to continuous illumination, whereas the first one is oppositely directed. The microseconds and ms stages were shown to correlate, in the first approximation, with formation and decomposition of the bacteriorhodopsin intermediate absorbing with 412 nm, respectively. Both the second and third phases of the photoelectric response are sums of at least two exponents. The third stage is specifically inhibition by La3+ ions which are also shown to decrease the rate of regeneration of the original bacteriorhodopsin absorbing at 570 nm from the intermediate absorbing at 412 nm. Acidification of the medium induces parallel inhibition of the second and third phases and of formation of the intermediate absorbing at 412 nm as if protonation of a group with pK = 3.6 were responsible for this inhibition. The first (opposite) phase survives acidification. It even increases at pH lower than 1.5. At such a low pH, one can show a good correlation of decays of photopotential and of a bacteriorhodopsin bathointermediate. The decays are biphasic (tau 1 = 200 microseconds and tau 2 = 2 ms), formation of both the photopotential and the bathointermediate being faster than 200 ns. At higher pH, when a three-phase photoelectric response is revealed, decay of the formed electric potential difference gives the average tau value of about 1 s. It can be accelerated by compounds that increase ionic conductance of biomembranes. At pH below 4, fluoride is found to completely inhibit the second and third phases, so that only the first phase is observed. The results are discussed in terms of a scheme postulating that the first electrogenic phase is a result of translocation of the protonated Schiff base inside the membrane due to a light-induced conformation change in retinal or protein. The second and third phases are explained by H+ transfer from the Schiff base to the outer membrane surface and from inner (cytoplasmic) surface of membrane to the Schiff base, respectively.

Quantum chemical studies of proton transport through biomembranes

A proposed mechanism of proton transport through biological membranes was investigated with the aid of ab initio molecular orbital methods. It requires the existence within a transmembrane protein of a hydrogen-bonded chain of residues. The full transport process was broken down into a number of simpler steps, each of which involves the transfer of a proton from one residue to the next along the chain. The hydroxyl-containing residues were modeled by water molecules. Linear hydrogen-bonded systems H+ (H2O)n, n = 2, 3, 4, 5 were studied using the 4-31G basis set. The dimer was shown to furnish an excellent model for study of proton transfer in larger systems. Deformations of the hydrogen bond lead to large increases in the energy barrier to proton transfer. Certain properties of the electron density distribution show a close correspondence with transfer energetics; consequently, they may have some predictive use. The transition state to double proton transfer in the trimer and pentamer involve partial transfer of only one proton. Implications of the above observations upon the proposed mechanism were discussed.

Competitive membrane adsorption of Na+, K+, and Ca2+ in smooth muscle cells

A theory for Na+, K+ and Ca2+ competitive adsorption to a charged membrane is used to explain a number of experimental observations in smooth muscle. Adsorption is described by Langmuir isotherms for mono- and divalent cations which in turn are coupled in a self-consistent way to the bulk solution through the diffuse double layer theory and the Boltzman equations. We found that the dissociation constants for binding of Na+, K+ and Ca2+ in guinea pig taenia coli are ca. 0.009, 1.0, and 4 X 10(-8) M, respectively. Furthermore, the effect of a Ca2+ pump that maintains free surface Ca2+ concentration constant is investigated. A decrease in intracellular Na+ content results in an increased Ca2+ uptake; part of this uptake is due to an increase in surface-bound Ca2+ in an intracellular compartment which is in contact with the myofilaments. Variations in the amount of charge available to bind Ca2+ and the surface charge density are studied and their effect interpreted in terms of different pharmacological agents.

Photocurrent response of bacteriorhodopsin adsorbed on bimolecular lipid membranes

The photo response of bacteriorhodopsin adsorbed on a bimolecular lipid membrane has been investigated using short-circuit current measurements. The results revealed a biphasic current vs. time curve for the photocurrent at pH values of approx. 7. This phenomenon could be modified by altering either the value of the external applied electrical field or the proton concentration differences. The observed effects of the external applied voltage, pH gradient and lipophilic proton carriers enabled us to conclude that the bacteriorhodopsin can be adsorbed in two different states, which give rise to a pumping effect and a flux of protons in opposite directions. A theoretical analysis of the photocycle in relation to the electrical field which acts on the proton uptake and release is proposed. The main effect of this field is to diminish the pumping rate due to the proton motive force resulting from the creation of space-charge in the vicinity of purple membrane fragments.