Models for the active transport of cations...the steady-state analysis

New free-exchange model of EmrE transport

EmrE is a small multidrug resistance transporter found in Escherichia coli that confers resistance to toxic polyaromatic cations due to its proton-coupled antiport of these substrates. Here we show that EmrE breaks the rules generally deemed essential for coupled antiport. NMR spectra reveal that EmrE can simultaneously bind and cotransport proton and drug. The functional consequence of this finding is an exceptionally promiscuous transporter: not only can EmrE export diverse drug substrates, it can couple antiport of a drug to either one or two protons, performing both electrogenic and electroneutral transport of a single substrate. We present a free-exchange model for EmrE antiport that is consistent with these results and recapitulates ∆pH-driven concentrative drug uptake. Kinetic modeling suggests that free exchange by EmrE sacrifices coupling efficiency but boosts initial transport speed and drug release rate, which may facilitate efficient multidrug efflux.

Allosteric Mechanisms of Molecular Machines at the Membrane: Transport by Sodium-Coupled Symporters

Solute transport across cell membranes is ubiquitous in biology as an essential physiological process. Secondary active transporters couple the unfavorable process of solute transport against its concentration gradient to the energetically favorable transport of one or several ions. The study of such transporters over several decades indicates that their function involves complex allosteric mechanisms that are progressively being revealed in atomistic detail. We focus on two well-characterized sodium-coupled symporters: the bacterial amino acid transporter LeuT, which is the prototype for the "gated pore" mechanism in the mammalian synaptic monoamine transporters, and the archaeal GltPh, which is the prototype for the "elevator" mechanism in the mammalian excitatory amino acid transporters. We present the evidence for the role of allostery in the context of a quantitative formalism that can reconcile biochemical and biophysical data and thereby connects directly to recent insights into the molecular structure and dynamics of these proteins. We demonstrate that, while the structures and mechanisms of these transporters are very different, the available data suggest a common role of specific models of allostery in their functions. We argue that such allosteric mechanisms appear essential not only for sodium-coupled symport in general but also for the function of other types of molecular machines in the membrane.

Simulating the function of sodium/proton antiporters

The molecular basis of the function of transporters is a problem of significant importance, and the emerging structural information has not yet been converted to a full understanding of the corresponding function. This work explores the molecular origin of the function of the bacterial Na+/H+ antiporter NhaA by evaluating the energetics of the Na+ and H+ movement and then using the resulting landscape in Monte Carlo simulations that examine two transport models and explore which model can reproduce the relevant experimental results. The simulations reproduce the observed transport features by a relatively simple model that relates the protein structure to its transporting function. Focusing on the two key aspartic acid residues of NhaA, D163 and D164, shows that the fully charged state acts as an Na+ trap and that the fully protonated one poses an energetic barrier that blocks the transport of Na+. By alternating between the former and latter states, mediated by the partially protonated protein, protons, and Na+ can be exchanged across the membrane at 2:1 stoichiometry. Our study provides a numerical validation of the need of large conformational changes for effective transport. Furthermore, we also yield a reasonable explanation for the observation that some mammalian transporters have 1:1 stoichiometry. The present coarse-grained model can provide a general way for exploring the function of transporters on a molecular level.

Keeping it simple, transport mechanism and pH regulation in Na+/H+ exchangers

Na⁺/H⁺ exchangers are essential for regulation of intracellular proton and sodium concentrations in all living organisms. We examined and experimentally verified a kinetic model for Na⁺/H⁺ exchangers, where a single binding site is alternatively occupied by Na⁺ or one or two H⁺ ions. The proposed transport mechanism inherently down-regulates Na⁺/H⁺ exchangers at extreme pH, preventing excessive cytoplasmic acidification or alkalinization. As an experimental test system we present the first electrophysiological investigation of an electroneutral Na⁺/H⁺ exchanger, NhaP1 from Methanocaldococcus jannaschii (MjNhaP1), a close homologue of the medically important eukaryotic NHE Na⁺/H⁺ exchangers. The kinetic model describes the experimentally observed substrate dependences of MjNhaP1, and the transport mechanism explains alkaline down-regulation of MjNhaP1. Because this model also accounts for acidic down-regulation of the electrogenic NhaA Na⁺/H⁺ exchanger from Escherichia coli (EcNhaA, shown in a previous publication) we conclude that it applies generally to all Na⁺/H⁺ exchangers, electrogenic as well as electroneutral, and elegantly explains their pH regulation. Furthermore, the electrophysiological analysis allows insight into the electrostatic structure of the translocation complex in electroneutral and electrogenic Na⁺/H⁺ exchangers.

The structural basis of secondary active transport mechanisms

Secondary active transporters couple the free energy of the electrochemical potential of one solute to the transmembrane movement of another. As a basic mechanistic explanation for their transport function the model of alternating access was put forward more than 40 years ago, and has been supported by numerous kinetic, biochemical and biophysical studies. According to this model, the transporter exposes its substrate binding site(s) to one side of the membrane or the other during transport catalysis, requiring a substantial conformational change of the carrier protein. In the light of recent structural data for a number of secondary transport proteins, we analyze the model of alternating access in more detail, and correlate it with specific structural and chemical properties of the transporters, such as their assignment to different functional states in the catalytic cycle of the respective transporter, the definition of substrate binding sites, the type of movement of the central part of the carrier harboring the substrate binding site, as well as the impact of symmetry on fold-specific conformational changes. Besides mediating the transmembrane movement of solutes, the mechanism of secondary carriers inherently involves a mechanistic coupling of substrate flux to the electrochemical potential of co-substrate ions or solutes. Mainly because of limitations in resolution of available transporter structures, this important aspect of secondary transport cannot yet be substantiated by structural data to the same extent as the conformational change aspect. We summarize the concepts of coupling in secondary transport and discuss them in the context of the available evidence for ion binding to specific sites and the impact of the ions on the conformational state of the carrier protein, which together lead to mechanistic models for coupling.

Coupling of secondary active transport with a deltamu-H+

Most nutrients and ions in bacteria, yeasts, algae, and plants are transported uphill at the expense of a gradient of the electrochemical potential of protons deltamu-H+ (a type of secondary active transport). Diagnosis of such transports rests on the determination of the transmembrane electrical potential difference deltapsi and the difference of pH at the two membrane sides. The behavior of kinetic parameters K(T) (the half-saturation constant) and J(max), (the maximum rate of transport) upon changing driving ion concentrations and electrical potentials may be used to determine the molecular details of the transport reaction. Equilibrium accumulation ratios of driven solutes are expected to be in agreement with the deltapsi and deltapH measured independently, as well as with the Haldane-type expression involving K(T) and J(max). Different stoichiometries of H+/solute, as well as intramembrane effects of pH and deltapsi, may account for some of the observed inconsistencies.

Cellular transport processes of aminoguanidine, a nitric oxide synthase inhibitor, in the opossum kidney cell culture line

Aminoguanidine has potential pharmacologic utility for diabetes and nitric oxide - mediated inflammation. Because aminoguanidine is positively charged at physiologic pH (pK(a) approximately 10), it is unlikely that simple diffusion is a predominant mechanism for cellular penetration. This study sought to determine the transport processes by which aminoguanidine, a cationic compound, traverses across cellular membranes. In cultured opossum kidney (OK) cell monolayers, aminoguanidine transport involved both saturable and non-saturable diffusion processes. At passage numbers below 67, the observed V(max) and K(m) for saturable influx were significantly lower than that observed at passages greater than 79 (V(max): low passage, 21.2+/-7.8 pmol/(min*mg protein), n=3; versus high passage, 129.7+/-24.3 pmol/(min*mg protein), n=3, P<0.05; K(m): low passage, 23.7+/-10.8 microM, n=3; versus high passage, 101.7+/-5.6 microM, n=3, P<0.05; mean+/-S.E.M.). Nonsaturable processes were not statistically different (k(ns): low passage, 1.6+/-0.1 pmol/(min*mg protein*microM), n=3; high passage, 1.1+/-0.2 pmol/(min*mg protein*microM) n=3). Saturable influx was temperature dependent, and independent of ATP energy, sodium gradients or changes in membrane potential. Other organic cations competitively inhibited and trans-stimulated saturable influx. Aminoguanidine influx was increased in the presence of an outwardly-directed proton gradient and was inhibited in the presence of an inwardly-directed proton gradient. Correspondingly, aminoguanidine efflux was trans79) express a saturable, bi-directional carrier-mediated process to transport aminoguanidine across cellular membranes.

Control analysis of enzyme mechanisms in terms of the classical steady-state description

The algebraic rate equations of steady-state enzyme kinetics generally allow the derivation of analytical expressions for the distribution of rate control among the elementary reactions defined by the kinetic mechanism. It is shown that these analytical expressions complete the macroscopic (probabilistic) description of enzyme-catalysed chemical reactions without involving any assumption at the microscopic (molecular) level. By also surveying some directly relevant results of the graph theoretical treatment of enzyme mechanisms, it is shown that control analysis is an integral part of steady-state enzyme kinetics.

Interpreting the effects of site-directed mutagenesis on active transport systems

Single amino acid substitutions in the lactose permease of Escherichia coli are known to elicit behaviour, such as the transformation of an active into a passive system, not explained by current co-transport models. The behaviour, it is shown, can be explained by an expanded reaction scheme that takes account of the required alternation of the carrier, in the course of the coupled reaction, between mobile and immobile conformations or between conformations that bind either only one substrate or both substrates. The extended model links such behaviour to altered conformational equilibria or binding regions. Thus, mutations that affect the equilibrium between a mobile one-site conformation of the free carrier and an immobile conformation having sites for both substrates allow passive transport of the second substrate in an ordered mechanism, and mutations in a secondary substrate binding region that affects this conformational change allow passive transport of the first substrate. Mutations in regions interacting with a substrate in the transition state in carrier movement, as well as in the initial binding sites, can also be distinguished. The analysis applies to both primary and secondary active transport.

The application of vectorial coupling theory to the calcium pump

Models for the calcium pump of the E1E2 type appear to be inconsistent with new evidence for the binding of internal and external calcium ions, simultaneously, to the free pump. The models are shown here to be incomplete but not necessarily wrong; they omit the required modulation of the mobility, specificity, and enzyme activity of the pump, which is brought about through substrate-controlled conformational changes. A reaction scheme based on the E1E2 model but incorporating the conformational equilibria in question is shown to account for a variety of experimental findings, including those at odds with the simple model: (i) binding of lumenal Ca2+ to the free as well as the phosphorylated pump; (ii) uncoupled exit of lumenal Ca2+ at high concentrations; (iii) the absence of any effect of lumenal Ca2+ on the binding of external Ca2+; (iv) uncoupled ATPase activity in dimethyl sulfoxide.

Coupling mechanisms in ATP-driven pumps

Because the kinetic reaction schemes for primary and secondary active transport can be identical, the same fundamental relationship holds among rate and equilibrium constants: the ratio of coupled to uncoupled flux is no greater than the ratio of substrate dissociation constants in an initial complex and a conformationally altered state. Further, the role played by each substrate in coupling depends in the same way on its order of addition to the carrier. It follows that the structural principles governing the design and operation of the carrier proteins are fundamentally alike. In either system, the strict control of the mobility and specificity of the carrier, a prerequisite for active transport, depends on the utilization of substrate binding forces to alter the protein conformation; and whether the driving substrate is transported or not and whether reversibly bound or covalently bound (like the phosphate group derived from ATP), the force producing the conformational change is derived from non-covalent interactions between the substrate (held at the substrate site) and other sections of the protein. The protein probably encloses the substrate, with a resulting increase in the binding force; the favourable energy of interaction balances the unfavourable energy involved in distorting the protein structure. The postulated complex can account for the 'occluded state' of transported cations and for the favourable reaction of inorganic phosphate with the calcium pump.

Coupling mechanisms in active transport

In primary and secondary active transport, the mobility and specificity of the carrier are controlled, over the course of the transport reaction, in accordance with a set of 'rules'. The rules are shown to depend on two mechanisms: a substrate--either the driving substrate (a transported ion or ATP) or the driven substrate--may shift a conformational equilibrium or accelerate a rate-limiting conformational change. From an analysis of coupling mechanisms the following conclusions emerge. (i) The ratio of coupled to uncoupled flux, which should be large, cannot be greater than the ratio of substrate dissociation constants in an initial complex and a conformationally altered state. A minimum value for the increased binding force can be estimated from steady-state constants. (ii) In an ordered mechanism, slippage is expected at high concentrations of the substrate adding to the carrier second, while slippage of the first substrate should remain low. (iii) Slippage in coupled transport is minimized if the driven substrate is last on in loading the carrier and last off in unloading, while the reverse order makes the affinity high in loading and low in unloading, as required for efficient transfer from one compartment to another; hence the preferred mechanism may depend on prevailing physiological conditions. (iv) A coupled transport system can be transformed into a facilitated system for one substrate or both if the control of carrier mobility is undermined through modification of the carrier.

Presteady-state kinetics and carrier-mediated transport: a theoretical analysis

Kinetic studies of cotransport mechanisms have so far been limited to the conventional steady-state approach which does not allow in general to resolve either isomerization or rate-limiting steps and to determine the values of the individual rate constants for the elementary reactions involved along a given transport pathway. Such questions can only be answered using presteady-state or relaxation experiments which, for technical reasons, have not yet been introduced into the field of cotransport kinetics. However, since two recent reports seem compatible with the observation of such transient kinetics, it would appear that theoretical studies are needed to evaluate the validity of such claims and to critically evaluate the expectations from a presteady-state approach. We thus report such a study which was performed on a simple four-state mechanism of carrier-mediated transport. The time-dependent equation for zero-trans substrate uptake was thus derived and then extended to models with p intermediary steps. It is concluded that (p-1) exponential terms will describe the approach to the steady state but that such equations have low analytical value since the parameters of the flux equation cannot be expressed in terms of the individual rate constants of the elementary reactions for models with p greater than 5. We thus propose realistic simplifications based on the time-scale separation hypothesis which allows replacement of the rate constants of the rapid steps by their equilibrium constants, thereby reducing the complexity of the kinetic system. Assuming that only one relaxation can be observed, this treatment generates approximate models for which analytical expressions can easily be derived and simulated through computer modeling. When performed on the four-state mechanism of carrier-mediated transport, the simulations demonstrate the validity of the approximate solutions derived according to this hypothesis. Moreover, our approach clearly shows that presteady-state kinetics, should they become applicable to (co)transport kinetics, could be invaluable in determining more precise transport mechanisms.

Nonequilibrium voltage fluctuations in biological membranes. I. General framework of charge transport in discrete systems and related voltage noise

This paper continues our work on the theory of nonequilibrium voltage noise generated by electric transport processes in membranes. Introducing the membrane voltage as a further variable, a system of kinetic equations linearized in voltage is derived by which generally the time-dependent behaviour of charge-transport processes under varying voltage can be discussed. Using these equations, the treatment of voltage noise can be based on the usual master equation approach to steady-state fluctuations of scalar quantities. Thus, a general theoretical approach to nonequilibrium voltage noise is presented, completing our approach to current fluctuations which had been developed some years ago. It is explicitly shown that at equilibrium the approach yields agreement with the Nyquist relation, while at nonequilibrium this relation is not valid. A further general property of voltage noise is the reduction of low-frequency noise with increasing number of transport units as a consequence of the interactions via the electric field. In a second paper, the approach will be applied for a number of special transport mechanisms, such as ionic channels, carriers or electrogenic pumps.

The thermostatics and thermodynamics of cotransport

The thermostatics of cotransport are reviewed. A static-head equilibrium state across a cotransport system, without leaks, is thought to occur when the electrochemical potential of the driven solute, B prevents net flow of the driving solute, A. For a symport this gives the relationship (formula: see text) Where n is the stoichiometric coefficient, namely the number of moles of A transported per mole of B. (2) If either a symporter with a 2:1 stoichiometric coefficient and a 1:1 symporter, or alternatively, a 1:1 symporter and a 1:1 antiporter are placed in a series membrane array, then the predicted static-head equilibrium across the entire array conflicts with the zeroth law of thermodynamics. (3) There are two major reasons for this failure of cotransport theory; these are: (A) the thermostatic relationships derived shown in Point 1 are based on the assumption that the cotransport process takes place within a closed system. However, the membrane and the external reservoirs are open to the cotransported ligands. It follows that A and B in the external reservoirs can vary independently of the changes within the cotransport process. As no chemical reaction between A and B occurs in the external solutions, reactions within the membrane phase do not affect the equilibrium between the transported ligands in the open reservoirs. (B) It is assumed that the law of mass action can be applied to the cotransport chemical reactions within the membrane phase, without any allowance for the fact that these reactions occur within a 'small thermodynamic system'. Any proper analysis of the chemical potential of the transported intermediate must consider the effects of lower order ligand-carrier forms, which coexist and compete for space with the higher order cotransported forms on the binding matrix. If account is taken of this necessity, then a simple extension of the work of Hill and Kedem (1966) J. Theor. Biol. 10, 399-441 shows that: (a) the static-head equilibrium state cannot exist; (b) the stoichiometry of cotransport, whether symport, or antiport, does not affect the static-head distribution of cotransported ligands; (c) the hypothetical net charge of the transported ligand-carrier complex does not affect static-head equilibrium; (d) the only equilibrium state where there is zero net flow of both driving and driven transported ligand is at true equilibrium when the ligands are uniformly distributed across the membrane. (4) It is deduced that cotransport is not entirely an affinity-driven, but is partially an entropy-driven process.(ABSTRACT TRUNCATED AT 400 WORDS)

Hydrogen ion dependence of carrier-mediated auxin uptake by suspension-cultured crown gall cells

1. The dependence on external hydrogen ion concentration of the carrier-mediated components of the uptakes of indol-3-yl acetic acid (IAA) and 2,4-dichlorophenoxyacetic acid (2,4D) by suspension-cultured crown gall cells from Parthenocissus tricuspidata Planch. is examined. The initiall rates of uptake of IAA and 2,4 D from 0.30 μmol/l solutions exhibit pH optima of approximately pH 5.0 and pH 4.0 respectively.-2. The inherent difficulties, especially at low pH, of estimating the carrier-mediated uptake component in the presence of the large diffusive uptake of undissociated acid are discussed.-3. At pH 5.0, the uptakes of the two auxins are characterised by similar "Michaelis Constants" (0.65 and 0.80 μmol/l) and "Maximum Velocities" (0.87 and 1.0 pmol/min/mg cells) for IAA and 2,4D respectively.-4. A dependence of carrier-mediated auxin uptake on cations other than hydrogen ions could not be demonstrated. It is suggested that uptake of auxin anions may occur by co-transport with hydrogen ions.