Simple Carrier Kinetics in Complex Membrane Transporters

The four-state simple carrier model (SCM) has been employed to describe facilitative transport of ligands across biological membranes. Two basic mechanisms have been invoked to account for carrier-mediated ligand translocation: (i) binding to a mobile carrier, and (ii) displacement determined by conformational changes of an integral protein. While translatory carriers may be accurately represented by a four-state diagram, it is unlikely that the transport process mediated by a complex membrane protein can be strictly described by the elementary SCM. The purpose of this article is to test whether facilitative transporters with a more complex kinetic design than the SCM can exhibit macroscopic kinetic properties indistinguishable from it. For this, I studied a ``general carrier model' (GCM), and evaluated whether the relevant kinetic parameters are subject to the same basic restrictions as in the SCM. The fundamental finding is that there is a general kinetic design embodied with SCM-like properties, that can be shared by many transporters. In particular, the classical SCM is shown here to represent a particular case of the GCM. A main conclusion of this work is therefore that the finding of a macroscopic SCM-like kinetic behavior for a particular process of facilitative transport does not represent a sufficient argument in favor of a particular type of mechanism, like the typical one involving a two-conformational single-site carrier. Received: 9 February 1998/Revised: 19 June 1998     

A General Channel Model Accounts for Channel,Carrier, Countertransport and Cotransport Kinetics

In this work we propose a unifying model of mediated membrane transport, based upon the idea that the integral membrane proteins involved in these processes operate via complex channel mechanisms. In the first part, we briefly review literature about the structural aspects of membrane transporters. We conclude that there is a substantial amount of evidence suggesting that most membrane proteins performing transport are embodied with channel-like structures that may constitute the translocation paths. This includes cases where the phenomenological transport kinetics do not correspond to the classical channel behavior. In the second part of this article we introduce the general channel model of mediated transport and employ it to derive specific examples, like simple one- or two-ligand channels, water-ligand channels, simple carriers, co- and counter-transport systems and more complex water-ligand carriers. We show that, for the most part, these particular cases can be obtained by the application of the techniques of diagram reduction to the full model. The necessary conditions for diagram reduction reflect physical properties of the protein and its surroundings.     

Modeling Facilitative Sugar Transporters: Transitions Between Single and Double Ligand Occupancy of Multiconformational Channel Models Explain Anomalous Kinetics

The four-state simple carrier model (SCM) is employed to describe ligand translocation by diverse passive membrane transporters. However, its application to systems like facilitative sugar transporters (GLUTs) is controversial: unidirectional fluxes under zero-trans and equilibrium-exchange experimental conditions fit a SCM, but flux data from infinite-cis and infinite-trans experiments appear not to fit the same SCM. More complex kinetic models have been proposed to explain this ``anomalous' behavior of GLUTs, but none of them accounts for all the experimental findings. We propose an alternative model in which GLUTs are channels subject to conformational transitions, and further assume that the results from zero-trans and equilibrium-exchange experiments as well as trans-effects corresponds to a single-occupancy channel regime, whereas the results from the infinite-cis and infinite-trans experiments correspond to a regime including higher channel occupancies. We test the plausibility of this hypothesis by studying a kinetic model of a two-site channel with two conformational states. In each state, the channel can bind the ligand from only one of the compartments. Under single-occupancy, for conditions corresponding to zero-trans and equilibrium-exchange experiments, the model behaves as a SCM capable of exhibiting trans-stimulations. For a regime including higher degrees of occupancy and infinite-cis and infinite-trans conditions, the same channel model can exhibit a behavior qualitatively similar to a SCM, albeit with kinetic parameters different from those for the single-occupancy regime. Numerical results obtained with our model are consistent with available experimental data on facilitative glucose transport across erythrocyte membranes. Hence, if GLUTs are multiconformational channels, their particular kinetic properties can result from transitions between single and double channel occupancies. Received: 12 April 1995/Revised: 28 August 1995     

Differential Transmembrane Diffusion of Triiodothyronine and Thyroxine in Liposomes: Regulation by Lipid Composition

How thyroid hormones move across biological or model membranes is a subject of controversy. The passage of the 3,5,3′triiodo l-thyronine and 3,5,3′,5′ tetraiodo l-thyronine across model membranes was evaluated by the addition of the hormones to liposomes containing 2,4,6-trinitrobenzene sulfonic acid. Results indicate that hormones can react with an amino-reactive compound pre-encapsulated into phosphatidylcholine liposomes. The transversal motions of thyroid hormones were characterized by using physiological concentration levels of (¹²⁵I) 3,5,3′triiodo l-thyronine and (¹²⁵I) 3,5,3′,5′ tetraiodo l-thyronine. The hormone distribution between the two monolayers was time-dependent and kinetic data were fitted to a single exponential. Results obtained show that 3,5,3′ triiodo l-thyronine can permeate phospholipid membranes and the diffusion time increases in the gel and liquid-ordered phase. On the contrary, 3,5,3′, 5′ tetraiodo l-thyronine could not diffuse the liposomal membrane from dimyristoyl and dipalmitoyl phosphatidylcholine in gel phase and egg yolk phosphatidylcholine:cholesterol in the liquid-ordered phase. Our results in the liquid-ordered phase suggest that diffusion movement of thyroid hormones across cell membranes depends on the amount of cholesterol in the bilayer. Received: 1 June 1998/Revised: 14 October 1998     

Kinetic Analysis of Ca2+/K+ Selectivity of an Ion Channel by Single-Binding-Site Models

Current-voltage relationships of a cation channel in the tonoplast of Beta vulgaris, as recorded in solutions with different activities of Ca²⁺ and K⁺ (from Johannes & Sanders 1995, J. Membrane Biol. 146:211–224), have been reevaluated for Ca²⁺/K⁺ selectivity. Since conversion of reversal voltages to permeability ratios by constant field equations is expected to fail because different ions do not move independently through a channel, the data have been analyzed with kinetic channel models instead. Since recent structural information on K⁺ channels show one short and predominant constriction, selectivity models with only one binding site are assumed here to reflect this region kinetically. The rigid-pore model with a main binding site between two energy barriers (nine free parameters) had intrinsic problems to describe the observed current-saturation at large (negative) voltages. The alternative, dynamic-pore model uses a selectivity filter in which the binding site alternates its orientation (empty, or occupied by either Ca²⁺ or K⁺) between the cytoplasmic side and the luminal side within a fraction of the electrical distance and in a rate-limiting fashion. Fits with this model describe the data well. The fits yield about a 10% electrical distance of the selectivity filter, located about 5% more cytoplasmic than the electrical center. For K⁺ translocation, reorientation of the unoccupied binding site (with a preference of about 6:5 to face the lumenal side) is rate limiting. For Ca²⁺, the results show high affinity to the binding site and low translocation rates (<1% of the K⁺ translocation rate). With the fitted model Ca²⁺ entry through the open channel has been calculated for physiological conditions. The model predicts a unitary open channel current of about 100 fA which is insensitive to cytoplasmic Ca²⁺ concentrations (between 0.1 and 1 μm) and which shows little sensitivity to the voltage across the tonoplast. Received: 19 February 1997/Revised: 19 May 1997     

Relations Between the Stage of Cell Maturation and Lactate Transporter Activities in Rat Neonatal Muscle Cells in Culture

Lactate transport was investigated in newborn rat muscle cells in culture. The aim was to study the lactate transport function at two stages of cell differentiation in culture: (i) during the proliferative phase characterized by myoblasts and myotubes (MyB/MyT2) obtained after 2–3 seedings, (ii) when myotubes (MyT1) grow old in culture after 8–9 seedings. In both developmental stages MyB/MyT2, lactate was carried following a saturable and sigmoidal velocity curve: the Hill and the Scatchard plot analyses confirmed an allosteric or multisite mechanism of lactate transport with two classes of carriers: one of low and one of high affinity i.e., 8.6 and 0.95 mm, respectively, which are associated with high and low transport capacities (V _m ) i.e., 9.1 and 0.67 nm/min/mg, respectively. With MyT1, the velocity curve of lactate transport presented a hyperbolic profile, and the Hill plot analysis gave a Hill number near one suggesting that for cell aging in culture the decrease in cooperativity shows that lactate transport essentially occurs through the low affinity transport system. Inhibitor effects also contributed to evidence for at least two systems of transport. Results obtained from primary cells give evidence for the early activity of lactate transport system at the Myb/MyT2 stage and its evolution during cell aging in culture (MyT1). Sarcolemmal lactate transport in primary cultures of myocytes is accomplished by multiple carriers, neither of which are MCT1 or MCT2 as confirmed by immunoblots. Received: 31 March 1999/Revised: 22 September 1999     

Characterization of Inverted Membrane Vesicles from the Halophilic Archaeon Haloferax volcanii

Membrane-related processes in archaea, the third and most-recently described domain of life, are in general only poorly understood. One obstacle to a functional understanding of archaeal membrane-associated activities corresponds to a lack of archaeal model membrane systems. In the following, characterization of inverted archaeal membrane vesicles, prepared from the halophilic archaeon Haloferax volcanii, is presented. The inverted topology of the vesicles was revealed by defining the orientation of membrane-bound enzymes that in intact cells normally face the cytoplasm or of other protein markers, known to face the exterior medium in intact cells. Electron microscopy, protease protection assays and lectin-binding experiments confirmed the sealed nature of the vesicles. Upon alkalinization of the external medium, the vesicles were able to generate ATP, reflecting the functional nature of the membrane preparation. The availability of preparative scale amounts of inverted archaeal membrane vesicles provides a platform for the study of various membrane-related phenomena in archaea. Received: 27 March 2001/Revised: 13 June 2001     

Electrogenic Properties of the Sodium Pump in a Dynamic Model of Membrane Transport

The general purpose of this theoretical work is to contribute to understand the physiological role of the electrogenic properties of the sodium pump, by studying a dynamic model that integrates diverse processes of ionic and water transport across the plasma membrane. For this purpose, we employ a mathematical model that describes the rate of change of the intracellular concentrations of Na⁺, K⁺ and Cl⁻, of the cell volume, and of the plasma membrane potential (V _m ). We consider the case of a nonexcitable, nonpolarized cell expressing the sodium pump; Na⁺, K⁺, Cl⁻ and water channels, and cotransporters of KCl and NaCl in its plasma membrane. We particularly analyze here the conditions under which the physiological V _m can be generated in a predominantly electrogenic fashion, as a result of the activity of the sodium pump. A major conclusion of this study is that, for the cell model considered, a low potassium permeability is not a sufficient condition for a predominantly electrogenic generation of the V _m by the sodium pump. The presence of an electroneutral exchange of Na⁺ and K⁺ represents a necessary additional requirement. Received: 8 September 1999/Revised: 21 March 2000     

Burst Kinetics of Co-expressed Kir6.2/SUR1 Clones: Comparison of Recombinant with Native ATP-sensitive K+ Channel Behavior

Co-expression of clones encoding Kir6.2, a K⁺ inward rectifier, and SUR1, a sulfonylurea receptor, reconstitutes elementary features of ATP-sensitive K⁺ (K_ATP) channels. However, the precise kinetic properties of Kir6.2/SUR1 clones remain unknown. Herein, intraburst kinetics of Kir6.2/SUR1 channel activity, heterologously co-expressed in COS cells, displayed mean closed times from 0.7 ± 0.1 to 0.4 ± 0.03 msec, and from 0.4 ± 0.1 to 2.0 ± 0.2 msec, and mean open times from 1.9 ± 0.4 to 4.5 ± 0.8 msec, and from 12.1 ± 2.4 to 5.0 ± 0.2 msec between −100 and −20 mV, and +20 to +80 mV, respectively. Burst duration for Kir6.2/SUR1 activity was 17.9 ± 1.8 msec with 5.6 ± 1.5 closings per burst. Burst kinetics of the Kir6.2/SUR1 activity could be fitted by a four-state kinetic model defining transitions between one open and three closed states with forward and backward rate constants of 1905 ± 77 and 322 ± 27 sec⁻¹ for intraburst, 61.8 ± 6.6 and 23.9 ± 5.8 sec⁻¹ for interburst, 12.4 ± 6.0 and 13.6 ± 2.9 sec⁻¹ for intercluster events, respectively. Intraburst kinetic properties of Kir6.2/SUR1 clones were essentially indistinguishable from pancreatic or cardiac K_ATP channel phenotypes, indicating that intraburst kinetics per se were insufficient to classify recombinant Kir6.2/SUR1 amongst native K_ATP channels. Yet, burst kinetic behavior of Kir6.2/SUR1 although similar to pancreatic, was different from that of cardiac K_ATP channels. Thus, expression of Kir6.2/SUR1 proteins away from the pancreatic micro-environment, confers the burst kinetic identity of pancreatic, but not cardiac K_ATP channels. This study reports the kinetic properties of Kir6.2/SUR1 clones which could serve in the further characterization of novel K_ATP channel clones. Received: 12 March 1997/Revised: 5 May 1997     

Determination of the Individual Electrical and Transport Properties of the Plasmalemma and the Tonoplast of the Giant Marine Alga Ventricaria ventricosa by Means of the Integrated Perfusion/Charge-Pulse Technique: Evidence for a Multifolded Tonoplast

The charge-pulse relaxation spectrum of nonperfused and perfused (turgescent) cells of the giant marine alga Ventricaria ventricosa showed two main exponential decays with time constants of approximately 0.1 msec and 10 msec, respectively, when the cells were bathed in artificial sea water (pH 8). Variation of the external pH did not change the relaxation pattern (in contrast to other giant marine algae). Addition of nystatin (a membrane-impermeable and pore-forming antibiotic) to the vacuolar perfusion solution resulted in the disappearance of the slow exponential, whereas external nystatin decreased dramatically the time constant of the fast one. This indicated (by analogy to corresponding experiments with Valonia utricularis, J. Wang, I. Spiess, C. Ryser, U. Zimmermann, J. Membrane Biol. 157: 311-321, 1997) that the fast relaxation must be assigned to the RC-properties of the plasmalemma and the slow one to those of the tonoplast. Consistent with this, external variation of [K+]o or of [Cl-]o as well as external addition of K+- or Cl--channel/carrier inhibitors (TEA, Ba2+, DIDS) affected only the fast relaxation, but not the slow one. In contrast, addition of these inhibitors to the vacuolar perfusion solution had no measurable effect on the charge-pulse relaxation spectrum. The analysis of the data in terms of the "two membrane model" showed that K+- and (to a smaller extent) Cl--conducting elements dominated the plasmalemma conductance. The analysis of the charge-pulse relaxation spectra also yielded the following area-specific data for the capacitance and the conductance for the plasmalemma and tonoplast (by assuming that both membranes have a planar surface): (plasmalemma) Cp = 0.82 * 10(-2) F m-2, Rp = 1.69 * 10(-2) Omega m2, Gp = 5.9 * 10(4) mS m-2, (tonoplast) Ct = 7. 1 * 10(-2) F m-2, Rt = 14.9 * 10(-2) Omega m2 and Gt = 0.67 * 10(4) mS m-2. The electrical data for the tonoplast show that (in contrast to the literature) the area-specific membrane resistance of the tonoplast of these marine giant algal cells is apparently very high as reported already for V. utricularis. The exceptionally high value of the area-specific capacitance could be explained - among other interpretations - by assuming a 9-fold enlargement of the tonoplast surface. The hypothesis of a multifolded tonoplast was supported by transmission electronmicroscopy of cells fixed under maintenance of turgor pressure and of the electrical parameters of the membranes. This finding indicates that the tonoplast of this species exhibited a sponge-like appearance. Taking this result into account, it can be easily shown that the tonoplast exhibits a high-resistance (1.1 Omega m2). Vacuolar membrane potential measurements (performed in parallel with charge-pulse relaxation studies) showed that the potential difference across the plasmalemma was mainly controlled by the external K+-concentration which suggested that the resting membrane potential of the plasmalemma is largely a K+-diffusion potential. After permeabilization of the tonoplast with nystatin the potential of the intact membrane barrier dropped from about slightly negative or positive (-5.1 to +18 mV, n = 13) to negative values (-15 up to -68 mV; n = 8). This indicated that the cytoplasm of V. ventricosa was apparently negatively charged relative to the external medium. Permeabilization of the plasmalemma by addition of external nystatin resulted generally in an increase in the potential to slightly more positive values (-0.8 to +4.3 mV; n = 5), indicating that the vacuole is positively charged relative to the cytoplasm. These findings apparently end the long-term debate about the electrical properties of V. ventricosa. The results presented here support the findings of Davis (Plant Physiol. 67: 825-831, 1981), but are contrary to the results of Lainson and Field (J. Membrane Biol. 29: 81-94, 1976).     

Toward Assigning Helical Regions in Alignments of Ribosomal RNA and Testing the Appropriateness of Evolutionary Models

We suggest a nucleotide substitution model that takes correlation between base-paired nucleotides into account. The model includes the estimation of the transition–transversion ratio and allows inference of the shape parameter of a discrete gamma distribution to include rate heterogeneity. A Cox-test statistic, applied to a diatom ribosomal RNA alignment, shows that the suggested correlation model explains evolution of the stem region better than usual independence models. Moreover, the Cox-test procedure is extended to shed some light upon the problem of assigning helical regions in a secondary structure based alignment. This approach provides an estimate of the percentage of stem positions that do not appear to be correlated. Received: 4 March 1999 / Accepted: 10 May 1999     

Modeling Plasmalemma Ion Transport of the Aquatic Plant Egeria densa

Fresh-water plants generate extraordinarily high electric potential differences at the plasma membrane. For a deeper understanding of the underlying transport processes a mathematical model of the electrogenic plasmalemma ion transport was developed based on experimental data mainly obtained from Egeria densa. The model uses a general nonlinear network approach and assumes coupling of the transporters via membrane potential. A proton pump, an outward-rectifying K⁺ channel, an inward-rectifying K⁺ channel, a Cl⁻ channel and a (2H-Cl)⁺ symporter are considered to be elements of the system. The model takes into consideration the effects of light, external pH and ionic content of the bath medium on ion transport. As a result it does not only satisfactorily describe the membrane potential as a function of these external physiological factors but also succeeds in simulating the effects of specific inhibitors as well as I-V-curves obtained with the patch-clamp technique in the whole cell mode. The quality of the model was checked by stability and sensitivity analyses. Received: 18 March 1996/Revised: 17 July 1996     

Mutants of the Lactose Carrier of Escherichia coli Which Show Altered Sugar Recognition Plus a Severe Defect in Sugar Accumulation

Lactose and melibiose are actively accumulated by the wild-type Escherichia coli lactose carrier, which is an integral membrane protein energized by the proton motive force. Mutants of the E. coli lactose carrier were isolated by their ability to grow on minimal plates with succinate plus IPTG in the presence of the toxic lactose analog β-thio-o-nitrophenylgalactoside (TONPG). TONPG-resistant mutants were streaked on melibiose MacConkey indicator plates, and red clones were picked. These melibiose positive mutants were then streaked on lactose MacConkey plates, and white clones were picked. Transport assays indicated that the mutants had altered sugar recognition and a defect in sugar accumulation. The mutants had a poor apparent K _m for both lactose and melibiose in transport. One mutant had almost no ability to take up lactose, but melibiose downhill transport was 58% (V _max ) of normal. All of the mutants accumulated methyl-α-d-galactopyranoside (TMG) to only 8% or less of normal, and two failed to accumulate. Immunoblot analysis of the mutant lactose carrier proteins indicated that loss of sugar transport activity was not due to loss of expression in the membrane. Nucleotide sequencing of the lacY gene from the mutants revealed changes in the following amino acids of the lactose carrier: M23I, W151L, G257D, A295D and G377V. Two of the mutants (G257D and G377V) are novel in that they represent the first amino acids in periplasmic loops to be implicated with changes in sugar recognition. We conclude that the amino acids M23, W151, G257, A295 and G377 of the E. coli lactose carrier play either a direct or an indirect role in sugar recognition and accumulation. Received: 12 October 1999/Revised: 21 December 1999     

Proton Inhibition of Sodium Channels: Mechanism of Gating Shifts and Reduced Conductance

Extracellular acidosis affects both permeation and gating of the expressed rat skeletal muscle Na⁺ channel (μ1). Reduction of the extracellular pH produced a progressive decrease in the maximal whole-cell conductance and a depolarizing shift in the whole-cell current-voltage relationship. A smaller depolarizing shift in the steady-state inactivation curve was observed. The pK of the reduction of maximal conductance was 6.1 over the pH range studied. An upper limit estimate of the pK of the shift of the half-activation voltage was 6.1. The relative reduction in the maximal whole-cell conductance did not change with higher [Na⁺] _o . The conductance of single fenvalerate-modified Na⁺ channels was reduced by extracellular protons. Although the single-channel conductance increased with higher [Na⁺] _o , the maximal conductances at pH 7.6, 7.0 and 6.0 did not converge at [Na⁺] _o up to 280 mm, inconsistent with a simple electrostatic effect. A model incorporating both Na⁺ and H⁺ binding in the pore and cation binding to a Gouy-Chapman surface charge provided a robust fit to the single-channel conductance data with an estimated surface charge density of 1e⁻/439?². Neither surface charge nor proton block alone suffices to explain the effects of extracellular acidosis on Na⁺ channel permeation; both effects play major roles in mediating the response to extracellular pH. Received: 14 May 1996/Revised: 19 September 1996     

1/f-Noise of Open Bacterial Porin Channels

General diffusion pores and specific porin channels from outer membranes of gram-negative bacteria were reconstituted into lipid bilayer membranes. The current noise of the channels was investigated for the different porins in the open state and in the ligand-induced closed state using fast Fourier transformation. The open channel noise exhibited 1/f-noise for frequencies up to 200 Hz. The 1/f-noise was investigated using the Hooge formula (Hooge, Phys. Lett. 29A: 139–140 (1969)), and the Hooge parameter α was calculated for all bacterial porins used in this study. The 1/f-noise was in part caused by slow inactivation and activation of porin channels. However, when care was taken that during the noise measurement no opening or closing of porin channels occurred, the Hooge Parameter α was a meaningful number for a given channel. A linear relationship was observed between α and the single-channel conductance, g, of the different porins. This linear relation between single-channel conductance and the Hooge parameter α could be qualitatively explained by assuming that the passing of an ion through a bacterial porin channel is—to a certain extent—influenced by nonlinear effects between channel wall and passing ion. Received: 8 May 1996/Revised: 27 January 1997     

Membrane Fusion and Rupture in Liposomes: Effect of Biodegradable pH-Sensitive Surfactants

Biodegradable pH-sensitive surfactants (BPS) are a unique family of easily metabolized compounds that demonstrate pH-dependent surface activity. These agents, in combination with other delivery systems, have demonstrated effects in enhancing transnucleic acid activity. The increased activity has been hypothesized to occur from a release of endosomal contents. Simply, the BPS delivery system containing nucleic acids enters the cell through an endocytotoic process. It encounters an acidic pH and becomes surface active leading to defects in the endosomal membrane. In the current study, an in vitro model membrane was used to better understand the liposome defect mechanisms that BPS elicit. Using this system, it is shown that BPS can induce both liposome fusion and rupture depending upon the pH and mole ratio of BPS to membrane lipids. Futhermore, liposome fusion induced by BPS was dependent on the total numbers of liposome particles while rupture was independent of interacting liposome particles. The generated data indicate that BPS agents act differently from other typical surface active agents and fuosgenic compounds. Instead of facilitating membrane fusion through the hexagonal II phase, BPS appeared to contribute and participate in the membrane fusion at different stages. Received: 18 February 1998/Revised: 14 July 1998