An extended kinetic analysis of valinomycin-induced Rb-transport through monoglyceride membranes

Summary The time course of the current following a voltage jump, which is applied to monoglyceride bilayers in the presence of valinomycin, shows two relaxation times. This is basically in agreement with a simple carrier model which has been described in full detail formerly. Relaxation times and amplitudes allow a calculation of the rate constants of the transport model. The presented data supplement an analysis which was hitherto based only on the slower relaxation process and on information derived from the nonlinearity of currentvoltage characteristics. The additional resolution of the faster relaxation time allowed an approximate determination of the voltage dependence of the translocation rate constant for the carrier-ion-complex and provided evidence for a small voltage dependence of the interfacial reaction. The dependence of the relaxation parameters on the ion concentration in the aqueous phase was interpreted assuming a saturation of the ion concentration at the reaction plane at high bulk concentrations.     

Relaxation studies of enzymes: concentration and pH dependence of isomerization phenomena.

Equations have been developed for the relaxation times for a variety of mechanisms involving enzyme isomerization coupled to proton transfers. The concentration and pH dependences of the relaxation time have been calculated and graphed for a number of representative mechanisms. We find that for most of the mechanisms examined, the relaxation time is not only pH but also strongly concentration dependent. The concentration dependence results from finite perturbations of the hydrogen ion concentration. For the systems tested, the relaxation time shows a clear concentration dependence at enzyme concentrations below 200 microM.     

Protonation dynamics of the alpha-toxin ion channel from spectral analysis of pH-dependent current fluctuations.

To probe protonation dynamics inside the fully open alpha-toxin ion channel, we measured the pH-dependent fluctuations in its current. In the presence of 1 M NaCl dissolved in H2O and positive applied potentials (from the side of protein addition), the low frequency noise exhibited a single well defined peak between pH 4.5 and 7.5. A simple model in which the current is assumed to change by equal amounts upon the reversible protonation of each of N identical ionizable residues inside the channel describes the data well. These results, and the frequency dependence of the spectral density at higher frequencies, allow us to evaluate the effective pK = 5.5, as well as the rate constants for the reversible protonation reactions: kon = 8 x 10(9) M-1 s-1 and koff = 2.5 x 10(4) s-1. The estimate of kon is only slightly less than the diffusion-limited values measured by others for protonation reactions for free carboxyl or imidazole residues. Substitution of H2O by D2O caused a 3.8-fold decrease in the dissociation rate constant and shifted the pK to 6.0. The decrease in the ionization rate constants caused by H2O/D2O substitution permitted the reliable measurement of the characteristic relaxation time over a wide range of D+ concentrations and voltages. The dependence of the relaxation time on D+ concentration strongly supports the first order reaction model. The voltage dependence of the low frequency spectral density suggests that the protonation dynamics are virtually insensitive to the applied potential while the rate-limiting barriers for NaCl transport are voltage dependent. The number of ionizable residues deduced from experiments in H2O (N = 4.2) and D2O (N = 4.1) is in good agreement.     

The voltage-dependent step of the chloride transporter of Valonia utricularis encounters a Nernst-Planck and not an Eyring type of potential energy barrier

Voltage-clamp experiments were performed on cells of the giant marine alga Valonia utricularis to study the voltage dependence of the previously postulated chloride transporter (Wang, J., G. Wehner, R. Benz, and U. Zimmermann. 1991. Biophys. J. 59:235-248). Only one exponential current relaxation (apart from the capacitive spike) could be resolved up to a clamp voltage of ~120 mV within the time resolution of our experimental instrumentation (100 μs). This means that the rate constants of the heterogeneous complexation, k_R (association) and k_D (dissociation), were too fast to be resolved. Therefore, the “Läuger” model for carrier-mediated ion transport with equilibrium heterogeneous surface reaction was used to fit the experimental results. The voltage dependence of the initial membrane conductance was used for the evaluation of the voltage dependence of the translocation rate constant of the complexed carriers, k_AS. The initial conductance was found to be independent on the clamp voltage, which means that the translocation rate constant k_AS is a linear function of the applied voltage and that the voltage dependence of the translocation of charged carriers through the plasmalemma could be explained by a square-type Nernst-Planck barrier. The movement of the complexed form of the carrier through the membrane may be explained by a diffusion process rather than by simple first-order kinetic jump across an Eyring-type potential well. The current relaxation after a voltage clamp was studied as a function of the external chloride concentration. The results allowed an estimation of the stability constant, K, of the heterogeneous complexation reaction and a calculation of the translocation rate constants of the free and the complexed carriers, k_s and k_AS, respectively.     

Voltage and Ca(2+) dependence of pre-steady-state currents of the Na-Ca exchanger generated by Ca(2+) concentration jumps

The Ca(2+) concentration and voltage dependence of the relaxation kinetics of the Na-Ca exchanger after a Ca(2+) concentration jump was measured in excised giant membrane patches from guinea pig heart. Ca(2+) concentration jumps on the cytoplasmic side were achieved by laser flash-induced photolysis of DM-nitrophen. In the Ca-Ca exchange mode a transient inward current is generated. The amplitude and the decay rate of the current saturate at concentrations >10 microM. The integrated current signal, i.e., the charge moved is fairly independent of the amount of Ca(2+) released. The amount of charge translocated increases at negative membrane potentials, whereas the decay rate constant shows no voltage dependence. It is suggested that Ca(2+) translocation occurs in at least four steps: intra- and extracellular Ca(2+) binding and two intramolecular transport steps. Saturation of the amplitude and of the relaxation of the current can be explained if the charge translocating reaction step is preceded by two nonelectrogenic steps: Ca(2+) binding and one conformational transition. Charge translocation in this mode is assigned to one additional conformational change which determines the equilibrium distribution of states. In the Na-Ca exchange mode, the stationary inward current depends on the cytoplasmic Ca(2+) concentration and voltage. The K(m) for Ca(2+) is 4 microM for guinea pig and 10 microM for rat myocytes. The amplitude of the pre-steady-state current and its relaxation saturate with increasing Ca(2+) concentrations. In this mode the relaxation is voltage dependent.     

Microscopic description of voltage effects on ion-driven cotransport systems

A microscopic model for the analysis of voltage effects on ion-driven cotransport systems is described. The model is based on the notion that the voltage dependence of a given rate constant is directly related to the amount of charge which is translocated in the corresponding reaction step. Charge translocation may result from the movement of an ion along the transport pathway, from the displacement of charged ligand groups of the ion-binding site, or from reorientation of polar residues of the protein in the course of a conformational transition. The voltage dependence of overall transport rate is described by a set of dimensionless coefficients reflecting the dielectric distances over which charge is displaced in the elementary reaction steps. The dielectric coefficients may be evaluated from the shape of the experimental flux-voltage curve if sufficient information on the rate constants of the reaction cycle is available. Examples of flux-voltage curves which are obtained by numerical simulation of the transport model are given for a number of limiting cases.     

Fractal analysis of a voltage-dependent potassium channel from cultured mouse hippocampal neurons.

The kinetics of ion channels have been widely modeled as a Markov process. In these models it is assumed that the channel protein has a small number of discrete conformational states and the kinetic rate constants connecting these states are constant. In the alternative fractal model the spontaneous fluctuations of the channel protein at many different time scales are represented by a kinetic rate constant k = At1-D, where A is the kinetic setpoint and D the fractal dimension. Single-channel currents were recorded at 146 mM external K+ from an inwardly rectifying, 120 pS, K+ selective, voltage-sensitive channel in cultured mouse hippocampal neurons. The kinetics of these channels were found to be statistically self-similar at different time scales as predicted by the fractal model. The fractal dimensions were approximately 2 for the closed times and approximately 1 for the open times and did not depend on voltage. For both the open and closed times the logarithm of the kinetic setpoint was found to be proportional to the applied voltage, which indicates that the gating of this channel involves the net inward movement of approximately one negative charge when this channel opens. Thus, the open and closed times and the voltage dependence of the gating of this channel are well described by the fractal model.     

Asymmetry of the gramicidin channel in bilayers of asymmetric lipid composition: I. Single channel conductance

Summary Gramicidin-doped asymmetric bilayers made by the Montal-Mueller method exhibited an asymmetric current-voltage relationship. The asymmetric conductance was shown to be the product of two components, a rectifying single-channel conductance and an asymmetric voltage dependence of the reaction which leads to the conducting channel. The single-channel conductance was asymmetric in both asymmetric bilayers made of charged lipids and asymmetric bilayers made only of neutral lipids. The single-channel asymmetry decreased with increasing ion concentration. From the comparison of the singlechannel conductance in symmetric and asymmetric bilayers and the dependence of the asymmetry on the solution ion concentrations, it was concluded that (1) the rate of ion entry into the channel is dependent on the lipid composition of the membrane and is asymmetric in asymmetric bilayers; (2) the entry step is rate determining at low ion concentrations; and (3) at higher ion concentrations the rate-determining step is the translocation across the main barrier in the membrane; and this translocation appears insensitive to lipid asymmetry.     

Gating kinetics of potassium channel in rat dorsal root ganglion neurons analyzed with fractal model

The kinetics of ion channels have been widely modeled as a Markov process. In these models it is assumed that the channel protein has a small number of discrete conformational states and kinetic rate constants connecting these states are constant. To study the gating kinetics of voltage-dependent K(+) channel in rat dorsal root ganglion neurons, K(+) channel current were recorded using cell-attached patch-clamp technique. The K(+) channel characteristic of kinetics were found to be statistically self-similar at different time scales as predicted by the fractal model. The fractal dimension D for the closed times and for the open times depend on the pipette potential. For the open and closed times of kinetic setpoint, it was found dependent on the applied pipette potential, which indicated that the ion channel gating kinetics had nonlinear kinetic properties. Thus, the open and closed durations, which had the voltage dependence of the gating of this ion channel, were well described by the fractal model.     

Electron spin resonance and magnetic relaxation studies of gadolinium(III) complexes with human transferrin

A human serum transferrin complex was prepared in which Gd(III) was substituted for Fe(III) at the two metal-binding sites. Characteristic changes upon metal binding in both the UV absorption of ligated tyrosines and the solvent proton longitudinal magnetic relaxation rates demonstrated 2/1 metal stoichiometry and pH-dependent binding constants. Binding studies were complicated both by binding of Gd(III) to nonspecific sites on transferrin at pH less than or equal to 7 and by complexation of the Gd(III) by the requisite bicarbonate anion at pH greater than or equal to 6.0. A unique Gd(III) electron spin resonance spectrum, with a prominent signal at g = 4.96, was observed for the specific Gd(III)-transferrin complex. The major features of this spectrum were fit successfully by a model Hamiltonian which utilized crystal field parameters similar to those determined for Fe(III) in transferrin [Aasa, R. (1970) J. Chem. Phys. 52, 3919-3924]. The magnetic field dependence of the solvent proton relaxation rate was measured as a function of both pH and metal ion concentration. An observed biphasic dependence of the relaxation rate on metal concentration is attributed to either sequential metal binding to the two iron-binding sites with different relaxation properties or random binding to two sites that are similar but show conformationally induced changes in relaxation properties as the second metal is bound. The increase in the solvent proton relaxation rate with pH is consistent with a model in which a proton of a second coordination sphere water molecule is hydrogen bonded to a metal ligand which becomes deprotonated at pH 8.5.     

Kinetics of the daunomycin--DNA interaction

The kinetics of the interaction of daunomycin with calf thymus DNA are described. Stopped-flow and temperature-jump relaxation methods, using absorption detection, were used to study the binding reaction. Three relaxation times were observed, all of which are concentration dependent, although the two slower relaxations approach constant values at high reactant concentrations. Relaxation times over a wide range of concentrations were gathered, and the data were fit by a minimal mechanism in which a rapid bimolecular association step is followed by two sequential isomerization steps. The six rate constants for this mechanism were extracted from our data by relaxation analysis. The values determined for the six rate constants may be combined to calculate an overall equilibrium constant that is in excellent agreement with that obtained by independent equilibrium measurements. Additional stopped-flow experiments, using first sodium dodecyl sulfate to dissociate bound drug and second pseudo-first-order conditions to study the fast bimolecular step, provide independent verification of three of the six rate constants. The temperature dependence of four of the six rate constants was measured, allowing estimates of the activation energy of some of the steps to be made. We speculate that the three steps in the proposed mechanism may correspond to a rapid "outside" binding of daunomycin to DNA, followed by intercalation of the drug, followed by either conformational adjustment of the drug or DNA binding site or redistribution of bound drug to preferred sites.     

Ferrocyanide carbon-13 NMR line broadening as a probe of electron transfer reactions

The electron transfer reaction between ferrocyanide ion and the blue copper protein, stellacyanin, has been investigated by means of 13C NMR line broadening of the inorganic oxidant. The temperature dependence of the ferrocyanide line broadening gives an activation energy for the electron transfer reaction of 17 +/- 3 kJ. The apparent rate constant decreases with increasing concentration of K4Fe(CN)6, a result which can be explained either by formation of a strong precursor ferrocyanide--stellacyanin [Cu(II)] complex or by increased formation of KFe(CN)3-6 ion pairs. The direct electron transfer between ferrocyanide and ferricyanide has also been studied by 13C NMR line broadening of the former species. The ferricyanide concentration dependence of the exchange line broadening yields a value for the apparent second-order rate constant at 25 degrees C of k = 1.65 . 10(3) M-1 . s-1, in agreement with previously reported values derived from 14N NMR and isotope exchange studies. This rate constant shows a linear dependence on the K+ concentration, independent of ionic strength, a result which confirms the importance of ion pair species such as KFe(CN)3-6 and KFe(CN)2-6 in the direct electron transfer mechanism. The general applications of the method are discussed, including the considerations which suggest that a wide range of electron transfer rates, from about 1 s-1 to 4 . 10(3) s-1, are, in principle, accessible to this technique. The potential utility of ferrocyanide 13C spin--lattice relaxation time measurements is decreasing the lower limit of this range is also discussed.     

An investigation of biooxidation ability of Acidithiobacillus ferrooxidans using NMR relaxation measurement

NMR relaxation measurements can provide a simple means for understanding biological activity of cells in solution with known composition. It has the advantage that it is an in situ, non-intrusive technique, and the acquisition is fast. The iron oxidation ability of Acidithiobacillus ferrooxidans was investigated using NMR relaxation measurements. The transversal relaxation is characterized by a time constant, T?, which is sensitive to the chemical environment. Fe3? ion has more significant T? shortening than Fe2? ion. In the presence of A. ferrooxidans in solutions containing Fe2? ion, T? shortening was found with increasing time as the bacteria oxidize Fe2? to Fe3? ions. In the optimal growth medium, the bacteria concentration increased 80 times and high iron oxidation rate was found. In 10 mM K?SO? medium, however, bacteria concentration remained almost unchanged and the iron oxidation rate was significantly lower.     

Inactivation viewed through single sodium channels

Recordings of the sodium current in tissue-cultured GH3 cells show that the rate of inactivation in whole cell and averaged single channel records is voltage dependent: tau h varied e-fold/approximately 26 mV. The source of this voltage dependence was investigated by examining the voltage dependence of individual rate constants, estimated by maximum likelihood analysis of single channel records, in a five-state kinetic model. The rate constant for inactivating from the open state, rather than closing, increased with depolarization, as did the probability that an open channel inactivates. The rate constant for closing from the open state had the opposite voltage dependence. Both rate constants contributed to the mean open time, which was not very voltage dependent. Both open time and burst duration were less than tau h for voltages up to -20 mV. The slowest time constant of activation, tau m, was measured from whole cell records, by fitting a single exponential either to tail currents or to activating currents in trypsin-treated cells, in which the inactivation was abolished. tau m was a bell-shaped function of voltage and had a voltage dependence similar to tau h at voltages more positive than -35 mV, but was smaller than tau h. At potentials more negative than about -10 mV, individual channels may open and close several times before inactivating. Therefore, averaged single channel records, which correspond with macroscopic current elicited by a depolarization, are best described by a convolution of the first latency density with the autocorrelation function rather than with 1 - (channel open time distribution). The voltage dependence of inactivation from the open state, in addition to that of the activation process, is a significant factor in determining the voltage dependence of macroscopic inactivation. Although the rates of activation and inactivation overlapped greatly, independent and coupled inactivation could not be statistically distinguished for two models examined. Although rates of activation affect the observed rate of inactivation at intermediate voltages, extrapolation of our estimates of rate constants suggests that at very depolarized voltages the activation process is so fast that it is an insignificant factor in the time course of inactivation. Prediction of gating currents shows that an inherently voltage-dependent inactivation process need not produce a conspicuous component in the gating current.     

A model study of the contribution of active Na-K transport to membrane repolarization in cardiac cells

A biochemical model of active Na-K transport in cardiac cells was studied in conjunction with a representation of the passive membrane currents and ion concentration changes. The active transport model is based on the thermodynamic and kinetic properties of a six-step reaction scheme for the Na,K-ATPase. It has a fixed Na:K stoechiometry of 3:2, and its activation is governed by three parameters: membrane potential intracellular Na+ concentration, and interstitial K+ concentration. The Na-K pump current is directly proportional to the density of Na,K-ATPase molecules. The passive membrane currents and ion concentration changes involve only Na+ and K+ ions, and no attempt was made to provide a precise representation of Ca2+ currents or Ca2+ concentration changes. The surface-to-volume ratio of the interstitial compartment is 55 times larger than that of the intracellular compartment. The flux balance conditions are such that the original equilibrium concentration values are re-established at each stimulation cycle. The underlying assumptions of the model were checked against experimental measurements on Na-K pump activity in a variety of preparations. In addition, the qualitative validation of the model was carried out by comparing its behavior following sudden frequency shifts to corresponding experimental observations. The overall behavior of the model is quite satisfactory and it is used to provide the following indications: (1) when the intracellular and interstitial volumes are relatively large, the ion concentration transients are small and the pumping rate depends essentially on average concentration levels. (2) An increase in internal Na+ concentration potentiates the response of the Na-K pump to rapid membrane depolarizations. (3) When the internal Na+ concentration is large enough, the Na-K pump current transient plays an important role in shaping the plateau and repolarization phase of the action potential. (4) A rapid increase in external K+ concentration during voltage clamp in multicellular preparations could saturate the Na-K pump response and lead to a fairly linear dependence of the pump activity on the internal Na+ concentration.     

Voltage-dependent formation of gramicidin channels in lipid bilayers.

The formation kinetics of gramicidin A channels in lipid bilayer membranes has been characterized as a function of voltage for different solution conditions and membrane composition. The frequency of channel events was measured during the application of voltage ramps and counted in given intervals, a procedure that eliminated the effects of drift in gramicidin concentration. The formation rate was found to increase strongly with voltages up to approximately 50 mV and then to level off slightly. The shape of the voltage dependence was independent of lipid solvent and ramp speed but differed for different ions and different solution concentrations. This suggested an ion occupancy effect on the formation rate that was further supported by the fact that the minimum of the formation rate was shifted toward the equilibrium potential in asymmetric solution concentrations. The effects are explained in terms of a model that contains two contributions to the voltage dependence, a voltage-dependent ion binding to the monomers and a polarization of monomers by the applied electric field and by the occupied ions. The theory is found to give a good fit to experimental data.     

Block by acetylcholine of mouse muscle nicotinic receptors,stably expressed in fibroblasts

We have measured the concentration and voltage dependence of block by acetylcholine (ACh) of fetal- and adult-type mouse muscle nicotinic receptors, expressed in a fibroblast cell line. Data, obtained at a transmembrane potential of -60 mV and with ACh concentrations of 1 mM and above, are broadly consistent with the occlusion of an open channel with a single ACh+ ion (simple open channel block). The rate of recovery from block is approximately 40,000s-1 and has only a weak voltage dependence. This is in contrast to the strong voltage dependence observed for the degree of block. Deviations from the predictions of the simple model are seen in data collected at positive transmembrane potentials and at negative potentials for ACh concentrations < 1 mM. Less concentration dependence is observed than expected. Of a number of models tested, we demonstrate that two models incorporating both a high and a low affinity blocking site can predict our data.     

Kinetics and mechanism of the acid transition of the active site in plastocyanin

Exchange on the microsecond time scale between the protonated and deprotonated forms of His92 in the copper site of reduced plastocyanin from the cyanobacteria Anabaena variabilis was monitored using 15N NMR relaxation measurements. On the basis of the dependence of the kinetics on pH and phosphate buffer concentration, we propose a two-step model for the protonation of the copper site in agreement with previous crystallographic studies. It is shown that the proton transfer is the rate-limiting step in the reaction at low buffer concentrations, whereas at high buffer concentrations, another step becomes rate-limiting. We suggest that the latter step is a concerted dissociation of His92 from the Cu(I) ion and a 180 degrees rotation of the imidazole ring, which precede the protonation. The first-order rate constant for the dissociation of His92 from the Cu(I) ion is estimated to be 2.4 x 10(4) s(-1). Also, a cooperative effect of the protonation of the remote His61 on the protonation of His92 and the redox properties of the protein was investigated by substituting His61 with asparagine. The mutation causes a modest change in both the pKa value of His92 and the redox potential of the protein.     

Evaluation of proximity inhibition of DNA synthesis in 3T3 cells.

A microphotometric technique that displays rapid length changes of Spirostomum has been used to follow the variation with temperature of three kinetic parameters of myonemal contraction: contraction rate, relaxation rate and stimulus duration at threshold. In each case the exponential form of the relationship indicated that the gross rate constant might be equated with the limiting rate constant, k, of a driving chemical reaction, and from standard expressions of chemical kinetics the change in activation free energy appropriate to this reaction has been computed. The thermal dependence of contraction is described by an activation enthalpy (ΔLH?) of 21.7 kcal mol^?1, and the activation entropy (ΔLS?) of 26.8 e.u. is consistent with a model of contraction requiring neutralization of fixed myonemal charges by divalent cations. The analysis of thermal dependence of relaxation gives a negative activation entropy, a result predicted for a rate-limiting reaction involving dissociation of a neutral molecule. On the other hand, values of ΔLS? and ΔLH? for relaxation fall close to an isokinetic correlation drawn in the literature from analysis of the thermal dependence of ciliary beat frequency in different organisms, and for which breakdown of an ATP-ATPase complex could be the common rate-limiting reaction. ΔLS? for stimulus duration suggests that the rate-limiting step in excitation-contraction coupling is a reaction between ions of like charge, or ion pair formation from a neutral molecule.     

Counter-ion dynamics in crosslinked poly(styrene sulfonate) systems studied by NMR

The field dependence of the longitudinal and transverse nuclear magnetic relaxation rates of 23Na+ in aqueous crosslinked Na-poly(styrene sulfonate) (PSS) systems (ion exchange resins) has been obtained as a function of the degree of crosslinking. The relaxation is considerably enhanced relative to solutions of non-crosslinked NaPSS at equal ionizable group concentration. This is due to the dynamic constraints of the polymer chains, which render the averaging of the counter-ion chain interaction less efficient. The field dependence of the relaxation rates in the crosslinked NaPSS systems reveals two processes that are out of the extreme narrowing limit. This is in contrast to the relaxation behavior found in non-crosslinked NaPSS systems. To characterize these processes their correlation times were combined with constants of selfdiffusion to estimate the distances diffused by an ion in order to average the electric field gradient at its nucleus. These two distances are interpreted as characteristic length scales in the network. At all degrees of crosslinking it was found that the smallest of these length scales is roughly equal to the distance between two neighbouring crosslinks. The largest characteristic distance extends over several crosslinks and reflects inhomogeneities in the crosslink concentration. These conclusions were also reached from similar experiments on 7Li+ in LiPSS systems.