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The combined kinetic analysis implies a simultaneous analysis of experimental data representative of the forward solid-state reaction obtained under any experimental conditions. The analysis is based on the fact that when a solid-state reaction is described by a single activation energy, preexponetial factor and kinetic model, every experimental T-alpha-dalpha/dt triplet should fit the general differential equation independently of the experimental conditions used for recording such a triplet. Thus, only the correct kinetic model would fit all of the experimental data yielding a unique activation energy and preexponential factor. Nevertheless, a limitation of the method should be considered; thus, the proposed solid-state kinetic models have been derived by supposing ideal conditions, such as unique particle size and morphology. In real systems, deviations from such ideal conditions are expected, and therefore, experimental data might deviate from ideal equations. In this paper, we propose a modification in the combined kinetic analysis by using an empirical equation that fits every f(alpha) of the ideal kinetic models most extensively used in the literature and even their deviations produced by particle size distributions or heterogeneities in particle morphologies. The procedure here proposed allows the combined kinetic analysis of data obtained under any experimental conditions without any previous assumption about the kinetic model followed by the reaction. The procedure has been verified with simulated and experimental data.
It has been found empirically that either average or minimum steady-state plasma concentrations (Css) of drugs obeying Michaelis-Menten elimination kinetics give essentially linear plots on semilogarithmic graph paper when Css is plotted versus the maintenance dose (D) or dose rate (R). The equations of such straight lines may be converted to the following nonlinear equation: Css = abD which fits the Css,D data essentially as well as D = VmCss/(Km + Css). The parameter b is analogous to unity plus the interest fraction in logarithmic growth or compound interest calculations, and each drug appears to have a characteristic value of this parameter, with extremely small intersubject variation. From the above equation the following equation, Dn+1 = Dn + 1n(Cn+1/Cn)1n b can be derived, which forms the basis of predicting the needed dosage, Dn+1, to obtain a desired steady-state concentration, Cn+1, using one initial steady-state concentration, Cn, obtained with dose, Dn, and using a population value of b for the drug. It appears that it is the value of the "initial capital" (i.e., a in relation to the initial dose) rather than the "interest fraction" (i.e., b - 1) that causes most of the intersubject variation in Css of a given drug. Several drugs illustrate the usefulness of the method. A semilogarithmic plot also appears to be an excellent method to distinguish simple Michaelis-Menten kinetics from parallel Michaelis-Menten and first order elimination kinetics and from simple first order kinetics with steady-state data in the range 0.3-3 Km.
Growth kinetics, i.e., the relationship between specific growth rate and the concentration of a substrate, is one of the basic tools in microbiology. However, despite more than half a century of research, many fundamental questions about the validity and application of growth kinetics as observed in the laboratory to environmental growth conditions are still unanswered. For pure cultures growing with single substrates, enormous inconsistencies exist in the growth kinetic data reported. The low quality of experimental data has so far hampered the comparison and validation of the different growth models proposed, and only recently have data collected from nutrient-controlled chemostat cultures allowed us to compare different kinetic models on a statistical basis. The problems are mainly due to (i) the analytical difficulty in measuring substrates at growth-controlling concentrations and (ii) the fact that during a kinetic experiment, particularly in batch systems, microorganisms alter their kinetic properties because of adaptation to the changing environment. For example, for Escherichia coli growing with glucose, a physiological long-term adaptation results in a change in KS for glucose from some 5 mg liter-1 to ca. 30 microg liter-1. The data suggest that a dilemma exists, namely, that either "intrinsic" KS (under substrate-controlled conditions in chemostat culture) or micromax (under substrate-excess conditions in batch culture) can be measured but both cannot be determined at the same time. The above-described conventional growth kinetics derived from single-substrate-controlled laboratory experiments have invariably been used for describing both growth and substrate utilization in ecosystems. However, in nature, microbial cells are exposed to a wide spectrum of potential substrates, many of which they utilize simultaneously (in particular carbon sources). The kinetic data available to date for growth of pure cultures in carbon-controlled continuous culture with defined mixtures of two or more carbon sources (including pollutants) clearly demonstrate that simultaneous utilization results in lowered residual steady-state concentrations of all substrates. This should result in a competitive advantage of a cell capable of mixed-substrate growth because it can grow much faster at low substrate concentrations than one would expect from single-substrate kinetics. Additionally, the relevance of the kinetic principles obtained from defined culture systems with single, mixed, or multicomponent substrates to the kinetics of pollutant degradation as it occurs in the presence of alternative carbon sources in complex environmental systems is discussed. The presented overview indicates that many of the environmentally relevant apects in growth kinetics are still waiting to be discovered, established, and exploited.
The purpose of this study was to analyze forces at the tibiofemoral joint during open and closed-kinetic-chain exercises. Five healthy subjects performed maximum isometric contractions at 30, 60, and 90 degrees of knee flexion during open-kinetic-chain extension, open-kinetic-chain flexion, and closed-kinetic-chain exercises. Electromyographic activity of the quadriceps and hamstrings, as well as load and torque-cell data, were recorded. Tibiofemoral shear and compression forces were calculated with use of a two-dimensional biomechanical model. The results showed that, during the open-kinetic-chain extension exercise, maximum posterior shear forces (the resisting forces to anterior drawer) of 285 +/- 120 newtons (mean and standard deviation) occurred at 30 degrees of knee flexion and maximum anterior shear forces (the resisting forces to posterior drawer) of 1780 +/- 699 newtons occurred at 90 degrees of knee flexion. The closed-kinetic-chain exercise produced significantly less posterior shear force at all angles when compared with the open-kinetic-chain extension exercise. In addition, the closed-kinetic-chain exercise produced significantly less anterior shear force at all angles except 30 degrees when compared with the open-kinetic-chain flexion exercise (p < 0.05). Analysis of tibiofemoral compression forces and electromyographic recruitment patterns revealed that the closed-kinetic-chain exercise produced significantly greater compression forces and increased muscular co-contraction at the same angles at which the open-kinetic-chain exercises produced maximum shear forces and minimum muscular co-contraction.(ABSTRACT TRUNCATED AT 250 WORDS)
Graphic methods have proved to be very useful in enzyme kinetics, as reflected in both raising the efficiency of performing calculations and aiding in the analysis of catalytic mechanisms. The kinetic relations among protein folding states are very similar to those between enzyme-catalyzed species. Therefore, it should be equally useful to provide a visually intuitive relation between kinetic calculations and folding mechanisms for protein folding kinetics, as manifested by the graphic rules in enzyme kinetics. It can actually be anticipated that, due to increasing interest in protein folding, the graphic method will become an important tool in folding kinetics as well. Based on the recent progress made in graphic methods of enzyme kinetics, in this review four graphic rules are summarized, which can be used to deal with protein folding systems as well as enzyme-catalyzed systems. Rules 1-3 are established for deriving the kinetic equations for steady-state processes and Rule 4 for those in the case of non-steady-state processes. In comparison with conventional graphic methods, which can only be applied to a steady-state system, the current rules have the following advantages: (1) Complicated and tedious calculations can be greatly simplified. (2) A lot of wasted labor can be turned away. (3) Final results can be double-checked by a formula provided in each of the graphic rules. (4) Transient kinetic systems can also be treated. The mathematical proof of Rules 1-4 is given in appendices A-D, respectively.
For practical applications of solid/solution adsorption processes, the kinetics of these processes is at least as much essential as their features at equilibrium. Meanwhile, the general understanding of this kinetics and its corresponding theoretical description are far behind the understanding and the level of theoretical interpretation of adsorption equilibria in these systems. The Lagergren empirical equation proposed at the end of 19th century to describe the kinetics of solute sorption at the solid/solution interfaces has been the most widely used kinetic equation until now. This equation has also been called the pseudo-first order kinetic equation because it was intuitively associated with the model of one-site occupancy adsorption kinetics governed by the rate of surface reaction. More recently, its generalization for the two-sites-occupancy adsorption was proposed and called the pseudo-second-order kinetic equation. However, the general use and the wide applicability of these empirical equations during more than one century have not resulted in a corresponding fundamental search for their theoretical origin. Here the first theoretical development of these equations is proposed, based on applying the new fundamental approach to kinetics of interfacial transport called the Statistical Rate Theory. It is shown that these empirical equations are simplified forms of a more general equation developed here, for the case when the adsorption kinetics is governed by the rate of surface reactions. The features of that general equation are shown by presenting exhaustive model investigations, and the applicability of that equation is tested by presenting a quantitative analysis of some experimental data reported in the literature.
The primary objective of the present study was to compare the effect of a neoprene sleeve on knee joint position sense during a sitting open kinetic chain test and a supine closed kinetic chain test. Young (24 +/- 2 years old), healthy subjects (18 men and 18 women) performed knee joint angle replication tests during open kinetic chain knee extension (sitting) and closed kinetic chain leg press (supine with an axial load of 15% body weight) before and after application of a neoprene sleeve over the dominant knee. The improvement in ability to replicate joint angles after application of the sleeve (sleeve effect) was significantly less during the supine closed kinetic chain test (0.3 degree +/- 1.4 degrees) than during the sitting open kinetic chain test (1.2 degrees +/- 1.1 degrees). The sleeve effect was inversely related to subjects' performance without the sleeve during both the sitting open kinetic chain and supine closed kinetic chain tests, suggesting that some people may derive greater benefit from the sleeve than others. Although the sleeve effects were small, particularly during the supine closed kinetic chain test, 72% of subjects felt that the sleeve improved their overall test performance. Future research is needed to establish the functional relevance of the small sleeve effects observed and to identify the characteristics of people who might derive greatest benefit from sleeve use.
A kinetic model for omega-transaminase from Bacillus thuringiensis JS64 was developed by using the King-Altman method to simulate the kinetic resolution of alpha-methylbenzylamine (alpha-MBA). Starting from a ping-pong bi-bi mechanism, a complete kinetic model including substrate inhibition only in the reverse reaction (i.e., transamination between acetophenone and L-alanine) was developed. The asymmetric synthesis of (S)-alpha-MBA proved to be difficult due to a much lower maximum reverse reaction rate than the maximum forward reaction rate, thermodynamically exergonic forward reaction (i.e., transamination between (S)-alpha-MBA and pyruvate), and the severe product and substrate inhibition of the reverse reaction. Experimental values for kinetic parameters show that the product inhibition constant of (S)-alpha-MBA is the most important parameter on determining the resolution reaction rate, suggesting that the resolution reaction rate will be very low unless (S)-alpha-MBA strongly inhibits the reverse reaction. Using the kinetic model, the kinetic resolution of alpha-MBA in aqueous buffer was simulated, and the simulation results showed a high degree of consistency with experimental data over a range of reaction conditions. Various simulation results suggest that the crucial bottleneck in the kinetic resolution of alpha-MBA lies mainly in the accumulation of acetophenone in reaction media as the reaction proceeds, whereas L-alanine exerts a little inhibitory effect on the reaction. The model predicts that removing acetophenone produced during the reaction can enhance the reaction rate dramatically. Indeed, the biphasic reaction system is capable of extracting acetophenone from the aqueous phase, showing a much higher reaction rate compared to a monophasic reaction system. The kinetic model was also useful in predicting the properties of other, better enzymes as well as the optimal concentrations of amino acceptor and enzyme in the resolution reaction.
Using simulation to study the folding kinetics of 20-mer poly-phenylacetylene (pPA) oligomers, we find a long time scale trapped kinetic phase in the cumulative folding time distribution. This is demonstrated using molecular dynamics to simulate an ensemble of over 100 folding trajectories. The simulation data are fit to a four-state kinetic model which includes the typical folded and unfolded states, along with an intermediate state, and most surprisingly, a kinetically trapped state. Topologically diverse conformations reminiscent of alpha helices, beta turns, and sheets in proteins are observed, along with unique structures in the form of knots. The nonhelical conformations are implicated, on the basis of structural correlations to kinetic parameters, to contribute to the trapped kinetic behavior. The strong solvophobic forces which mediate the folding process and produce a stable helical folded state also serve to overstabilize the nonhelical conformations, ultimately trapping them. From our simulations, the folding time is predicted to be on the order of 2.5-12.5 mus in the presence of the trapped kinetic phase. The folding mechanism for these 20-mer chains is compared with the previously reported folding mechanism for the pPA 12-mer chains. A linear scaling relationship between the chain length and the mean first passage time is predicted in the absence of the trapped kinetic phase. We discuss the major implications of this discovery in the design of self-assembling nanostructures.
The principles of structural kinetics allow one to define the thermodynamic conditions that are sufficient to generate a certain type of kinetic behavior. If subunits are loosely coupled, that is if no quaternary constraint exists between them, the kinetic behavior of the polymeric enzyme is qualitatively defined by the behavior of an ideal dimer. The nature and the extent of the kinetic cooperativity are defined by the energy of interaction, delta G rho, between two subunits. This energy of interaction is that of an ideal dimer relative to that of the A2 and B2 states. This thermodynamic formulation of a given type of cooperativity holds whatever the degree of polymerization of the enzyme. Under these conditions of loose coupling between subunits, positive kinetic cooperativity cannot be associated with any sigmoidicity of the rate curve. The range of energy coupling where positive kinetic cooperativity must, of necessity, be observed becomes more and more narrow as the number of subunit interactions is increased. This range, however, is independent of the number of subunits. The same situation is not observed for negative cooperativity which appears to be independent of both the number of subunits and the number of subunit interactions. If the subunits are tightly coupled, that is if quaternary constraints exist between them, three thermodynamic parameters, delta G' rho, delta G lambda, delta G mu, are required to define the nature of kinetic cooperativity. delta G' rho is the free energy of an ideal strained dimer relative to that of strained A2 and B2 states. delta G lambda and delta G mu represent the difference of strain energies between conformations A and B and B and B relative to that existing between conformations A and A. One may determine in the parametric space (delta G' rho, delta G lambda, delta G mu) the boundaries between the sufficient conditions that generate a certain type of cooperativity and the lack of these conditions. The kinetic parameters of the rate equation are not all independent. A number of constraint conditions exist between them which depend upon the subunit design of the polymeric enzyme. The existence of these constraint conditions may be diagnostic of a certain type of subunit interactions.
Cytochrome P450 (CYP) enzymes represent a superfamily of hemoproteins that are involved in the metabolism of a wide variety of endogenous and exogenous compounds. For a given CYP enzyme, kinetic properties of a substrate are usually related to substrate lipophilicity (log P or log D(7.4)). In this review, enzyme kinetic parameters (K(m), V(max), and V(max)/K(m)) of 215 CYP3A4-mediated metabolic reactions of 113 drugs in human liver microsomes were obtained from the literature, and lipophilicity values of the 113 drugs were calculated using the ACD/Labs 8.0 program. A low degree of K(m)- or (V(max)/K(m))-lipophilicity correlation, but no V(max)-lipophilicity correlation, is exhibited for the CYP3A4-mediated reactions. Overall, K(m) decreases, but V(max)/K(m) increases, with increasing substrate lipophilicity, and V(max) appears to be independent of substrate lipophilicity. In other words, a low K(m) generally confers a high V(max)/K(m) ratio for a substrate. The degree of lipophilicity-kinetics correlations is related to both reaction types (or reaction mechanisms) and regiochemical positions (or physicochemical properties) of the reaction groups of the substrates. Among the categorized CYP3A4-mediated reactions, the best lipophilicity-kinetics correlation is achieved for carbon hydroxylation, followed by N-dealkylation. No or little lipophilicity-kinetics correlations are seen for N, S-oxidation and other reactions. Within the hydroxylation group, aliphatic hydroxylation shows the best lipophilicity-kinetics correlation while hydroxylation on a carbon atom adjacent to an aromatic ring does not show any lipophilicity-kinetics correlation. The detailed structural and kinetic data sets of the human liver microsomal CYP3A4-mediated reactions represent a specialized database useful for researchers working in the area of structure-metabolism relationship modeling and analysis.
The kinetic mechanism by which Escherichia coli RecBCD helicase unwinds duplex DNA was studied using a fluorescence stopped-flow method. Single turnover DNA unwinding experiments were performed using a series of fluorescently labeled DNA substrates containing duplex DNA regions ranging from 24 bp to 60 bp. All or no DNA unwinding time courses were obtained by monitoring the changes in fluorescence resonance energy transfer between a Cy3 donor and Cy5 acceptor fluorescent pair placed on opposite sides of a nick in the duplex DNA. From these experiments one can determine the average rates of DNA unwinding as well as a kinetic step-size, defined as the average number of base-pairs unwound between two successive rate-limiting steps repeated during DNA unwinding. In order to probe how the kinetic step-size might relate to a mechanical step-size, we performed single turnover experiments as a function of [ATP] and temperature. The apparent unwinding rate constant, kUapp, decreases with decreasing [ATP], exhibiting a hyperbolic dependence on [ATP] (K1/2=176(+/-30) microM) and a maximum rate of kUapp=204(+/-4) steps s(-1) (mkUapp=709(+/-14) bp s(-1)) (10 mM MgCl2, 30 mM NaCl (pH 7.0), 5% (v/v) glycerol, 25.0 degrees C). kUapp also increases with increasing temperature (10-25 degrees C), with Ea=19(+/-1) kcal mol(-1). However, the average kinetic step-size, m=3.9(+/-0.5) bp step(-1), remains independent of [ATP] and temperature. This indicates that even though the values of the rate constants change, the same elementary kinetic step in the unwinding cycle remains rate-limiting over this range of conditions and this kinetic step remains coupled to ATP binding. The implications of the constancy of the measured kinetic step-size for the mechanism of RecBCD-catalyzed DNA unwinding are discussed.
Stopped-flow kinetic studies of the reductive half-reaction of methylamine dehydrogenase from Paracoccus denitrificans yielded kinetic constants for the reversible formation of the imine intermediate formed between the substrate and the tryptophan tryptophylquinone (TTQ) prosthetic group and for the hydrogen abstraction step which occurs concomitantly with TTQ reduction. When CD3NH2 was used as a substrate, deuterium kinetic isotope effects of 4.2 and 3.8, respectively, were measured for the rate constants that correspond to the formation and dissociation of the iminoquinone intermediate. A deuterium kinetic isotope effect of 17.2 was measured for the hydrogen abstraction step. The maximum deuterium kinetic isotope effect which was measured in steady-state kinetic experiments was 3.0. These data are discussed in relation to the reaction mechanism of methylamine dehydrogenase and the similar large deuterium kinetic isotope effect for hydrogen abstraction which has been observed for another quinoprotein, plasma amine oxidase.
The Escherichia coli Rep protein is a DNA helicase that functions as a homodimer to catalyze the unwinding of duplex DNA during DNA replication in a reaction that is coupled to the binding and hydrolysis of ATP. As a first step toward a molecular understanding of the interactions of Rep with adenine nucleotides, we have investigated the kinetic mechanism of adenine nucleotide binding to the Rep monomer, which is the state of the protein in the absence of DNA. Although ATP binding to Rep does not significantly change the intrinsic tryptophan fluorescence, the binding of the fluorescent nucleotide analogue, 2'(3')-O-(N-methylanthraniloyl)-ATP (mantATP) is associated with a large increase in mant nucleotide fluorescence intensity [lambda ex = 290 nm, lambda em > 420 nm; Moore, K. J. M., & Lohman, T. M. (1994) Biochemistry (preceding article in this issue)]. We have used the fluorescence signal from mantATP binding to monitor the kinetics of nonfluorescent nucleotide binding to Rep by a kinetic competition approach. The simultaneous and parallel binding of a mixture of mantATP and ATP to the Rep monomer is associated with a complex triphasic fluorescence transient during the approach to equilibrium. Global analysis of the fluorescence transients over a range of [ATP] by numerical integration techniques was used to define the kinetic mechanism of ATP binding and to determine the elementary rate constants. Using this approach, the kinetic rate constants for ADP, ATP gamma S, AMPPNP, AMP, adenosine, and inorganic phosphate were also determined at 4 degrees C in 20 mM Tris.HCl (pH 7.5), 6 mM NaCl, 10% (v/v) glycerol, and 5 mM MgCl2. The kinetics of adenine nucleotide binding to the Rep monomer are similar to those observed with the mant nucleotides under identical experimental conditions (Moore & Lohman, 1994). The kinetic competition data are consistent with the following two-step mechanism for the binding of ATP, ADP, and ATP gamma S, where P is the Rep monomer and A is the adenine nucleotide: P+A [formula: see text] P-A [formula: see text] (P-A). In the presence of 5 mM MgCl2, the values of K+1 (approximately 10(7) M-1 s-1) and k+2 (approximately 10 s-1) are comparable for each nucleotide, whereas k+2 > k-1 for ATP and ATP gamma S while for ADP k+2 << k-1; hence, differences in the overall equilibrium binding affinities of these nucleotides are primarily due to changes in k-1.(ABSTRACT TRUNCATED AT 400 WORDS)
The kinetics of CO binding to human cytochrome P450 3A4 was examined by the flash photolysis technique, employing the membrane-bound P450 expressed in baculovirus-infected SF9 insect cells. Triexponential kinetics was observed, indicating that P450 3A4 is composed of multiple, kinetically distinguishable conformers. To define the substrate specificity of individual P450 3A4 conformers we evaluated the effect of a series of substrates of varying sizes and structures on the CO binding kinetics. The rate of CO binding to the total mixture of P450 3A4 conformers was increased in the presence of nifedipine and erythromycin, decreased by quinidine, testosterone, and warfarin, and unaffected by cimetidine and 17 alpha-ethynylestradiol. A recently developed kinetic difference method (Koley, A. P., Robinson, R. C., Markowitz, A., and Friedman, F. K. (1994) Biochemistry 33, 2484-2489) was used to define the kinetic parameters of individual P450 3A4 conformers. The results showed that different conformers have distinct substrate specificities. The substrates had markedly variable effects on the CO binding kinetics of their target P450 3A4 conformers and thus differentially modulate their conformations. These results demonstrate that the interaction of a particular substrate with a specific P450 3A4 conformer can be assessed in the presence of multiple conformers.
A recent trend in occupational safety and health has focused on the use of respiratory protective equipment to supplant engineering controls as the primary means of protecting workers from toxic substances. Respirator adsorbent cartridges have been demonstrated to have a finite capacity to adsorb toxic vapors. The knowledge of when this limit is approached or has been exceeded is crucial to the user. The Wheeler kinetic breakthrough model has been shown to describe accurately organic vapor penetration through beds of activated carbon. The model, however, does not account for competitive adsorption of water vapor or other organic vapors. The investigations reported here demonstrate the effect of adsorbed water vapor on the kinetic adsorption parameters (kinetic rate constant and kinetic saturation capacity) of the Wheeler equation. Adsorbent beds were equilibrated at varying concentrations of water vapor and then challenged with carbon tetrachloride vapor-laden air. Dry carbon had an initial rate constant of 62.5 s-1 and a kinetic adsorption capacity of 0.36 g of adsorbed CCl4/gram (g/g) of adsorbent. These parameters decreased in proportion to the amount of water vapor adsorbed, with the minimum predicted values occurring at 100% relative humidity. The minimum experimental value for the kinetic rate constant was 17.6 s-1, a decrease of 73% from the dry carbon values. The minimum predicted value for the kinetic adsorption capacity was 0.16 g/g, a decrease of 45%.
Solute uptake in many cells is characterized by a series of additive Michaelis-Menten functions. Several explanations for these kinetics have been advanced: unstirred layers, transport across more than one membrane, effects of solute concentration on membrane potential, numerous carrier systems. Although each of these explanations might suffice for individual cases, none provides a comprehensive basis for interpretation of the kinetics. The most common mechanism of solute absorption involves cotransport of solute with a driver ion. A model is developed in which solute and driver ion bind randomly to a membrane-bound carrier which provides a single transmembrane pathway for transport. The kinetic properties of the model are explored with particular reference to its capacity to generate additive Michaelian functions for initial rate measurements of isotopic solute influx. In accord with previous analysis of ordered binding models (Sanders, D., Hansen, U.-P., Gradmann, D., Slayman, C.L. (1984) J. Membrane Biol. 77:123), the conventional assumption that transmembrane transit rate-limits transport has not been applied. Random binding carriers can exhibit single or multiple Michaelian kinetics in response to changing substrate concentration. These kinetics include high affinity/low velocity and low affinity/high velocity phases (so-called "dual isotherms") which are commonly observed in plant cells. Other combinations of the Michaelis parameters can result in cis-(substrate) inhibition. Despite the generality of the random binding scheme and the complexity of the underlying rate equation, a number of predictive and testable features emerge. If external driver ion concentration is saturating, single Michaelian functions always result and increasing internal substrate concentration causes uncompetitive inhibition of transport. Numerical analysis of the model in conditions thought to resemble those in many experiments demonstrates that small relative differences in a few key component rate constants of the carrier reaction cycle are instrumental in generation of dual isotherms. The random binding model makes the important prediction that the contributions of the two isotherms show opposing dependence on external concentration of driver ion as this approaches saturation. In the one case in which this dependence has been examined experimentally, the model provides a good description of the data. Charge translocation characteristics of the carrier can be determined from steady-state kinetic data on the basis of the response of substrate flux to modulation of internal driver ion concentration.(ABSTRACT TRUNCATED AT 400 WORDS)