Kinetic analysis of a reaction model with two binding sites for acetylcholinesterase

After having suggested a kinetic model with two binding sites for acetylcholinesterase, the authors obtained the various function of [I] (1/vi; (vo/vi-1)/[I]; 1/Vi; Ki/Vi) starting from the velocity equation. An analytical study was then carried out showing the theoretical shape of such functions at different values of the kinetic parameters.     

Determination of the Catalytic Mechanism for Mitochondrial Malate Dehydrogenase

The kinetics of malate dehydrogenase (MDH) catalyzed oxidation/reduction of L-malate/oxaloacetate is pH-dependent due to the proton generated/taken up during the reaction. Previous kinetic studies on the mitochondrial MDH did not yield a consensus kinetic model that explains both substrate and pH dependency of the initial velocity. In this study, we propose, to our knowledge, a new kinetic mechanism to explain kinetic data acquired over a range of pH and substrate concentrations. Progress curves in the forward and reverse reaction directions were obtained under a variety of reactant concentrations to identify associated kinetic parameters. Experiments were conducted at physiologically relevant ionic strength of 0.17 M, pH ranging between 6.5 and 9.0, and at 25°C. The developed model was built on the prior observation of proton uptake upon binding of NADH to MDH, and that the MDH-catalyzed oxidation of NADH may follow an ordered bi-bi mechanism with NADH/NAD binding to the enzyme first, followed by the binding of oxaloacetate/L-malate. This basic mechanism was expanded to account for additional ionic states to explain the pH dependency of the kinetic behavior, resulting in what we believe to be the first kinetic model explaining both substrate and pH dependency of the reaction velocity.     

A closed-form analytic expression for FRAP formula for the binding diffusion model

One of the most dominant methods cells use for a large class of cellular processes is reaction (or binding) diffusion kinetics, which are controlled by kinetic constants such as diffusion coefficients and on/off binding rate constants. Fluorescence recovery after photobleaching (FRAP) can be used to determine these kinetic constants in living cells. While an analytic expression for FRAP formulae for pure diffusion has been available for some time, an analytic FRAP formula for the binding diffusion model has not been reported yet. Here, we present an analytic FRAP formula for the binding diffusion model in an explicit form allowing for diffusion of the bound complex for either a uniform circle laser profile or a Gaussian laser profile.     

Lumped parameter model for prediction of initial breakthrough profiles for the chromatographic capture of antibodies from a complex feedstock

A simple mathematical model to predict initial breakthrough profiles from preparative chromatographic separations of biological macromolecules has been developed. A lumped parameter approach was applied, employing Langmuirian adsorption kinetics to describe the rate of mass transfer (MT) from the bulk liquid in the column to the bound state. Equilibrium and kinetic adsorption data were determined for six different packed bed chromatographic adsorbents: two derivatised with rProtein A; and four functionalised with synthetic low molecular weight ligands. All adsorption isotherms were well described by the Langmuir model, whereas the data fitting to kinetic batch experiments showed that the model was inadequate after the first approximately 25 min of adsorption for four of the six adsorbents. The model underestimated the dynamic Ig breakthough on packed beds of rProtein A Sepharose FF, MabSelect, MBI HyperCel, and MabSorbent A1P, applying a feedstock of 20-100% (v/v) clarified rabbit antiserum. However, when employing a maximum adsorption capacity 25% greater than that determined in batch binding studies, excellent agreement was obtained at all antiserum strengths for most adsorbents. Useful insights into scale-up and process design can be obtained by applying the model, without determining tentative parameters specific for each adsorbent and target protein concentration. However, the model parameters are solvent dependent so a prerequisite for its true applicability is that binding is both Langmuirian and essentially independent of the ionic strength of the feedstock applied.     

Concurrent binding to multiple ligands: kinetic rates of CD16b for membrane-bound IgG1 and IgG2

CD16b (FcgammaRIIIb) is the most common receptor for the Fc domain of IgG on leukocytes. The binding of Fc receptors to immunoglobulin triggers a wide array of immune responses. In published assays measuring the reaction of CD16b with isotypes of soluble IgG, the affinity for IgG1 was low and that for IgG2 was undetectable. Here we report the first measurement of kinetic rates of CD16b binding to membrane-bound IgG isotypes-a physically distinct and physiologically more relevant presentation-using a recently developed micropipette method. In contrast to the soluble data, we found clearly measurable IgG2 binding, with a forward kinetic rate six-fold lower than that of IgG1 but with an equilibrium affinity only threefold lower. This suggests a nonnegligible role for IgG2 in Fc-mediated immune responses, particularly in longer duration contacts. The binding constants were measured from two sets of experiments. Single-isotype experiments were analyzed by an existing model (, Biophys. J. 75:1553-1572). The resulting kinetic rates were used as input to an extended model (, Biophys. J. 79:1850-1857.) to predict the results of mixed-isotype experiments. This design enabled rigorous validation of the concurrent binding model through a test of its predictive ability.     

Detection and kinetics of mucosal pathogenic bacteria binding with polysaccharides

The detection and kinetics of mucosal pathogenic bacteria binding on polysaccharide ligands were studied using a surface plasmon resonance biosensor. The kinetic model applied curve-fitting to the experimental surface plasmon resonance sensorgrams to evaluate the binding interactions. The kinetic parameters for the mucosal pathogenic bacteria (Pseudomonas aeruginosa, Pseudomonasfluorescens, Serratia marcescens) with the alginate ligand were determined from a kinetic model. In addition, the binding interactions of the mucosal pathogenic bacteria with polysaccharide binding pairs (Pseudomonas aeruginosa/alginate, Streptococcus pneumoniae/pneumococcal polysaccharide, Staphylococcus aureus/pectin) were also compared with their kinetic parameters. The rate constants of association for Pseudomonas aeruginosa with the alginate ligand were higher than those for Pseudomonas fluorescens. Serratia marcescens had no detectable interaction with the alginate ligand. The adhesion affinity of Pseudomonas aeruginosa with alginate was higher than that for the other binding pairs. The binding affinities of the pathogenic bacteria with their own polysaccharide were higher than that of Staphylococcus aureus with pectin. Measuring the contact angle was found to be a feasible method for detecting binding interactions between analytes and ligands.     

Insulin receptor processing as a function of erythrocyte age. A kinetic model for down-regulation

The effects of cell aging on insulin binding and on insulin receptor processing in human erythrocytes were studied. Erythrocytes were found to exponentially lose equal proportions of both high and low affinity receptors as a function of age. The affinities of remaining surface receptors did not change significantly. The maximum extent of insulin receptor down-regulation that could be induced decreased linearly with age over the range studied. Together with dose-response and time course studies, these age-related changes in insulin binding and receptor down-regulation were used to develop a kinetic model in which receptor internalization is a function of surface receptor concentration. The ability of the model to predict the behavior of a heterogeneous population suggests that changes in receptor processing with age may be attributed to changes in the surface receptor concentration.     

Simple models for the analysis of binding protein-dependent transport systems.

Mathematical modeling was used to evaluate experimental data for bacterial binding protein-dependent transport systems. Two simple models were considered in which ligand-free periplasmic binding protein interacts with the membrane-bound components of transport. In one, this interaction was viewed as a competition with the ligand-bound binding protein, whereas in the other, it was considered to be a consequence of the complexes formed during the transport process itself. Two sets of kinetic parameters were derived for each model that fit the available experimental results for the maltose system. By contrast, a model that omitted the interaction of ligand-free binding protein did not fit the experimental data. Some applications of the successful models for the interpretation of existing mutant data are illustrated, as well as the possibilities of using mutant data to test the original models and sets of kinetic parameters. Practical suggestions are given for further experimental design.     

A proposed mechanism for myosin magnesium adenosine triphosphatase activity

A formal mechanism for the myosin MgATPase is proposed. The basic characteristics of this mechanism require that the binding of substrate at either one of two equivalent nucleotide sites of uncomplexed myosin prevents binding of substrate at the other unoccupied site (i.e. negative cooperativity) and that the rapid formation of a myosin-product complex permits binding of substrate at the unoccupied site. Analogue computer kinetic simulations indicate that the proposed mechanism is compatible with the observed transient phase kinetics characterizing the interaction of the enzyme with MgATP. In addition, analysis of the derived rate equation show that the mechanism is also consistent with existing steady-state kinetic data for the myosin MgATPase. A simpler mechanism is proposed for the subfragment-1 MgATPase that is shown to be compatible with the existing kinetic data. Features of the proposed myosin MgATPase mechanism are incorporated into a model of contraction which utilizes the bipartite structure and nucleotide site interaction of the myosin crossbridge to provide an efficient utilization of ATP in the contraction cycle.     

Differential dissociation kinetics explain the binding preference of insulin-like growth factor binding protein-6 for insulin-like growth factor-II over insulin-like growth factor-I

Insulin-like growth factor binding protein-6 binds insulin-like growth factor-II with a marked preferential affinity over insulin-like growth factor-I. The kinetic basis of this binding preference was studied using surface plasmon resonance. Binding of insulin-like growth factor-I and insulin-like growth factor-II to immobilized insulin-like growth factor binding protein-6 fitted a two-site binding kinetic model. Insulin-like growth factor-I and insulin-like growth factor-II association rates were similar whereas the dissociation rate was approximately 60-fold lower for insulin-like growth factor-II, resulting in a higher equilibrium binding affinity for insulin-like growth factor-II. The equilibrium binding affinities of a series of insulin-like growth factor-II mutants were also explained by differential dissociation kinetics. O-glycosylation had a small effect on the association kinetics of insulin-like growth factor binding protein-6. The insulin-like growth factor binding properties of insulin-like growth factor binding protein-6 are explained by differential dissociation kinetics.     

A kinetic study of analyte-receptor binding and dissociation for biosensor applications: a fractal analysis for two different DNA systems

A fractal analysis of DNA binding and dissociation kinetics on biosensor surfaces is presented. The fractal approach provides an attractive, convenient method to model the kinetic data taking into account the effects of surface heterogeneity brought about by ligand immobilization. The fractal technique can be used in conjunction or as an alternate approach to conventional modeling techniques, such as the Langmuir model, saturation model, etc. Examples analyzed include a DNA molecular beacon biosensor and a plasmid DNA-(cationic polymer) interaction biosensor. The molecular beacon example provides some insights into the nature of the surface and how it influences the binding rate coefficients. The DNA-cationic polymer interaction example provides some quantitative results on the binding and dissociation rate coefficients. Data taken from the literature may be modeled, in the case of binding, using a single-fractal analysis or a dual-fractal analysis. The dual-fractal analysis results indicate a change in the binding mechanism as the reaction progresses on the surface. A single-fractal analysis is adequate to model the dissociation kinetics in the example presented. Relationships are presented for the binding rate coefficients as a function of their corresponding fractal dimension, D(f), which is an indication of the degree of heterogeneity that exists on the surface. When analyte-receptor binding is involved, an increase in the heterogeneity of the surface (increase in D(f)) leads to an increase in the binding rate coefficient.     

O-phospho-L-serine and the thiocarboxylated sulfur carrier protein CysO-COSH are substrates for CysM, a cysteine synthase from Mycobacterium tuberculosis

The kinetic pathway of CysM, a cysteine synthase from Mycobacterium tuberculosis, was studied by transient-state kinetic techniques. The expression of which is upregulated under conditions of oxidative stress. This enzyme exhibits extensive homology with the B-isozymes of the well-studied O-acetylserine sulfhydrylase family and employs a similar chemical mechanism involving a stable alpha-aminoacrylate intermediate. However, we show that specificity of CysM for its amino acid substrate is more than 500-fold greater for O-phospho-L-serine than for O-acetyl-L-serine, suggesting that O-phospho-L-serine is the likely substrate in vivo. We also investigated the kinetics of the carbon-sulfur bond-forming reaction between the CysM-bound alpha-aminoacrylate intermediate and the thiocarboxylated sulfur carrier protein, CysO-COSH. The specificity of CysM for this physiological sulfide equivalent is more than 3 orders of magnitude greater than that for bisulfide. Moreover, the kinetics of this latter reaction are limited by association of the proteins, while the reaction with bisulfide is consistent with a rapid equilibrium binding model. We interpret this finding to suggest that the CysM active site with the bound aminoacrylate intermediate is protected from solvent and that binding of CysO-COSH produces a conformational change allowing rapid sulfur transfer. This study represents the first detailed kinetic characterization of sulfide transfer from a sulfide carrier protein.     

1-Deoxy-D-xylulose 5-phosphate synthase catalyzes a novel random sequential mechanism

Emerging resistance of human pathogens to anti-infective agents make it necessary to develop new agents to treat infection. The methylerythritol phosphate pathway has been identified as an anti-infective target, as this essential isoprenoid biosynthetic pathway is widespread in human pathogens but absent in humans. The first enzyme of the pathway, 1-deoxy-D-xylulose 5-phosphate (DXP) synthase, catalyzes the formation of DXP via condensation of D-glyceraldehyde 3-phosphate (D-GAP) and pyruvate in a thiamine diphosphate-dependent manner. Structural analysis has revealed a unique domain arrangement suggesting opportunities for the selective targeting of DXP synthase; however, reports on the kinetic mechanism are conflicting. Here, we present the results of tryptophan fluorescence binding and kinetic analyses of DXP synthase and propose a new model for substrate binding and mechanism. Our results are consistent with a random sequential kinetic mechanism, which is unprecedented in this enzyme class.     

Kinetics of gonadotropin binding by receptors of the rat testis. Analysis by a nonlinear curve-fitting method.

The kinetics of the reaction between human chorionic gonadotropin (hCG) and specific gonadotropin receptors in the rat testis were determined at 24 and 37 degrees, over a wide range of hormone concentrations. Hormone concentrations were corrected for the binding activity of the (-125I)hCG tracer preparations. Analysis of the experimental data was performed with an interactive nonlinear curve fitting program, based upon the second-order chemical kinetic differential equation. The mean values for the association rate constant (k1) were 4.7 x 10-7 M-1 min-1 at 24 degrees, and 11.0 x 10-7 M-1 min-1 at 37 degrees. At both temperatures, the values of kl were independent of hormone concentration. Initial dissociation rates were consistent with first order kinetics, with dissociation rate constant (k2) of 1.7 x 10 minus -3 and 4.6 x 10 minus -3 min minus -1 at 24 and 37 degrees, respectively. When studied over longer periods at 24 degrees, the dissociation process appeared to be multiexponential. The kinetics of degradation of (-125I)hCG and receptors were determined at both temperatures, and a mathematical model was developed by modification of the second-order chemical kinetic differential equation to take these factors into account. The application of such a model to hCG kinetic binding data demonstrated that reactant degradation had little significant effect on the derivation of the association rate constant (k1), but caused significant overestimation of the dissociation rate constant (k2) values derived from association experiments. The model was also applied by computer simulation to a theoretical analysis of the effects of degradation of free hormone and receptor sites upon kinetic and steadystate binding data. By this method, the initial velocities of hormone binding were shown to be less affected by degradation than the steady-state levels of hormone-receptor complex. Also, reactant degradation in simulated steady-state experiments caused an underestimate of the apparent equilibrium association constant, but had relatively less effect on the determination of binding site concentration.     

Diffusion-controlled association of a dye, 1-anilinonaphthalene-8-sulfonic acid, to a protein, bovine serum albumin, using a fast-flow microsecond mixer and stopped-flow

The kinetic constants of the two fastest reactions of 1-anilinonaphthalene-8-sulfonic acid binding to bovine serum albumin are derived from the results of experiments with a microsecond fast-flow mixing technique and a stopped-flow method. The experiments are interpreted in terms of rapid bimolecular diffusion-controlled associations to two independent regions on the protein surface; this reaction mechanism contrasts with previous kinetic studies of ligand binding to bovine serum albumin which have not demonstrated the fastest kinetic processes.     

Enhancer and competitive allosteric modulation model for G-protein-coupled receptors

A new mathematical model, referred to as Enhancer and Competitive Allosteric Modulator (ECAM) model, developed with the aim of quantitatively describing the interaction of an allosteric modulator with both enhancer and competitive properties towards G-protein-coupled receptors is described here. Model simulations for equilibrium (displacement-like and saturation-like), and kinetic (association and dissociation) binding experiments were performed. The results showed the ability of the model to interpret a number of possible ligand-receptor binding behaviors. In particular, the binding properties of PD81723, an enhancer and competitive allosteric modulator for the adenosine A₁ receptor, were experimentally evaluated by radioligand binding assays and interpreted by the ECAM model. The results also offer a theoretical background enabling the design and optimization of compounds endowed with allosteric enhancer, competitive, agonist, antagonist, and inverse agonist properties.     

A kinetically defined Na+/H+ antiporter within a mathematical model of the rat proximal tubule

The luminal membrane antiporter of the proximal tubule has been represented using the kinetic formulation of E. Heinz (1978. Mechanics and Engergetics of Biological Transport. Springer-Verlag, Berlin) with the assumption of equilibrium binding and 1:1 stoichiometry. Competitive binding and transport of NH+4 is included within this model. Ion affinities and permeation velocities were selected in a least-squares fit to the kinetic parameters determined experimentally in renal membrane vesicles (Aronson, P.S., M.A. Suhm, and J. Nee. 1983. Journal of Biological Chemistry. 258:6767-6771). The modifier role of internal H+ to enhance transport beyond the expected kinetics (Aronson, P.S., J. Nee, and M. A. Suhm. 1982. Nature. 299:161-163) is represented as a velocity effect of H+ binding to a single site. This kinetic formulation of the Na+/H+ antiporter was incorporated within a model of the rat proximal tubule (Weinstein, A. M. 1994. American Journal of Physiology. 267:F237-F248) as a replacement for the representation by linear nonequilibrium thermodynamics (NET). The membrane density of the antiporter was selected to yield agreement with the rate of tubular Na+ reabsorption. Simulation of 0.5 cm of tubule predicts that the activity of the Na+/H+ antiporter is the most important force for active secretion of ammonia. Model calculations of metabolic acid-base disturbances are performed and comparison is made among antiporter representations (kinetic model, kinetic model without internal modifier, and NET formulation). It is found that the ability to sharply turn off Na+/H+ exchange in cellular alkalosis substantially eliminates the cell volume increase associated with high HCO3- conditions. In the tubule model, diminished Na+/H+ exchange in alkalosis blunts the axial decrease in luminal HCO3- and thus diminishes paracellular reabsorption of Cl-. In this way, the kinetics of the Na+/H+ antiporter could act to enhance distal delivery of Na+, Cl-, and HCO3- in acute metabolic alkalosis.     

The membrane-binding properties of a class A amphipathic peptide

The membrane-binding properties of a class A amphipathic peptide (18D) were investigated using two different immobilized model membrane systems. The first system involved the use of surface plasmon resonance (SPR) to study the binding of 18D to dimyristylphosphatidylcholine (DMPC) and dimyristylphosphatidylglycerol (DMPG), which allowed peptide binding to be monitored in real time. The SPR experiments indicated stronger binding of 18D to DMPG than DMPC, which kinetic analysis revealed was due to a faster on-rate. The second model membrane system involved immobilized membrane chromatography in which the binding of 18D to either DMPC or DMPG monolayers covalently linked to silica particles was analysed by elution chromatography. Stronger binding affinity of 18D was also obtained with the negatively charged phosphatidylglycerol (PG) monolayer compared to the phosphatidylcholine (PC) monolayer, which was consistent with the SPR results. Non-linear binding behaviour of 18D to the immobilized lipid monolayers was also observed, which suggests that the peptide undergoes conformational and orientational changes upon binding to the immobilized PC and PG ligands. Significant band broadening was also observed on both monolayers, with larger bandwidths obtained on the PC surface, indicating slower binding and orientation kinetics with the zwitterionic surface. The dependence of logk' on the percentage of methanol also demonstrated a bimodal interaction whereby hydrophobic forces predominated at higher temperatures and methanol concentrations, while at lower temperatures, electrostatic and other polar forces also made a contribution to the affinity of the peptides for the lipid monolayer particularly. Overall, these results demonstrate the complementary use of these two lipid biosensors which allows the role of hydrophobic and electrostatic forces in peptide–membrane interactions to be studied and insight gained into the kinetic factors associated with these interactions.