Determination of rate constants of antigen-antibody reaction. A theory

A new method of determination of rate constants for antigen-antibody interactions is proposed. This method is based on a solid phase immunoenzymatic analysis of the dynamics of elution of immobilized antigen-bound antibodies in the presence of a free antigen. The kinetics of this process is described by a system of differential equations, whose solution results in expression defining the dynamics of antibody interaction with immobilized and free antigens. Simple formulas were derived for the calculation of the rate and equilibrium constants for the antibody-antigen reaction on the basis of experimental kinetic curves. The use of theoretical kinetic curves for antibody elution showed that these formulas reflect with a high degree of accuracy the kinetic properties of the reaction under study.     

Determination of equilibrium constants and maximum binding capacities in complexIn vitro systems: I. The mammillary system

It is shown that in a system containingn types of mutually noninteracting binding sites, the association constants are then roots of annth order polynomial while the maximum binding capacities can be evaluated by solving a set ofn simultaneous linear equations. Thenth order polynomial and the system ofn linear equations are defined in terms of 2n intermediate coefficients, the coefficients being themselves evaluated by substituting 2n sets of appropriate experimental data into an auxiliary system of 2n linear equations. The existence and uniqueness of the solutions are established.     

Identifiability and interval identifiability of mammillary and catenary compartmental models with some known rate constants

The identifiability problem is addressed for n-compartment linear mammillary and catenary models, for the common case of input and output in the first compartment and prior information about one or more model rate constants. We first define the concept of independent constraints and show that n-compartment linear mammillary or catenary models are uniquely identifiable under n-1 independent constraints. Closed-form algorithms for bounding the constrained parameter space are then developed algebraically, and their validity is confirmed using an independent approach, namely joint estimation of the parameters of all uniquely identifiable submodels of the original multicompartmental model. For the noise-free (deterministic) case, the major effects of additional parameter knowledge are to narrow the bounds of rate constants that remain unidentifiable, as well as to possibly render others identifiable. When noisy data are considered, the means of the bounds of rate constants that remain unidentifiable are also narrowed, but the variances of some of these bound estimates increase. This unexpected result was verified by Monte Carlo simulation of several different models, using both normally and lognormally distributed data assumptions. Extensions and some consequences of this analysis useful for model discrimination and experiment design applications are also noted.     

Determination the rate constants of some biexponential reactions

Reactions that are described by biexponential functions are typical for many biological processes. The kinetics of these reactions is described by transcendental irrational equations interconnecting the reagent concentrations, time and rate constants. Meantime, their graphical representation in the semi-logarithmic coordinates can be decomposed into two straight lines that intercept at some angle. New simple methods for asymptotic numerical solution of the equations describing these reactions are suggested. These methods permit determining the rate constants using the kinetic data of initial substance concentration, which transform into final product according to a two-component model, a sequential model or a competitive model.     

Determination of rate constants for the reaction of hydroxyl radicals with some purines and pyrimidines using sunlight

Sunlight mediated hydroxyl radical production from aqueous ferric perchlorate at low pH has been investigated using deoxyribose-thiobarbituric acid assay. The rate of production of hydroxyl radical was found to be dependent on the time of irradiation. Hydroxyl radical scavengers can compete with deoxyribose for hydroxyl radicals produced in the system leading to a decreased yield of thiobarbituric acid chromogen. The second-order rate constants of the added scavengers can be determined using a simple competition kinetic method. The rate constants for the reaction of hydroxyl radical with a number of purine and pyrimidine derivatives were determined using this method. The rate constants obtained (1-7 x 10(9) dm(3) mol(-1) s(-1)) were found to be in good agreement with those reported using pulse radiolysis technique. The rate constants of dimethyluracil, xanthosine, amino and methyl substituted pyrimidines, cytidine monophosphate and uridine monophosphate were also determined by this method. It is proposed that sunlight mediated production of hydroxyl radical coupled with deoxyribose-thiobarbituric acid assay is a simple and efficient method for the determination of rate constants for the reaction of hydroxyl radical with a wide range of biomolecules.     

Determination of rate constants in carrier-mediated diffusion through lipid bilayers

In this work data are presented on the relaxation current, under a voltage step, through soybean lipid bilayers in the presence of the carrier valinomycin. Measurements of voltage-dependent steady-state conductance have also been performed. These measurements are sufficient to calculate the full set of kinetic parameters determining the transport.The data are analyzed according to the kinetic model, based on an Eyring treatment of the carrier-mediated diffusion. Complementary measurements of conductance as a function of antibiotic concentration have also been reported. These data allow one to calculate the membrane-solution partition coefficient of the carrier and the surface charge density of the membrane. The results are compared with those previously obtained with membranes of different lipid composition.     

Calculating reaction rate constants and estimating the efficacy of selective enzyme inhibitors

The dynamic steady state of a pair of forward and backward enzymatic reactions is dependent on the balance between the enzymes catalyzing the reactions. By selectively inhibiting one or more of the enzymes involved, this balance is shifted into a new steady state, making it possible to calculate the reaction rate constants after measurement of the reactants. Ideally, the inhibitors should completely eliminate either reaction, but this is often not the case. Here we present and discuss a method for calculating the reaction rate constants and, thus, for evaluating the efficacy of one or more inhibitors when introduced to a forward-backward pair of enzymatic reactions.     

Determination of rate constants for the irreversible inhibition of acetylcholine esterase by continuously monitoring the substrate reaction in the presence of the inhibitor

The kinetics of the irreversible inhibition of acetylcholinesterase (acetylcholine acetylhydrolase, EC 3.1.1.7) by diisopropyl fluorophosphate and paraoxon have been studied by the approach of following the substrate reaction continuously in the presence of both the substrate and the inhibitor based on kinetic equations previously derived (Tsou, C.-L. (1965) Acta Biochim. Biophys. Sinica 5, 387-417). From determinations of the effects of different concentrations of substrate and the inhibitors on the apparent rate constants for the irreversible inhibition reactions it can be shown that these inhibitors are of the competitive complexing type. Both the reversible dissociation constant for the enzyme inhibitor complex and the rate constant for the subsequent phosphorylation step can be obtained from suitable plots of the experimental data.     

Determination of the two-dimensional interaction rate constants of a cytokine receptor complex

Ligand-receptor interactions within the plane of the plasma membrane play a pivotal role for transmembrane signaling. The biophysical principles of protein-protein interactions on lipid bilayers, though, have hardly been experimentally addressed. We have dissected the interactions involved in ternary complex formation by ligand-induced cross-linking of the subunits of the type I interferon (IFN) receptors ifnar1 and ifnar2 in vitro. The extracellular domains ifnar1-ectodomain (EC) and ifnar2-EC were tethered in an oriented manner on solid-supported lipid bilayers. The interactions of IFNalpha2 and several mutants, which exhibit different association and dissociation rate constants toward ifnar1-EC and ifnar2-EC, were monitored by simultaneous label-free detection and surface-sensitive fluorescence spectroscopy. Surface dissociation rate constants were determined by measuring ligand exchange kinetics, and by measuring receptor exchange on the surface by fluorescence resonance energy transfer. Strikingly, approximately three-times lower dissociation rate constants were observed for both receptor subunits compared to the dissociation in solution. Based on these directly determined surface-dissociation rate constants, the surface-association rate constants were assessed by probing ligand dissociation at different relative surface concentrations of the receptor subunits. In contrast to the interaction in solution, the association rate constants depended on the orientation of the receptor components. Furthermore, the large differences in association kinetics observed in solution were not detectable on the surface. Based on these results, the key roles of orientation and lateral diffusion on the kinetics of protein interactions in plane of the membrane are discussed.     

Determination of rate constants for the antigen-antibody reaction. Kinetic characteristics of interaction of soluble and corpuscular antigen with specific antibodies

Using the previously developed procedure, the rate and equilibrium constants for the interaction of antibodies with soluble or corpuscular antigens were determined. Cow milk casein was used as a soluble antigen, while heat-inactivated Staphylococcus aureus cells--as a corpuscular antigen. The values of kinetic constants for the above reactions are close to those for various antigen--antibody pairs obtained by other investigators.     

An alternative method for determining inhibition rate constants by following the substrate reaction

An alternative plotting method is described by which microscopic inhibition rate constants can be determined by following the substrate reaction in the presence of the irreversible inhibitor. Not only does this method keep the advantage of Tsou's original method (Tsou, 1965a. Acta Biochem. biophys. Sin. 5, 1028-1032; 1965b. Acta Biochem. biophys. Sin 5, 409-417), but also is suitable for the cases where the consumption of substrate and accumulation of product must be taken into account.     

Acetylcholinesterase inhibition by eserine: rate constants of reaction. Part II

The inhibition of eel acetylcholinesterase by physostigmine at 20 degrees and 25 degrees C have been investigated. In our evaluation the unimolecular reactivation rate constant, k3, the carbamylation rate constant, k2, and the binding constant, Ka, are the first simultaneously determined. The mechanism of this reaction is discussed.     

Determination of equilibrium and individual rate constants for subtilisin-catalyzed transesterification in anhydrous environments

We report here the first determinations of individual rate constants and equilibrium constants for enzymatic reactions in essentially anhydrous organic solvents. Using the added nucleophile method we have measured the effect of changing solvent on the binding and catalytic steps for subtilisin-catalyzed transesterification of N-protected amino acid esters. The detailed information generated indicates that once the substrate has bound to the enzyme, the catalytic machinery can work at rates equivalent to those in water. The decreased overall rates for subtilisin suspended in anhydrous solvents are merely the result of extremely high values for K(s), in most cases, coupled with low concentrations of nucleophile ( approximately 1.0M in organic solvents, and 55M in water). The method described, which is generally applicable, and straightforward experimentally, will, we believe, enable a clearer understanding of how changing solvent can predictably affect the activity and specificity of the enzyme. (c) 1992 John Wiley & Sons, Inc.     

Determination of association and dissociation rate constants for bilirubin--bovine serum albumin.

The association rate constant for the binding of bilirubin to bovine serum albumin has been determined in a continuous-flow experiment. The value obtained is 0.9 x 10⁶m^?1S^?1. Furthermore the dissociation rate constant is determined from the rate of the peroxidase-catalyzed oxidation of bilirubin in a bilirubin-albumin solution. This figure is 3.1 × 10^?2s ¹. Calculation of the apparent binding equilibrium constant from the two rate constants gives 2.9 x 10⁷m^?1. The above mentioned peroxidase oxidation has also been used for a direct estimation of the binding equilibrium constant giving 2.7 × 10⁷m^?1. All experiments are carried out at 36 °C and pH 7.4.     

Determination of rate constants for nucleotide dissociation from Na,K-ATPase.

A method for determining individual rate constants for nucleotide binding to and dissociation from membrane bound pig kidney Na,K-ATPase is presented. The method involves determination of the rate of relaxation when Na,K-ATPase in the presence of eosin is mixed with ADP or ATP in a stopped-flow fluorescence apparatus. It is shown that the nucleotide dependence of this rate of relaxation--taken together with measured equilibrium binding values for eosin and ADP--makes possible a reasonably reliable determination of the rate constant for dissociation of nucleotide, i.e., determination of the rate constant k-1 in the following model (where E denotes Na,K-ATPase): [formula: see text] All experiments are carried out at about 4 degrees C in a buffer containing 200 mM sucrose, 10 mM EDTA, 25 mM Tris and 73 mM NaCl (pH 7.4). Values obtained for the rate constants for dissociation are about 6 s-1 for ADP and 2-3 s-1 for ATP.     

Determination of kinetic constants of hybrid textile wastewater treatment system

The present study is related to treatment of textile wastewater in microaerophilic–aerobic hybrid reactor. The study showed the effectiveness of biological treatment of wastewater involving appropriate microorganism and suitable reactors. COD and color were reduced to 82–94%, and 99% respectively for textile wastewater. The reactor was operated at highest loading of 16.4 g COD g l⁻¹ d⁻¹ and obtained 80% COD and 72% color removal. Biokinetic models were applied to data obtained from experimental studies in continuously operated hybrid reactor. Treatment efficiencies of the reactor were investigated at different hydraulic retention times (2.3–9.1 d) and organic loading rates (2.6–16.4 g COD l⁻¹ d⁻¹). Second-order and a Stover–Kincannon models were best fitted to the hybrid column reactor. The second-order substrate removal rate constant (k_2(S)) was found as 41.44 d⁻¹ for hybrid reactor. Applying the modified Stover–Kincannon model to the hybrid reactor, the maximum removal rate constant (U_max) and saturation value constant (K_B) were found to be 212 g l⁻¹ d⁻¹ and 22.89 g l⁻¹ d⁻¹, respectively.