Iterative Approximate Solutions of Kinetic Equations for Reversible Enzyme Reactions

We study kinetic models of reversible enzyme reactions and compare two techniques for analytic approximate solutions of the model. Analytic approximate solutions of non-linear reaction equations for reversible enzyme reactions are calculated using the Homotopy Perturbation Method (HPM) and the Simple Iteration Method (SIM). The results of the approximations are similar. The Matlab programs are included in appendices.Comment: 28 pages, 22 figure

Principal basis for enzyme power

The reaction rate enhancement that enzymes produce had not been fully appreciated. The object of the article is to present the mechanism of the enormous catalytic power of the enzymes. I conclude that during substrate conversion to product the enzyme transfers firstly some additional small reactant group that must be initially presented in the active site of the enzyme to bound substrate (i) ; the enzyme regenerates during second substrate group transfer (ii); the active enzyme acts as a reactant of the enzymatic reaction (iii). The detailed chemical mechanisms of enzymatic reactions, such as a the well-studied reaction of the serine proteases family, the peptide bond hydrolysis catalyzed by α-chymotrypsin, and the glyceraldehyde-3-phosphate interconversion step in glycolysis, are in accordance with my conclusion

Enzymatic activity toward poly(L-lactic acid) implants

Tissue reactions toward biodegradable poly(L-lactic acid) implants were monitored by studying the activity pattern of seven enzymes as a function of time: alkaline phosphatase, acid phosphatase, -naphthyl acetyl esterase, -glucuronidase, ATP-ase, NADH-reductase, and lactate dehydrogenase. Cell types were identified by their specific enzyme patterns, their morphology and location. Special attention was paid to the enzyme patterns of macrophages, fibroblasts and polymorphonuclear granulocytes (PMNs), being involved in foreign body reactions or inflammatory responses. One day after implantation, an influx of neutrophilic and eosinophilic granulocytes was observed, coinciding with activity of alkaline phosphatase (PMN's) and -glucuronidase (eosinophils). From day 3 on, macrophages containing ATP-ase, acid phosphatase and esterase could be observed. From day 7 on, lactate dehydrogenase, the enzyme normally involved in the conversion of lactic acid, and its coenzyme NADH-reductase were observed in macrophages and fibroblasts. These two enzymes demonstrated more activity than expected on basis of wound-healing reactions upon implantation of a nonbiodegradable, inert biomaterial (as, e.g., Teflon). It is concluded that the biodegradable poly (L-lactic acid) used in these implantation studies is tissue compatible, and evokes a foreign body reaction with minor macrophage and giant cell activity, as observed during this 3-week implantation period. Most enzyme patterns were simply due to a wound-healing reaction. The slightly increased levels of LDH and NADH suggest the release of lactic acid from the implant, and thus confirms the biodegradable nature of this polymer

Stochastic theory of large-scale enzyme-reaction networks: Finite copy number corrections to rate equation models

Chemical reactions inside cells occur in compartment volumes in the range of atto- to femtolitres. Physiological concentrations realized in such small volumes imply low copy numbers of interacting molecules with the consequence of considerable fluctuations in the concentrations. In contrast, rate equation models are based on the implicit assumption of infinitely large numbers of interacting molecules, or equivalently, that reactions occur in infinite volumes at constant macroscopic concentrations. In this article we compute the finite-volume corrections (or equivalently the finite copy number corrections) to the solutions of the rate equations for chemical reaction networks composed of arbitrarily large numbers of enzyme-catalyzed reactions which are confined inside a small sub-cellular compartment. This is achieved by applying a mesoscopic version of the quasi-steady state assumption to the exact Fokker-Planck equation associated with the Poisson Representation of the chemical master equation. The procedure yields impressively simple and compact expressions for the finite-volume corrections. We prove that the predictions of the rate equations will always underestimate the actual steady-state substrate concentrations for an enzyme-reaction network confined in a small volume. In particular we show that the finite-volume corrections increase with decreasing sub-cellular volume, decreasing Michaelis-Menten constants and increasing enzyme saturation. The magnitude of the corrections depends sensitively on the topology of the network. The predictions of the theory are shown to be in excellent agreement with stochastic simulations for two types of networks typically associated with protein methylation and metabolism.Comment: 13 pages, 4 figures; published in The Journal of Chemical Physic

Insolubilization process increases enzyme stability

Enzymes complexed with polymeric matrices contain properties suggesting application to enzyme-controlled reactions. Stability of insolubilized enzyme derivatives is markedly greater than that of soluble enzymes and physical form of insolubilized enzymes is useful in column and batch processes

Enzyme kinetics for a two-step enzymic reaction with comparable initial enzyme-substrate ratios

We extend the validity of the quasi-steady state assumption for a model double intermediate enzyme-substrate reaction to include the case where the ratio of initial enzyme to substrate concentration is not necessarily small. Simple analytical solutions are obtained when the reaction rates and the initial substrate concentration satisfy a certain condition. These analytical solutions compare favourably with numerical solutions of the full system of differential equations describing the reaction. Experimental methods are suggested which might permit the application of the quasi-steady state assumption to reactions where it may not have been obviously applicable before