A fast method to estimate kinetic constants for enzyme inhibitors

Natural Parameter Conditions for Singular Perturbations of Chemical and Biochemical Reaction Networks

We consider reaction networks that admit a singular perturbation reduction in a certain parameter range. The focus of this paper is on deriving "small parameters" (briefly for small perturbation parameters), to gauge the accuracy of the reduction, in a manner that is consistent, amenable to computation and permits an interpretation in chemical or biochemical terms. Our work is based on local timescale estimates via ratios of the real parts of eigenvalues of the Jacobian near critical manifolds. This approach modifies the one introduced by Segel and Slemrod and is familiar from computational singular perturbation theory. While parameters derived by this method cannot provide universal quantitative estimates for the accuracy of a reduction, they represent a critical first step toward this end. Working directly with eigenvalues is generally unfeasible, and at best cumbersome. Therefore we focus on the coefficients of the characteristic polynomial to derive parameters, and relate them to timescales. Thus, we obtain distinguished parameters for systems of arbitrary dimension, with particular emphasis on reduction to dimension one. As a first application, we discuss the Michaelis-Menten reaction mechanism system in various settings, with new and perhaps surprising results. We proceed to investigate more complex enzyme catalyzed reaction mechanisms (uncompetitive, competitive inhibition and cooperativity) of dimension three, with reductions to dimension one and two. The distinguished parameters we derive for these three-dimensional systems are new. In fact, no rigorous derivation of small parameters seems to exist in the literature so far. Numerical simulations are included to illustrate the efficacy of the parameters obtained, but also to show that certain limitations must be observed.

Sequence to structure approach of estrogen receptor alpha and ligand interactions

Estrogen receptors (ERs) are steroid receptors located in the cytoplasm and on the nuclear membrane. The sequence similarities of human ERα, mouse ERα, rat ERα, dog ERα, and cat ERα are above 90%, but structures of ERα may different among species. Estrogen can be agonist and antagonist depending on its target organs. This hormone play roles in several diseases including breast cancer. There are variety of the relative binding affinity (RBA) of ER and estrogen species in comparison to 17β-estradiol (E2), which is a natural ligand of both ERα and ERβ. The RBA of the estrogen species are as following: diethyl stilbestrol (DES)>hexestrol>dienestrol>17β-estradiol (E2)>17-estradiol>moxestrol>estriol (E3)>4-OH estradiol>estrone-3-sulfate. Estrogen mimetic drugs, selective estrogen receptor modulators (SERMs), have been used as hormonal therapy for ER positive breast cancer and postmenopausal osteoporosis. In the postgenomic era, in silico models have become effective tools for modern drug discovery. These provide three dimensional structures of many transmembrane receptors and enzymes, which are important targets of de novo drug development. The estimated inhibition constants (Ki) from computational model have been used as a screening procedure before in vitro and in vivo studies.

Validity of the Michaelis-Menten equation--steady-state or reactant stationary assumption: that is the question

The Michaelis-Menten equation is generally used to estimate the kinetic parameters, V and K(M), when the steady-state assumption is valid. Following a brief overview of the derivation of the Michaelis-Menten equation for the single-enzyme, single-substrate reaction, a critical review of the criteria for validity of the steady-state assumption is presented. The application of the steady-state assumption makes the implicit assumption that there is an initial transient during which the substrate concentration remains approximately constant, equal to the initial substrate concentration, while the enzyme-substrate complex concentration builds up. This implicit assumption is known as the reactant stationary assumption. This review presents evidence showing that the reactant stationary assumption is distinct from and independent of the steady-state assumption. Contrary to the widely believed notion that the Michaelis-Menten equation can always be applied under the steady-state assumption, the reactant stationary assumption is truly the necessary condition for validity of the Michaelis-Menten equation to estimate kinetic parameters. Therefore, the application of the Michaelis-Menten equation only leads to accurate estimation of kinetic parameters when it is used under experimental conditions meeting the reactant stationary assumption. The criterion for validity of the reactant stationary assumption does not require the restrictive condition of choosing a substrate concentration that is much higher than the enzyme concentration in initial rate experiments.

A test for measuring the effects of enzyme inactivation

In the single-enzyme, single-substrate reaction with non-mechanism-based enzyme inactivation, the formation of the product and inactivation of the enzyme occur independently. For this reaction, we show that the steady-state hypothesis is applicable even when degradation of the enzyme occurs. An equation for the rate of product formation has been derived and it shows Michaelis-Menten kinetics with an apparent Michaelis-Menten constant K(M)(app)=K(M)+K(delta) where K(delta) is the enzyme inactivation constant. Use of a Lineweaver-Burk plot yields values for K(M)(app), which can be used to estimate K(delta) and, consequently, the degree of enzyme inactivation in a particular experiment. We employ this methodology to estimate the inactivation constant for the arsenate reductase catalyzed production of arsenite with appreciable enzyme inactivation.

Susceptibilities of an Irreversible Michaelis – Menten Enzyme

The nonlinear response of the simplest irreversible Michaelis-Menten enzyme is considered. In the context of metabolic networks, i.e. in vivo, the enzyme is subject to sustained, frequently time-dependent, input fluxes that keep the system out of equilibrium. The connection between the fluxes and the response is investigated by means of a new sensitivity analysis. The kinetics of the enzyme is simple enough to allow for the computations to be carried out analytically. In particular, a set of sensitivities of the response with respect to the substrate influx, the susceptibilities, is derived. The susceptibilities are multivariate functions and thus are suitable for predicting complete progress curves of several variables of biochemical interest, namely, rates and concentrations. This is shown by means of an example. The relationship between the susceptibilities and the stoichiometry of the reaction is also taken into account. Moreover, all the required information comes from decay experiments of initial concentrations, which are common in enzymological setups.