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Slow-Onset Enzyme Inhibition and Inactivation

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Slow-Onset Enzyme Inhibition and Inactivation 55 Experimental Standard Conditions of Enzyme Characterization Beilstein-Institut September 12th –16th, 2011, Ru¨desheim/Rhein, Germany Slow-onset Enzyme Inhibition and Inactivation Antonio Baici Department of Biochemistry, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland E-Mail: [email protected] Received: 16th February 2012/Published: 15th February 2013 Abstract Interactions between modifiers and enzymes can either occur rapidly, on the time scale of diffusion-controlled reactions, or they can be slow processes observable on the steady-state time scale. Slow interactions in hysteretic enzymes serve to dampen cellular responses to rapid changes in metabolite concentration as part of regulatory mechanisms. Naturally occurring inhibitors of several enzymes, such as the macro- molecular proteinaceous inhibitors of peptidases, may act slowly when forming complexes with their targets. To allow physiologically mean- ingful rates of enzyme inhibition, the modifier concentration is kept at high levels in nature but problems arise when these levels drop for some reason. The slow-onset inhibitory behavior of enzyme modifiers used as drugs may represent a handicap if their concentration at the target site is insufficient and/or the kinetic constants are inadequate to warrant pharmacologically meaningful rates of enzyme inhibition. A truthful knowledge of mechanisms and kinetic constants of such sys- tems is mandatory for making predictions on the efficiency of the modifiers in vivo. Introduction Slow interactions in enzymology gained popularity after Frieden coined the term hysteretic enzymes for ‘‘... those enzymes which respond slowly (in terms of some kinetic character- istic) to a rapid change in ligand, either substrate or modifier, concentration’’ [1]. http://www.beilstein-institut.de/escec2011/Proceedings/Baici/Baici.pdf 56 Baici, A. Frieden also derived an integrated rate equation, see equation (1) below, which relates the increase of product concentration with time. This equation was later shown to apply to a vast group of enzymatic mechanisms, whether or not enzyme hysteresis was involved, and the necessary mathematical background for inhibitors was further developed by Cha [2 – 4] and Morrison et al.[5–7]. Reversible enzyme inhibitors have been classified by Morrison in four categories (Table 1) depending on the rate of formation of their complexes with enzymes [5]. There are many instances in which the binding step of modifiers to enzymes occurs rapidly, whereas the sluggishness of the process is due to events other than the formation of the first complex. For this reason, the more general expression slow-onset inhibition will be used in place of slow- binding inhibition. The term ‘slow’ is vague as the time taken by these reactions varies from seconds to hours. However, it is generally agreed that slow-onset inhibition represents transient kinetics observed on the steady-state time scale and that the slowness of inhibition is understood in terms relative to the catalytic step, which is usually a faster process. There is no clear demarcation between the slow and fast categories in Table 1. For classical inhibitors the condition [I] » [I]t (the subscript means total concentration) could be trusted if it were not for the relative magnitudes of [E]t, [I]t and Ki, which are not considered in Morrison’s classification. In fact, a classical inhibitor can manifests tight-binding properties if [E]t is comparable in magnitude to Ki. On the other hand, typical high-affinity inhibitors show their efficiency already for [I]t [E]t at low enzyme concentrations to meet the condition [I]t [E]t Ki. Then, the relationships for the tight-binding and the slow, tight-binding classes of inhibitors in Table 1are better appreciated with the modification [I]t [E]t and Ki in place of [I]t [E]t. Table 1. Classification of the reversible enzyme inhibitors according to Morrison [5]. The original relationship between the total enzyme and inhibitor concentrations for the tight-binding and the slow, tight-binding cases, [I]t » [E]t, is changed here into [I]t » [E]t and Ki. Type of inhibition Relationship between [E]t and [I]t Rate of formation of the inhibited complex Classical [I]t >> [E]t fast Tight-binding [I]t » [E]t and Ki fast Slow-binding [I]t >> [E]t slow Slow, tight-binding [I]t » [E]t and Ki slow Irreversible enzyme inhibition, more appropriately called inactivation, is typically a slow process under in vitro conditions and can be treated analogously to slow-onset inhibition. The term modifier describes in general inhibition, inactivation and activation. This chapter is dedicated to slow-onset inhibition and inactivation, while slow-onset activation will not be 57 Slow-onset Enzyme Inhibition and Inactivation treated. Steady-state and pre-steady-state equations for slow-onset activation have been derived by Hijazi and Laidler [8], and an overview of hysteretic, allosteric activators has been published by Neet et al. [9]. General Aspects of Slow-onset Inhibition There are several reasons why an inhibitor acts ‘slowly’, including (1) the existence of an intermediate whose structure recalls that of the transition state; (2) the inhibitor equilibrates rapidly between two or more forms, one of which makes up only a small proportion of all forms and interacts with the enzyme; (3) binding of the modifier to the enzyme to form an intermediate adsorption complex is a fast process, which is followed by a slow structural rearrangement to a second inhibitory complex; (4) only a rare form of the enzyme, which equilibrates between conformers, interacts with the modifier; (5) more trivially, it may be impossible to achieve sufficiently high modifier concentrations so that the rate of the second- order association reaction with enzyme is slow. The information supplied by the analysis of the transient phase in slow-onset inhibition experiments is superior to that gained from steady-state data because the exponential approach to steady-state can be used for calculating at least some individual rate constants for the inhibitory steps. The mechanism of inhibition and kinetic constants can be extracted from data either using integrated rate equations, when available, or by numerical integration. For some mechanisms, integrated rate equations can be derived under restrictive assump- tions but this is not always possible. The assumptions require [S] » [S]t and [I] » [I]t, which means [S]t, [I]t >> [E]t, i.e. experiments must be properly designed to avoid excessive substrate turnover (say £ 10%) and to circumvent tight-binding between enzyme and inhi- bitor. In the presence of a slow-onset inhibitor, an enzyme-catalyzed reaction in which substrate is transformed into product (P) can be described by Frieden’s equation mentioned above, which reads zÀs Àt (1) ½P¼st þ 1 À e þ d, where vs and vz are the velocities at steady-state and at time zero, respectively, and l is the frequency constant of the exponential phase with reciprocal time as dimension. The para- meter d, for displacement, was added to the original equation to account for any non-zero value of [P] or background of measured signal proportional to it at time zero. If an integrated rate equation exists and experiments can be set up to fulfill the assumptions, the equation can be fitted to progress curves by non-linear regression. In several cases, unambiguous diagnosis of the mechanism is possible by extracting the information contained in the expressions of the parameters vs, vz and l. These are functions of inhibitor and substrate 58 Baici, A. concentrations for a given mechanism and allow the calculation of rate constants. The graphical representation of slow-onset inhibition according to equation (1) is shown in Figure 1. Figure 1. Progress curves for a generic slow-onset inhibition mechanism. The curve in (b) is obtained when substrate and inhibitor are mixed and reaction is started by adding enzyme. Curve (c) represents a reaction started by adding substrate to enzyme and inhibitor that had been preincubated for a sufficiently long tome to allow complex formation. The dashed line (a) is the tangent at time zero for curve (b) and dashed line (d) is the corresponding tangent for curve (c). All mechanisms discussed below are drawn as the simplest one-substrate/one-product reac- tion for purely practical reasons with the implicit agreement that the same mechanisms can be applied to multi-reactant enzymes. For instance, in the case of a two-substrate/two- product enzymatic reaction, one substrate is kept at a constant concentration (not shown in the scheme) while the concentrations of the second substrate and inhibitor are varied. The measurements are then repeated exchanging the roles of the varied substrate. The most frequent mechanism of slow-onset inhibition, both among naturally occurring and synthetic inhibitors, is of the linear competitive type. A general form is shown in Scheme 1, panel M11, in which no assumptions are made about the relative rates of equilibration of the two inhibitory steps. For this mechanism, a progress curve consisting of a double exponen- tial followed by a linear steady-state release of product is expected but the derivation of an integrated rate equation is bound to restrictions, of which the absence of tight-binding between enzyme and inhibitor is the most important. However, it is right M1 in Scheme 1 that is often characterized by tight-binding. 1 Reaction mechanisms, labeled Mx, where x is a progressive number, are grouped in this chapter as composite schemes to allow easier finding and cross-referencing 59 Slow-onset Enzyme Inhibition and Inactivation Scheme 1. Mechanisms giving rise to slow-onset inhibition. The labels M1 through M12 are introduced for facilitating cross-referencing, e.g. M3 is read ‘mechanism 3’. E = enzyme, S = substrate, P = product, I = inhibitor. The steps labeled slow indicate qualitatively their relative rate of equilibration with respect to the other steps, which are assumed to be much faster.
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