Enzyme Arrhenius equation

Enzymatic reactions frequently undergo a phenomenon referred to as substrate inhibition. Here, the reaction rate reaches a maximum and subsequently falls as shown in Eigure 11-lb. Enzymatic reactions can also exhibit substrate activation as depicted by the sigmoidal type rate dependence in Eigure 11-lc. Biochemical reactions are limited by mass transfer where a substrate has to cross cell walls. Enzymatic reactions that depend on temperature are modeled with the Arrhenius equation. Most enzymes deactivate rapidly at temperatures of 50°C-100°C, and deactivation is an irreversible process. 

Other factors that can impact these constants relate to reaction solution conditions. We have already discussed how temperature can affect the value of kCM and kcJKM according to the Arrhenius equation (vide supra). Because enzymes are composed of proteins, and proteins undergo thermal denaturation, there are limits on the range of temperature over which enzymes are stable and therefore conform to Arrhenius-like behavior. The practical aspects of the dependence of reaction velocity on temperature are discussed briefly in Chapter 4, and in greater detail in Copeland (2000). 

The rate of enzyme-mediated reactions, like most other types of reaction, depends on temperature. Over a limited temperature range, the reaction may follow the Arrhenius equation ... 

The increase in energy content of an atom, ion, or molecular entity or the process that makes an atom, ion, or molecular entity more active or reactive. In enzymology, activation often refers to processes that result in increased enzyme activity. For example, increasing temperature often can have a positive effect on enzyme activity (See Arrhenius Equation). Other examples of enzyme activation include (1) proteolysis of zymogens (2) alterations in ionic strength (3) alterations due to pH changes (4) activation in cooperative systems (5) lipid or membrane interface activation (6) metal ion effects (7) autocatalysis and (8) covalent modification. 

Finally, yet another issue enters into the interpretation of nonlinear Arrhenius plots of enzyme-catalyzed reactions. As is seen in the examples above, one typically plots In y ax (or. In kcat) versus the reciprocal absolute temperature. This protocol is certainly valid for rapid equilibrium enzymes whose rate-determining step does not change throughout the temperature range studied (and, in addition, remains rapid equilibrium throughout this range). However, for steady-state enzymes, other factors can influence the interpretation of the nonlinear data. For example, for an ordered two-substrate, two-product reaction, kcat is equal to kskjl ks + k ) in which ks and k are the off-rate constants for the two products. If these two rate constants have a different temperature dependency (e.g., ks > ky at one temperature but not at another temperature), then a nonlinear Arrhenius plot may result. See Arrhenius Equation Owl Transition-State Theory van t Hoff Relationship... 

Free energy diagrams for enzymes REACTION COORDINATE DIAGRAM ENZYME ENERGETICS POTENTIAL-ENERGY SURFACES TRANSITION-STATE THEORY ARRHENIUS EQUATION VAN T HOFF RELATIONSHIP... 

Decarboxylase reaction Kinetic constants The optimum pH of the decarboxylase reaction was determined with the natural substrates of both enzymes, pyruvate (PDC) and benzoylformate (BFD). Both enzymes show a pH optimum at pH 6.0-6.5 for the decarboxylation reaction [4, 5] and investigation of the kinetic parameters gave hyperbolic v/[S] plots. The kinetic constants are given in Table 2.2.3.1. The catalytic activity of both enzymes increases with the temperature up to about 60 °C. From these data activation energies of 34 kj moT (PDC) and 38 kJ mol (BFD) were calculated using the Arrhenius equation [4, 6-8]. 

In the Arrhenius equation (equation 5.1)Ar can be replaced by cat and, at constant enzyme concentration, EioX will be directly related to Kmax... 

Most enzymes show a 50-300% increase in reaction rate when the temperature is increased by 10°, and the ratio of rate constants at two temperatures 10° apart is usually between 1.5 and 4.0 for most enzymes. This value is termed Q10 and is derived from the Arrhenius equation [Equation (5.9)], which can be integrated to give... 

For chemical reactions, the Arrhenius equation describes the relationship between the rate constant of the reaction and the absolute temperature. This equation, which is empirical and has no theoretical basis, was developed in 1889 by Arrhenius to define the activation energy of a reaction. The role of enzymes in chemical reactions is to lower the activation energy. In fact, the activation energy of enzyme-catalyzed reactions appear to be more characteristic of the enzyme than of the substrates involved in the reaction. For most enzyme-catalyzed reactions, the activation energies are between 6,000 and 15,000 cal/mol (24). 

Temperature. In general, the dependence of enzyme activity on temperature will be described by the curve illustrated in Figure 11-13. At the lower temperatures, the temperature dependence of VmAX will be described by the Arrhenius equation (Equation 11-20). 

Solution According to the Arrhenius equation, k = AeEa/ RT Let ke and kn be the rate constants of the enzyme-catalysed and non-catalysed reactions, respectively. Assuming that the Arrhenius pre-exponential factor A is the same in both cases, we have... 

In enzyme kinetics the rate of reaction (fe) is related to the energy of activation (E) by the Arrhenius equation ... 

In a diffusion-free enzyme reaction the reaction rate increases up to a certain critical value exponentially and is described by the Arrhenius equation [82]. In diffusion-controlled reactions the reaction rate is a matter of the efficiency factor ri [see Eqs. (3 - 5)]. In more detail, the maximum reaction rate is expressed within the root of Eq. (4). Conclusively, the temperature dependence is a function of the square root of the enzyme activity. In practice, immobilized enzymes are much less temperature dependent when their reaction rate is diffusion controlled. 

Temperature effects can be either negative or positive on the or the fccat of the reaction but can only be negative on the enzyme (denaturation). If = Ks, K may be determined at various temperatures. The /Ccat can be established directly from the Arrhenius equation (eq. 1) ... 

Traditional literature treats enzyme catalyzed reactions, including hydrogen transfer, in terms of transition state theory (TST) [4, 34, 70]. TST assumes that the reaction coordinate may be described by a free energy minimum (the reactant well) and a free energy maximum that is the saddle point leading to product. The distribution of states between the ground state (GS, at the minimum) and the transition state (TS, at the top of the barrier) is assumed to be an equilibrium process that follows the Boltzmann distribution. Consequently, the reaction s rate is exponentially dependent on the reciprocal absolute temperature (1/T) as reflected by the Arrhenius equation ... 

AT any biochemical processes involve very rapid reactions and transient intermediates. Frequently the rapidity of the reaction causes major technical difficulties in ascertaining the details of the events occurring in the process. One approach to overcome this inherent problem is to utilize the fact that most chemical reactions are temperature dependent. This relationship is quantitatively described by the Arrhenius equation, k = Ae E /RT, where k represents the rate constant, A is a constant (the frequency factor), and Ea is the energy of activation. Consequently, by initiating the reaction at a sufficiently low temperature, interconversion of the intermediates may be effectively stopped and they may be accumulated and stabilized individually. Although the focus of this article is on the application of this low-temperature approach to the study of enzyme catalysis, that is, cryoenzymology, the technique is potentially of much wider biological application (1, 2,3). 

Enzyme activity decay can be expressed in terms of the Arrhenius Equation ... 

In the absence of significant denaturation or degradation of an enzyme during the assay, the rate of an enzyme-catalyzed reaction will increase with a rise in temperature in a manner empirically described by the Arrhenius equation ... 

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