Inactivation, enzyme, rate equation

According to Equation 17.47, an affinity label should exhibit time- and concentration-de-pendent inactivation. The rate of inactivation is proportional to low concentrations of inhibitor, whereas at high inhibitor concentrations saturation occurs and no further increase in the rate of inactivation is observed. A typical pseudo first-order plot of log enzyme activity vs. time is illustrated in Fig. 17.26. In some cases nonlinear plots may be obtained, particularly for mechanism-based inhibitors (166, 167). 

The forth prerequisite is that the enzyme should be stable to validate Equ.(2), or else the inactivation kinetics of the enzyme should be included in the kinetic model. Enzyme stability should be checked before kinetic analysis of reaction curve. When the inactivation kinetics of an enzyme is included in a kinetic model for kinetic analysis of reaction curve, the integrated rate equation is usually quite complex or even inaccessible if the inactivation kinetics is too complex. For kinetic analysis of reaction curve of complicated kinetics, numerical integration to produce calculated reaction curves for NLSF to a reaction curve of interest, instead of NLSF with Equ. (4), can be used to estimate parameters (Duggleby, 1983, 1994 Moruno-Davila, et al., 2001 Varon, et al., 1998 Yang, et al., 2010). 

This equation will describe the loss of enzyme activity, if the affinity label is binding at the active site. Moreover, reversibly bound ligands capable of occupying the same site as the affinity label will competitively inhibit the rate of enzyme inactivation. 

By integrating the second equation first, we get [R] = [R]initiaie 2 thus, we may substitute this expression for [R] into the first differential equation to obtain the rate law that allows for enzyme inactivation by a reagent which itself is undergoing deactivation. After separating variables and integrating the combined expression, we obtain... 

Dekker et al. [170] studied the extraction process of a-amylase in a TOMAC/isooctane reverse micellar system in terms of the distribution coefficients, mass transfer coefficient, inactivation rate constants, phase ratio, and residence time during the forward and backward extractions. They derived different equations for the concentration of active enzyme in all phases as a function of time. It was also shown that the inactivation took place predominantly in the first aqueous phase due to complex formation between enzyme and surfactant. In order to minimize the extent of enzyme inactivation, the steady state enzyme concentration should be kept as low as possible in the first aqueous phase. This can be achieved by a high mass transfer rate and a high distribution coefficient of the enzyme between reverse micellar and aqueous phases. The effect of mass transfer coefficient during forward extraction on the recovery of a-amylase was simulated for two values of the distribution coefficient. These model predictions were verified experimentally by changing the distribution coefficient (by adding... 

Thermal inactivation of EcaL-ASNase was monitored by activity measurements. Samples of the enzyme, in potassium phosphate buffer (lOmM, pH 7), were incubated at a range of temperatures from 35 °C to 50 °C. The rates of inactivation were followed by periodically removing samples for assay of enzymatic activity. Observed rates of inactivation (ki ) were deduced from plots of log (% remaining activity) versus time. To obtain the thermodynamic parameters from these inactivation rates, two analyses were carried out according to Stein and Staros (1996). An empirical activation energy, Ea, for the inactivation process can be obtained from an Arrhenius plot according to the equation ... 

If the rate of metabolite formation can be determined over a time period that is sufficiently short that significant enzyme inactivation does not occur (fccat > inacl), then the exponential term in Eq. (12) approaches unity and may be ignored. Equation (12) illustrates that the apparent Vmax for formation of a metabolite will decline as the incubation time increases when simultaneous enzyme inactivation occurs (Fig. 4). 

Enzyme activity may be inhibited by substances that inactivate the enzyme or occupy the active site of the enzyme before the substrate has a chance. As a result, the rate of transformation of the substrate to product is slowed. In competitive inhibition, similar substrates (or analogs) can bind to the same active site on the enzyme. Therefore, they compete with each other for the same active sites. This inhibition process is reversible and can be prevented or slowed by increasing the substrate concentration or by diluting the inhibitor in the solution. In this case, the enzyme already bound to the substrate is not inhibited. The effect of the competitive inhibitor (I) on the rate of enzyme reaction in Equation (5.129), Equation (5.130), Equation (5.131), and Equation (5.132) yields ... 

Enzymes involved in steroid biosynthesis have proved to be good targets, both for therapeutic intervention and for mechanism-based inactivators (2). Aromatase, for example, catalyzes the final, rate-limiting step in estrogen biosynthesis (Equation 17.55). Aromatase has proved susceptible to mechanism-based inhibitors such as formestane and ex-emestane. These are now both used in the treatment of breast cancer (210). 

For operation of continuous bioreactors, the solvent type employed has a significant effect on the water retention during esterification. One role of the flowing solvent is to remove the generated water. However, when the solvent is lipophilic, snch as hexane, its water capacity is too small to remove the water at a rate eqnal to water prodnction hence, water accumulates in the solid enzyme phase and leads to irreversible inactivation. The inclusion of a polar co-solvent, or the use of a solvent of intermediate polarity, can improve water removal. The optimal concentration of polar co-solvent is predetermined by equating water removal rate of the co-solvent mixtnre s (water solnbility multiplied by the flow rate) with the water generation rate. Water accnmnlation also occurs when the polarity of the fluid phase decreases... 

Kinetic model for mechanism-based inhibition is proposed in Scheme 16.3 (Waley, 1980 Walsh et al., 1978). Inactivation of the enzyme is an irreversible process over the time scale of the experiment. At the given concentrations of inhibitor and enzyme, the reactions indicated in Scheme 16.3 are governed by the first-order rate constants k, k, 2, k, and 4, respectively. The rate of enzyme inactivation can be introduced by Equation 16.3 (Jxmg and Metcalf, 1975 Kitz and Wilson, 1962). 

Usually, Nr -h 1 reactors will be required to absorb non-productive time (discharge, cleaning and filling of reactor). Solving the equation that represents enzyme inactivation under operation conditions (i.e. Eq. 5.76) and the equation that model conversion profiles within the biocatalyst bed in CPBR (Eq. 5.79), residual enzyme activity in each bioreactor after each time interval can be determined and feed flow-rate to each bioreactor during each interval calculated as ... 

Equation 1 indicates the proportionality between the radical concentration and the active enzyme concentration in the reaction system studied. As evident from Figure 2, this equation is a key to the rate analyses of all three post-enzymatic reactions involving die phenoxy radical i.e., enzyme inactivation and NEP fomation via self-coupling and/or cross-cotqiling reactions. Enzyme inactivation resulting from radical attack, for exanqile, can be eiqiressed as... 

Equation 2 was shown to provide a good descr on of die rate behaviors of enzyme inactivation observed in our eariier study, and will be applied in analyses of the rate information developed in the present study. 

---