The present communication describes a novel method for estimating initial velocities (v) of enzyme-catalysed reactions. It is based on an approximation of experimental data obtained by the cubic spline function. The initial velocity of a reaction is calculated as a derivative of the approximating function at a time value equal to zero. The proposed method is usable on a computer with a FORTRAN IV program. The method can be successfully used in such cases as substantial extents of substrate conversion, the inactivation of an enzyme in the course of a reaction, the existence of large experimental error or when the reaction mechanism is unknown.
A D-hydantoinase (5,6-dihydropyrimidine amidohydrolase) was purified to homogeneity from Bacillus circulans. Purification of two hundred forty-three-fold was achieved with an overall yield of 12%. The relative molecular mass of the native enzyme is 212,000 and that of the subunit is 53,000. This enzyme is an acidic protein with an isoelectric point of 4.55. The enzyme is sensitive to thiol reagent and requires metal ions for its activity. The optimal conditions for the hydantoinase activity are pH 8.0-10.0 and a temperature of 75 degrees C. The enzyme is the most stable in a pH range of 8.5-9.5 and up to 60 degrees C. The enzyme is significantly stable not only at high temperatures but also on treatment with protein denaturant SDS. These remarkable properties are used for the purification procedure.
The precise description of the course of the deactivation of biocatalysts is very important from a practical viewpoint. At present, the first-order kinetics is most frequently accepted when a quantitative expression isHowever, in many cases, experimental data do not correspond to simple first-order kinetics, especially when dealing with immobilized enzymes. The reasons for deviation may be various. For example, it may be an intrinsic heterogeneity of partially purified enzymes, the presence of enzyme fractions with a different degree of chemical modification (taking place during immobilization), the presence of different enzymes catalysing the same reaction, the complexity of the mechanism of deactivation, and many others. Very often the course of deactivation can be adequately described by eq. (2), which characterizes two fractions of the biocatalyst differing in activity and ~tability~,~:A typical two-stage deactivation curve is presented in Figure 1. Constants kb and b are usually determined by plotting logarithmic activity data against time at large values of t.4,5 It is assumed that for the experimental points applied, a exp{ -k,t} = 0. Then, by a subsequent linearization of In (A, -b exp{ -kbt}) vs. t one can find the constant k,. The value of a can be obtained from the material balance equation a + b = Ao.The determination of kinetic constants of deactivation by the linearization method may often lead to erroneous results. Relatively good results can be obtained only when constants kb and b are determined from experimental points in which the activity of the labile fraction is close to zero. It requires a high degree of deactivation and is experimentally inconvenient. In most cases, the separation of two fractions is also unachievable. The deactivation
MODELThe dimensionless activity is given byLet us suppose that kinetic constants are determined by the linearization method. For simplicity, the data at two values of time tl and t2 (tl < t2) are used (Fig. 1). Then
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