Sequential models, enzyme kinetics

More detailed analysis of the difference between symmetry and sequential models could be found in specialized literature (V.Leskovac, Comprehensive enzyme kinetics, Kluwer Academic/Plenum publishers, New York, 2003). 

Substituting Eq. 5.86, 5.87 and 5.88 in Eq. 5.85 and using a suitable model for enzyme inactivation (i.e. Eq. 5.76 for modulated two-stage sequential inactivation kinetics) batch enzyme reactor performance will be described by the resolution of differential Eqs. 5.85 and 5.76. The same procedure can be used considering other mechanisms of enzyme kinetics and enzyme inactivation. We have constructed a didactic software game in Visual Basic in which kinetic and inactivation parameters can be modified at will and analyze its impact on enzyme reactor performance. 

Anti-cancer drugs that are sulfamate esters, ROSO2NH2, appear to act by inhibition of sulfatases. Now, kinetic studies of the aminolysis of p-nitrophenyl sulfamate (109) by secondary alicyclic amines in MeCN at 310 K are reported that model the enzyme reaction. The Brpnsted-type plot was biphasic, the break point at w 18.2 more or less corresponding to the pKa of the ester (109) (17.8). The proposed mechanism (Scheme 30) involves a sequential double deprotonation of (109) leading first, via (110), to the sulfenamine (112) and at higher basic strength to (111) and thence to a novel anionic sulfenamine (113), the products in each case being an V, V-dialkylsulfamide (114) and p-nitrophenol.114... 

Thus, the kinetics of conversions In metabolic cellular sequences, and even in whole cell kinetics, at or near steady state may be expected to resemble the kinetic rate form appropriate to one or a very small number of sequential enzyme catalyzed steps. The implications of this point in kinetic models of structured cell systems are reflected in later contributions in this conference. 

Eq. 6.2.6 was solved analytically to obtain the operation curve of the reactor (X vs t). Lumped kinetic parameters were determined by non-linear regression of experimental data using the numerical method of Newton-Raphson with first-order Taylor series expansion. Lumped parameters were smooth functions of temperature all parameters were adequately fitted to second order polynomials except for D that required a fourth order polynomial. The model can be used for reactor temperature optimization and can be extended to prolonged sequential batch operation provided that a sound model for enzyme inactivation is validated (Illanes et al. 2005b). 

The application of immobilized model systems for investigation of the kinetics of sequential enzyme reactions has been reviewed. 

Cooperative substrate binding results in sigmoidal v versus [S] curves (Fig. 8.1). The Michaelis-Menten model is therefore not appMcable to cooperative enzymes. Two major equihbrium models have evolved to describe the catalytic behavior of cooperative enzymes the sequential interaction and concerted transition models. The reader should be aware that other models have also been developed, such as equilibrium association-dissociation models, as well as several kinetic models. These are not discussed in this chapter. 

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