Classical methods, parameter estimation kinetic parameters, determination

In general, full rate laws for the various reactions of an intact system have not been determined under physiological conditions. This is true of the more complex enzymes even under standard experimental conditions in vitro because of limitations in the classical methods for estimating the value of kinetic parameters and the large number of assays required for such estimations. 

The first two sections of Chapter 5 give a practical introduction to dynamic models and their numerical solution. In addition to some classical methods, an efficient procedure is presented for solving systems of stiff differential equations frequently encountered in chemistry and biology. Sensitivity analysis of dynamic models and their reduction based on quasy-steady-state approximation are discussed. The second central problem of this chapter is estimating parameters in ordinary differential equations. An efficient short-cut method designed specifically for PC s is presented and applied to parameter estimation, numerical deconvolution and input determination. Application examples concern enzyme kinetics and pharmacokinetic compartmental modelling. 

Experimentally, water exchange rate constants are mainly determined from nuclear magnetic resonance measurements [6, 7]. Other techniques are restricted to very slow reactions (classical kinetic methods using isotopic substitution) or are indirect methods, such as ultrasound absorption, where the rate constants are estimated from complex-formation reactions with sulfate [3]. The microscopic nature of the mechanism of the exchange reaction is not directly accessible by experimental methods. In general, reaction mechanisms can be deduced by experimentally testing the sensitivity of the reaction rate to a variety of chemical and physical parameters such as temperature, pressure, or concentration. 

---