Quasi steady state assumption , enzyme

In addition to the thermodynamic constraints on the reaction kinetics, a number of assumptions (including quasi-equilibrium binding and quasi-steady state assumptions) are often invoked in computer modeling of enzyme kinetics. Analysis of enzyme kinetics is treated in greater depth in Chapter 4. 

This need not be true in vivo where the concentrations of reactants and their enzymes in some cases are nearly comparable. Under these conditions, the nominal concentration of substrate could be significantly greater than the level of unbound substrate, and the reaction rate calculated with nominal concentrations inserted into the rate law clearly would overestimate the rate observed in vivo (Wright et al., 1992 Shiraishii and Savageau, 1993). This condition does not alter the basic chemical kinetic equations that describe the mechanism, but it does mean that the quasi-steady state assumption (e.g., see Peller and Alberty, 1959 Segel and Slemrod, 1989) may be inappropriate when reaction rates change with time in vivo. 

In general, such nonlinear differential equations are difficult to solve exactly. Therefore, Michaelis and Menten (1913) made the simplifying assumption that the intermediate complex is in equilibrium with the free enzyme and substrate (the quasi-equilibrium postulate). While this is not strictly true, it is nearly so when k2 is much less than k i or ki, as was the case for Michaelis and Menten, who were concerned with the enzyme invertase. More often valid is the quasi-steady state postulate, which was first developed in detail by Briggs and Haldane (1925). 

The validity of the quasi-steady-state approximation, has already been mentioned in Subsection 4.8.7. A detailed analysis of enzyme kinetics is given in Heineken et al. (1967), Walter (1977) and Segel (1984). The strict mathematical basis of the assumption is based on a theorem by Tikhonov (1952). He investigated the assumptions leading to separation of the fast and slow components of the solutions of the system... 

In Michaelis and Menten s (1913) analysis, the equilibrium between the complex formation and its dissociation is assumed to exist. However, in some cases, this assumption does not hold, especially when the product formation rate from the complex (fcj) is close to the rate of complex dissociation to the enzyme and substrate In such cases, a more general assumption, known as quasi-steady state, is used. 

The derivation of initial velocity equations invariably entails certain assumptions. In fact, these assumptions are often conditions that must be fulfilled for the equations to be valid. Initial velocity is defined as the reaction rate at the early phase of enzymic catalysis during which the formation of product is linear with respect to time. This linear phase is achieved when the enzyme and substrate intermediates reach a steady state or quasi-equilibrium. Other assumptions basic to the derivation of initial rate equations are as follows ... 

The steady-state kinetic treatment of random reactions is complex and gives rise to rate equations of higher order in substrate and product terms. For kinetic treatment of random reactions that display the Michaelis-Menten (i.e. hyperbolic velocity-substrate relationship) or linear (linearly transformed kinetic plots) kinetic behavior, the quasi-equilibrium assumption is commonly made to analyze enzyme kinetic data. 

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