Enzyme kinetics cellular metabolic modeling

Often the key entity one is interested in obtaining in modeling enzyme kinetics is the analytical expression for the turnover flux in quasi-steady state. Equations (4.12) and (4.38) are examples. These expressions are sometimes called Michaelis-Menten rate laws. Such expressions can be used in simulation of cellular biochemical systems, as is the subject of Chapters 5, 6, and 7 of this book. However, one must keep in mind that, as we have seen, these rates represent approximations that result from simplifications of the kinetic mechanisms. We typically use the approximate Michaelis-Menten-type flux expressions rather than the full system of equations in simulations for several reasons. First, often the quasi-steady rate constants (such as Ks and K in Equation (4.38)) are available from experimental data while the mass-action rate constants (k+i, k-i, etc.) are not. In fact, it is possible for different enzymes with different detailed mechanisms to yield the same Michaelis-Menten rate expression, as we shall see below. Second, in metabolic reaction networks (for example), reactions operate near steady state in vivo. Kinetic transitions from one in vivo steady state to another may not involve the sort of extreme shifts in enzyme binding that have been illustrated in Figure 4.7. Therefore the quasi-steady approximation (or equivalently the approximation of rapid enzyme turnover) tends to be reasonable for the simulation of in vivo systems. 

Metabolic networks can be quantitatively and qualitatively studied without enzyme kinetic parameters by using a constraints-based approach. Metabolic networks must obey the fundamental physicochemical laws, such as mass, energy, redox balances, diffusion, and thermodynamics. Therefore, when kinetic constants are unavailable, cellular function can still be mathematically constrained based on the mass and energy balance. Flux balance analysis (FBA) is a mathematical modeling framework that can be used to study the steady-state metabolic capabilities of cell-based physicochemical constraints. ... 

The addition of new biochemical pathways, or the modification of existing pathways, is likely to affect the rest of the cellular metabolism. The new or altered pathways may compete with other reactions for intermediates or cofactors. To precisely predict the impact of the manipulation of a metabolic network is virtually impossible since it would require a perfect model of all enzyme kinetics and of the control of gene expression. Flowever, attempts have been made to develop modeling techniques to predict the behavior of altered organisms [29]. 

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. 

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