Biochemical kinetics reaction fluxes

The data and associated model fits used to obtain these kinetic constants are shown in Figures 4.10 through 4.12. These data on quasi-steady reaction flux as functions of reactant and inhibitor concentrations are obtained from a number of independent sources, as described in the figure legends. Note that the data sets were obtained under different biochemical states. In fact, it is typical that data on biochemical kinetics are obtained under non-physiological pH and ionic conditions. Therefore the reported kinetic constants are not necessarily representative of the biochemical states obtained in physiological systems. 

One can view biochemical systems as represented at the most basic level as networks of given stoichiometry. Whether the steady state or the kinetic behavior is explored, the stoichiometry constrains the feasible behavior according to mass balance and the laws of thermodynamics. As we have seen in this chapter, some analysis is possible based solely on the stoichiometric structure of a given system. Mass balance provides linear constraints on reaction fluxes non-linear thermodynamic constraints provide information about feasible flux directions and reactant concentrations. 

The obvious advantage is that the steady-state solution of an S-system model is accessible analytically. However, while the drastic reduction of complexity can be formally justified by a (logarithmic) expansion of the rate equation, it forsakes the interpretability of the involved parameters. The utilization of basic biochemical interrelations, such as an interpretation of fluxes in terms of a nullspace matrix is no longer possible. Rather, an incorporation of flux-balance constraints would result in complicated and unintuitive dependencies among the kinetic parameters. Furthermore, it must be emphasized that an S-system model does not necessarily result in a reduced number of reactions. Quite on the contrary, the number of reactions r = 2m usually exceeds the value found in typical metabolic networks. 

A commonly held belief is that, for an enzyme reaction within a metabolic pathway, a large excess of catalytic capacity relative to a pathway s metabolic flux ensures that a given step is at or near thermodynamic equilibrium. Brooks recently treated the kinetic behavior of reaction schemes one might judge to be at equilibrium, and he showed that individual steps can remain far from equilibrium, even at a high ratio of an enzyme s flux to a pathway s steady-state flux. His calculations indicate that whether a reaction is near equilibrium depends on (a) the overall flux through the enzyme locus and (b) the kinetic parameters of the other enzymes in the pathway. S. P. Brooks (1996) Biochem. Cell Biol. 74, 411. 

Although these arguments have been presented for reaction systems whose rates are forced by an external oscillator, they remain true for autonomous biochemical oscillations where ot and are nonlinear functions of metabolite concentrations. That is, the rate of removal of a labeled compound through a reaction step whose rate is oscillating due to nonlinear kinetics will be enhanced over an equivalent system that maintains the same mean chemical flux and mean concentrations of metabolites but does not oscillate. This has been demonstrated numerically ( 6) on the reaction system (1) from the previous section using the full kinetic equations... 

There is almost no biochemical reaction in a cell that is not catalyzed by an enzyme. (An enzyme is a specialized protein that increases the flux of a biochemical reaction by facilitating a mechanism [or mechanisms] for the reaction to proceed more rapidly than it would without the enzyme.) While the concept of an enzyme-mediated kinetic mechanism for a biochemical reaction was introduced in the previous chapter, this chapter explores the action of enzymes in greater detail than we have seen so far. Specifically, catalytic cycles associated with enzyme mechanisms are examined non-equilibrium steady state and transient kinetics of enzyme-mediated reactions are studied an asymptotic analysis of the fast and slow timescales of the Michaelis-Menten mechanism is presented and the concepts of cooperativity and hysteresis in enzyme kinetics are introduced. 

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. 

Appropriate expressions for the fluxes of each of the reactions in the system must be determined. Typically, biochemical reactions proceed through multiple-step catalytic mechanisms, as described in Chapter 4, and simulations are based on the quasi-steady state approximations for the fluxes through enzyme-catalyzed reactions. (See Section 3.1.3.2 and Chapter 4 for treatments on the kinetics of enzyme catalyzed reactions.)... 

If enough fluxes are measured at a metabolic steady state, MFA [11,12] can be used to estimate the fluxes through the remainder of the metabolic reaction network (Figure 15.1). This analysis is powerful because only the stoichiometry of the biochemical reaction network is required, and no knowledge of the chemical reaction kinetics is needed. MFA is usually formulated as a matrix equation ... 

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