The physical constraint constant

The argument that flux-force relations can be taken as approximately linear, because they can be approximated as the first order term in the expansion series of the real flux-force relation is relatively trivial. It would be more satisfactory if the linear approximation could be shown to be better than that. Van der Meer et al. [13], stressing that a metabolically important physical constraint is that of conservation of substrate plus product concentration, demonstrated such a better linear approximation for the enzyme-catalyzed reaction (see also Ref. 11)  

Here E is the enzyme and ES and EP are the enzyme-substrate and the enzyme-product complex, respectively. The rate of such a reaction (e.g., if [P] = 0) approaches a maximum value, at increasing substrate concentrations. Similarly, the backward reaction (i.e., at [S] = 0) has a maximum rate Vp at high P concentrations. With the introduction of the Michaelis-Menten constants  

In the literature a distinction is sometimes made between irreversible and reversible reactions. Such a distinction is in apparent contradiction with the principle of microscopic reversibility [1,18] if substrate and product concentrations were chosen 

Until recently, non-equilibrium thermodynamic treatments always formulated the dependence of the rates of individual reactions on the free-energy difference (AG) across them in the same manner  

Differences between different enzymes were supposed to be confined to differences in L they were not supposed to affect the form, or position of the dependence of the reaction rate on AG. However, for the dashed curve in Fig. 1.1, the part where the approximation by this equation would be reasonable, is at very small reaction rates. In the presumably functionally more relevant part (v/V between 0.1 and 0.9), this equation (i.e., a straight line through the origin) is a completely unsatisfactory approximation of the actual relationship between v and AG. Yet, around = 0.5 a different, though linear, approximation would seem possible. Below, we shall further substantiate this alternative approximation. 

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