Hyperbolic inhibition in bisubstrate reactions

Let us, now, depart from monosubstrate reactions and turn our attention to a much more realistic case of a hyperbolic inhibition in bisubstrate reactions (Segel, 1975 Dixon Webb, 1979 f rich Allison, 2000). In the rapid equilibrium reaction (6.14), A and B are the substrates while I is a nonexclusive inhibitor  

The interaction factors a, p, and y represent, respectively, the effect of A on the binding of B, the effect of I on the binding of B, and the effect of I on the binding of A. The factor d represents the effect of I on the catalytic activity of the EABI complex. The derivation of rate equation for reaction (6.14) would be extremely laborious from the steady-state assumptions. Therefore, the general velocity equation is derived from Ae rapid equilibrium assumptions  

The rate equations in the reciprocal form, derived from Eq. (6.15), are extremely 

Similarly as for the nonlinear inhibition with a single substrate and a single inhibitor molecule (Section 6.1), the double reciprocal plots of i/vo versus 1/A or i/u versus 1/B, are a family of straight lines with a single intersection point to the left of the vertical axis. Also, the slope and intercept replots are hyperbolic. 

In the general case, when both complexes EAB and EABI are c ytically active, the inhibitor constants are conveniently obtained from replots of i/A Slope and i/A Intercept versus 1/7, obtained at saturating concentration of one constant substrate, while the other is varied. Under sueh conditions, the system behaves as a single substrate, hyperbolic noncompetitive inhibition system. In this case, the inhibition with respeet to a varied ligand cannot be overcome by saturation with the nonvaried ligand. 

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