The classical Botts-Morales theory for the action of a modifier on the catalytic properties of an enzyme has been extended to deal with allosteric effects in serine proteases. The exact analytical solution derived for the linkage scheme at steady state provides a rigorous framework for the study of many biologically relevant systems, including enzymes activated by monovalent cations and cofactor-controlled protease-zymogen interactions in blood coagulation. When the enzyme obeys Michaelis-Menten kinetics, the exact solution of the kinetic linkage scheme simplifies considerably. Of particular importance for practical applications is a simple equation expressing the dependence of the specificity constant of the enzyme, kcat/Km, on the concentration of the modifier, from which the equilibrium binding constant for the formation of the enzyme-modifier complex can be estimated. Analysis of the allosteric changes in thrombin activity induced by thrombomodulin and Na+ in terms of this equation yields accurate determinations of the equilibrium binding constants for both effectors.