On the existence of a steady state in a biological system

This paper deals with the existence, uniqueness, and stability of a critical point (steady state) in the case of a macromolecular system, such as an allosteric or polysteric protein, for which the first-order kinetic equations are nonlinear. It presents a brief outline of a rigorous proof (to be given in full elsewhere) that, in a restricted but not unrepresentative system of this kind, there always exists one and only one positive critical point and that this point is asymptotically stable in the large: no matter what its starting point, the system will always approach this point by some kind of relaxation process, however complex.