Multiple equilibria in complex chemical reaction networks: extensions to entrapped species models

In two earlier papers, means were provided to decide the capacity of complex chemical reaction networks, taken with mass-action kinetics, to admit multiple equilibria in the context of the isothermal homogeneous continuous flow stirred tank reactor (CFSTR). In such a reactor, all species are deemed to be in the outflow, a fact which has an important bearing on the nature of the governing equations. In contrast, one can imagine CFSTR-like models of the cell in which certain large molecules (e.g., enzymes) remain entrapped within the cell, whereas smaller ones (e.g., metabolites) are free to diffuse through the cell boundary. Although such models bear a strong physical resemblance to the classical CFSTR picture, there are substantive differences in the corresponding mathematics. Without a presumption of mass-action kinetics, this research is intended to indicate a general way in which results about uniqueness of equilibria in the classical CFSTR context extend to entrapped species models.