On physiological multiplicity and population heterogeneity of biological systems

Abstract

The theory of steady-state multiplicity has been used to analyze the adaptive behavior associated with two experimentally well characterized biological systems; the bacteriophage γ and the Escherichia coli lactose operon. The ability to observe such systems in distinct physiological forms within a unique environment was found to be consistent with the existence of multiple stable solutions of the representative balance equations. Additionally, transitions between physiological states were found to be controlled by threshold mechanisms that altered the steady-state solution structure in a manner analogous to the ignition-extinction behavior exhibited by non-isothermal chemical reactors. These findings indicate that the population heterogeneity observed in these systems can be explained on the basis of steady-state multiplicity whereby a nonuniform population response acts to generate a culture comprised of physiologically distinct forms. Since multiple solutions of the conservation equations were found to orginate from interactions between conserved nonlinear kinetic and feedback mechanisms, these results appear general and the conclusions derived should be applicable to other less characterized biological systems. These findings also suggest that the physiological homogeneity assumption routinely employed in theoretical and experimental analysis of cellular behavior may lack theoretical justification.