Internal regulation of a modular system: the different faces of internal control

Abstract

The living cell houses a multitude of molecular processes that operate simultaneously in a mutually consistent fashion. A certain degree of organization stands out, e.g. in terms of the various metabolic pathways, transcription versus translation, signal transduction versus metabolism. This paper shows that by taking one of the aforementioned organizational principles into account, the complexity of understanding cell function quantitatively may be reduced significantly. To this aim the definition of the corresponding type of organization is refined and the conceptual tools used in the analysis of the control of cell function are adjusted. The approach is elaborated for a theoretical model of cell function, in which the latter depends on a constellation of interdependent but unconnected modules. The organization of a system is reduced to global control within a limited set of partaking modules and the links between them. Information about the systems total internal control and regulability is then drastically reduced to the information specifying global control and the regulability of the pathways that constitute the system. It is shown quantitatively how control at a lower level of organization bears on the control of the cell as a whole. The approach centers on writing the product of control (matrix) and elasticity (matrix) at a number of different levels of aggregation; these products equalling the identity (matrix) under different conditions. We demonstrate that there are at least three ways in which control and regulability of a system can be matched. In one, the true control within and between the modules of the systems is the inverse of the primary regulability (i.e. elasticity plus stoichiometry). In a second, the control internal to a module (but partly determined through the other modules) is matched by the inverse of newly defined `global' regulabilities for each module separately, which comprise the regulatory impact of the remainder of the system. In the third, the regulabilities are the ones intrinsic to the module and the control is taken equal to the control that would reign in the absence of the regulatory interactions between the units. In making these distinctions, it becomes transparent how much control stems from control within the organizational modules, and how much derives from the regulatory interactions between them. Control through other modules turns out to be equivalent, at steady state, to control within a module. The implications of this type of cellular organization for the location of the steady-state operating point is discussed.