Controlling networks of nonlinearly-coupled nodes using response surfaces

Network modulation at stable states

Advances in microarray and sequencing technologies have made possible the interrogation of biological processes at increasing levels of complexity. The underlying biomolecular networks contain large numbers of nodes, yet interactions within the networks are not known precisely. In the absence of accurate models, one may inquire if it is possible to find relationships between the states of such networks under external changes, and in particular, if such relationships can be model-independent. In this paper we introduce a class of such relationships. The results are based on the observation that changes to the equilibrium state of a network due to an alteration in an external input are "small" compared to the change in the input, a phenomenon we refer to as network modulation. It relies on the stability of the state. One consequence of network modulation is that response surfaces containing expression profiles of different mutants of an organism are low-dimensional linear subspaces. As an example, the expression profile of a double-knockout mutant generally lies close to the plane defined by the expression profiles of the wild-type and those of the two single-knockout mutants. This assertion is validated using experimental data from the sleep-deprivation network of Drosophila and the oxygen-deprivation network of Escherichia coli. The linearity of response surfaces is crucial in the design of a feedback control algorithm to move the underlying network from an initial state to a prespecified target state.