Collective modes and wavelike solutions to cellular control equations

A living cell is viewed as a system of biochemical reaction pathways which are self- and mutually-regulating. A matrix differential equation is proposed which governs the system behavior. A periodic boundary condition is introduced which allows the equation to be solved for its eigenvalues and eigenvectors. The nature of the solution is such that a set of coordinates representing strongly interacting chemical populations is converted into a set of collective coordinates representing weakly interacting oscillatory modes. The modes are travelling waves which transport matter through an open loop and information through a closed loop. The validity of the model is examined, as is the relation to other models of the cellular regulatory apparatus. An experiment is outlined which should detect these modes if they are present in living cells. The main impediment to their detection is nonlinearity, which produces decay of the modes. Several predictions of the model may be associated with specific cellular attributes. The “growth mode” belongs to zero frequency. An unstable mode acts like a switch causing a cell to enter a new phase. Cell division is seen as such a phase transition. Although there is discontinuity in the global aspect (one cell becoming two), there is still a slow variation in chemical concentrations, in keeping with biochemical evidence.