On the generalisation of the metabolic thermodynamic theory of the cell cycle

In a recent Letter, we have shown how a thermodynamic-like theory can be developed starting from the periodic production of certain proteins in the cell cycle [Chem. Phys. Lett. 377 (2003) 627]. The kinetic equations for two protein complexes regulating the cell cycle were assumed to be in Hamiltonian form. This implies that the underlying system is conservative, a hypothesis which is by no means verified by biological systems. The only justification we had for such a choice was the necessity to keep the derivation as simple as possible, so that the essence of the methodology and its development were not shadowed by complicated mathematics. In this short communication, we revisit the theory presented and we generalise it to the case when the system is dissipative. We also show that the theory still holds when the system is not at equilibrium.