Intrinsic noise modulation in closed oligomerization-type systems

Abstract

How random fluctuations impact on biological systems and what is their relationship with complexity and energetic cooperativity are challenging questions that are far from being elucidated. Using the stochastic differential equation formalism, we studied analytically the effect of fluctuations on a series of oligomerization processes, in which several molecules of the same or different species interact to form complexes, without interaction with the environment. The conservation of the total number of molecules within the systems imposes constraints on the stochastic quantities, among which the negativity of the covariances and the vanishing of the determinant of the covariance matrix. The intrinsic noise on the number of molecules of each species is represented by the Fano factor, defined as the variance to mean ratio. At the equilibrium steady states, the sum of the Fano factors of all molecular species is equal to the rank of the system, independently of the parameters. The Fano factors of the individual molecular species are, however, parameter dependent. We found that when the free energy cooperativity of the reactions increases, the intrinsic noise on the oligomeric product decreases, and is compensated by a higher noise on the monomeric reactants and/or intermediate states. The noise reduction is moreover more pronounced for higher complexity systems, involving oligomers of higher degrees.