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.

Deciphering noise amplification and reduction in open chemical reaction networks

“…Two features are shown to be crucial for the noise modulation in the systems analyzed: the deficiency δ and the type of oligomers. On the basis of the results obtained in this paper and in [31,32], we propose the following conclusions and tentative generalizations:…”

“…Thus, when s=1, the number of molecules of each species follows a Poisson distribution [21,22]. For closed systems, we showed in [31] the weaker result…”

“…Note that this is only true for open systems. For closed systems, we showed in [23] the weaker result i F(U i ) = χ since in this case, the number of molecules follow a multinomial distribution constrained by the conservation of the total number of molecules [14].…”

“…It has furthermore been shown that the increase of the network complexity tends to decrease the intrinsic noise as well as to reduce the effect of the extrinsic noise for some multistable model systems [29], whereas a dependence of the noise reduction or amplification on the system parameters has been found in [30].This paper focuses on a class of biological networks linking several molecular species, which are produced, degraded and undergo homo-or hetero-oligomerizationtype reactions. It builds on our earlier works, in which we used the stochastic differential equation formalism to study the intrinsic noise in a series of closed [31] and open systems [32]. Here we computed the noise reduction or amplification on every individual molecular species at the steady state, and related the fluctuation levels to some structural characteristics of the reaction network and to the reaction fluxes flowing between the species.…”

“…This paper focuses on a class of biological networks linking several molecular species, which are produced, degraded and undergo homo-or hetero-oligomerizationtype reactions. It builds on our earlier works, in which we used the stochastic differential equation formalism to study the intrinsic noise in a series of closed [31] and open systems [32]. Here we computed the noise reduction or amplification on every individual molecular species at the steady state, and related the fluctuation levels to some structural characteristics of the reaction network and to the reaction fluxes flowing between the species.…”