Cell systems consist of a huge number of various molecules that display
specific patterns of interactions, which have a determining influence on the
cell's functioning. In general, such complexity is seen to increase with the
complexity of the organism, with a concomitant increase of the accuracy and
specificity of the cellular processes. The question thus arises how the
complexification of systems - modeled here by simple interacting birth-death
type processes - can lead to a reduction of the noise - described by the
variance of the number of molecules. To gain understanding of this issue, we
investigated the difference between a single system containing molecules that
are produced and degraded, and the same system - with the same average number
of molecules - connected to a buffer. We modeled these systems using Ito
stochastic differential equations in discrete time, as they allow
straightforward analytical developments. In general, when the molecules in the
system and the buffer are positively correlated, the variance on the number of
molecules in the system is found to decrease compared to the equivalent system
without a buffer. Only buffers that are too noisy by themselves tend to
increase the noise in the main system. We tested this result on two model
cases, in which the system and the buffer contain proteins in their active and
inactive state, or protein monomers and homodimers. We found that in the second
test case, where the interconversion terms are non-linear in the number of
molecules, the noise reduction is much more pronounced; it reaches up to 20%
reduction of the Fano factor with the parameter values tested in numerical
simulations on an unperturbed birth-death model. We extended our analysis to
two arbitrary interconnected systems.Comment: 38 pages, 5 figures, to appear in J. Theor. Bio
