Constraints on Fluctuations in Sparsely Characterized Biological Systems
Andreas Hilfinger,1 Thomas M. Norman, 1 Glenn Vinnicombe, 2 and Johan Paulsson 1,*
1 Department of Systems Biology, Harvard University, 200 Longwood Avenue, Boston, Massachusetts 02115, USA
2 Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, United Kingdom
(Received 27 August 2015; published 1 February 2016)
Biochemical processes are inherently stochastic, creating molecular fluctuations in otherwise identical cells. Such “noise” is widespread but has proven difficult to analyze because most systems are sparsely characterized at the single cell level and because nonlinear stochastic models are analytically intractable. Here, we exactly relate average abundances, lifetimes, step sizes, and covariances for any pair of components in complex stochastic reaction systems even when the dynamics of other components are left unspecified. Using basic mathematical inequalities, we then establish bounds for whole classes of systems. These bounds highlight fundamental trade-offs that show how efficient assembly processes must invariably exhibit large fluctuations in subunit levels and how eliminating fluctuations in one cellular component requires creating heterogeneity in another.
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