Title: Coherence of Biochemical Oscillations is Bounded by Driving Force and Network Topology,
Abstract: Biochemical oscillations are prevalent in living organisms. Systems with a
small number of constituents cannot sustain coherent oscillations for an
indefinite time because of fluctuations in the period of oscillation. We show
that the number of coherent oscillations that quantifies the precision of the
oscillator is universally bounded by the thermodynamic force that drives the
system out of equilibrium and by the topology of the underlying biochemical
network of states. Our results are valid for arbitrary Markov processes, which
are commonly used to model biochemical reactions. We apply our results to a
model for a single KaiC protein and to an activator-inhibitor model that
consists of several molecules. From a mathematical perspective, based on strong
numerical evidence, we conjecture a universal constraint relating the imaginary
and real parts of the first non-trivial eigenvalue of a stochastic matrix.