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Biochemical processes typically involve huge numbers of individual reversiblesteps, each with its own dynamical rate constants. For example, kineticproofreading processes rely upon numerous sequential reactions in order toguarantee the precise construction of specific macromolecules. In this work, westudy the transient properties of such systems and fully characterize theirfirst passage (completion) time distributions. In particular, we provideexplicit expressions for the mean and the variance of the completion time for akinetic proofreading process and computational analyses for more complicatedbiochemical systems. We find that, for a wide range of parameters, as thesystem size grows, the completion time behavior simplifies: it becomes eitherdeterministic or exponentially distributed, with a very narrow transitionbetween the two regimes. In both regimes, the dynamical complexity of the fullsystem is trivial compared to its apparent structural complexity. Similarsimplicity is likely to arise in the dynamics of many complex multi-stepbiochemical processes. In particular, these findings suggest not only that onemay not be able to understand individual elementary reactions from macroscopicobservations, but also that such understanding may be unnecessary.

Simplicity of Completion Time Distributions for Common Complex Biochemical Processes