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Center for Nonlinear Studies |
Biochemical processes typically involve huge numbers of individual steps, each with its own dynamical rate constants. For example, kinetic proofreading processes rely upon numerous sequential reactions in order to guarantee the precise construction of specific macromolecules. In this work, we study the transient properties of such systems and fully characterize their first passage time (completion) distributions. In particular, we provide explicit expressions for the mean and the variance of the kinetic proofreading completion time. We find that, for a wide range of parameters, as the system size grows, the completion time behavior simplifies: it becomes either deterministic or exponentially distributed, with a very narrow transition between the two regimes. In both regimes, the full system dynamical complexity is trivial compared to its apparent structural complexity. We also show that similar simplification arises in the dynamics of other complex biochemical processes in particular multi-branch kinetic proofreading. These findings suggest not only that one may not be able to understand individual elementary reactions from macroscopic observations, but also that such understanding may be unnecessary.