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 Hopfield, 1974 . 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. Similar simplicity will arise in the dynamics of other complex biochemical processes. In particular, 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.
Biochemical processes typically involve huge numbers of individual reversible 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 (completion) time distributions. In particular, we provide explicit expressions for the mean and the variance of the completion time for a kinetic proofreading process and computational analyses for more complicated biochemical systems . 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 dynamical complexity of the full system is trivial compared to its apparent structural complexity. Similar simplicity is likely to arise in the dynamics of many complex multi-step biochemical processes. In particular, 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.
A
reversible
D
Hopfield, 1974
D
time
A
time
R
kinetic proofreading completion time
completion time for a kinetic proofreading process and computational analyses for more complicated biochemical systems
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full system dynamical complexity
dynamical complexity of the full system
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will
is likely to
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other complex
many complex multi-step