Simplicity of Completion Time Distributions for Common Complex Biochemical Processes

TL;DR

This paper characterizes the distribution of completion times in complex biochemical processes, revealing that as systems grow large, their timing behavior simplifies to either deterministic or exponential, despite underlying complexity.

Contribution

It provides explicit formulas for mean and variance of completion times and demonstrates the emergence of simple timing distributions in large biochemical systems.

Findings

Completion times become either deterministic or exponentially distributed as system size increases.

The transition between regimes is very narrow, indicating a sharp simplification.

Full system complexity is trivial compared to apparent structural complexity.

Abstract

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.