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The simplicity of completion time distributions for common complex biochemical processes.
Golan Bel1, Brian Munsky, Ilya Nemenman
1Center for Nonlinear Studies and the Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA. golanbel@gmail.com
Physical Biology
|December 23, 2009
Summary
Complex biochemical processes simplify as they grow larger. Their completion times become either deterministic or exponentially distributed, suggesting macroscopic understanding may suffice over detailed elementary steps.
Area of Science:
- Biochemistry and Biophysics
- Chemical Kinetics
- Systems Biology
Background:
- Biochemical pathways involve numerous reversible steps with distinct rate constants.
- Kinetic proofreading relies on sequential reactions for accurate macromolecule synthesis.
Purpose of the Study:
- To investigate transient properties and completion time distributions in complex biochemical systems.
- To derive explicit expressions for mean and variance of completion times in kinetic proofreading.
- To analyze computational models of intricate biochemical processes.
Main Methods:
- Mathematical derivation of completion time distributions for kinetic proofreading.
- Computational analysis of complex multistep biochemical systems.
- Analysis of system size effects on transient dynamics.
Main Results:
- Explicit expressions for mean and variance of completion time derived for kinetic proofreading.
- Completion time behavior simplifies to deterministic or exponential distributions as system size increases.
- A narrow transition zone exists between deterministic and exponential regimes.
Conclusions:
- Dynamical complexity becomes trivial relative to structural complexity in large biochemical systems.
- Simplification of dynamics is likely prevalent in many complex multistep biochemical processes.
- Macroscopic observation may be sufficient for understanding, rendering detailed elementary reaction analysis unnecessary.
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