Related Experiment Videos
Concentration fluctuations in a mesoscopic oscillating chemical reaction system
Hong Qian1, Saveez Saffarian, Elliot L Elson
1Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA. qian@amath.washington.edu
Summary
Stochastic models reveal that small biochemical systems exhibit cyclic random walks, regardless of deterministic steady or oscillating states. This clarifies fluctuations in nonequilibrium systems and their relevance to spectroscopy and metabolic networks.
Area of Science:
- Biochemical reaction kinetics
- Nonlinear dynamics
- Stochastic modeling
Background:
- Macroscopic nonlinear biochemical systems far from equilibrium exhibit either steady states or sustained oscillations.
- Deterministic kinetics based on the law of mass action describe these macroscopic behaviors.
- At the mesoscopic level, small concentrations of species lead to significant random fluctuations.
Purpose of the Study:
- To investigate the behavior of mesoscopic biochemical systems with small concentrations of dynamic species (X and Y).
- To replace deterministic mass action kinetics with a stochastic model to account for random fluctuations.
- To analyze the impact of stochasticity on systems that would be steady or oscillating in the macroscopic limit.
Main Methods:
- Development of a stochastic model for a two-species (X and Y) mesoscopic system.
- Analysis of probability distributions and correlation functions for species concentrations over time.
- Derivation of a diffusion-like equation for probability in the two-dimensional phase plane.
- Examination of system behavior in the limit of large species concentrations.
Main Results:
- Species concentrations execute cyclic random walks in the phase plane, irrespective of the deterministic steady or oscillating state.
- Probability distributions and correlation functions show quantitative, not qualitative, differences between steady and oscillating macroscopic counterparts.
- A diffusion equation accurately describes the probability of states in the phase plane.
- The deterministic nonlinear kinetics are recovered in the limit of large concentrations.
Conclusions:
- Stochastic fluctuations fundamentally alter the behavior of mesoscopic biochemical systems, leading to random walks.
- The distinction between "thermal stochasticity" and "temporal complexity" in oscillating nonequilibrium systems is clarified.
- Findings are relevant for understanding fluorescence correlation spectroscopy and metabolic reaction networks.