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Rigorous elimination of fast stochastic variables from the linear noise approximation using projection operators
Philipp Thomas1, Ramon Grima, Arthur V Straube
1Department of Physics, Humboldt University of Berlin, Newtonstr. 15, D-12489 Berlin, Germany. philippocampus@gmail.com
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 11, 2012
Summary
The slow-scale linear noise approximation (ssLNA) rigorously derives from the standard LNA for biochemical networks with timescale separation. This reduced model simplifies intrinsic noise analysis in these systems.
Area of Science:
- Biochemical network modeling
- Stochastic systems analysis
- Computational biology
Background:
- The linear noise approximation (LNA) is used to study intrinsic noise in biochemical networks.
- A simplified version, the slow-scale LNA (ssLNA), was previously proposed based on physical arguments for systems with timescale separation.
Purpose of the Study:
- To provide the first rigorous mathematical derivation of the slow-scale LNA (ssLNA).
- To establish the conditions under which ssLNA is valid and its relationship to other reduction techniques.
Main Methods:
- Projection operator technique
- Analysis of timescale separation conditions
- Comparison with deterministic quasi-steady-state approximation
Main Results:
- The ssLNA is rigorously derived from the standard LNA under timescale separation conditions.
- These conditions are identical to those for the deterministic quasi-steady-state approximation.
- The large molecule number limit of other stochastic reduction methods is shown to be a special case of ssLNA.
Conclusions:
- The ssLNA provides a mathematically sound and simplified approach for analyzing intrinsic noise in biochemical systems exhibiting timescale separation.
- This work unifies several stochastic model reduction techniques under the framework of ssLNA.
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