A local polynomial moment approximation for compartmentalized biochemical systems.
Tommaso Bianucci1, Christoph Zechner1
1Max Planck Institute of Molecular Cell Biology and Genetics, Pfotenhauerstraße 108, 01307, Dresden, Germany; Center for Systems Biology Dresden, Pfotenhauerstraße 108, 01307, Dresden, Germany; Cluster of Excellence Physics of Life, TU Dresden, Arnoldstraße 18, 01307, Dresden, Germany.
Mathematical Biosciences
|November 30, 2023
Summary
This study introduces a systematic method to analyze complex biochemical reactions in biological compartments. The new approach provides accurate predictions for systems with varying molecular content and compartment numbers, aiding in understanding cellular dynamics.
Area of Science:
- Biochemistry
- Systems Biology
- Mathematical Biology
Background:
- Compartmentalized biochemical reactions are fundamental to biological systems, exhibiting complex dynamics influenced by chemical and compartmental factors.
- Analyzing these systems mathematically, especially with inherent stochasticity, is challenging.
- Existing moment equation approaches are limited to polynomial rate laws and require difficult-to-find moment closure approximations.
Purpose of the Study:
- To develop a systematic method for deriving closed moment dynamics in compartmentalized biochemical systems.
- To overcome limitations of previous approaches regarding rate law restrictions and moment closure approximations.
- To enable more accurate mathematical analysis of stochasticity in biological compartmentalized systems.
Main Methods:
- Proposed a systematic method to derive closed moment dynamics for compartmentalized biochemical systems.
- Exploited the factorization structure of moment equations involving molecular content and compartment number distributions.
- Utilized polynomial expansions to approximate functions, resulting in a closed system of moment equations.
Main Results:
- Successfully derived closed moment dynamics for compartmentalized biochemical systems.
- Demonstrated the method's applicability to systems inspired by cell populations and organelle networks.
- Validated the accuracy of the method across different dynamical regimes.
Conclusions:
- The developed method provides a systematic way to derive closed moment equations for compartmentalized biochemical systems.
- This approach enhances the ability to analyze the statistical properties of complex biological systems.
- The findings offer a valuable tool for studying cellular and organelle network dynamics with improved accuracy.
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