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Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
Published on: December 7, 2021
Patterns of stochastic behavior in dynamically unstable high-dimensional biochemical networks
1National Cancer Institute, EPN 3108, 6130 Executive Blvd, Rockville, MD 20892, USA. sr212a@nih.gov
Gene Regulation and Systems Biology
|October 20, 2009
Summary
Large biochemical networks are often dynamically unstable, exhibiting pseudo-random fluctuations. These fluctuations follow specific statistical distributions, explaining biological burstiness in gene expression.
Area of Science:
- Biochemistry
- Chemical Kinetics
- Systems Biology
Background:
- Large biochemical networks often exhibit complex dynamics.
- Asymptotic stability criteria are rarely met in multidimensional chemical kinetic systems.
- Dynamical instability does not always lead to system collapse.
Purpose of the Study:
- To investigate the stochastic behavior of large biochemical networks.
- To explore the implications of dynamical instability in biochemical systems.
- To connect theoretical dynamics to observed biological phenomena like gene expression burstiness.
Main Methods:
- Analysis of differential equations in chemical kinetics.
- Application of stability criteria (Routh-Hurwitz, Lyapunov, Feinberg's Deficiency Zero theorem).
- Computer simulations to model system dynamics.
- Statistical analysis using Langevin and Fokker-Plank equations.
Main Results:
- Stringent asymptotic stability conditions are unlikely in complex biochemical networks.
- Dynamically unstable systems can exhibit pseudo-random fluctuations resembling shot noise.
- Simulated processes follow Generalized Pareto Distribution and Poisson processes.
- These dynamics explain the burstiness observed in gene expression.
Conclusions:
- Biochemical network dynamics are often inherently unstable.
- Pseudo-stochastic behavior and burstiness are natural outcomes of these unstable dynamics.
- Langevin and Fokker-Plank equations provide a suitable framework for describing these systems.
- The findings offer insights into intracellular dynamics and gene expression regulation.
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