Time-dependent propagators for stochastic models of gene expression: an analytical method

Area of Science:

• Systems Biology
• Computational Biology
• Biophysics

Background:

• Gene expression exhibits inherent stochasticity within regulatory networks, impacting species dynamics.
• Propagators, describing network evolution, are typically solutions to the chemical master equation (CME).
• Exact CME solutions are often intractable due to high dimensionality.

Purpose of the Study:

• To develop an efficient analytical method for approximating propagators in stochastic gene expression models.
• To provide a generalized framework for analyzing complex biological networks.

Main Methods:

• Introduced a probability-generating function to transform the CME into partial differential equations (PDEs).
• Applied the method of characteristics to derive ordinary differential equations (ODEs) solvable via dynamical systems techniques.
• Reconstructed propagator probabilities numerically using the Cauchy integral formula.

Main Results:

• Developed a closed-form solution for the generating function.
• Generated a 'library' of propagators for specific stochastic gene expression models.
• Demonstrated the method's applicability to two established gene expression models.

Conclusions:

• The proposed analytical method offers an efficient way to approximate propagators for stochastic gene expression.
• The technique is adaptable for Bayesian parameter inference and can be extended to other stochastic models.
• This work provides a valuable tool for analyzing complex biological systems with inherent randomness.