DeepCME: A deep learning framework for computing solution statistics of the chemical master equation.

Area of Science:

• Computational Biology
• Systems Biology
• Synthetic Biology

Background:

• Stochastic models are crucial for understanding low copy-number reactions in biological systems.
• The Chemical Master Equation (CME) describes probability distributions but often results in high-dimensional systems, making solutions computationally challenging.
• Current methods often rely on intensive stochastic simulations.

Purpose of the Study:

• To develop a novel deep learning approach for computing solution statistics of high-dimensional Chemical Master Equations (CMEs).
• To reformulate stochastic dynamics using Kolmogorov's backward equation for improved approximation.
• To enable efficient estimation of expectations and sensitivities for CME solutions.

Main Methods:

• Reformulation of stochastic dynamics using Kolmogorov's backward equation.
• Application of Deep Neural Networks (DNNs) to approximate CME solutions.
• Algorithm based on reinforcement learning for training DNNs with moderate simulations.

Main Results:

• Successfully estimated expectations for user-defined functions of the state-vector under CME solutions.
• Demonstrated the ability to compute sensitivities with respect to reaction network parameters.
• Validated the methodology with four illustrative examples.

Conclusions:

• The proposed deep learning method offers an efficient alternative to traditional simulations for high-dimensional CMEs.
• This approach facilitates accurate computation of solution statistics and parameter sensitivities.
• Paves the way for further research in applying deep learning to complex biological models.