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A differentiable Gillespie algorithm for simulating chemical kinetics, parameter estimation, and designing synthetic

Krishna Rijal¹, Pankaj Mehta¹

¹Department of Physics, Boston University, Boston, Massachusetts 02215, USA.

Biorxiv : the Preprint Server for Biology

|July 19, 2024

Summary

We introduce a differentiable Gillespie algorithm (DGA) using deep learning to analyze complex chemical reactions. This method accurately learns kinetic parameters and designs biochemical networks for systems biology applications.

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Area of Science:

Systems Biology
Computational Chemistry
Machine Learning

Background:

The Gillespie algorithm is a standard for simulating chemical reaction networks.
Deep learning offers new approaches for analyzing complex systems.
Current methods lack differentiability for gradient-based optimization.

Purpose of the Study:

To develop a differentiable variant of the Gillespie algorithm (DGA).
To enable gradient-based learning of kinetic parameters and network design.
To apply DGA to stochastic models in systems and synthetic biology.

Main Methods:

Leveraging deep learning to approximate discontinuous operations in the Gillespie algorithm with smooth functions.
Implementing backpropagation for gradient calculation.
Applying DGA to stochastic gene promoter models.

Main Results:

Successfully learned kinetic parameters from experimental mRNA expression data for *E. coli* promoters.
Designed nonequilibrium promoter architectures with specific input-output relationships.
Demonstrated DGA's accuracy and speed in parameter learning and network design.

Conclusions:

The differentiable Gillespie algorithm (DGA) provides a powerful new tool for analyzing stochastic chemical kinetics.
DGA facilitates gradient-based optimization for parameter inference and synthetic biology design.
This approach has broad applicability in systems biology and related fields.