Chemical master equation parameter exploration using DMRG.

Area of Science:

• Computational chemistry
• Biophysics
• Systems biology

Background:

• Chemical reaction networks (CRNs) exhibit complex dynamics with correlated species fluctuations.
• Monte Carlo methods are standard for analyzing CRN stochastic trajectories.
• Approximating joint distributions over large state spaces using tensor networks is an emerging area.

Purpose of the Study:

• To apply tensor network methods for analyzing the steady-state distribution of a seven-species gene toggle switch CRN.
• To determine the conditions for bistability in the CRN model as a function of decomposition rates.
• To demonstrate the capability of tensor networks in capturing stochastic effects and enabling parameter exploration.

Main Methods:

• Utilizing tensor network strategies, specifically the density matrix renormalization group (DMRG) algorithm, to compute steady-state distributions.
• Analyzing a seven-species gene toggle switch CRN model.
• Employing excited-state DMRG to calculate relaxation timescales.

Main Results:

• The tensor network approach successfully determined the steady-state distribution of the gene toggle switch CRN.
• Bistability was identified as a function of two decomposition rates, with tensor networks capturing stochastic effects beyond mean-field approximations.
• The method demonstrated efficient projection to an order parameter for identifying bimodality and calculated a relaxation timescale.

Conclusions:

• Tensor networks provide a powerful tool for computing steady-state distributions of CRNs, offering insights into stochastic dynamics.
• This approach surpasses mean-field analysis in accuracy for systems with significant fluctuations.
• The developed techniques facilitate parameter exploration and analysis of complex CRN models, including bistable systems.