Sampling rare events in stochastic reaction-diffusion systems within trajectory looping.

Area of Science:

• Computational chemistry
• Biophysics
• Chemical kinetics

Background:

• Bistable reaction-diffusion systems exhibit slow state transitions compared to chemical equilibration.
• Estimating transition rates via explicit Brownian dynamics is computationally expensive.

Purpose of the Study:

• To develop a computationally efficient method for sampling rare chemical kinetic processes.
• To enhance the simulation of long-timescale events in systems with constant molecule numbers, like signal transduction.

Main Methods:

• A novel trajectory looping technique is presented.
• This method reuses a single diffusive trajectory by looping chemical states from the end to the beginning.
• The approach is applied to bistable systems, including autophosphorylating kinases.

Main Results:

• The method enables sampling of chemical kinetics on timescales orders of magnitude longer than the original diffusive trajectory.
• State-to-state transition rates and traveling wave velocities were calculated for a model system.
• An open-source implementation is provided.

Conclusions:

• Trajectory looping offers a significant computational advantage for simulating rare events in biochemical systems.
• This technique is applicable to various systems with conserved molecular numbers, such as cellular signaling.
• The method facilitates more accessible and efficient study of complex kinetic processes.