Multi-dimensional, mesoscopic Monte Carlo simulations of inhomogeneous reaction-drift-diffusion systems on...

Area of Science:

• Computational Biology
• Biophysics
• Mathematical Biology

Background:

• Macroscopic models are insufficient for many biological applications requiring stochastic simulation.
• Existing stochastic algorithms are computationally expensive and struggle with large particle numbers.
• Simulating reaction-drift-diffusion systems is crucial for understanding biological processes.

Purpose of the Study:

• To present a novel, genuine stochastic, multi-dimensional algorithm for reaction-drift-diffusion systems.
• To address the computational expense and limitations of existing stochastic methods.
• To enable simulations in previously inaccessible parameter regimes.

Main Methods:

• Developed a multi-dimensional stochastic algorithm for inhomogeneous, non-linear drift-diffusion problems.
• Integrated the algorithm into an operator-splitting approach to decouple reactions and spatial evolution.
• Leveraged data-parallel hardware architectures, specifically graphics processing units (GPUs).

Main Results:

• The algorithm successfully solves inhomogeneous, non-linear drift-diffusion problems on a mesoscopic level.
• Demonstrated validity and applicability through a suite of standard test problems.
• Quantified the numerical accuracy of the proposed method.

Conclusions:

• The new algorithm offers a computationally efficient and accurate approach for stochastic reaction-drift-diffusion simulations.
• The method is well-suited for GPU implementation, enhancing accessibility for researchers.
• Future integration into web services like Inchman will further facilitate parallel simulations on GPU clusters.