Point-particle method to compute diffusion-limited cellular uptake.

Area of Science:

• Computational physics and chemistry
• Biophysics and biochemical engineering

Background:

• Reaction-diffusion processes are fundamental to cellular uptake and biochemical reactions.
• Simulating diffusion-limited absorption by particles, like cellular uptake, is computationally challenging.

Purpose of the Study:

• To introduce an efficient point-particle simulation method for reaction-diffusion processes.
• To model cellular uptake by spherical absorbing particles in the diffusion-limited regime.
• To calibrate the numerical method using exact solutions for single absorbers.

Main Methods:

• Developed an efficient point-particle approach calibrated against exact solutions.
• Simulated multiple absorbers with increasing complexity to validate performance.
• Implemented the method within a pseudospectral solver, extensible to fluid motion.

Main Results:

• The method accurately links numerical parameters to physical properties like particle radius and uptake rate.
• Demonstrated the ability to resolve complex diffusive interactions, quantified by the Sherwood number.
• Successfully simulated uptake rate in a linear shear flow as a test case.

Conclusions:

• The point-particle approach is a powerful and flexible tool for simulating reaction-diffusion systems.
• The method can be generalized to include fluid dynamics, enhancing its applicability.
• Enables investigation of complex biological and chemical phenomena, including cellular uptake and transport.