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

## TL;DR

This paper introduces an efficient point-particle computational method for simulating diffusion-limited cellular uptake, accurately capturing interactions among multiple absorbers and adaptable to include fluid flow effects.

## Contribution

The paper presents a novel, calibrated point-particle approach for simulating diffusion-limited absorption, validated against analytical results, and extendable to fluid flow scenarios.

## Key findings

- Accurately models multiple absorbers and their interactions.
- Demonstrates the method's effectiveness in complex configurations.
- Shows potential for studying cellular uptake in flow conditions.

## Abstract

We present an efficient point-particle approach to simulate reaction-diffusion processes of spherical absorbing particles in the diffusion-limited regime, as simple models of cellular uptake. The exact solution for a single absorber is used to calibrate the method, linking the numerical parameters to the physical particle radius and uptake rate. We study configurations of multiple absorbers of increasing complexity to examine the performance of the method, by comparing our simulations with available exact analytical or numerical results. We demonstrate the potentiality of the method in resolving the complex diffusive interactions, here quantified by the Sherwood number, measuring the uptake rate in terms of that of isolated absorbers. We implement the method in a pseudo-spectral solver that can be generalized to include fluid motion and fluid-particle interactions. As a test case of the presence of a flow, we consider the uptake rate by a particle in a linear shear flow. Overall, our method represents a powerful and flexible computational tool that can be employed to investigate many complex situations in biology, chemistry and related sciences.