Effective simulations of interacting active droplets

TL;DR

This paper introduces an efficient modeling approach for simulating interacting active droplets in cells by focusing on key degrees of freedom, significantly reducing computational costs compared to traditional methods.

Contribution

The authors develop a simplified dynamical model based on analytical solutions that accurately captures droplet interactions and dynamics with lower computational expense.

Findings

The method accurately reproduces fully-resolved simulation results.

It reduces computational costs by a significant margin.

The approach can incorporate additional biological processes in future work.

Abstract

Droplets form a cornerstone of the spatiotemporal organization of biomolecules in cells. These droplets are controlled using physical processes like chemical reactions and imposed gradients, which are costly to simulate using traditional approaches, like solving the Cahn-Hilliard equation. To overcome this challenge, we here present an alternative, efficient method. The main idea is to focus on the relevant degrees of freedom, like droplet positions and sizes. We derive dynamical equations for these quantities using analytical solutions to simplified situations. We verify our method against fully-resolved simulations and show that it can describe interacting droplets under the influence of chemical reactions and external gradients using only a fraction of the computational costs of traditional methods. Our method can be extended to include other processes in the future and will thus serve as a relevant platform for understanding the dynamics of droplets in cells.