Conservative finite volume method on deforming geometries: The case of protein aggregation in dividing yeast cells

Abstract

Motivated by experimental observations of asymmetric protein aggregates distributions in dividing yeast cells, we present a conservative finite volume approach for reaction-diffusion systems defined over deforming geometries. The key idea of our approach is to use spatio-temporal control volumes instead of integrating the time-discretized equations in space, as it is common practice. Both our theoretical and computational results demonstrate the convergence of our method and highlight how traditional approaches can lead to inaccurate solutions. We employ this novel approach to investigate the partitioning of protein aggregates in dividing yeast cells, leveraging the flexibility of the level set method to construct realistic biological geometries. Using a simple reaction-diffusion model, we find that spatial heterogeneity in yeast cells during division can alone create asymmetries in the concentration of protein aggregates. Moreover, we find that obstructing intracellular entities, such as nuclei or insoluble protein compartments, amplify these asymmetries, suggesting that they may play an essential role in regulating molecular partitioning. Beyond these findings, our results illustrate the flexibility of our approach and its potential to design realistic predictive tools to explore intracellular bio-mechanisms.