期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2022
卷号：119
期号：33
DOI：10.1073/pnas.2206888119
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：Significance
Biological processes operate in a spatially and temporally ordered manner to reliably fulfill their function. This is achieved by pattern formation, which generally involves many different spatial and temporal scales. The resulting multiscale patterns exhibit complex dynamics for which it is difficult to find a simplified description at large scales while preserving information about the patterns at small scales. Here, we introduce an approach for mass-conserving reaction–diffusion systems that is based on a linear theory and therefore conceptually simple to apply. We investigate multiscale patterns of the Min protein system and show that our approach enables us to explain and predict the intricate dynamics from the large-scale mass redistribution of the total protein densities.
Self-organized pattern formation is vital for many biological processes. Reaction–diffusion models have advanced our understanding of how biological systems develop spatial structures, starting from homogeneity. However, biological processes inherently involve multiple spatial and temporal scales and transition from one pattern to another over time, rather than progressing from homogeneity to a pattern. To deal with such multiscale systems, coarse-graining methods are needed that allow the dynamics to be reduced to the relevant degrees of freedom at large scales, but without losing information about the patterns at small scales. Here, we present a semiphenomenological approach which exploits mass conservation in pattern formation, and enables reconstruction of information about patterns from the large-scale dynamics. The basic idea is to partition the domain into distinct regions (coarse grain) and determine instantaneous dispersion relations in each region, which ultimately inform about local pattern-forming instabilities. We illustrate our approach by studying the Min system, a paradigmatic model for protein pattern formation. By performing simulations, we first show that the Min system produces multiscale patterns in a spatially heterogeneous geometry. This prediction is confirmed experimentally by in vitro reconstitution of the Min system. Using a recently developed theoretical framework for mass-conserving reaction–diffusion systems, we show that the spatiotemporal evolution of the total protein densities on large scales reliably predicts the pattern-forming dynamics. Our approach provides an alternative and versatile theoretical framework for complex systems where analytical coarse-graining methods are not applicable, and can, in principle, be applied to a wide range of systems with an underlying conservation law.
关键词：enpattern formationmultiscale systemsreaction–diffusion dynamicsin vitro Min systemreduced dynamics
