Kavli Affiliate: Cees Dekker
| First 5 Authors: Laeschkir Würthner, Fridtjof Brauns, Grzegorz Pawlik, Jacob Halatek, Jacob Kerssemakers
| Summary:
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 the small scales. Here, we present a
semi-phenomenological approach which exploits mass-conservation in pattern
formation, and enables to reconstruct 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.
| Search Query: ArXiv Query: search_query=au:”Cees Dekker”&id_list=&start=0&max_results=3