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.
Mathematical modeling using reaction-diffusion models has 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. One possibility to
deal with multiscale systems is to use coarse-graining methods that allow the
dynamics to be reduced to the relevant degrees of freedom at large scales.
Unfortunately, these approaches have the major disadvantage that the eliminated
scales cannot be reconstructed from the large-scale dynamics and thus one loses
the information about the patterns. Here, we present an approach for
mass-conserving reaction-diffusion systems that overcomes this issue and allows
one to reconstruct information about patterns from the large-scale dynamics. We
illustrate our approach by studying the Min protein 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. On the basis of 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. Since conservation laws
are inherent in many different physical systems, we believe that our approach
can be generalized and contribute to uncover underlying physical principles in
multiscale pattern-forming systems.
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