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All biological systems are subject to perturbations arising from thermal fluctuations, external environments, or mutations. Yet, while biological systems consist of thousands of interacting components, recent high-throughput experiments have shown that their response to perturbations is surprisingly low dimensional: confined to only a few stereotyped changes out of the many possible. In this review, we explore a unifying dynamical systems framework—soft modes—to explain and analyze low dimensionality in biology, from molecules to ecosystems. We argue that this soft mode framework makes nontrivial predictions that generalize classic ideas from developmental biology to disparate systems, namely phenocopying, dual buffering, and global epistasis. While some of these predictions have been borne out in experiments, we discuss how soft modes allow for a surprisingly far-reaching and unifying framework in which to analyze data from protein biophysics to microbial ecology.
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Puckering and wrinkling in a growing composite ring
Pattern formation driven by differential strain in constrained elastic systems is a common motif in many technological and biological systems. Here we introduce a biologically motivated case of elastic patterning that allows us to explore the conditions for the existence of local puckering and global wrinkling patterns: a soft growing composite ring adhered elastically to a constraining rigid ring. We explore how differential growth of the soft ring and the elastic resistance to shear and stretching deformations induced by soft adherence lead to a range of phenomena that include uniform aperture-like modes, localized puckers that are Nambu–Goldstone-like modes and global wrinkles in the system. Our analysis combines computer simulations of a discrete rod model with a nonlinear stability analysis of the differential equations in the continuum limit. We provide phase diagrams and scaling relations that reveal the nature and extent of the deformation patterns. Overall, our study reveals how geometry and mechanics conspire to yield a rich phenomenology that could serve as a guide to the design of programmable localized elastic deformations while being relevant for the mechanical basis of biological morphogenesis.
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- Award ID(s):
- 1922321
- PAR ID:
- 10296200
- Date Published:
- Journal Name:
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Volume:
- 477
- Issue:
- 2248
- ISSN:
- 1364-5021
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1098/rspa.2020.0999
