skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


This content will become publicly available on May 6, 2026

Title: Soft Modes as a Predictive Framework for Low-Dimensional Biological Systems Across Scales
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.  more » « less
Award ID(s):
2317138
PAR ID:
10595345
Author(s) / Creator(s):
; ;
Publisher / Repository:
Annual Reviews
Date Published:
Journal Name:
Annual Review of Biophysics
Volume:
54
Issue:
1
ISSN:
1936-122X
Page Range / eLocation ID:
401 to 426
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Sato, Brian (Ed.)
    As biological science rapidly generates new knowledge and novel approaches to address increasingly complex and integrative questions, biology educators face the challenge of teaching the next generation of biologists and citizens the skills and knowledge to enable them to keep pace with a dynamic field. Fundamentally, biology is the science of living systems. Not surprisingly, systems is a theme that pervades national reports on biology education reform. In this essay, we present systems as a unifying paradigm that provides a conceptual framework for all of biology and a way of thinking that connects and integrates concepts with practices. To translate the systems paradigm into concrete outcomes to support instruction and assessment in the classroom, we introduce the biology systems-thinking (BST) framework, which describes four levels of systems-thinking skills: 1) describing a system’s structure and organization, 2) reasoning about relationships within the system, 3) reasoning about the system as a whole, and 4) analyzing how a system interacts with other systems. We conclude with a series of questions aimed at furthering conversations among biologists, biology education researchers, and biology instructors in the hopes of building support for the systems paradigm. 
    more » « less
  2. We develop a framework to understand the mechanics of metamaterial sheets on curved surfaces. Here we have constructed a continuum elastic theory of mechanical metamaterials by introducing an auxiliary, scalar gauge-like field that absorbs the strain along the soft mode and projects out the stiff ones. We propose a general form of the elastic energy of a mechanism based metamaterial sheet and specialize to the cases of dilational metamaterials and shear metamaterials conforming to positively and negatively curved substrates in the Föppl–Von Kármán limit of small strains. We perform numerical simulations of these systems and obtain good agreement with our analytical predictions. This work provides a framework that can be easily extended to explore non-linear soft modes in metamaterial elasticity in future. 
    more » « less
  3. Abstract Motivation The inference of gene regulatory networks (GRNs) from DNA microarray measurements forms a core element of systems biology-based phenotyping. In the recent past, numerous computational methodologies have been formalized to enable the deduction of reliable and testable predictions in today’s biology. However, little focus has been aimed at quantifying how well existing state-of-the-art GRNs correspond to measured gene-expression profiles. Results Here, we present a computational framework that combines the formulation of probabilistic graphical modeling, standard statistical estimation, and integration of high-throughput biological data to explore the global behavior of biological systems and the global consistency between experimentally verified GRNs and corresponding large microarray compendium data. The model is represented as a probabilistic bipartite graph, which can handle highly complex network systems and accommodates partial measurements of diverse biological entities, e.g. messengerRNAs, proteins, metabolites and various stimulators participating in regulatory networks. This method was tested on microarray expression data from the M3D database, corresponding to sub-networks on one of the best researched model organisms, Escherichia coli. Results show a surprisingly high correlation between the observed states and the inferred system’s behavior under various experimental conditions. Availability and implementation Processed data and software implementation using Matlab are freely available at https://github.com/kotiang54/PgmGRNs. Full dataset available from the M3D database. 
    more » « less
  4. Agent-based models provide a flexible framework that is frequently used for modelling many biological systems, including cell migration, molecular dynamics, ecology and epidemiology. Analysis of the model dynamics can be challenging due to their inherent stochasticity and heavy computational requirements. Common approaches to the analysis of agent-based models include extensive Monte Carlo simulation of the model or the derivation of coarse-grained differential equation models to predict the expected or averaged output from the agent-based model. Both of these approaches have limitations, however, as extensive computation of complex agent-based models may be infeasible, and coarse-grained differential equation models can fail to accurately describe model dynamics in certain parameter regimes. We propose that methods from the equation learning field provide a promising, novel and unifying approach for agent-based model analysis. Equation learning is a recent field of research from data science that aims to infer differential equation models directly from data. We use this tutorial to review how methods from equation learning can be used to learn differential equation models from agent-based model simulations. We demonstrate that this framework is easy to use, requires few model simulations, and accurately predicts model dynamics in parameter regions where coarse-grained differential equation models fail to do so. We highlight these advantages through several case studies involving two agent-based models that are broadly applicable to biological phenomena: a birth–death–migration model commonly used to explore cell biology experiments and a susceptible–infected–recovered model of infectious disease spread. 
    more » « less
  5. In recent years, non-reciprocally coupled systems have received growing attention. Previous work has shown that the interplay of non-reciprocal coupling and Goldstone modes can drive the emergence of temporal order such as traveling waves. We show that these phenomena are generically found in a broad class of pattern-forming systems, including mass-conserving reaction--diffusion systems and viscoelastic active gels. All these systems share a characteristic dispersion relation that acquires a non-zero imaginary part at the edge of the band of unstable modes and exhibit a regime of propagating structures (traveling wave bands or droplets). We show that models for these systems can be mapped to a common ``normal form'' that can be seen as a spatially extended generalization of the FitzHugh--Nagumo model, providing a unifying dynamical-systems perspective. We show that the minimal non-reciprocal Cahn--Hilliard (NRCH) equations exhibit a surprisingly rich set of behaviors, including interrupted coarsening of traveling waves without selection of a preferred wavelength and transversal undulations of wave fronts in two dimensions. We show that the emergence of traveling waves and their speed are precisely predicted from the local dispersion relation at interfaces far away from the homogeneous steady state. The traveling waves are therefore a consequence of spatially localized coalescence of hydrodynamic modes arising from mass conservation and translational invariance of displacement fields. Our work thus generalizes previously studied non-reciprocal phase transitions and identifies generic mechanisms for the emergence of dynamical patterns of conserved fields. 
    more » « less