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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. 

Microbial ecosystems are commonly modeled by fixed interactions between species in steady exponential growth states. However, microbes in exponential growth often modify their environments so strongly that they are forced out of the growth state into stressed, nongrowing states. Such dynamics are typical of ecological succession in nature and serial-dilution cycles in the laboratory. Here, we introduce a phenomenological model, the Community State Model, to gain insight into the dynamic coexistence of microbes due to changes in their physiological states during cyclic succession. Our model specifies the growth preference of each species along a global ecological coordinate, taken to be the biomass density of the community, but is otherwise agnostic to specific interactions (e.g., nutrient starvation, stress, aggregation), in order to focus on self-consistency conditions on combinations of physiological states, “community states,” in a stable ecosystem. We identify three key features of such dynamical communities that contrast starkly with steady-state communities: enhanced community stability through staggered dominance of different species in different community states, increased tolerance of community diversity to fast growing species dominating distinct community states, and increased requirement of growth dominance by late-growing species. These features, derived explicitly for simplified models, are proposed here as principles aiding the understanding of complex dynamical communities. Our model shifts the focus of ecosystem dynamics from bottom–up studies based on fixed, idealized interspecies interaction to top–down studies based on accessible macroscopic observables such as growth rates and total biomass density, enabling quantitative examination of community-wide characteristics. 

Abstract The backpropagation method has enabled transformative uses of neural networks. Alternatively, for energy-based models, local learning methods involving only nearby neurons offer benefits in terms of decentralized training, and allow for the possibility of learning in computationally-constrained substrates. One class of local learning methodscontraststhe desired, clamped behavior with spontaneous, free behavior. However, directly contrasting free and clamped behaviors requires explicit memory. Here, we introduce ‘Temporal Contrastive Learning’, an approach that uses integral feedback in each learning degree of freedom to provide a simple form of implicit non-equilibrium memory. During training, free and clamped behaviors are shown in a sawtooth-like protocol over time. When combined with integral feedback dynamics, these alternating temporal protocols generate an implicit memory necessary for comparing free and clamped behaviors, broadening the range of physical and biological systems capable of contrastive learning. Finally, we show that non-equilibrium dissipation improves learning quality and determine a Landauer-like energy cost of contrastive learning through physical dynamics. 

Abstract Microbial communities experience environmental fluctuations across timescales from rapid changes in moisture, temperature, or light levels to long-term seasonal or climactic variations. Understanding how microbial populations respond to these changes is critical for predicting the impact of perturbations, interventions, and climate change on communities. Since communities typically harbor tens to hundreds of distinct taxa, the response of microbial abundances to perturbations is potentially complex. However, while taxonomic diversity is high, in many communities taxa can be grouped into functional guilds of strains with similar metabolic traits. These guilds effectively reduce the complexity of the system by providing a physiologically motivated coarse-graining. Here, using a combination of simulations, theory, and experiments, we show that the response of guilds to nutrient fluctuations depends on the timescale of those fluctuations. Rapid changes in nutrient levels drive cohesive, positively correlated abundance dynamics within guilds. For slower timescales of environmental variation, members within a guild begin to compete due to similar resource preferences, driving negative correlations in abundances between members of the same guild. Our results provide a route to understanding the relationship between functional guilds and community response to changing environments, as well as an experimental approach to discovering functional guilds via designed nutrient perturbations to communities. 

A new paradigm for generating adaptive functionality in materials. 

Abstract Inspired by biology’s most sophisticated computer, the brain, neural networks constitute a profound reformulation of computational principles^1–3. Analogous high-dimensional, highly interconnected computational architectures also arise within information-processing molecular systems inside living cells, such as signal transduction cascades and genetic regulatory networks^4–7. Might collective modes analogous to neural computation be found more broadly in other physical and chemical processes, even those that ostensibly play non-information-processing roles? Here we examine nucleation during self-assembly of multicomponent structures, showing that high-dimensional patterns of concentrations can be discriminated and classified in a manner similar to neural network computation. Specifically, we design a set of 917 DNA tiles that can self-assemble in three alternative ways such that competitive nucleation depends sensitively on the extent of colocalization of high-concentration tiles within the three structures. The system was trained in silico to classify a set of 18 grayscale 30 × 30 pixel images into three categories. Experimentally, fluorescence and atomic force microscopy measurements during and after a 150 hour anneal established that all trained images were correctly classified, whereas a test set of image variations probed the robustness of the results. Although slow compared to previous biochemical neural networks, our approach is compact, robust and scalable. Our findings suggest that ubiquitous physical phenomena, such as nucleation, may hold powerful information-processing capabilities when they occur within high-dimensional multicomponent systems. 

Life is chemical intelligence. What is the source of intelligent behavior in molecular systems? Here we illustrate how, in contrast to the common belief that energy use in non-equilibrium reactions is essential, the detailed balance equilibrium properties of multicomponent liquid interactions are sufficient for sophisticated information processing. Our approach derives from the classical Boltzmann machine model for probabilistic neural networks, inheriting key principles such as representing probability distributions via quadratic energy functions, clamping input variables to infer conditional probability distributions, accommodating omnidirectional computation, and learning energy parameters via a wake phase / sleep phase algorithm that performs gradient descent on the relative entropy with respect to the target distribution. While the cubic lattice model of multicomponent liquids is standard, the behaviors exhibited by the trained molecules capture both previously-observed phenomena such as core-shell condensate architectures as well as novel phenomena such as an analog of Hopfield associative memories that perform recall by contact with a patterned surface. Our final example demonstrates equilibrium classification of MNIST digits. Experimental implementation using DNA nanostar liquids is conceptually straightforward. 

Our planet is a self-sustaining ecosystem powered by light energy from the sun, but roughly closed to matter. Many ecosystems on Earth are also approximately closed to matter and recycle nutrients by self-organizing stable nutrient cycles, e.g., microbial mats, lakes, open ocean gyres. However, existing ecological models do not exhibit the self-organization and dynamical stability widely observed in such planetary-scale ecosystems. Here, we advance a conceptual model that explains the self-organization, stability, and emergent features of closed microbial ecosystems. Our model incorporates the bioenergetics of metabolism into an ecological framework. By studying this model, we uncover a crucial thermodynamic feedback loop that enables metabolically diverse communities to almost always stabilize nutrient cycles. Surprisingly, highly diverse communities self-organize to extract $\approx$10 $\%$of the maximum extractable energy, or $\approx$100 fold more than randomized communities. Further, with increasing diversity, distinct ecosystems show strongly correlated fluxes through nutrient cycles. However, as the driving force from light increases, the fluxes of nutrient cycles become more variable and species-dependent. Our results highlight that self-organization promotes the efficiency and stability of complex ecosystems at extracting energy from the environment, even in the absence of any centralized coordination. 

Learning is traditionally studied in biological or computational systems. The power of learning frameworks in solving hard inverse problems provides an appealing case for the development of physical learning in which physical systems adopt desirable properties on their own without computational design. It was recently realized that large classes of physical systems can physically learn through local learning rules, autonomously adapting their parameters in response to observed examples of use. We review recent work in the emerging field of physical learning, describing theoretical and experimental advances in areas ranging from molecular self-assembly to flow networks and mechanical materials. Physical learning machines provide multiple practical advantages over computer designed ones, in particular by not requiring an accurate model of the system, and their ability to autonomously adapt to changing needs over time. As theoretical constructs, physical learning machines afford a novel perspective on how physical constraints modify abstract learning theory.