Cilia-driven flows in corals are crucial for exchanging nutrients, removing waste, and maintaining the ambient conditions necessary for corals' survival. While various studies have identified that ciliary activity can influence mass transport, the effect of local ciliary orientation and heterogeneity remains relatively unexplored. In this study, we combine noninvasive experimental measurements of ciliary distribution and alignment, with quantification of flow fields and spatial oxygen distributions among several species of reef-building corals, and develop a mathematical model based on singularity solutions of the Stokes equations to investigate mass transport near the coral's surface. Our findings reveal that counter-rotating vortices robustly emerge in three dimensions as a result of the ciliary arrangement on the coral surface. The rate at which ciliated tissue can exchange nutrients with the surrounding fluid depends strongly on the diffusivity of the dissolved organic matter and is enhanced through the inherent heterogeneity in ciliary orientation—for nutrients with low molecular diffusivity, ciliary heterogeneity increases mass transport by more than 50%. However, the presence of an externally imposed shear flow serves to diminish the overall rate of mass transport across all cases studied. This study highlights the critical role of ciliary orientation in modulating transport processes and exemplifies the role of ciliary transport, particularly in low-flow regimes.

Waddington's epigenetic landscape has served as biology's central metaphor for cellular differentiation for over half a century, depicting mature cell types as balls resting in stable valley floors. Boolean networks—introduced by Kauffman in 1969 to model gene regulatory dynamics—provide a mathematical formalization of this landscape, where attractors represent phenotypes, and basins of attraction correspond to developmental valleys. Traditional stability measures quantify robustness by perturbing arbitrary states, yet biological systems typically reside at attractors rather than in transient states. Here we formalize and systematically analyze attractor coherence, a stability measure Kauffman originally envisioned but never rigorously developed, which quantifies how likely it is that a perturbation of an attractor state causes phenotype switching. Analyzing 95 expert-curated biological Boolean models, we reveal a striking paradox: attractors representing mature cell types are consistently less stable than the developmental trajectories approaching them. Large-scale simulations of random networks demonstrate that this coherence gap arises from canalization—a hallmark of biological regulation where individual genes can override other genes. While canalization increases overall network stability, it disproportionately stabilizes transient states, positioning attractors near basin boundaries. The gap's magnitude is almost perfectly predicted by network bias (Spearman's $\rho$ = –0.997), itself modulated by canalization. These findings revise Waddington's landscape: canalization carves deep protective valleys ensuring developmental robustness, yet simultaneously flattens ridges near valley floors, facilitating phenotypic plasticity when multiple fates coexist. This explains how biological systems achieve both reliable development and plasticity, with implications for understanding development, disease-related transitions, and designing robust yet controllable synthetic gene circuits.

Advances in large-scale neural recordings have expanded our ability to describe the activity of distributed brain circuits. However, understanding how neural population dynamics differ across regions and behavioral contexts remains challenging. Here, we surveyed neuronal population dynamics across multiple mouse brain areas (visual cortex, hippocampus, thalamus, and midbrain) using spike data from local ensembles. Two complementary measures were used to characterize these dynamics: the coefficient of variation (CV), a classical indicator of spike-time variability, and statistical complexity, an information-theoretic quantifier of organizational structure. To probe stimulus-dependent activity, we segmented and concatenated recordings from behavioral experiments into distinct time series corresponding to natural image presentations, blank screens during visual task, and spontaneous activity. While the CV failed to discriminate between these conditions, statistical complexity revealed clear, stimulus-specific motifs in population activity. These results indicate that information-theoretic measures can uncover structured, stimulus-dependent patterns in neural population dynamics that remain unobserved in traditional variability metrics.

The positioning of nucleosomes, the most abundant nucleoprotein complex in eukaryotes, and their physical properties are strongly influenced by sequence-dependent geometric and elastic properties of the wrapped DNA. At present, the theoretical study of this system is largely limited to numerical computation, and access to entropic contributions has been challenging. In particular, the toolset for the systematic introduction of binding-site-mediated constraints that retains analytical tractability—beyond uniform superhelical wrapping—is currently lacking. Here, we present a mathematical framework for introducing such constraints in the context of the rigid-base-pair model that permits local DNA relaxation and yields closed-form expressions for elastic binding free energies. Importantly, the methodology enables the evaluation of individual contributions to the free energy, including entropy. Benchmarking against numerical solutions obtained via Monte Carlo sampling and validation with experimental data ranging from competitive nucleosome reconstitution to spontaneous nucleosome breathing and force-induced unwrapping demonstrates quantitative fidelity. The approach enables genome-wide evaluation of nucleosome binding affinities and can be readily extended to noncanonical and epigenetically modified DNA or histone cores. While the present study is based on the rigid-base-pair model, the same ideas extend to any rigid-body-based model, opening a route to a broad class of problems in biomolecular modeling.

Temperature dependence is a central constraint on biological timing, particularly in ectothermic development where reaction rates directly set developmental pace. A widely used framework for describing temperature dependence is the Arrhenius equation, which predicts an exponential increase in rates with temperature. However, biological rates often deviate from this prediction when measured across broader temperature ranges. While negative apparent activation energies are often attributed to protein denaturation, this cannot explain the similar behavior observed at temperatures where enzymes remain stable. These broader scaling patterns remain mechanistically unexplained. Here we present a general Markov chain framework for modeling biological timing as cascades of reversible, temperature-dependent steps. Across datasets, we identify a three-regime scaling structure: Arrhenius-like behavior at low and high temperatures, separated by a quadratic-exponential regime at intermediate temperatures. We show that this pattern arises naturally from differences in activation energies across steps in the network. The quadratic exponential regime is an emergent feature of averaging across many steps and is robust to variation across network realizations. In contrast, Arrhenius-like scaling at the extremes tends to be more variable and originates from smaller subnetworks. Apparent negative activation energies arise from network topology and reversibility in multi-step processes, even without protein denaturation. Our framework provides a general mechanistic framework for diverse temperature-scaling behaviors in biology and may help predict how developmental and physiological processes respond to environmental change. Although we focus on development, the model is broadly applicable to biological systems governed by multi-step reaction networks.

How do single-celled organisms adapt and learn to survive in unpredictable environments without the benefit of a nervous system? In this study, we provide experimental and theoretical evidence that single bacterial cells exhibit sophisticated learninglike behavior in changing environments. Using a custom microfluidic platform, we tracked individual E. coli cells in fluctuating nutrient conditions and found that bacteria do not merely react to the present; they integrate their environmental history to tune their future growth. We show that this adaptation process is scale-free, meaning cells possess a memory that stretches across multiple timescales, from minutes to hours. To explain this, we developed a mathematical framework based on fractional-order dynamics, demonstrating that a dynamic, power-law memory governs how cells integrate environmental history, which we validate with additional nutrient perturbation experiments. We demonstrate that this memory emerges naturally from the cell's internal machinery, specifically a heterogeneous population of ribosomes that react at different speeds. This mechanism reveals a strategic tradeoff between cellular adaptation speed and growth rate, which we confirm experimentally in pulsatile nutrient environments. By mapping the reaction-network architecture underlying bacterial physiology onto the logic of artificial recurrent neural networks, we show that even the simplest unicellular organisms implement complex computational strategies. Our findings establish a new foundation for understanding learning in non-neuronal systems, revealing how single cells use their history to navigate a changing environment.

Biomolecular condensates frequently rely on membrane interactions for recruitment, localization, and biochemical substrates. Many of these interactions are mediated by membrane-anchored molecules such as proteins or specific lipids, which we refer to as “mobile tethers” since they can typically diffuse within the membrane while still interacting with the condensate. The presence of mobile tethers creates a surface with dynamic and spatially inhomogeneous wetting properties that are typically overlooked by traditional wetting theories. Here, we propose a general theoretical framework to study how mobile tethers impact both equilibrium and dynamic properties of condensate wetting. We show that a favorable tether-condensate interaction leads to tether enrichment at the condensate-membrane interface, which modifies the equilibrium condensate–membrane surface tension and contact angle. Increasing tether abundance on the membrane can drive transitions between wetting regimes, with only a modest tether density and binding energy required for biologically relevant scenarios. Furthermore, tethers modulate how condensates react to complex membrane geometries. By helping condensates coat membranes, mobile tethers can facilitate condensate localization to junctions of membrane structures, such as the reticulated membranes inside the algal pyrenoid. Both tether abundance and mobility affect how droplets interact with complex membrane geometries, such as droplet migration along membrane tubules of varying radii. These results provide a framework to study the implications of tether-mediated condensate-membrane interactions for cellular organization and function.

In broad terms, the goal of a sensory system is to allow an organism to gain information about the external world, taking into account the physical processes that intervene between the sources of the signals and the organism's receptors. In olfaction, these transformations may be particularly complex, as they include the fluid mechanics of odorant transport, which is often turbulent. Here we focus on this transformation, viewing it as an inescapable signal processing stage that occurs before sensory transduction. The typically passive nature of an odorant (i.e., that it is carried by the flow, but does not affect the flow) allows for a concise characterization of how flow transforms the temporal characteristics of odorant concentration at the source into its temporal characteristics downstream. Specifically, the power spectrum (but not the odor concentration time series itself) is transformed in a linear fashion: Spectral components at the source are filtered and mapped to other frequencies at a downstream sensor. We characterize the dominant processes in the mapping as (1) frequency filtering acting as a low-pass filter on the source signal, (2) frequency spreading that redistributes power about the source frequency, and (3) frequency production of an underlying spectrum regardless of input frequency. Each of these processes arises naturally from the multiscale nature of turbulent flow environments. This machinery provides a framework for comparison with active sensation, viewed as another form of signal processing that occurs prior to sensory transduction.

The adaptive immune system can mount pathogen-specific responses against a vast world of evolving pathogens (antigens). The humoral immune system is a part of adaptive immunity. It has the remarkable ability to learn about an antigen after exposure to it through a mutation-selection evolutionary process, resulting in more potent responses than those that emerge initially. Recent studies have revealed that upon reexposure to antigens, feedback regulation mediated by past responses steers the evolutionary learning algorithm to generate new responses. This feature enables the immune system to learn to generalize responses to target unseen variants of the original pathogen upon “training” with a limited number of samples. We summarize these new findings and suggest new questions that emerge from them. This is the right time to address these questions by bringing together statistical physics, machine learning, immunology, and evolutionary biology.

Formulating quantitative and predictive models for tissue development requires consideration of complex, stochastic gene expression dynamics, their regulation via cell-cell interactions, and cell proliferation. Including all of these processes in a practical mathematical framework requires complex expressions that are difficult to apply. We construct a theory that incorporates intracellular stochastic gene expression dynamics, signaling chemicals that influence these dynamics and mediate cell-cell interactions, and cell proliferation and its accompanying differentiation. The dynamics of cellular states are described by a Waddington vector field, where no landscape assumption is made. We provide a procedure to systematically simplify the theory by applying explicit assumptions—this can reduce the theory to a master equation or even to a system of ordinary differential equations. We define an epigenetic fitness landscape that describes the proliferation of different cell types and elucidate how this fitness landscape is related to Waddington's vector field. We illustrate the applicability of our framework by analyzing two model systems: an interacting two-gene differentiation process and a spatiotemporal organism model inspired by planaria.

Biological systems maintain long-term memories that guide future behavior but face the challenge of retaining beneficial memories while eliminating harmful ones. This challenge is exemplified in gene silencing mechanisms, which must suppress deleterious genetic elements without affecting essential genes. These systems face a fundamental credit assignment problem, as the fitness consequences of individual memory units are revealed only through aggregate physiological outcomes such as cellular growth or DNA damage. We propose that eukaryotic gene silencing mechanisms address this challenge through fluctuation-driven feedback. Silenced genomic regions are memory units whose stability depends on fluctuating residual transcription, and different genomic regions are coupled through shared epigenetic modifiers that respond to global stress signals. Our analysis shows that this feedback loop preferentially stabilizes the silencing of harmful elements, enabling adaptive refinement of the memory repertoire over time. The model explains the paradoxical reliance of stable silencing on residual transcription and the adaptive role of stress-induced desilencing, makes specific testable predictions, and illustrates how fluctuation-driven feedback can shape memory repertoires in biological systems.

The day–night cycle drives the largest biomass migration on Earth: the diel vertical migration (DVM) of aquatic organisms. Here, we present a three-dimensional agent-based model that incorporates photokinesis, gyrotaxis, and stochastic reorientation to explore how individual-level swimming behaviors give rise to population-scale DVM patterns. By solving Langevin equations for swarms of swimmers, we identify four distinct regimes—surface accumulation, shallow DVM, deep DVM, and sinking—governed by two key dimensionless parameters: the Péclet number ($\text{Pe}$), representing motility persistence, and the vertical swimming asymmetry ratio ($W=w_{\text{down}}/w_{\text{up}}$), encoding photokinetic bias. These regimes emerge from nonlinear interactions between light-driven navigation and active noise, diagnosed through topological and statistical features of vertical distributions. A critical feedback is uncovered: upward-biased swimming ($W<1$) promotes surface aggregation, while excessive downward bias ($W>1$) leads to irreversible sinking. Analytical estimates link regime boundaries to gyrotactic alignment and velocity reversals. Together, our results provide a mechanistic framework to interpret DVM diversity and emphasize the central role of light gradients—beyond absolute intensity—in shaping ecological self-organization.

Neuronal activity is found to lie on low-dimensional manifolds embedded within the high-dimensional neuron space. Variants of principal component analysis are frequently employed to assess these manifolds. These methods are, however, limited by assuming a Gaussian data distribution and a flat manifold. In this study, we introduce a method designed to satisfy three core objectives: (1) extract coordinated activity across neurons, described either statistically as correlations or geometrically as manifolds; (2) identify a small number of latent variables capturing these structures; and (3) offer an analytical and interpretable framework characterizing statistical properties by a characteristic function and describing manifold geometry through a collection of charts. To this end, we employ normalizing flows (NFs), which learn an underlying probability distribution of data by an invertible mapping between data and latent space. Their simplicity and ability to compute exact likelihoods distinguish them from other generative networks. We adjust the NF's training objective to distinguish between relevant (in manifold) and noise dimensions (out of manifold). Additionally, we find that different behavioral states align with the components of the latent Gaussian mixture model, enabling their treatment as distinct curved manifolds. Subsequently, we approximate the network for each mixture component with a quadratic mapping, allowing us to characterize both neural manifold curvature and non-Gaussian correlations among recording channels. Applying the method to recordings in macaque visual cortex, we demonstrate that state-dependent manifolds are curved and exhibit complex statistical dependencies. Our approach thus enables an expressive description of neural population activity, uncovering nonlinear interactions among groups of neurons.

In physics we often use very simple models to describe systems with many degrees of freedom, but it is not clear why or how this success can be transferred to the more complex biological context. We consider models for the joint distribution of many variables, as with the combinations of spiking and silence in large networks of neurons. In this probabilistic framework, we argue that simple models are possible if the mutual information between two halves of the system is consistently subextensive, and if this shared information is compressible. These conditions are not met generically, but they are met by real-world data, such as natural images and the activity in a population of retinal output neurons. We introduce compression strategies that combine the information bottleneck with an iteration scheme inspired by the renormalization group, and we find that the number of parameters needed to describe the distribution of joint activity scales with the square of the number of neurons, even though the interactions are not well approximated as pairwise. Our results also show that this shared information is essentially equal to the information that individual neurons carry about natural visual inputs, which has surprising implications for the neural code.

To reliably transmit information, cells exploit nonequilibrium drives to reduce errors. Kinetic proofreading is a classic mechanism that sharpens ligand discrimination by T lymphocytes, yet it remains unclear whether adaptive immunity relies on kinetic proofreading alone to achieve high fidelity. Here, we propose an alternative: an enhanced form of mechanical proofreading (MPR), in which adaptive force generation during dynamic cell-cell contact enables faithful selection of high-affinity B lymphocytes. Using a coarse-grained model validated by experiments, we show that adaptive MPR, characterized by mechanical feedback between force exertion and contact formation, supports robust discrimination of receptor quality regardless of ligand quantity. While MPR generally balances tradeoffs between speed and fidelity, a negative scaling of contact duration with ligand abundance reveals the presence of feedback. By modulating interactions among distinct ligands that share mechanical load at membrane contacts, adaptive MPR may help mitigate autoimmunity or enhance multivalent vaccines. Overall, this work generalizes proofreading to include cellular designs that operate across scales to reconcile competing functional demands at the systems level.

Learning is based on synaptic plasticity, which affects and is driven by neural activity. Because pre- and postsynaptic spiking activity is shaped by randomness, the synaptic weights follow a stochastic process, requiring a probabilistic framework to capture the noisy synaptic dynamics. We consider a paradigmatic supervised learning example: a presynaptic neural population impinging in a sequence of episodes on a recurrent network of integrate-and-fire neurons through synapses undergoing spike-timing-dependent plasticity (STDP) with additive potentiation and multiplicative depression. We first analytically compute the drift and diffusion coefficients for a single synapse within a single episode (microscopic dynamics), mapping the true jump process to a Langevin and the associated Fokker-Planck equations. Leveraging recent analytical tools, we include spike-time-resolving cross-correlations between pre- and postsynaptic spikes, which corrects substantial deviations seen in standard theories purely based on firing rates. We then apply this microdynamical description to the network setup in which hetero-associations are trained over one-shot episodes into a feed-forward matrix of STDP synapses connecting to neurons of the recurrent network (macroscopic dynamics). By mapping statistically distinct synaptic populations to instances of the single-synapse process above, we self-consistently determine the joint neural and synaptic dynamics and, ultimately, the time course of memory degradation and the memory capacity. We demonstrate that specifically in the relevant case of sparse coding, our theory can quantitatively capture memory capacities which are strongly overestimated if spike-time–resolving cross-correlations are ignored. On the single-synapse level, our theory predicts a transition between acceleration and deceleration of the synaptic weight, and a possibly nonmonotonic dependence of the finite-time diffusion coefficient on the synaptic weight. On the memory level, we showcase two complementary roles of homeostatic plasticity: namely, it is both responsible for forgetting and a requirement for the ability to learn. Additionally, we show how strength of plasticity and duration of exposure to stimuli must be scaled to evade a tradeoff dilemma between memory capacity and early accuracy. We conclude with a discussion of the many directions in which our framework can be extended.

The collective construction of complex architectures by social insects involves the use of decentralized spatiotemporal signals in a dynamical environment that changes the behavior of the insects and is changed by them. Inspired by this original example of “stigmergy,” we show that a robot collective can nucleate, construct, and deconstruct aggregates via a trapping instability by simply altering their local transport behavior. We quantify these observations in terms of a two-dimensional phase space that encompasses agent-agent interaction and the agent-environment interaction (collection and deposition). Our results show how coordinated function can emerge spontaneously through simple local rules for sensing and action without the need for global representation, planning, or optimization/control algorithms, in sharp contrast with the traditional views of complex task execution. More broadly, our study shows that embodied collectives can leverage the environment as both a communication channel and a spatiotemporal memory, coupling organismal behavior to environmental remodeling leading to “exbodied intelligence.”

Biological systems have evolved to amazingly complex states, yet we do not understand in general how evolution operates to generate increasing genetic and functional complexity. Molecular recognition sites are short genome segments or peptides that can bind a cognate recognition target of sufficient sequence similarity, thereby inducing a target-dependent function. Such sites are simple, ubiquitous modules of sequence information, cellular physiology, and evolution. Here we show that recognition sites, if coupled to a time-dependent recognition target, can rapidly evolve to complex states with larger code length and smaller coding density than sites recognizing a static target. Such processes take place in a new mode of molecular evolution called an adaptive ratchet, characterized by asymmetric selection for code extensions and compressions. The underlying evolutionary model contains selection for recognition depending on the site-target binding affinity and mutations with a separation of timescales between changes of binding function and complexity changes. We show that ratchet evolution increases the number of mutational paths available for adaptive code changes, thereby accelerating the response to moving targets and facilitating refinement and innovation of recognition functions. We apply these results to the recognition of fast-evolving antigens by the human immune system. Our analysis shows how molecular complexity can evolve as a collateral to selection for function in a dynamic environment.

Living matter consumes energy to build and actuate dynamic protein machines, but the way energy enters these systems is often assumed to be externally imposed and independent of state. This review advances a unifying perspective, that across diverse cytoskeletal active matter, energy injection itself is state dependent, regulated by the mechanical and organizational configuration of the system, rather than acting as a fixed external bath. We synthesize recent experimental evidence, from excitable cortical waves in vivo to reconstituted actomyosin networks in vitro, showing that feedback between system state and energy input leads to nonmonotonic dissipation, selective energy routing, and relaxation-driven contractility. By organizing these findings within a common framework, we highlight how state-dependent energy injection challenges classical nonequilibrium assumptions and opens new questions for the design and control of active matter.

To rapidly coordinate collective behaviors in tissues, cells communicate with one another through traveling fronts of signaling activity called trigger waves. The stimulus threshold for wave propagation is a key biological parameter that determines when the system produces a global response to a local stimulus. However, it is unclear how this stimulus threshold is determined by the properties of the underlying signaling network. To address this gap, we studied a model of trigger waves with a realistic Hill-type autoactivation function. We obtained an analytic expression for the wave ignition threshold in one dimension (1D) and numerical solutions in 2D and 3D. In the limit of high sensitivity, we found that the trigger wave threshold depends on both the effective dissociation constant, $K_D$, and the effective Hill coefficient, $n$, of the positive feedback circuit, with the dominant contribution scaling as $K_D^{n/(n-1)}$ in all dimensions. This result leads to a simple method for predicting the trigger wave ignition threshold from bulk activation data and is potentially of use for developing synthetic trigger wave circuits with desired sensitivities.