Many natural complex systems exhibit synchronization, characterized by temporal coherence among the dynamics of their units. In ant colonies, synchronization manifests through activity bursts: sudden, sharp spikes of motion by a significant portion of workers throughout the nest, followed by durations of quiescence. These activity bursts were discovered three decades ago and studied since then; yet, the mechanisms that lead to their emergence remain elusive. Here, we present a model of ant activity that integrates both the motion of individuals within the nest and the transitions between behavioral states. By balancing microscopic behaviors in the model, we identify a nest-level phase transition from unsynchronized to synchronized activity and draw several connections between model predictions and empirical observations in the literature. Our analysis begets two key insights: (i) activity bursts emerge as a balance between the responsiveness of the colony to the first ant that activates and the ability of the colony to completely deactivate before the onset of the next burst, and (ii) the timescale of the motion of individuals through the nest is faster than that of the burst, suggesting that ants operate in a high-speed interaction regime where new behaviors are near-instantaneously transferred through the nest. We relate these findings to the broader literature on synchronization in complex systems, highlighting the need for periods of quiescence followed by the rapid communication of a new behavior through a population of connected units.

Elastic networks can be tuned to exhibit complex mechanical responses and have been extensively used to study protein allostery, where a localized strain regulates the conformation at a distant site. We show that cooperative binding, where one site enhances the other's ability to function, can be improved by tuning for bidirectional allostery: a symmetric coupling where the strain propagated between the two sites is independent of which site is perturbed. We identify a crossover temperature above which functionality breaks down due to thermal fluctuations. We introduce a modified tuning process to increase this crossover temperature, showing that function can be robust at biologically relevant temperatures if thermal stability is important.

Accurate sensing of chemical concentrations is essential for numerous biological processes. The accuracy of this sensing, for small numbers of molecules, is limited by shot noise. Corresponding theoretical limits on sensing precision, as a function of sensing duration, have been well studied in the context of quasistatic and randomly fluctuating concentrations. However, during development and in many other cases, concentration profiles are not random but exhibit predictable spatiotemporal patterns. We propose that leveraging prior knowledge of these structured profiles can improve and accelerate concentration sensing by utilizing information from current molecular binding events to predict future concentrations. By framing the constrained sensing problem as Bayesian inference over an allowed class of spatiotemporal profiles, we derive new theoretical limits on sensing accuracy. Our analysis reveals that maximum a posteriori estimation can outperform the classical Berg-Purcell and maximum-likelihood (Poisson counting) limits, achieving a sensing precision of $\delta c/c=1/\sqrt{a^{2}N}$, where $N$ is the number of binding events, and $a>1$ in certain cases. Thus knowledge of the statistical structure of concentration profiles enhances sensing precision, providing a potential explanation for the rapid yet highly accurate cell fate decisions observed during development.

Raster image correlation spectroscopy (RICS) is a nondestructive, fluorescence-based method to probe molecular diffusion and effective viscosity in biomolecular condensates. By measuring fluorescence intensity autocorrelations of fluorescent probes in a scanning confocal microscope image, RICS enables the calculation of effective, local condensate viscosities both in reconstituted condensates and in living cells. Here we demonstrate the use of RICS as a powerful tool to probe local diffusion and length-scale-dependent viscosities in multiphase coacervates and stress granules without disrupting them. We quantify the local viscosity in core and shell regions of multiphase coacervates, and inside stress granules and the surrounding cytoplasm in HEK293T cells without relying on labeled proteins. By comparing different probe types, we further show that globular probes such as folded proteins and quantum dots experience a length-scale-dependent viscosity in condensates, whereas dextran-based polymeric probes exhibit an apparent size-independent diffusivity over three orders of magnitude in molecular weight. We attribute these findings to a progressive collapse with increasing size of the polymer chains inside condensates, combined with a weakening of sticky probe-condensate interactions. These findings emphasize the need for due care when using probes to characterize condensate properties. Altogether, our results show that RICS is a useful tool for studying condensate properties in situ that can be accessed on conventional confocal microscopes.

An increasing number of biomolecules have been shown to phase-separate into biomolecular condensates—membraneless subcellular compartments capable of regulating distinct biochemical processes within living cells. The speed with which they exchange components with the cellular environment can influence how fast biochemical reactions occur inside condensates and how fast condensates respond to environmental changes, thereby directly impacting condensate function. While fluorescence recovery after photobleaching (FRAP) experiments are routinely performed to measure this exchange timescale, it remains a challenge to distinguish the various physical processes limiting fluorescence recovery and identify each associated timescale. Here, we present a reaction-diffusion model for condensate exchange dynamics and show that such exchange can differ significantly from that of conventional liquid droplets due to the presence of a percolated molecular network, which gives rise to different mobility species in the dense phase. In this model, exchange can be limited by diffusion of either the high- or low-mobility species in the dense phase, diffusion in the dilute phase, or the attachment (detachment) of molecules to (from) the network at the surface or throughout the bulk of the condensate. Combining analytic derivations and numerical simulations, we quantify the contributions of these distinct physical processes to the overall exchange timescale and predict an experimentally testable scaling relationship between the exchange timescale and condensate size. Our theory suggests that the exchange dynamics can be accelerated via a pore-mediated pathway in which molecules pass through the pores of the meshwork and attach directly in the condensate interior. Notably, this pathway permits a parameter regime in which the exchange timescale becomes independent of condensate size, a scaling behavior that is supported by our FRAP measurements on a biosynthetic DNA nanostar system. Our work offers insight into the rate-limiting physical processes that can control condensate material exchange, with implications for natural and engineered systems.

Protein folding is governed by distinct subcellular environments with unique biochemical compositions. Unfavorable conditions can lead to unfolding and aggregation, and cells deploy spatially targeted protein quality control mechanisms to promote folding. Understanding how proteostasis is balanced across diverse cellular conditions requires novel techniques that measure protein folding with high spatiotemporal resolution in living cells. Here we introduce confocal fast relaxation imaging (cFReI), which eliminates wide-field signal averaging compared to previous fast relaxation imaging approaches and enables quantification of biomolecular folding stability with enhanced axial resolution in three dimensions. We apply cFReI to monitor the folding stability of a destabilized monomeric apo variant of SOD1 ($\mathrm{SOD}{1}_{\mathrm{bar}}$) inside stress granules (SGs), comparing the measurements simultaneously to the surrounding cytoplasmic fluid of a single living cell. Surprisingly, $\mathrm{SOD}{1}_{\mathrm{bar}}$ is not destabilized in SGs relative to the cytoplasm, contrary to expectations from previous in vitro studies. The study demonstrates that cFReI is a pioneering technique for measuring folding kinetics and thermodynamics of fluorescently labeled biomolecules in different biomolecular condensates compared to their respective intracellular fluids.

The formation of polarized signaling domains on cell membranes is a fundamental example of biological pattern formation. While such patterns resemble structures from equilibrium phase separation, they are intrinsically nonequilibrium, driven by energy-consuming enzymatic cycles that switch molecules like phosphoinositides or small GTPases between distinct states. Here, we develop a minimal model of this enzyme-driven phase-ordering process. Starting from microscopic reaction kinetics, we derive a mesoscopic theory that belongs to the class of active model A with a global constraint. This framework yields an explicit mean-field phase diagram and closed-form expressions for key observables, such as interfacial tension, domain fractions, and phase-coexistence boundaries, in terms of kinetic rates. In this context, phase coexistence is controlled by nonequilibrium parameters such as- catalytic rates and enzymatic asymmetry, rather than equilibrium parameters such as saturation concentrations. The resulting phase-separated domains rapidly exchange material with their surroundings. Their maintenance requires a continuous power input determined by enzymatic kinetics. The predicted phenomenology is consistent with experimental observations on reconstituted systems of phosphoinositide and Rab5 membrane patterning. We further study how metastable uniform states decay via nucleation of minority-phase domains and subsequent coarsening, driven by an effective interfacial tension. Using largedeviation theory, we derive the critical nucleation radius under the action of the intrinsic, multiplicative chemical noise. The analytical results are quantitatively confirmed by stochastic simulations of the process. Our work provides a theoretical framework identifying key biochemical parameters controlling active phase separation on membrane scaffolds, offering testable predictions for experiments.

Single-cell experiments in yeast reveal two distinct heritable phenotypes—‘‘arresters’’ and ‘‘recoverers’’—when a clonal population experiences a negative shift in its growth environment. Recoverers exhibit a variable yet finite lag before resuming growth in the new environment, whereas arresters remain in a nongrowing, arrested state until more favorable conditions return. Although the diversification of individual cells into arresters and recoverers is a robust phenomenon, it remains unclear whether this coexistence constitutes an evolutionarily stable strategy. Here, we demonstrate that a heterogeneous strategy composed of both arrester and recoverer phenotypes maximizes long-term population fitness across a broad spectrum of growth-lag trade-offs. Our analysis employs a dynamic programming framework to identify the fitness-maximizing distribution of phenotypes for populations that stochastically switch between preferred and nonpreferred environments. We propose a minimal model incorporating metabolism, growth, and enzyme allocation to explain the physiological origin of a power-law growth-lag trade-off that favors phenotypic heterogeneity. The theory predicts a nontrivial relationship between the fraction of recoverers and their lag time, which aligns with existing data from wild yeast strains, evolved isolates, and variations in preshift growth conditions. This relationship suggests an evolutionary ‘‘rheostat’’-like mechanism that enables populations to rapidly adapt to changing environmental conditions.

Type IA topoisomerases relieve torsional stress in DNA by a strand-passage mechanism, using the strain in the DNA to drive relaxation. The topoisomerase IAs of the Mycobacterium genus have distinct C-terminal domains which are crucial for successful strand passage. We used single molecule magnetic tweezers to observe supercoil relaxation by wild type Mycobacterium smegmatis topoisomerase IA and two C-terminal truncation mutants. We recorded distinct behaviors from each truncation mutant. We calculated the free energy stored in the DNA as it is twisted under force to examine the differences between the proteins. Based on our results, we propose a modified model of the strand-passage cycle.

Identifying the network of species interactions is a fundamental step toward understanding ecosystem stability and biodiversity. However, the interpretability of empirical interaction measures remains a major challenge. Experimental estimates frequently exhibit puzzling temporal fluctuations, including sign shifts typically interpreted as transitions between competition and facilitation. Here, we analyze the temporal behavior of pairwise interaction measures to demonstrate that these fluctuations—and apparent shifts in ecological roles—can emerge intrinsically from standard population dynamics, without any underlying change in the actual ecological relationships. We show that inferred interactions are heavily distorted by experimental protocol choices, particularly the duration of observation and microbial growth constraints. By systematically evaluating interactions across timescales, we uncover a principled mechanism to mitigate these biases: short-term measurements reliably isolate direct, pairwise species couplings, whereas longer-term observations inevitably absorb indirect community feedbacks and systemic experimental constraints. By disentangling direct couplings from indirect network effects, our framework provides a robust, timescale-aware approach to interpreting empirical interaction matrices, offering critical quantitative guidance for experimental design and predictive ecosystem modeling.

Cellular symmetry breaking or polarization is a key process that underlies many types of cellular behavior like division, migration, and differentiation. In budding yeast, polarization is required for bud site selection. Polarization of key regulator Cdc42 has been molecularly dissected for decades, yet current data provide insufficient constraints to quantitatively differentiate between pattern-forming mechanisms and models. Here we present a phenomenological description of polarization in terms of physical characteristics using live cell microscopy and quantitative analysis. We identify multiple phases of Cdc42 polarization and derive mesoscale observables that describe each phase, yielding a basal framework to systematically characterize symmetry-breaking phenotypes. We then apply this description to two case studies in which the wildtype polarity network is perturbed: a small perturbation after eliminating spatial cue communication and a larger perturbation involving removal of near-essential scaffold Bem1. This confirms the applicability of the framework in nonwildtype contexts while revealing differences between genetic backgrounds. Finally, we study the dynamics of other polarizing components by extending our analysis to the Gic2 PBD domain, a Cdc42-GTP biosensor, and to polarisome component Spa2, highlighting variation in spot dynamics between protein species while also showing similarities to Cdc42. Our approach enables standardized comparison of polarization between diverse molecular backgrounds at the mesoscale and helps constrain future modeling efforts.

Biomolecular condensates formed by phase separation are key players in cellular organization, yet their interfacial mechanics remain poorly understood. Here we show that both synthetic and endogenous nuclear condensates exhibit critical-like interfacial behaviors near the phase boundary, including enhanced capillary fluctuations and reduced surface tension. By combining optogenetic control with submicron-resolution fluctuation spectroscopy, we quantitatively estimate surface tension, bending rigidity, and effective viscosity. Surface tension diminishes as the system approaches the critical composition, consistent with classical theories of phase separation. Notably, bending elasticity emerges as an unexpected feature of these nuclear liquidlike structures, suggesting the formation of structured interfacial layers that progressively weaken near criticality. Among these condensates, the nucleolus displays exceptionally high viscosity, which may arise in part from viscoelastic coupling to the surrounding perinucleolar heterochromatin, effectively increasing the apparent viscosity in the long-time fluctuation regime. This noninvasive approach enables probing condensate mechanics in living cells and may provide a basis for diagnosing or modulating condensates in biomedical contexts.

Neuronal cultures exhibit a complex activity, bursts, or avalanches, characterized by the coexistence of scale invariance and synchronization, quite stable with the percentage of inhibitory neurons. While this bistable behavior has been already observed in the past, the characterization of the statistical properties of avalanche activity and their temporal organization is still lacking, as well as a model able to reproduce these dynamics. Here we analyze experimental data of human neuronal cultures with controlled percentage of inhibitory neurons and characterize their statistical properties and dynamical organization. In order to model the experimental data, we propose a novel version of the Kuramoto model for two populations of oscillators, excitatory and inhibitory, implementing successfully the inhibition dynamics. The model can fully reproduce the experimental results, confirming the existence of correlations in the temporal organization of avalanche activity and the presence of an amplification-attenuation regime, as found in the human brain.

How biological brains become operational from development and onwards is an unresolved issue. Here we explored the emerging effects in a brain circuit model that received simulated touches through a biological skin model, which featured the potentially critical aspect of sensory dependencies resulting from mechanical couplings across a tissue patch. Our skin model system was connected to a generic, primitive cortical-like subnetwork that was composed of fully connected excitatory and inhibitory neurons, where each individual synapse was subject to continuous, independent, Hebbian-like learning. We used continuous random mechanical activations of the skin model, in this regard mimicking behavioral patterns of early brain development observed in infants, and let the neuron-independent learning define the function that emerged in the network. Remarkably, we found that the network could rapidly learn to separate various naive dynamic skin inputs and solve a kinematics task it had never encountered, even when substantial parts of the sensor population or even network connections were removed post-training. We propose that autonomous learning from a sensor population with intrinsic, time-evolving dependencies could cause the extensively recursive cortical network to gradually adapt its intrinsic dynamics to better mirror the various dynamics of whatever body it is connected to, which results in many biologically useful features for the early acquisition of brain circuitry function.

Many living and artificial systems improve their fitness or performance by adapting to changing environments or diverse training data. However, it remains unclear how environmental variation shapes adaptation, what is learned, and when memory of past conditions is retained. Here we show how cyclic environmental change can produce robust memory. Using a model athermal disordered solid trained by inverse design to attain target elastic properties over a prescribed range, we find that the system evolves toward a marginally absorbing manifold (MAM), meaning that training is reversible within the training range but not beyond it, which encodes a memory of that range. We further propose a general mechanism for MAM formation and memory encoding based on discontinuities in the gradient of the trained quantity. These results provide a simple, broadly applicable physical framework for how adaptive systems learn under changing environments and retain memory of past conditions.

A common underlying assumption in evolutionary thought is that adaptation generally drives an increase in biological complexity. However, the rules governing the evolution of complexity appear more nuanced, and the forces that drive the increase or decrease in organismal complexity are not fully understood. Evolution is deeply connected to learning, where complexity, as well as its origins and consequences, are much better understood, with established results on the optimal complexity appropriate for a given learning task in various settings. In this work, we suggest a mathematical framework for studying the relationship between organismal complexity and the complexity of the environment in which the organisms evolve by leveraging an existing mathematical isomorphism between evolutionary dynamics and learning theory, specifically an isomorphism between the replicator equation and sequential Bayesian learning, with evolving types corresponding to competing hypotheses, and fitness in a given environment corresponding to the likelihood of observed evidence. In Bayesian learning, implicit regularization prevents overfitting and drives the inference of hypotheses whose complexity matches the learning challenge. We show how these results naturally carry over to the evolutionary setting, where they are interpreted as organism complexity evolving to match the complexity of the environment, with organisms that are too complex or too simple for their environment suffering from effects we term overfitness and underfitness, respectively. Other aspects, peculiar to evolution and not to learning, reveal additional trends. One such trend is that frequently changing environments decrease selected complexity, a result with potential implications in both evolution and learning. Together, our results suggest that the balance between complex organisms that may overadapt to transient environmental features, and simple organisms that may be insufficiently flexible in responding to environmental challenges, drives the emergence of optimal complexity that reflects environmental structure. This mathematical framework offers new ways to think about biological complexity, and it suggests new potential causes for an increase or decrease in complexity in different selective environments.

The E. coli chemosensory lattice, consisting of receptors, kinases, and adaptor proteins, is an important test case for biochemical signal processing. Kinase output is characterized by precise adaptation to a wide range of background ligand levels and large gain in response to small relative changes in concentration. Existing models of this lattice achieve their gain through allosteric interactions between either receptors or core units of receptors and kinases. Here we introduce a model which operates through an entirely different mechanism in which receptors gate inherently far from equilibrium enzymatic reactions between neighboring kinases. Our lattice model achieves gain through a mechanism more closely related to zero-order ultrasensitivity than to allostery. Thus, we call it lattice ultrasensitivity (LU). Unlike other lattice models with critical points, the LU model can achieve arbitrarily high gain through timescale separation, rather than through finely tuned allosteric interactions. The model also captures qualitative experimental results which are difficult to reconcile with existing models. We discuss possible implementations in the lattice's baseplate where long flexible linkers could potentially mediate interactions between neighboring core units.

Decision-making is the process of selecting an action among alternatives, allowing biological and artificial systems to navigate complex environments and optimize behavior. While neural systems rely on neuron-based sensory processing and evaluation, decision-making also occurs in organisms without a centralized organizing unit, such as the unicellular slime mold Physarum polycephalum. Unlike neural systems, P. polycephalum relies on rhythmic peristaltic contractions to drive internal flows and redistribute mass, allowing it to adapt to its environment. However, while previous studies have focused on the outcomes of these decisions, the underlying mechanical principles that govern this mass relocation remain unknown. Here, we investigate the exploration process of P. polycephalum confined by blue light into polygonal shapes up to its escape. While the escape occurs along the longest axis of the polygons, independent of confinement shape, the exploration process prior to escape extends protrusions almost everywhere around a shape boundary. We find protrusions to align with the direction of peristaltic contraction waves driving mass relocation. Mapping out contraction modes during exploration in detail we observe an ongoing switching between different dominant principle contraction modes. Only over the course of time does the organism ultimately settle on the contraction mode most efficient for transport, which coincides with the escape. Thus, we find that only harsh environmental confinement triggers optimal behavior which is reached by long time reorganization of the flow patterns. Our findings provide insights into the mechanics of decision-making in non-neuronal organisms, shedding light on how decentralized systems process environmental constraints to drive adaptive behavior.

Evolutionary change is shaped not only by genetic variation and selection across generations but also by phenotypic plasticity, niche construction, and nongenetic inheritance. Here we develop a quantitative, falsifiable framework that models individual organisms as learners that infer hidden environmental states from noisy cues and update phenotype strategies within a lifetime. We introduce Markovian, Bayesian Agents (MBAs), which combine regret-gated stochastic exploration with genetic assimilation, and compare them to nonlearning Blind Agents (BAs). Agent-based simulations reveal that MBAs outperform BAs when cue-stress correlations are high, but lose their advantage above a critical environmental stochasticity threshold ($\varepsilon \approx 0.2$). We then test a central prediction in the unicellular holozoan Capsaspora owczarzaki using a smart-incubator conditioning assay: cultures trained with predictive cue-stress pairing show significantly reduced mortality relative to nonpredictive controls (Mann-Whitney $U$, $p=1.07\times {10}^{-8}$). Together, model and experiment link within-lifetime inference to cross-generational adaptation in a single-celled system.

Ribosome-targeting antibiotics, such as chloramphenicol, stall elongating ribosomes during protein synthesis, disrupting mRNA translation. These antibiotic-induced pauses occur stochastically, alter collective ribosome dynamics, and transiently block protein production on the affected transcript. Existing models of ribosome traffic often rely on idealized assumptions, such as infinitely long and stable mRNAs and simplified pausing dynamics, overlooking key biological constraints. Here, we develop a totally asymmetric simple exclusion process that incorporates stochastic particle pausing and lattice degradation, using experimentally determined pausing and unpausing rates to model the effects of ribosome-targeting antibiotics. We introduce a single-cluster approximation, which is analytically treatable, tailored to capture the biologically relevant regime of rare and long antibiotic-induced pauses. This biologically constrained model reveals three key insights: (i) the inhibition of antibiotic-induced translation strongly depends on transcript length, with longer transcripts being disproportionately affected; (ii) reducing ribosome initiation rates significantly mitigates antibiotic vulnerability; and (iii) inhibition of translation is governed more by collective ribosome dynamics than by single-ribosome properties. Our analytical predictions match Gillespie simulations, align quantitatively with experimental observations, and yield testable hypotheses for future experiments. These findings may have broader implications for the mechanistic modeling of other biological transport processes (e.g., RNAP dynamics), and more generally for the community studying traffic models.