Noise is a ubiquitous feature of the physical world. As a result, the first prerequisite of life is fault tolerance: maintaining integrity of state despite external bombardment. Recent experimental advances have revealed that some biological systems achieve fault tolerance by implementing mathematically intricate error correcting codes and by organizing in a modular fashion that physically separates functionally distinct subsystems. These elaborate structures represent a vanishing volume in the massive genetic configuration space. How is it possible that the primitive process of evolution, by which all biological systems evolved, achieved such unusual results? In this work, through experiments in Boolean networks, we show that the simultaneous presence of error correction and modularity in biological systems is no coincidence. Rather, it is a typical co-occurrence in noisy dynamic systems undergoing evolution. From this, we deduce the principle of error correction enhanced evolvability: systems possessing error correcting capabilities are more effectively improved by evolution than those without.

We present a methodology that leverages the zero-crossing time gaps of electric-field molecular fingerprints from liquid biopsies to extract information about their molecular composition. By analyzing zero-crossing timings, we demonstrate that these temporal features encode all medically relevant information contained in the original time traces. A clinical study targeting lung cancer detection using human blood samples reveals that aberrations in zero-crossing time gaps are associated with the presence of the disease and its progression. The proposed approach to discretizing continuous molecular signals through zero-crossing analysis enables compact representation of physiological signatures and can facilitate integration with other omics technologies, opening pathways for comprehensive, multidimensional biological insights.

Hair cells actively drive oscillations of their mechanosensitive organelles—the hair bundles that enable hearing and balance sensing in vertebrates. Why and how some hair cells expend energy by sustaining this oscillatory motion in order to fulfill their function as sensors and amplifiers remains unknown. Here, we develop a stochastic thermodynamic theory to describe flows of mechanical energy in a periodically driven hair bundle. Our analysis of thermodynamic fluxes associated with hair-bundle motion and external sinusoidal stimulus reveals that these organelles function as thermodynamic work-to-work machines under different operational modes. One mode allows the cell to harvest energy of the external signal, whereas another channels the power supplied by the cell into the signal. These two regimes might represent thermodynamic signatures of signal sensing and amplification, respectively, which we further connect to the receptor currents through ion channels controlled by the hair bundles. In addition to energy harvesting and work transduction, our model also substantiates the capability of hair cells to operate as heaters and, at the expense of external driving, as active feedback refrigerators. We quantify the performance and robustness of the mechanical work-to-work conversion by hair bundles, whose thermodynamic efficiency in some conditions exceeds 80% of the applied power.

The eukaryotic cytoskeleton consists of three filament types: actin filaments, microtubules, and intermediate filaments (IFs). IF proteins are expressed in a cell-type-specific manner, and keratins are found in epithelial cells. In certain cell types, keratin forms a layer close to the membrane which may be referred to as an “IF-cortex.” It is hypothesized that this IF-cortex arranges with radial bundles in a “rim-and-spokes” structure in epithelia. Based on this hypothesis, IFs and actin filaments might add complementary mechanical properties to the cortex. It was previously shown that single IFs in vitro remain undamaged at high strains and display a nonlinear stretching behavior. We now ask whether this unique force-extension behavior of single IFs is also relevant in the context of a filament network within a cell. We show that keratin-deficient (KO) Madin-Darby canine kidney II cells readily form two-dimensional (2D) cell layers and 3D cysts and withstand high equibiaxial strains. High-resolution imaging using STED microscopy reveals altered actin cortex structures in KO cells, presumably in response to the missing keratin. We investigate the influence of the equibiaxial strain on the viscoelastic properties of wild-type (WT) and KO cells using atomic force microscopy. We find that the KO cells exhibit a higher prestress than the WT cells, likely due to the change of the cortical structure. Interestingly, both the prestress and the fluidity of the KO cells are altered already at intermediate strains, whereas the WT cells show a response only at high strain. Upon stretching, the WT cysts retain their intraluminal fluid, i.e., they possess tight cell-cell contacts, whereas a part of the KO cysts release the fluid due to deficient cell-cell contacts. The compressibility modulus is analyzed in a spatially resolved manner and we find this modulus to be increased at the cell rim, compared to the inside region, due to the geometry of the cell layer. Our results indicate that KO cells remodel their actin cytoskeleton to maintain function, but nevertheless the whole tissue is very sensitive to external strain. The intricate interplay between the actin and keratin cortices in WT cells preserves their mechanical state and the cell layer stability.

Across development, the formation of fluid-filled lumina enclosed by epithelial tissues is inextricably linked to the establishment of apicobasal cell polarity. Here, we reveal how the mechanical differences between cell surfaces resulting from this polarity enter the interplay of lumen pressure, mechanics of the cell cortex, and cell-cell adhesion that determines lumen morphology: Madin–Darby canine kidney cysts under tight junction perturbations display a shape instability of apical surfaces that is associated with changes of cyst pressure and apical belt tension [Mukenhirn et al., Dev. Cell 59, 2886 (2024)]. Here, we discover that the cysts also respond to these perturbations by significant modulations of lateral and basal surface tensions. We develop a mean-field three-dimensional vertex model of these cysts that reproduces the experimental shape space and instability quantitatively. This model explains the observed increase of lateral contractility to be a cellular response that counters the instability. Our work thus shows how regulation of the mechanics of all cell surfaces conspires to control lumen morphology.

Biology stores information and computes at the molecular scale, yet the ways in which it does so are often distinct from human-engineered computers. Mapping biological computation onto architectures familiar to computer science remains an outstanding challenge. Here, inspired by Crick's proposal for molecular memory, we analyze a thermodynamically consistent model of a protein complex subject to driven, nonequilibrium enzymatic reactions. In the strongly driven limit, we find that the system maps onto a stochastic, asynchronous variant of cellular automata, where each rule corresponds to a different set of enzymes being present. We find a broad class of phenomena in these “molecular automata” that can be exploited for molecular computation, including error-tolerant memory via multistable attractors, and long transients that can be used as molecular stopwatches. By systematically enumerating all possible dynamical rules, we identify those that allow molecular automata to implement simple computational architectures such as finite-state machines. Overall, our results provide a framework for engineering synthetic molecular automata and offer a route to building protein-based computation in living cells.

This tutorial covers the emerging field of coarse-grained cellular growth modeling, and aims to bridge the gap between theoretical foundations and practical application. By adopting an original “cookbook” approach, it is designed to offer a hands-on guide for constructing and analyzing different key aspects of cellular growth, focusing on available results for bacteria and beyond. The tutorial is structured as a series of step-by-step “recipes,” and covers essential concepts, recent literature, and key challenges. It aims to empower a broad audience, from students to seasoned researchers, to replicate, extend, and innovate in this scientific area. Specifically, each section provides detailed, bare-bones models to start working in each area, from basic steady-state growth to variable environments and focusing on different key layers relevant to biosynthesis, transcription, translation, nutrient sensing, and protein degradation, links between cell cycle and growth, ending with ecological insights.

It is well established from in vitro studies of immune cells that stimulation by a wide range of potential signals leads to motility and morphology changes. How these physical behaviors manifest inside a living animal remains unclear due to limitations of conventional imaging and analysis approaches. Here, we establish a quantitative framework for imaging and tracking neutrophil and macrophage dynamics in larval zebrafish, spanning a large fraction of the animal for multihour timescales with few-minute temporal resolution. We focus especially on the gut, examining innate immune responses to different preparations of the intestinal microbiome. Using light sheet fluorescence microscopy and trajectory analysis of hundreds of individual cells, we characterize speeds, directional persistence measures, and cellular morphology to reveal distinct population behaviors. Individual immune cells exhibit stable motility phenotypes, favoring predominantly motile or nonmotile states rather than frequent transitions between them. Gut architecture constrains migration patterns as demonstrated by preferential anterior-posterior movement and a high probability of cells remaining in the vicinity of the gut throughout the imaging duration. Macrophages display significantly reduced sphericity during motile periods compared to nonmotile periods, providing a morphological signature that may enable inference of dynamic behavior from static snapshots. Surprisingly, migration patterns remain consistent across diverse microbial conditions—germ-free, conventionally reared, and colonized by two strains of a zebrafish-native Vibrio species—indicating that tissue structure exerts a stronger influence than bacterial stimuli on immune surveillance dynamics. Previously observed tissue damage by the wild-type Vibrio strain, and the resulting recruitment of immune cells toward the damage site, provide the only microbe-specific cellular behavior. These findings reveal innate immune surveillance as a stereotyped process whose characteristics reflect both cellular decision-making and larger-scale anatomical structure.

Soil microbial communities regulate critical ecological processes, including nutrient cycling, carbon sequestration, and plant growth. However, due to the opacity and structural complexity of soil, how physical constraints imposed by pore geometry influence bacterial motility and chemotactic recruitment to plant roots remains poorly understood. We use a transparent soil mimic composed of cryolite grains that replicates the structural characteristics of natural soils while enabling direct visualization of bacterial dynamics. Using Escherichia coli as a model bacterium, we combine macroscopic spreading assays with microscopic tracking of cellular trajectories to characterize how soil texture affects motility across pore scales. We find that bacterial motility shifts from run-and-tumble behavior in large, open pores to frequent trapping in smaller, more confined spaces. This transition is governed by the pore size distribution and leads to reduced effective diffusivity and slower population-scale spreading. Moreover, pore-scale confinement hinders the chemotactic recruitment of bacteria to Arabidopsis thaliana roots: recruitment is robust in sandy and loamy soils but negligible in highly confining textures. Our results establish soil texture as a critical factor regulating microbial dynamics and ecological interactions in the rhizosphere. This mechanistic understanding complements genomic surveys by identifying physical confinement as an ecological filter that shapes root-associated microbiomes. These findings highlight the essential and previously underappreciated role of soil texture, suggesting new strategies for managing microbial communities to promote plant health and sustainable agriculture.

Chromosomal crossovers play a crucial role in meiotic cell division, as they ensure proper chromosome segregation and increase genetic variability. Experiments have consistently revealed two key observations across species: (i) the number of crossovers per chromosome is typically small, but at least one, and (ii) crossovers on the same chromosome are subject to interference, i.e., they are more separated than expected by chance. These observations can be explained by a recently proposed coarsening model, where the dynamics of droplets associated with chromosomes designate crossovers. We here introduce an extended coarsening model, which includes material exchanges between droplets, the synaptonemal complex, and the nucleoplasm. Using a comprehensive analysis, including scaling laws for the crossover count, allows us to analyze data across species. Moreover, our model provides a coherent explanation of experimental data across mutants, including the wild type and zyp1 mutant of Arabidopsis thaliana. Consequently, the extended coarsening model provides a solid framework for investigating the underlying mechanisms of crossover placement.

We investigate the hydrodynamic stability and the formation of patterns in a continuum model of epithelial layers, able to account for the interplay between mechanical activity, lateral adhesion, and the sixfold orientational order originating from the hexagonal morphology of the cells. Unlike in other models of active liquid crystals, the balance between energy injection and dissipation can here involve multiple length scales, resulting in a large spectrum of dynamical behaviors. When kinetic energy is dissipated by the cells' adhesive interactions at a rate higher than at which is injected by active stresses, the quiescent state of the cellular layer is generically stable: i.e., hydrodynamically stable regardless of its size. However, as the cellular layer becomes progressively more active, this homeostatic condition is altered by a hierarchy of pattern-forming instabilities, where the system organizes in an increasingly large number of counterflowing lanes of fixed width. In two-dimensional periodic domains, the latter organization is itself unstable to the proliferation of vortices and the dynamics of the cellular layer becomes eventually chaotic and yet different from the more common active turbulence.

Living systems operate far from thermodynamic equilibrium. Movements in cells are always driven by thermal forces but, more importantly, also by motor-generated active forces in the cytoplasm. How intracellular structures respond to these forces depends on their mechanical properties. Intracellular dynamics remain challenging to understand because, in most cases, neither local forces nor local material response properties are known, and imaging of fluctuations is typically not sufficient to measure both. While some subcellular structures such as actin filaments and microtubules, which form the major cytoskeletal networks, have been extensively studied in vitro, their mechanical properties in living cells where they are regulated by post-translational modifications and association with regulatory factors remain poorly understood. Here we present an alternative approach that uses nonequilibrium bending fluctuations of rod-shaped structures to characterize their mechanical properties and those of their surroundings and to estimate driving forces. We demonstrate that, when one of the three factors—two material properties and one driving force—is determined independently, the other two can be derived from observed fluctuations. By applying our method to microtubules in living cells we find that polyglutamylation, a post-translational modification enriched on microtubules that need to withstand large deformation forces like those in axons or cilia, increases microtubule stiffness. In contrast, tubelike mitochondria, lipid membrane-bounded organelles which easily deform, yielded a bending stiffness significantly lower than that of microtubules. Our method opens the door to a quantitative understanding of the effects of cellular factors on the mechanical properties of filaments and organelles in cells.

Elucidating the complex relationships between genotypes, phenotypes, and fitness remains one of the fundamental challenges in evolutionary biology. Part of the difficulty arises from the enormous number of possible genotypes and the lack of understanding of the underlying phenotypic differences driving adaptation. Here we present a computational method that takes advantage of modern high-throughput fitness measurements to learn a map from high-dimensional fitness profiles to a low-dimensional latent space in a geometry-informed manner. We demonstrate that our approach using a Riemannian Hamiltonian variational autoencoder outperforms traditional linear dimensionality reduction techniques by capturing the nonlinear structure of the phenotype-fitness map. When applied to simulated adaptive dynamics, we show that the learned latent space retains information about the underlying adaptive phenotypic space and accurately reconstructs complex fitness landscapes. We then apply this method to a dataset of high-throughput fitness measurements of Escherichia coli under different antibiotic pressures and demonstrate superior predictive power for out-of-sample data compared to linear approaches. Our work provides a data-driven implementation of Fisher's geometric model of adaptation, transforming it from a theoretical framework into an empirically grounded approach for understanding evolutionary dynamics using modern deep learning methods.

To survive, animals must be able to quickly infer the state of their surroundings. For example, to successfully escape an approaching predator, prey must quickly estimate the direction of approach from incoming sensory stimuli and guide their behavior accordingly. Such rapid inferences are particularly challenging because the animal has only a brief window of time to gather sensory stimuli, and yet the accuracy of inference is critical for survival. Due to evolutionary pressures, nervous systems have likely evolved effective computational strategies that enable accurate inferences under strong time limitations. Traditionally, the relationship between the speed and accuracy of inference has been described by the “speed-accuracy tradeoff” (SAT), which quantifies how the average performance of an ideal observer improves as the observer has more time to collect incoming stimuli. While this trial-averaged description can reasonably account for individual inferences made over long timescales, it does not capture individual inferences on short timescales, when trial-to-trial variability gives rise to diverse patterns of error dynamics. We show that an ideal observer can exploit this single-trial structure by adaptively tracking the dynamics of its belief about the state of the environment, which enables it to speed its own inferences and more reliably track its own error, but also causes it to violate the SAT. We show that these features can be used to improve overall performance during rapid escape. The resulting behavior qualitatively reproduces features of escape behavior in the fruit fly Drosophila melanogaster, whose escapes have presumably been highly optimized by natural selection.

The CRISPR-Cas9 nuclease system is currently the most powerful tool in genome engineering. Existing data-driven learning and thermal equilibrium-based modeling cannot capture the kinetic mechanism of the gene cleavage process. This study integrates large-scale genome editing data with a random forest approach—a supervised ensemble learning algorithm—and free energy landscape analysis to uncover the kinetic pathways and pivotal steps that govern cleavage efficiency. Major findings highlight a direct correlation between CRISPR cleavage efficiency and R-loop unfolding rate, establishing the R-loop unfolding rate as the critical factor in gene editing performance. The kinetic model significantly improves over other methods in predicting both on- and off-target gene editing efficiencies. Furthermore, energy landscape analysis reveals a novel three-state mechanism and identifies key nucleotides essential for gene editing. These insights lay the biophysical groundwork for new strategies to enhance CRISPR-Cas9 accuracy and efficiency, offering new avenues for single guide RNA design and target site selection.

Biological and artificial networks routinely make reliable distinctions between similar inputs, and the rules for making these distinctions are learned. In some ways, self/nonself discrimination in the immune system is similar, being both reliable and (partly) learned through thymic selection. In contrast to other examples, we show that the distributions of self- and nonself-peptides are nearly identical but strongly inhomogeneous. Reliable discrimination is possible only because self-peptides are a particular finite sample drawn from this distribution, and T cells can target the “spaces” between these samples. In conventional learning problems, this would constitute memorization or overfitting and lead to disaster. Here, the strong inhomogeneities imply instead that the immune system gains by targeting peptides that are similar to self, with maximum sensitivity for sequences just one or two substitutions away. This model of the structure of the underlying distribution in sequence space predicts, for example, the observed ability of the immune system to respond to mutation-derived cancer neoantigens.

Multicomponent phase-separating molecular systems play a key role as membraneless organelles in living cells. Phase diagrams are indispensable for probing the concentration-dependent behavior of these condensates, yet their interpretation has remained largely qualitative due to challenges of modeling complex, multicomponent interactions. Here, we present a generic framework for quantitative analysis and interpretation of phase diagrams. We derive an analytical expression for the phase boundary normal vector, which reveals two distinct scaling regimes: one for associative phase separation, characterized by a power-law scaling analogous to mass-action kinetics that allows for direct extraction of dense phase solute molar ratios, and another for condensate dissolution, where an exponential scaling quantifies three-body repulsion effects triggered by the addition of a new component. We analyze a wide range of experimentally measured phase diagrams, covering proteins NSP5, NSP2, FUS, Whi3, G3BP1, and antimicrobial peptides, and we demonstrate that the additional quantitative insights can aid the mechanistic interpretation of their phase behavior.

Mechanosensitive (MS) ion channels are crucial for translating mechanical stimuli into cellular responses; however, their dynamic properties pose significant challenges for experimental investigations. This study introduces two enhanced anisotropic network models (ANMs) that incorporate membrane contact probability (MCP) to more effectively capture the influence of the cell membrane on protein dynamics. MCP-ANM and MCP-multiscale ANM (mANM) outperform traditional ANM models that do not explicitly consider membranes when predicting the flexibility of various types of membrane proteins. Furthermore, by integrating MCP-mANM with perturbation response scanning, we are able to efficiently simulate the conformational changes of MS proteins subjected to different mechanical forces. This methodology allows for the examination of various gating mechanisms, including force-from-lipids and force-from-tether, across multiple MS ion channels such as no mechanoreceptor potential C, mechanosensitive channel of small conductance, and Piezo-type mechanosensitive ion channel. The calculated mechanosensitivity of the MS channels aligns well with the experimental findings. These results demonstrate the effectiveness of MCP-incorporated ANM in linking mechanical stimuli to protein dynamics, providing a reliable and efficient framework for understanding the mechanotransduction and gating mechanisms of MS ion channels.

Across the living world, from cell biology and morphogenesis to behavior and cognition, system dynamics is often directed towards functionally important goals one might call target states. Dynamics towards such target states is never in equilibrium, always nonstationary, and typically swiftly over, terminating once the goal is reached. Complicating data-driven inference of effective dynamical models, trajectories of living systems homing in on target states are not only brief but exhibit initial conditions that are typically intrinsically heterogeneous and experimentally uncontrollable. Here we present a reverse-time stochastic dynamics theory for ensembles of target state directed processes, and uncover a universal space-time core of such ensembles that is independent of initial conditions. Examining this core structure, we demonstrate that the landscape of conceivable target state directed dynamics decomposes into sectors that qualitatively differ in their accessibility to data-driven inference. Ensembles undergo a phase transition from an opaque phase, in which their space-time core is uninformative about the underlying dynamics, to a transparent phase, in which the dynamics is directly encoded in its low-order moment functions. We use the reverse-time theory of target state directed processes to construct core-based methods for data-driven dynamical systems inference. Applied to biophysical models of cytokinesis, a directed process for which different regimes of actomyosin turnover cause distinct types of terminal dynamics, our approach precisely identifies the underlying molecular mechanism. Reverse-time ensemble theory establishes a versatile toolset for understanding target state directed biological processes and reveals that the mere presence of target states in living systems induces a novel kind of phase transition in dynamical systems inference.

Diversity exists throughout biology, playing an important role in maintaining robustness and stability. The same is true of the brain, as has become increasingly apparent in recent years with the accumulation of datasets of unparalleled resolution. These datasets show widespread neural heterogeneity, spanning cells, circuits, and system dynamics, marking it as an unavoidable component of the brain's composition. Recent experiments found that declines in heterogeneity among neurons may accompany pathological states. While heterogeneity has been linked to stability, robustness, and increased computational potential, the loss of biophysical diversity was found conducive to the onset of seizurelike activity, suggesting an important functional role. Despite this, how changes in heterogeneity arise remains unknown. Oftentimes considered a static metaparameter resulting from solely genetic disposition, heterogeneity is, in fact, a highly dynamic property of biological networks arising from various sources. Here, we consider this through the lens of intrinsic plasticity, the activity-dependent modulation of neuron biophysical properties, which we propose allows the degree of biophysical diversity to fluctuate in time. Using a network of Poisson neurons endowed with intrinsic plasticity, we combine analytical and numerical approaches to measure the effect of input statistics on the excitability of individual cells, and how this translates into changes in network heterogeneity at the population scale. Our results indicate that, through intrinsic plasticity, diversity in synaptic inputs promotes heterogeneity in cell-to-cell excitability due to changes in the statistics of presynaptic firing rates and network topology. In contrast, whenever the statistics of synaptic input between cells were too similar, intrinsic plasticity promoted the decline in heterogeneity. Further, we show that changes in heterogeneity can coexist with degeneracy in the firing rate between neurons. Taken together, understanding how input statistics affect neuronal network heterogeneity may provide key insights into brain function, resilience, and the manipulability of neural diversity through intrinsic plasticity.