Bacterial drug resistance is a major global health emergency that requires newer approaches for its detection, especially those that are rapid and sensitive at the single cell level. One of the major limitations of existing antimicrobial resistance (AMR) screening is that it relies on culturing bacterial samples, which is time- and resource-intensive, or on detection of known mutations that impart resistance. Here we provide the first evidence for the existence of direct correlations between nanoscale dynamical reorganization in Gram-negative bacterial cell membranes with their evolution of phenotypic resistance under sublethal dosage of the last-line antibiotic Colistin. While super-resolution fluorescence microscopy in combination with fluorescence correlation spectroscopy enables probing dynamical lipid nanodomains on single E. coli cells undergoing AMR evolution, high-resolution atomic force microscopy provides information on nanoscale morphological changes in the same cell population. Interestingly, our study also reveals intricate correlations between nanoscale bacterial membrane organization and biochemical signaling responses that eventually drive the evolution of antimicrobial resistance. In addition, we detect signatures of cooperative lipid motion and dynamic heterogeneity as quantified through the non-Gaussian parameter, ${\alpha }_2$, for lipid number fluctuations in the illumination volume. Further, this parameter is also correlated with the evolution of resistance in the strains. Our study suggests a subtle feedback mechanism for the emergence of antimicrobial resistance which is initiated by membrane nanoscale organization and lipid dynamics leading to biochemical signaling that leads to membrane compositional changes. These compositional changes alter these membrane nanoscale parameters to mitigate the antibiotic mediated stress, and they increase the survival probability of the cell population, which thus becomes more resistant. Our study could thus lead to the development of a fundamentally new approach with high resolution and sensitivity that could be used to infer about antimicrobial resistance evolution, which could also be applicable to other Gram-negative strains and membrane-targeting antibiotics.

A central question in neuroscience is which neuronal and connectivity properties determine a network's ability to store information. The theory of Hopfield models has provided powerful tools to investigate this question. Here, we generalize classical results on the memory capacity of homogeneous Hopfield models to a broader class of heterogeneous networks. We derive an analytical formula for the maximal capacity of networks with arbitrary, and generally heterogeneous, activation rates (coding levels) of neurons in memory patterns, as well as arbitrary connectivity architectures. We use this result to make normative predictions about the properties that maximize capacity in brain-inspired networks. We show that, although heterogeneity in neuron coding levels and inward connection counts (in-degrees) generally reduces capacity, maximal capacity is retained when these two parameters are correlated. This prediction holds across various biologically relevant scenarios, including the storage of independent patterns in both classical and dendritic networks, as well as the storage of example patterns clustered around prototypes representing concepts. In the latter case, heterogeneity similarly affects the capacity for both examples and concepts. Finally, we analyze bipartite models of the CA3-DG circuit in the hippocampus, known to be crucial for memory encoding. In these networks, capacity is maximized by a quasi-indexing encoding scheme, where each neuron in the DG binds subsets of features from a few memory patterns stored in CA3. Compared to a complete-indexing scheme, where each DG unit binds all the features of a single pattern, quasi-indexing significantly improves both network capacity and memory robustness to neuron ablation. These findings introduce new dimensions to the hippocampal index theory of memory encoding and retrieval, while suggesting specific neural substrates for these functions.

When analyzing the individual positional dynamics of an ensemble of moving objects, the extracted parameters that characterize the motion of individual objects, such as the mean-squared instantaneous velocity or the diffusivity, exhibit a spread that is due to the convolution of three different effects: (i) Motion stochasticity, caused by the fluctuating environment and enhanced by limited observation time, (ii) measurement errors that depend on details of the detection technique, and (iii) the intrinsic parameter variance that characterizes actual differences between individual objects, which is the quantity of ultimate interest. We develop the theoretical framework to separate these three effects based on the generalized Langevin equation, which constitutes the most general description of active and passive dynamics, as it derives from the underlying general many-body Hamiltonian for the studied system without approximations. We apply our methodology to determine intrinsic cell-to-cell differences of living and actively moving human breast-cancer cells, algae cells, and, as a benchmark, size differences of passively moving polystyrene beads in water. We find algae and human breast-cancer cells to exhibit significant individual differences, reflected by the spread of the intrinsic mean squared instantaneous velocity over two orders of magnitude, which is remarkable in light of the genetic homogeneity of the investigated breast-cancer cells and highlights their phenotypical diversity. Quantification of the intrinsic variance of single-cell properties is relevant for infection biology, ecology, and medicine, and it opens up new possibilities to estimate population heterogeneity on the single-organism level in a nondestructive manner. Our framework is not limited to motility properties but can be readily applied to other experimental time-series data.

Complex, high-dimensional data are often analyzed by grouping their constituent units into components, sometimes referred to as latent features, which afford physical or biological interpretation. However, a priori many different types of latent features and data decompositions can be defined, and one typically uses a trial-and-error approach to determine a decomposition that is natural to the system and its data. A principled understanding of which decomposition is appropriate for a given dataset is needed. In this work, we take a step in this direction and argue that sample-sample correlations carry important information to this effect. We construct a generative random latent feature matrix model of high-dimensional data based on linear mixing of latent features. As a key ingredient, we allow for a statistical dependence between the mixing coefficients. We argue that, with only two parameters (latent dimensionality and the structure of the statistical dependence), the resulting model captures characteristic properties found in many types of natural data. Specifically, the model can produce (overlapping) clusters, sparse mixing, and constrained (non-negative) mixing. We describe typical correlations and eigenvalue distributions of each pattern. Finally, we fit the model on correlation patterns in a benchmark natural images dataset, and we find a good match between the data and the sparse mixing regime of our model. This is in line with the well-known sparse coding structure in natural images, arguing that our approach identifies a correct latent decomposition of these data. We believe that our work will deliver similar insights for other diverse datasets.

Understanding protein conformation is key to understanding their function. Importantly, most proteins adopt multiple conformations with nontrivial ensemble distributions that change depending on their environment to perform functions like catalysis, signaling, and transport. Recently, machine learning techniques, especially deep generative models, have been employed to develop protein conformation generators. These models, known as unified protein ensemble samplers, are trained on the Protein Data Bank (PDB) dataset and can generate diverse protein conformation ensembles given a protein sequence. However, their reliance solely on structural data from the PDB, which primarily captures folded protein states, restricts the diversity of the generated ensembles and can result in physically unrealistic conformations. In this paper, we overcome these challenges by introducing ExEnDiff, an experiment-guided diffusion model for protein conformation generation. ExEnDiff integrates experimental measurements as a physical prior, enabling the generation of protein conformations with desired properties. Our experiments on a variety of fast-folding and intrinsically disordered proteins demonstrate that ExEnDiff significantly advances the capabilities of current unified protein ensemble samplers. With little computational cost, ExEnDiff can capture important proteins' configuration properties and the underlying Boltzmann distribution, paving the way for a next-generation molecular dynamics engine. We further demonstrate the effectiveness of ExEnDiff to capture conformational changes in the presence of mutations and as an efficient tool for determining a reasonable collective variable space for protein ensembles. With these results, ExEnDiff is well poised to push the study of protein ensembles into a data-rich regime currently available to few problems in biology.

The human large intestine harbors a highly dynamic microbial ecosystem in which growing microbes regularly replenish biomass lost via feces. Elucidating these population dynamics is important as studies increasingly indicate a direct link between microbial density imbalances in the large intestine and host immune responses, colonic cell physiology, as well as disease development. However, given the strong changes in microbial growth, biomass, and intestinal fluid flow throughout the day, gaining a better understanding of these population dynamics remains a major challenge. Leveraging experimental data on fluid turnover, nutrient supply, and microbial growth, we here derive a biophysical model of microbial population dynamics in the proximal large intestine. We show how the digestion of meals in batches triggers strong fluctuations in fluid movement and bacteria growth. Comparing different model scenarios, we further analyze how the expandable nature of the proximal large intestine, the presence of a pouch-like cecum off major flow paths, and the periodic exit of luminal content via “mass movements” are required in combination to maintain the high microbial population observed in the proximal large intestine. As the microbial population undergoes several bottlenecks followed by rapid growth each day, the effective population size in the proximal large intestine is small, $N_e\sim {10}^7-{10}^{11}$, promoting the rapid evolution of microbes. The diurnal fluctuations in flow also hamper the accumulation of slower-growing bacteria and lead to substantial variations in the uptake of fermentation products by the host. Our findings underscore the complex interplay between population dynamics of the gut microbiota, fluid flow, and bacterial growth with important consequences for the microbiome and the host.

Viruses like influenza have long coevolved with host immune systems, gradually shaping the evolutionary trajectory of these pathogens. Host immune systems develop immunity against circulating strains, which in turn avoid extinction by exploiting antigenic escape mutations that render new strains immune to existing antibodies in the host population. Infected hosts are also mobile, which can spread the virus to regions without developed host immunity, offering additional reservoirs for viral growth. While the effects of migration on viral persistence have been investigated, we know little about how antigenic escape coupled with migration changes the survival and spread of emerging viruses. By considering the two processes on equal footing, we show that on short timescales an intermediate host mobility rate increases the survival probability of the virus through antigenic escape. We show that more strongly connected migratory networks decrease the survival probability of the virus. Using data from high traffic airports, we argue that current human migration rates are beneficial for viral survival.

Analyzing the kinetics of biological processes plays a significant role in understanding fundamental cellular functions. Many physics-based technologies used to study such processes are limited by the shot noise inherent to the coherent states of light. These technologies can greatly benefit from leveraging quantum probes to improve the sensitivity of measurements in cellular biology. The surface plasmon resonance technique has been used effectively to achieve label-free, real-time measurements of protein binding kinetics, which constitutes an important biological phenomenon occurring near the cell membrane. Here, we demonstrate the integration of this technique with the two-mode bright squeezed state having fewer fluctuations as compared to the coherent state to improve the sensitivity of measurement in studying a protein-gold adsorption process. We show 4 dB of squeezing as we record the signal-to-noise ratio as the function of time, and it is maintained throughout the kinetic process. The improved signal-to-noise ratio leads to a $60\%$ improvement in the sensitivity of measuring the observable rate constant $k_s$. The quantum advantage as shown in terms of squeezing is achieved despite the total absorption of $74\%$ from the source until the final detection after the sensor. Overall, we provide the most practical setup for improving the sensitivity of the time-dependent measurements involved in various biological processes at the molecular level.

The release of the AlphaFold database, which contains 214 million predicted protein structures, represents a major leap forward for proteomics and its applications. However, the lack of comprehensive protein annotation limits its accessibility and usability. Here, we present DPCstruct, an unsupervised clustering algorithm designed to provide domain-level classification of protein structures. Using structural predictions from AlphaFold2 and comprehensive all-against-all local alignments from Foldseek, DPCstruct identifies and groups recurrent structural motifs into domain clusters. When applied to the Foldseek Cluster database, a representative set of proteins from the AlphaFoldDB, DPCstruct successfully recovers the majority of protein folds catalogued in established databases such as SCOP and CATH. Out of the 28 246 clusters identified by DPCstruct, 24% have no structural or sequence similarity to known protein families. Supported by a modular and efficient implementation, classifying 15 million entries in less than 48 h, DPCstruct is well suited for large-scale proteomics and metagenomics applications. It also facilitates the rapid incorporation of updates from the latest structural prediction tools, ensuring that the classification remains up-to-date. The DPCstruct pipeline and associated database are freely available in a dedicated repository, enhancing the navigation of the AlphaFoldDB through domain annotations and enabling rapid classification of other protein datasets.

Networks of excitatory and inhibitory (EI) neurons form a canonical circuit in the brain. Seminal theoretical results on the dynamics of such networks are based on the assumption that synaptic strengths depend on the type of neurons they connect, but are otherwise statistically independent. Recent synaptic physiology datasets, however, highlight the prominence of specific connectivity patterns that go well beyond what is expected from independent connections. While decades of influential research have demonstrated the strong role of the basic EI cell type structure, the extent to which additional connectivity features influence dynamics remains to be fully determined. Here we examine the effects of pairwise connectivity motifs on the linear dynamics in excitatory-inhibitory networks using an analytical framework that approximates the connectivity in terms of low-rank structures. This low-rank approximation is based on a mathematical derivation of the dominant eigenvalues of the connectivity matrix, and it predicts the impact on responses to external inputs of connectivity motifs and their interactions with cell-type structure. Our results reveal that a particular pattern of connectivity, namely chain motifs, have a much stronger impact on dominant eigenmodes than other pairwise motifs. In particular, an over-representation of chain motifs induces a strong positive eigenvalue in inhibition-dominated networks, and it generates a potential instability that requires revisiting the classical excitation-inhibition balance criteria. Examining the effects of external inputs, we show that chain motifs can on their own induce paradoxical responses, where an increased input to inhibitory neurons leads to a decrease in their activity due to the recurrent feedback. These findings have direct implications for the interpretation of experiments in which responses to optogenetic perturbations are measured and used to infer the dynamical regime of cortical circuits.

This work probes the role of cell geometry in orienting self-organized fluid flows in the late-stage Drosophila oocyte. Recent theoretical work has shown that a model, which relies only on hydrodynamic interactions of flexible, cortically anchored microtubules and the mechanical loads from molecular motors moving upon them, is sufficient to generate observed flows. While the emergence of flows has been studied in spheres, oocytes change shape during streaming, and it was unclear how robust these flows are to the geometry of the cell. Here we use biophysical theory and computational analysis to investigate the role of geometry and find that the axis of rotation is set by the shape of the domain and that the flow is robust to biologically relevant perturbations of the domain shape. Using live imaging and three-dimensional flow reconstruction, we test the predictions of the theory/simulation, finding consistency between the model and live experiments, further demonstrating a geometric dependence on flow direction in late-stage Drosophila oocytes.

The ability to store continuous variables in the state of a biological system (e.g., a neural network) is critical for many behaviors. Most models for implementing such a memory manifold require hand-crafted symmetries in the interactions or precise fine-tuning of parameters. We present a general principle that we refer to as frozen stabilization (FS), which allows a family of neural networks to self-organize to a critical state exhibiting multiple memory manifolds without parameter fine-tuning or symmetries. Memory manifolds arising from FS exhibit a wide range of emergent relaxational timescales and can be used as general purpose integrators for inputs aligned with the manifold. Moreover, FS allows robust memory manifolds in small networks, and is therefore relevant to debates about implementing continuous attractors with a small number of neurons in light of recent experimental discoveries.

Assessing the similarity of matrices is valuable for analyzing the extent to which data sets exhibit common features in tasks such as data clustering, dimensionality reduction, pattern recognition, group comparison, and graph analysis. Methods proposed for comparing vectors, such as cosine similarity, can be readily generalized to matrices. However, this approach usually neglects the inherent two-dimensional structure of matrices. Here we propose singular angle similarity (SAS), a measure for evaluating the structural similarity between two arbitrary, real matrices of the same shape based on singular value decomposition. After introducing the measure, we compare SAS with standard measures for matrix comparison and show that only SAS captures the two-dimensional structure of matrices. Further, we characterize the behavior of SAS in the presence of noise, as a function of matrix dimensionality, and when singular values are degenerate. Finally, we apply SAS to two use cases: square nonsymmetric matrices of probabilistic network connectivity, and nonsquare matrices representing neural brain activity. For synthetic data of network connectivity, SAS matches intuitive expectations and allows for a robust assessment of similarities and differences. For experimental data of brain activity, SAS captures differences in the structure of high-dimensional responses to different stimuli. We conclude that SAS is a suitable measure for quantifying the shared structure of matrices with arbitrary shape.

The formation, dissolution, and dynamics of multiparticle complexes is of fundamental interest in the study of stochastic chemical systems. In 1976, Masao Doi introduced a Fock space formalism for modeling classical particles. Doi's formalism, however, does not support the assembly of multiple particles into complexes. Starting in the 2000s, multiple groups developed rule-based methods for computationally simulating biochemical systems involving large macromolecular complexes. However, these methods are based on graph-rewriting rules and/or process algebras that are mathematically disconnected from the statistical physics methods generally used to analyze equilibrium and nonequilibrium systems. Here we bridge these two approaches by introducing an operator algebra for the rule-based modeling of multiparticle complexes. Our formalism is based on a Fock space that supports not only the creation and annihilation of classical particles but also the assembly of multiple particles into complexes, as well as the disassembly of complexes into their components. Rules are specified by algebraic operators that act on particles through a manifestation of Wick's theorem. We further describe diagrammatic methods that facilitate rule specification and analytic calculations. We demonstrate our formalism on systems in and out of thermal equilibrium, and for nonequilibrium systems we present a stochastic simulation algorithm based on this formalism. The results provide a unified approach to the mathematical and computational study of stochastic chemical systems in which multiparticle complexes play an important role.

Aligning EM density maps and fitting atomic models are essential steps in single-particle cryogenic electron microscopy (cryo-em), with recent methods leveraging various algorithms and machine learning tools. As aligning maps remains challenging in the presence of a map that only partially fits the other (e.g., one subunit), we here propose a procedure, em partial alignment with optimal transport (EMPOT), for partial alignment of three-dimensional (3D) maps. EMPOT finds a coupling between 3D point-cloud representations, which is associated with their so-called unbalanced Gromov Wasserstein divergence, and uses this coupling to find an optimal rigid body transformation. On running and benchmarking our method with experimental maps and structures, we show that EMPOT outperforms standard methods for aligning density maps and fitting atomic models to a density map, suggesting potential applications of partial optimal transport for improving cryo-em pipelines.

Animal morphogenesis often involves significant shape changes of epithelial tissue sheets. Great progress has been made in understanding the underlying cellular driving forces and their coordination through biomechanical feedback loops. However, our quantitative understanding of how cell-level dynamics translate into large-scale morphogenetic flows remains limited. A key challenge is finding the relevant macroscopic variables (order parameters) that retain the essential information about cell-scale structure. To address this challenge, we combine symmetry arguments with a stochastic mean-field model that accounts for the relevant microscopic dynamics. Complementary to previous work on the passive fluid- and solidlike properties of tissue, we focus on the role of actively generated internal stresses. Centrally, we use the timescale separation between elastic relaxation and morphogenetic dynamics to describe tissue shape change in the quasistatic balance of forces within the tissue sheet. The resulting geometric structure—a triangulation in tension space dual to the polygonal cell tiling—proves ideal for developing a mean-field model. All parameters of the coarse-grained model are calculated from the underlying microscopic dynamics. Centrally, the model explains how active plastic flow driven by autonomous active cell rearrangements becomes self-limiting as previously observed in experiments and simulations. Additionally, the model quantitatively predicts tissue behavior when coupled with external fields, such as planar cell polarity and external forces. We show how such fields can sustain oriented active cell rearrangements and thus overcome the self-limited character of purely autonomous active plastic flow. These findings demonstrate how local self-organization and top-down genetic instruction together determine internally driven tissue dynamics.

Undulation is a form of propulsion in which waves of bending propagate along an elongated, slender body. This locomotor strategy is used by organisms that span orders of magnitude in size and represent diverse habitats and species. Despite this diversity, common neuromechanical phenomena have been observed across biologically disparate undulators, as a result of common mechanics. For example, neuromechanical phase lags (NPL), a phenomenon where waves of muscle contraction travel at different speeds than the corresponding body bends, have been observed in fish, lamprey, and lizards. Existing theoretical descriptions of this phenomenon implicate the role of physical body-environment interactions. However, systematic experimental variation of body-environment interactions and measurement of the corresponding phase lags have not been performed. Using the nematode Caenorhabditis elegans we measured phase lags across a range of environmental interaction regimes, performing calcium imaging in body wall muscles in fluids of varying viscosity and on agar. A mechanical model demonstrates that the measured phase lags are controlled by the relative strength of elastic torques within the body and resistive forces within the medium. We further show that the phase lags correspond with a difference in the wave number of the muscle activity and curvature patterns. Hence, the environmental forces that create NPL also act as a filter that shapes and modulates the gait articulated by the nervous system. Beyond nematodes, the simplicity of our model suggests that tuning body elasticity may serve as a general means of controlling the degree of mechanical wave modulation in other undulators.

In biology, data are conceptualized using diagrams that capture protein-protein, enzyme-substrate, and regulator-target interactions, among many others. These interaction diagrams are every bit as complicated as wiring diagrams in modern electronic circuits—in many cases, even more so. Yet, in contrast to electronic circuits, living systems must also autonomously reproduce; some part of the “wiring diagram” of life must be devoted to reproducing itself. A greatly simplifying principle in the analysis of these biological wiring diagrams is that of “balanced growth,” in which network flows are balanced according to the requirements of biomass production, leading to the exponential accumulation of cells. In microbial cells, exponential growth greatly simplifies the underlying biochemical networks, because when its mathematical description is combined with kinetic descriptions of underlying enzyme-mediated reactions, macroscale constraints on physiology emerge. As is demonstrated in this tutorial, these constraints are mathematically and conceptually equivalent to Kirchhoff's circuit laws and Ohm's constitutive equation. Consequently, bacterial growth physiology can be approached with the same quantitative rigour as electrical circuit analysis. In this tutorial, this “Ohmics” approach is developed in detail, and its power in simplifying complex physiology is demonstrated through two case studies.

Proteins fold to a specific functional conformation with a densely packed core that controls their stability. Despite their importance, we lack a quantitative explanation for why all protein cores, regardless of their overall fold, possess the same average packing fraction $\langle \varphi \rangle \approx 0.55$. However, important developments in the physics of jamming in particulate systems can shed light on the packing of protein cores. Here, we extend the framework of jamming to describe core packing in collapsed polymers, as well as in all-atom models of folded proteins. First, we show in a spherical bead-spring polymer model (with and without bond-angle constraints) that as the hydrophobic interactions increase relative to thermal fluctuations, a jamming-like transition occurs when the core packing fraction exceeds ${\varphi }_c$ with the same power-law scaling behavior for the potential energy $V_r$, excess contact number $\mathrm{\Delta }N$, and characteristic frequency of the vibrational density of states ${\omega }^{*}$ versus $\mathrm{\Delta }\varphi =\varphi -{\varphi }_c$ as that for jammed particulate systems. Then, we develop an all-atom model for proteins and find that, above ${\varphi }_c\sim 0.55$, protein cores undergo a jamming-like transition, but with anomalous power-law scaling for $V_r, \mathrm{\Delta }N$, and ${\omega }^{*}$ versus $\mathrm{\Delta }\varphi$. The all-atom protein model remains close to the native protein structure during jamming and accurately refolds from partially unfolded states.

Biological systems rely on robust perfect adaptation (RPA) to maintain stability despite external disturbances, a property critical for their survival. In biochemical networks, achieving RPA without fine-tuning parameters presents a significant challenge due to complex reaction dynamics and nonlinear interactions. This study introduces a framework for characterizing RPA mechanisms in deterministic chemical reaction networks, utilizing topological invariants to systematically identify all structural configurations that enable robustness. We establish that each structural RPA property corresponds to a specific subnetwork with unique topological features, which we term “labeled buffering structures.” This correspondence allows us to map and enumerate all such RPA properties by analyzing network topology alone, independent of kinetic details. We further identify integral feedback controllers associated with each RPA mechanism, demonstrating their alignment with the Internal Model Principle of control theory. Our findings offer a complete characterization of kinetics-independent robustness in biochemical networks, paving the way for the rational design of synthetic controllers and providing insights into the fundamental architectures of resilience in biological systems. This work lays the groundwork for understanding RPA as a universal topological principle in dynamical systems, which we propose as the “Robust Adaptation is Topological” (RAT) principle.