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.

Spontaneous waves are ubiquitous during early brain development and are hypothesized to drive the development of receptive fields (RFs). Different stages of retinal waves, characterized by activity patterns in the retina and downstream areas, coincide with key developments along the visual pathway. Stage II waves, in particular, have been linked to a possible early synaptic pruning process; however, the mechanisms underlying their activity-dependent effects on thalamocortical synapses remain poorly understood. In this work, we develop a biologically constrained model of thalamocortical synapse formation driven by stage II retinal waves. Using this, alongside a reduced rate-based model, we propose mechanisms underlying the formation of distinct RF structures, including transitions from a disklike RF to a ringlike RF, modulated by learning parameters and initial synaptic connection strengths. We leverage the mechanisms uncovered through the reduced model to make two predictions: gap junctions promote local retinotopic refinement during stage II waves, and the resulting RF structure established during this stage controls the emergence of orientation selectivity later in development. Mechanisms identified here may aid in the understanding of developing synaptic structures across various cortical regions.

A central challenge in modeling neurodegenerative diseases is connecting cellular-level mechanisms to tissue-level pathology, in particular to determine whether pathology is driven primarily by cell-autonomous triggers or by propagation from cells that are already in a pathological, runaway aggregation state. To bridge this gap, we develop here a bottom-up physical model that explicitly incorporates these two fundamental cell-level drivers of protein aggregation dynamics. We show that our model naturally explains the characteristic long, slow development of pathology followed by a rapid acceleration, a hallmark of many neurodegenerative diseases. Furthermore, the model reveals the existence of a critical switch point at which the system's dynamics transition from being dominated by slow, spontaneous formation of diseased cells to being driven by fast propagation. We explore the different limiting behaviours of this model, derive approximate analytical solutions for several observables, and demonstrate the parallels to models used in population epidemiology. This framework offers a method to simulate disease propagation and intervention in silico and provides a robust physical foundation for interpreting pathological data.

Cells transform complex environmental stimuli into physiological responses. In dynamic environments, or when a motile cell moves in a static setting, stimuli change over time. Here we introduce a concept, “reverse opto-chemical engineering,” which uses temporal light patterns and photo-triggers to create virtual sensory landscapes for cells. This allows us to record their physiological responses and motor behavior in real time. Using this approach, we studied cyclic-nucleotide signaling in sperm cells and mapped their stimulus-response transfer function. The technique can be employed for remote control of motility by light. Exploiting the chemotactic signaling backbone, we enable sperm to navigate in light gradients, making them attracted to light. This method offers possibilities for uncovering the mechanisms and signaling molecules behind rapid cellular computations, helping to understand the wiring diagram of cellular networks.

The big potassium (BK) channels remain open with a small limiting probability of $P_{\mathrm{o}}\sim {10}^{-7}$ at minimal $\mathrm{C}{\mathrm{a}}^{2+}$ and negative voltages below $-100\mathrm{mV}$. The molecular origin of such an “intrinsic opening” is not understood. Here, free-energy analysis of ${\mathrm{K}}^{+}$ permeation shows that the intrinsic opening of BK channels is likely an inherent property of the vapor barrier, generated by hydrophobic dewetting of the inner pore in the $\mathrm{C}{\mathrm{a}}^{2+}$-free state. The vapor barrier only gives rise to a finite free-energy barrier, of $\sim 8\mathrm{kcal}$/mol, and it cannot completely shut down ${\mathrm{K}}^{+}$ flow even when the voltage sensor domains are fully deactivated. The resulting “leaking” currents can be measured at negative voltages as intrinsic opening. The shallow limiting slope of $P_{\mathrm{o}}$ at negative voltages arises primarily from the electric field effects on the permeating ion through the vapor barrier. We further demonstrate that the vapor barrier can be perturbed by truncation of the cytosolic domains, inner pore mutations, and ligand binding to the pore, leading to predicable changes in limiting slope measurements highly consistent with existing experimental data. Therefore, the intrinsic opening paves the way for direct experimental study of hydrophobic gating in BK and many other ion channels.

DNA methylation is a primary layer of epigenetic modification that plays a pivotal role in the regulation of development, aging, and cancer. The concurrent activity of opposing enzymes that mediate DNA methylation and demethylation gives rise to a biochemical cycle and active turnover of DNA methylation. While the ensuing biochemical oscillations have been implicated in the regulation of cell differentiation, their functional role and spatiotemporal dynamics are unknown. In this work, we demonstrate that chromatin-mediated coupling between these local biochemical cycles can lead to the emergence of phase-locked domains, regions of locally synchronized turnover activity, whose coarsening is arrested by genomic heterogeneity. We introduce a minimal model based on stochastic oscillators with constrained long-range and nonreciprocal interactions, shaped by the local chromatin organization. Through a combination of analytical theory and stochastic simulations, we predict both the degree of synchronization and the typical size of emergent phase-locked domains. We qualitatively test these predictions using single-cell sequencing data. Our results show that DNA methylation turnover exhibits surprisingly rich spatiotemporal patterns that may be used by cells to control cell differentiation.

We study the equilibrium phases of a generalized Lotka-Volterra model characterized by a species interaction matrix which is random, sparse, and symmetric. Dynamical fluctuations are modeled by a demographic noise with amplitude proportional to the effective temperature $T$. The equilibrium distribution of species abundances is obtained by means of the cavity method and the Belief Propagation equations, which allow for an exact solution on sparse networks. Our results reveal a rich and nontrivial phenomenology that deviates significantly from the predictions of fully connected models. Consistently with data from real ecosystems, which are characterized by sparse rather than dense interaction networks, we find strong deviations from Gaussianity in the distribution of abundances. In addition to the study of these deviations from Gaussianity, which are not related to multiple equilibria, we also identified a novel topological multiple-attractor phase, present at both finite temperature, as shown here and at $T=0$, as previously suggested in the literature. The peculiarity of this phase, which differs from the multiple-equilibria phase of fully connected networks, is its strong dependence on the presence of extinctions. These findings provide new insights into how network topology and disorder influence ecological networks, particularly emphasizing that sparsity is a crucial feature for accurately modeling real-world ecological phenomena.

Neurons are spatially extended cells. Different parts of a neuron have specific voltage dynamics. Important types of neurons even generate different spikes in different parts of the cell. Neurons' inputs are also often spatially compartmentalized, with different sources targeting different locations on the cell. Classic mean-field theories for neural population activity, however, rely on point-neuron models with at most one type of spike, the sodium-potassium action potential. Here, we develop a statistical field-theoretic approach to understanding collective activity in networks of compartmental neurons, including those generating multiple types of spikes. We use this to examine simple models of cortical networks with pyramidal cells that generate dendritic calcium spikes. In the weakly coupled regime, we uncover an exact mean-field limit for these networks that maps them to a marked point process. We use this mean-field limit to compare the impact of compartmentalized recurrent excitatory and inhibitory connectivity on the equilibrium phase diagram. This exposes regions of metastability between various activity states, including activity with silent vs active dendrites, with and without inhibitory activity, and oscillations.

During development, highly ordered structures emerge as cells collectively coordinate with each other. While recent advances have clarified how individual cells process and respond to external signals, understanding collective cellular decision making remains a major challenge. Here, we introduce a minimal, analytically tractable model of cell patterning via local cell-cell communication. Using this framework, we identify a trade-off between the speed and accuracy of collective pattern formation and, by adapting techniques from stochastic chemical kinetics, quantify how information flows between cells during patterning. Our analysis reveals counterintuitive features of collective patterning: globally optimized solutions do not necessarily maximize intercellular information transfer and individual cells may appear suboptimal in isolation. Moreover, the model predicts that instantaneous information shared between cells can be nonmonotonic in time as patterning occurs. An analysis of recent experimental data from lateral inhibition in Drosophila pupal abdomen finds a qualitatively similar effect.

The growth and scaling of organs is a fundamental aspect of animal development. However, how organs grow to the right size and shape required by physiological demands, remains largely unknown. Here we provide a framework combining theory and experiment to study the scaling of branched organs. As a biological model, we focus on the branching morphogenesis of the planarian gut, which is a highly branched organ responsible for the delivery of nutrients. Planarians undergo massive body size changes requiring gut morphology to adapt to these size variations. Our experimental analysis shows that various gut properties scale with organism size according to power laws. We introduce a theoretical framework to understand the growth and scaling of branched organs. Our theory considers the dynamics of the interface between organ and surrounding tissue to be controlled by a morphogen and illustrates how a shape instability of this interface can give rise to the self-organized formation and growth of complex branched patterns. Considering the reaction-diffusion dynamics in a growing domain representative of organismal growth, we show that a wide range of scaling behaviors of the branching pattern emerges from the interplay between interface dynamics and organism growth. Our model can recapitulate the scaling laws of planarian gut morphology that we quantified and also opens new directions for understanding allometric scaling laws in various other branching systems in organisms.

In many viruses, hundreds of proteins assemble an outer shell (capsid) around the viral nucleic acid to form an infectious virion. How the assembly process selects the viral genome amidst a vast excess of diverse cellular nucleic acids is poorly understood. It has recently been discovered that many viruses perform assembly and genome packaging within liquid-liquid phase separated biomolecular condensates inside the host cell. However, the role of condensates in genome packaging is poorly understood. Here, we construct equilibrium and dynamical rate equation models for condensate-coupled assembly and genome packaging. We show that when the viral genome and capsid proteins favorably partition into the condensate, assembly rates, yields, and packaging efficiencies can increase by orders of magnitude. Selectivity is further enhanced by the condensate when capsid proteins are translated during assembly and packaging. Our results suggest that viral condensates provide a mechanism to ensure robust and highly selective assembly of virions around viral genomes. More broadly, our results may apply to other types of selective co-assembly processes that occur within biomolecular condensates and suggest that liquid-liquid phase-separated condensates could be exploited for selective encapsulation of microscopic cargo in human-engineered systems.

Uncovering the rules governing the nonequilibrium dynamics of the membranes that define biological cells is of central importance to understanding the physics of living systems. We theoretically and computationally investigate the behavior of flexible quasispherical vesicles that exchange membrane constituents, internal volume, and heat with an external reservoir. The excess chemical potential and osmotic pressure difference imposed by the reservoir act as generalized thermodynamic driving forces that modulate vesicle morphology. We show that the renormalization of membrane mechanical properties by nonequilibrium driving gives rise to a morphological transition between a weakly driven regime, in which growing vesicles remain quasispherical, and a strongly driven regime, in which vesicles accommodate rapid membrane uptake by developing surface wrinkles. Additionally, we propose a minimal vesicle growth-shape law, derived using insights from stochastic thermodynamics, that robustly describes vesicle growth dynamics even in strongly driven, far-from-equilibrium regimes.

The organization of neurons into functionally related assemblies is a fundamental feature of cortical networks, yet our understanding of how these assemblies maintain distinct identities while sharing members remains limited. Here we analyze how spike timing-dependent plasticity (STDP) shapes the formation and stability of overlapping neuronal assemblies in recurrently coupled networks of spiking neuron models. Using numerical simulations and an associated mean-field theory, we demonstrate that the temporal structure of the STDP rule, specifically its degree of causality, critically determines whether assemblies that share neurons maintain segregation or merge together after training is completed. We find that causal STDP rules, where potentiation or depression occurs strictly when presynaptic spikes precede or follow postsynaptic spikes, allow assemblies to remain distinct even with substantial overlap in membership. This stability arises because causal STDP effectively cancels the symmetric correlations introduced by common inputs from shared neurons. In contrast, acausal STDP rules lead to assembly fusion when overlap exceeds a critical threshold, due to unchecked growth of common input correlations. Our results provide theoretical insight into how spike timing-dependent learning rules can support distributed representations where individual neurons participate in multiple assemblies while maintaining functional specificity.

Motivated by recent experiments on growing fibroblasts, we examine the development of nematic order in a colony of elongated cells proliferating on a nematic elastomer substrate. After sparse seeding, the cells divide and grow into locally ordered but randomly oriented domains that then interact with each other and the substrate. Global alignment with the substrate is only achieved above a critical density, suggesting a collective mechanism for the sensing of substrate anisotropy. The system jams at high density, where both reorientation and proliferation stop. Using a continuum model of a proliferating nematic liquid crystal, we examine the competition between growth-driven alignment and substrate-driven alignment in controlling the density and structure of the final jammed state. We propose that anisotropic traction forces and the tendency of cells to align perpendicular to the direction of density gradients act in concert to provide a mechanism for collective cell alignment.

Developmental patterning comprises processes that range from purely instructed, where external signals specify cell fates, to fully self-organized, where spatial patterns emerge autonomously through cellular interactions. We propose that both extremes—as well as the continuum of intermediate cases—can be conceptualized as information-processing systems, whose operation can be described using “Marr's three levels of analysis”: the computational problem being solved, the algorithms employed, and their molecular implementation. At the first level, we argue that normative theories, such as information-theoretic optimization principles, provide a formalization of the computational problem. At the second level, we show how simplified information-processing architectures provide a framework for developmental algorithms, which are formalized mathematically using dynamical systems theory. At the third level, the implementation of developmental algorithms is described by mechanistic biophysical and gene regulatory network models.

Cells integrate signals and make decisions about their future state in short amounts of time. A lot of theoretical effort has gone into asking how to best design gene regulatory circuits that fulfill a given function, yet much less is known about the constraints that performing that function in a small amount of time imposes on circuit architectures. Using an optimization framework, we explore the properties of a class of promoter architectures that distinguish small differences in transcription factor concentrations under time constraints. We show that the full temporal trajectory of gene activity allows for faster decisions than its integrated activity represented by the total number of transcribed mRNA. The topology of promoter architectures that allow for rapidly distinguishing low transcription factor concentrations results in a low, shallow, and noncooperative response, while at high concentrations, the response is high and cooperative. In the presence of noncognate ligands, networks with fast and accurate decision times need not be optimally selective, especially if discrimination is difficult. While optimal networks are generically out of equilibrium, the energy associated with that irreversibility is only modest and negligible at small concentrations. Instead, our results highlight the crucial role of rate-limiting steps imposed by biophysical constraints.

Animals rely on their sense of smell to survive, but important olfactory cues are mixed with confounding background odors that fluctuate due to atmospheric turbulence. It is unclear how the olfactory system habituates to such stochastic backgrounds to detect behaviorally important odors. Here, we explicitly consider the high-dimensional nature of odor coding, the natural statistics of odor fluctuations, and the architecture of the early olfactory pathway. We show that their combination favors a manifold learning mechanism for olfactory habituation over alternatives based on predictive filtering. Manifold learning is implemented in our model by a biologically plausible network of inhibitory interneurons in the early olfactory pathway. We demonstrate that plasticity rules based on the Intrator, Bienenstock, Cooper, and Munro (IBCM) model or an online principal components analysis algorithm are effective at implementing this mechanism in turbulent conditions and outperform previous models relying on mean background subtraction. Interneurons with an IBCM plasticity rule acquire selectivity to independently varying odors. This manifold learning mechanism offers a path toward distinguishing plasticity rules in experiments and could be leveraged by other biological circuits facing fluctuating environments.

Mesoscopic models of finite-size neuronal populations are crucial to understand the dynamics of neural networks in the brain, especially their fluctuations and response to stimuli. However, current theories to derive such models are based on the assumption of homogeneous all-to-all (full) connectivity, neglecting the variance in the connectivity of biologically realistic networks with connection probabilities $p<1$ (nonfull connectivity). To gain insight into the different fluctuation mechanisms underlying the neural variability of populations of spiking neurons, we derive and analyze a stochastic mean-field model for finite-size networks of Poisson neurons with random connectivity (including nonfull connectivity), external noise, and disordered mean inputs. We treat the quenched disorder of the connectivity by an annealed approximation enabling a doubly stochastic description of synaptic inputs for finite network size. A further reduction leads to a low-dimensional closed system of coupled Langevin equations for the mean and variance of the neuronal membrane potentials as well as a variable capturing finite-size fluctuations arising specifically in the case of connectivity disorder. Comparing to microscopic simulations, we find that the mesoscopic model describes the fluctuations and nonlinearities well and outperforms previous mesoscopic models that neglected the variance in the connectivity. The joint effect of connectivity disorder and finite network size can be analytically understood by a softening of the effective nonlinearity and the multiplicative character of spiking noise. The mesoscopic theory shows that quenched disorder can stabilize the asynchronous state, and it correctly predicts large quantitative and nontrivial qualitative effects of connection probability on the variance of the population firing rate and its dependence on stimulus strength. Our theory thus elucidates how disordered connectivity shapes nonlinear dynamics and fluctuations of neural populations at the mesoscopic scale and showcases a useful mean-field method to treat random connectivity in finite-size, spiking neural networks.