Communications Physics

F1-ATPase, the catalytic domain of ATP synthase, is pivotal for mechanochemical energy conversion in mitochondria. Aiming at a minimal yet quantitative and thermodynamically consistent model for its rotary catalysis mechanism, here we developed a chemo-mechanical Markov model incorporating essential conformational and chemical degrees of freedom. By systematically evaluating over 14,000 model variants via Bayesian inference and cross-validation, we find that a fully functional minimal model requires four functionally distinct {beta}-subunit conformations. Our model reconciles the decade-long bi-site versus tri-site controversy, showing that both pathways contribute depending on ATP concentration. Furthermore, our model suggests a Brownian-ratchet-like mechanism that explains the observation that one ATP hydrolysis event can trigger larger than 120{degrees} rotations, thereby explaining seemingly over 100% efficiency. Beyond this prototypic example of a complex biomolecular machine, our approach should enable one to study other enzymatic mechanisms that implement close coupling between conformational motions, substrate binding, and chemical reactions.

Neural oscillations are thought to play a central role in encoding and transmitting cognitive information across large-scale brain networks, yet the relative contributions of phase synchrony and amplitude co-modulations to distributed coding remain unclear. A key obstacle is the absence of tools that can simultaneously quantify task-relevant information in the frequency domain and disentangle its phase and amplitude components across pairwise and higher-order interactions. Here, we introduce a spectral partial information decomposition framework (named NeOPID) for quantifying information about cognitive variables in power and phase contributions, and to quantify redundant and synergistic information in brain relations, from pairwise to higher-order interactions. We validated the approach on Kuramoto and Stuart-Landau oscillator networks, including a whole-brain model constrained by macaque anatomical connectivity. NeOPID accurately recovers ground-truth encoding schemes and reveals that phase relations and amplitude co-modulations act as complementary coding channels with both redundant and synergistic components. NeOPID further extends this decomposition to higher-order functional interactions enabling the characterization of how cognitive information is collectively distributed across multiple oscillatory edges via redundant and synergistic encoding. To illustrate biological applicability, we applied NeOPID to local field potentials (LFPs) recorded from the macaque fronto-parietal network during a working memory task. In this dataset, NeOPID identified beta-band amplitude co-modulations as the primary carrier of stimulus information, and revealed that higher-order phase interactions exhibit both redundant and synergistic structure during the memory delay. These results establish NeOPID as a principled tool for dissecting the informational architecture about cognitive processes of oscillatory brain networks.

Temporal gradient sensing is a fundamental capability observed across diverse natural biological systems, contributing to the coordination of their functions. Harnessing this ability is also of significant interest in synthetic biology, particularly for sensing and control applications. In this work, we focus on a biomolecular topology that exemplifies a broader class of signal-differentiating architectures, while introducing a structural variant of it. We examine their behavior under both nominal and non-ideal conditions, accounting for stochastic noise arising from different sources. Our investigation includes scenarios where these topologies operate independently, as well as when embedded within minimal regulatory architectures based on negative as well as positive feedback. We analyze the stability of the resulting macroscopic dynamics--a prerequisite for practical deployment--and quantify stochastic fluctuations in system output, providing comparisons with the corresponding input/unregulated process. Importantly, our results demonstrate that signal differentiation can be effectively implemented in a biomolecular setting without incurring deleterious noise amplification--a major concern in the utilization of derivative action across disciplines.

This Perspective formally proposes Particle Biology as a unifying theoretical framework to address the critical bottleneck in current life science research. Current life science research has reached a critical bottleneck. While the field has advanced to the study of 3D genomic spatial configurations and chromosomal organization, it remains largely descriptive and confined to the macromolecular level. This approach lacks a first-principles understanding of the underlying physical forces that drive biological processes. This Perspective formally proposes Particle Biology as a unifying theoretical framework. We establish an axiomatic system positing that life phenomena are fundamentally emergent spatiotemporal patterns of electromagnetic forces among atoms, electrons, and nuclei operating far from thermodynamic equilibrium. By defining biological states through the Biological Hamiltonian and mapping biochemical pathways to multidimensional Potential Energy Surfaces (PES), we bridge the gap between descriptive biology and predictive physics. We categorize core research technologies into three modalities--seeing, computing, and controlling particles--facilitated by advancements in Cryo-EM, AlphaFold 3, and Boron Neutron Capture Therapy (BNCT). Ultimately, the trajectory of molecular biology has evolved from cells to DNA and onto the 3D spatial genome, yet it cannot go deeper within current paradigms. The next logical evolution is to move beyond the macromolecular bottleneck to focus on the electromagnetic interactions between atoms and ions--the true Particle Biology level--to redefine disease and intervention.

A longstanding puzzle in cortical research is how the cerebral cortex, having largely uniform interconnected architecture, gives rise to such diverse yet highly structured spatiotemporal activity. Here, we propose that local cortical networks distance from criticality (DTC) provides a unifying principle related to this conundrum. Analyzing resting-state fMRI BOLD signals and leveraging simple network models of randomly connected recurrent units, we show that DTC robustly explains key dynamical features, in particular, local power spectra and functional connectivity, across the full set of 360 cortical areas. Our analysis shows that a rank-order distribution of DTC values is highly conserved across subjects. Moreover, the empirical analysis of cortical slow dynamics and its fitted network simulations demonstrate similar power-laws across hierarchies of the cortical sheet. These results suggest that recurrent neuronal networks, operating close to criticality, can generate a remarkably rich dynamical repertoire which fit the entire range of experimentally observed cortical dynamics. Our findings underscore the importance of DTC as a powerful, fundamental generator underlying the spectrum of diverse cortical dynamics. HighlightsO_LISpontaneous (resting-state) activity in the human cortex is shown to be organized along a conserved spatial gradient of distance from criticality (DTC), with regions exhibiting a stable cross-individual rank order along this axis. C_LIO_LIMulti-subject fMRI data of regional power spectra and functional connectivity can be fitted with a single parameter simulation model based on DTC. C_LIO_LIQuantitative estimation of the DTC across cortical regions can be achieved using a simple sparse recurrent neural network model. C_LIO_LIThe model fits the power spectra of low frequency fluctuations and the distribution of functional connectivity. C_LIO_LIShape collapse analysis of the power spectrum demonstrates a universal profile across the resting cortex depending only on the DTC. C_LI

Multivalent ligand-receptor interactions underlie most forms of cell-cell communication, yet a general quantitative framework for "avidity" has remained elusive for over a century. Here, we derive closed-form expressions for signaling potency (EC50) in multivalent systems directly from first principles, extending exact analytical models of ternary complex equilibria to account for receptor confinement at cell surfaces. These equations unify antibody-antigen and cytokine-receptor interactions under a common mathematical framework in which potency emerges as a function of binding constants and receptor density. In contrast to monovalent models, EC50 is no longer equal to the dissociation constant (Kd), but instead reflects receptor-dependent avidity effects that vary across cellular contexts. We validate these predictions across biophysical measurements, in vitro binding and signaling assays, in vivo murine cytokine perturbation data, and human spatial transcriptomic datasets. The framework explains longstanding empirical observations, including enhanced antibody potency through avidity and asymmetric control of cytokine signaling by receptor subunits. By embedding these equations within a regression-compatible formulation, we enable inference of signaling drivers from single-cell and spatial transcriptomic data. This work establishes a mechanistic bridge between molecular binding, receptor context, and tissue-level signaling, providing a quantitative foundation for interpreting and modeling intercellular communication in health and disease.

Frustrated phagocytosis occurs when phagocytes fail to fully engulf large targets, yet the geometric origins of this physical limit remain poorly defined. Here we present a geometric model that identifies the cell nucleus as an intracellular constraint on engulfment. Extending membrane-limited frameworks, we distinguish an intrinsic phagocytic capacity set by membrane availability from an apparent capacity reduced by nuclear exclusion. Using minimal geometric assumptions, we derive closed-form expressions linking experimentally measurable parameters, including target coverage, volume ratio, and size, to phagocytic capacity and a normalized axial separation that quantifies nuclear accommodation. The model predicts a size- and curvature-independent geometric criterion for nuclear involvement applicable to both spherical and planar targets. These results establish nuclear geometry as a fundamental physical bottleneck in phagocytosis and provide a quantitative framework for interpreting stalled engulfment and nuclear deformation-dependent responses.

When three cyanobacterial proteins--KaiA, KaiB, and KaiC--are incubated with ATP in vitro, the phosphorylation level of KaiC exhibits stable circadian oscillations. Biochemical and structural analyses have shown that KaiCs ATPase activity is crucial for these oscillations, leading to the hypothesis that ATP-consuming dynamics function as a molecular clock, determining the oscillation period of individual molecules. Moreover, these molecular clocks synchronize with one another, resulting in collective oscillations at the ensemble level. In this study, we develop a theoretical model to test this molecular clockwork hypothesis. Our model clarifies the relationship between the oscillation period and ATPase activity, explaining the significant changes in the period induced by amino-acid substitutions near the CI-CII domain boundary of the KaiC hexamer. Furthermore, the model addresses the physical basis for temperature compensation concerning both the oscillation period and ATPase activity. Thus, the molecular clockwork perspective provides a framework for understanding the atomic design behind collective oscillations.

Structural Maintenance Complexes (SMC) are energy consuming motors that are important in folding the genome by loop extrusion (LE) in all stages of the cell cycle. Single molecule magnetic tweezer pulling experiments have revealed that condensin, a member of the SMC family involved in mitosis, takes occasional backward steps, thus coughing up the gains in the length of the extruded loop. To reveal the mechanism of the forward and backward steps simultaneously, we developed a theory using the stochastic kinetic model and the scrunching mechanism for LE. The calculations quantitatively account for the measured force-dependent step size and dwell time distributions in both the directions. By postulating the existence of an intermediate state in the ATP-driven cycle that is poised to take a forward or a backward step, we predict that its lifetime increases as the external mechanical force increases till a critical value and subsequently decreases at higher forces. The surprising finding of lifetime increase in an active motor, at sub-piconewton forces, is the characteristic of catch bonds, known in force-induced rupture of several passive protein complexes. The identification of catch bond-like states in condensin not only expands our understanding of LE but also highlights the significance of mechanical forces in regulating genome organization.

The hierarchical organization of multiphase biomolecular condensates into core-shell architectures is a fundamental problem in soft matter and biophysics. While classical explanations rely on hierarchies of interfacial tension ({gamma}) between coexisting liquids, the ultralow tensions of condensates (0.1-1 {micro}N/m) render such hierarchies potentially fragile. We introduce a robust assembly principle based on Polymer-Assisted Condensation (PAC), in which a single polymer species dictates the entire structure. The polymer nucleates a dense core by recruiting a condensation-incompetent protein (P1). A second incompetent protein (P2), which is repelled or otherwise thermodynamically disfavored from entering the polymer-rich core, is nonetheless recruited to the interface by weak attraction to P1, forming a stable shell. This effective repulsion-driven layering operates across a wide parameter space without requiring{gamma} asymmetries and yields a robust structure that is impervious to concentration fluctuations and environmental perturbations. Phase-field modeling and molecular simulations establish this mechanism and capture key features of nucleolar organization. Our work reveals a general physical pathway for encoding spatial order in soft, multicomponent fluids.

Genomic organization within the nucleus is crucial for gene regulation and cell health, as disruptions in this organization are linked to genetic disorders and cancers. Recent studies suggest that molecular-scale organization of chromatin near the nuclear periphery (lamina-associated domains, LADs) affects gene regulation, providing transciptional supression, but the biophysical mechanisms of supression behind remain unclear. LADs are large heterochromatic regions near the nuclear lamina, where transcriptional factors and RNA polymerase are scarce, implying a nonspecific filtering property. Here, we investigate the steric filtering capabilities of LADs by performing coarse-grained polymer simulations. Our results show that LAD thickness can be affected by the interaction between chromatin and nuclear periphery as well as chromatin self-compaction. Regardless, the LAD layer acts as a size-selective steric partitioning environment for protein particles limiting their access to nuclear periphery. Notably, increasing bulk protein levels enhances protein access linearly. These results align with experimental observations and suggest that LADs could control the presence of transcription machinery on the periphery of the nucleus, providing a polymer-physical mechanism for gene regulation in nuclei.

Transcription factors organize into liquid-like condensates to facilitate gene expression, yet the physical mechanisms governing their formation and properties remain poorly understood. We study the size statistics of transcriptional condensates in human HAP1 cells using widefield and super-resolution microscopy tagging the epigenetic reader BRD4. We find that hubs that appear monolithic in widefield resolve into clusters of smaller droplets that resist coarsening. We link this size control to Active Model B+, a non-equilibrium field theory that captures a regime of reverse Ostwald ripening out of thermal equilibrium. In this regime, chemically driven currents cause larger droplets to transfer mass back to smaller ones, stabilizing a state of microphase segregation. The observed exponential size distribution of BRD4 foci quantitatively matches our numerical simulations, suggesting a universal physical picture for the non-equilibrium self-limitation of cellular condensates.

How can simple organisms lacking nervous systems encode and transmit environmental signals to generate complex, adaptive behaviours? Using the unicellular organism Physarum polycephalum as a model, we identify a unifying mechanochemical mechanism that links intracellular calcium oscillations to large-scale behavioural coordination. We first demonstrate experimentally that local perturbation of the actomyosin cortex is sufficient to induce symmetry breaking and directed migration, even in the absence of nutrient cues. Building on evidence linking calcium concentration to actin depolymerization and contractile relaxation, we develop a mechanochemical tubule model in which self-sustained calcium oscillations are coupled to pressure-driven mechanics. We show that environmental cues, encoded through the local modulation of these oscillations, give rise to directed transport and the redistribution of biomass. By extending this framework to a two-dimensional phase-field model, we demonstrate that this mechanism is sufficient to generate a diverse set of slime mould behaviours, including chemotaxis, network formation, and balancing exploration-exploitation trade-offs. In doing so, we provide a single mechanistic framework linking intracellular dynamics to organism-scale behaviour across spatial and temporal scales. Our work shows that these sophisticated behaviours can emerge from the modulation of self-sustained oscillations coupled by diffusion, providing a physically grounded mechanism for information processing in non-neural organisms and offering insight into the evolutionary origins of coordinated behaviour.

Humans and animals often face risky situations that require decision-making. Such decisions can be high-risk, high-return at some times, and low-risk, low-return at other times, depending on the balance between optimism and pessimism. However, how this optimism-pessimism bias is regulated across contexts remains unclear. Here, we introduced a computational model of decision-making in a risk-taking task based on the free-energy principle, together with a machine-learning framework that inversely estimates cognitive updating and optimism-pessimism bias from behavioral data. Applying this framework to monkey behavioral data, we found that a monkey quickly and accurately recognized the degree of risk, while frequently switching between optimism and pessimism during the task. In addition, we identified a characteristic control rule for optimism-pessimism bias that is distinct from reward-dependent regulation. Our framework provided a principled tool for understanding the latent cognitive processes underlying risky decision-making in animals and humans.

Nitrogen is essential for all life forms, and microorganisms prefer ammonium as a nitrogen source. Due to the low affinity of glutamine synthetase (GS) for ammonium, E. coli must maintain high intracellular ammonium (NH4+) concentrations to sustain its rapid growth. Under ammonium limitation, E. coli imports ammonium through the transporter AmtB and incorporates it into glutamine by using GS. On the basis of structural and mutagenesis information, mechanisms have been proposed for the transport of ammonia (NH3) and protons by AmtB through spatially (partly) separate routes. These mechanisms do not explain the required coupling between proton and ammonia transports. How does the membrane potential push the ammonia inward so as to attain high concentrations near GS? We here compare six candidate kinetic models of E. coli ammonium transport and assimilation in terms of how they reproduce experimental data from the literature: three variants of the electro-binding model in which the membrane potential affects AmtB-NH4+ binding, and three variants of the electro-flipping model in which it influences the conformational flip of the transporter. The computer simulations decide that the electro-binding models are 28 times more plausible than the electro-flipping models and suggest that the transmembrane electric potential affects AmtB-NH4+ binding from the cytoplasmic side. The addition of kinetic and thermodynamic features to existing structural information plus our requirement of an explanation of the coupling, suggest a new spatiotemporal mechanism of coupling of ammonia and proton flows in AmtB. Further simulations show that GS and AmtB regulation is coordinated via both the uridylyltransferase/uridylyl-removing enzyme (UTase) and 2-oxoglutarate binding, allowing the cell to minimize futile cycling while maintaining rapid growth. The free energy cost of transport-related futile cycling exceeded that of the GS reaction itself. Moreover, AmtB enabled robust growth under varying ammonium concentrations and pH levels, albeit at a cost of futile cycling that became substantial at low ammonium. These findings highlight the crucial roles of GS and AmtB in E. colis adaptations and provide new insights into the trade-off mechanism between nutrient acquisition and energy efficiency.

Cerebellar neural circuit dynamics rely on a rich repertoire of synaptic and excitability mechanisms, which are thought to determine network computation in physiological and pathological conditions. In this work, we develop and validate a biologically-grounded spiking neural network of the cerebellar cortex, embedding key mechanisms of cellular excitability and synaptic transmission, and assess their impact on signal processing. Neuronal input-output functions, short-term synaptic plasticity, receptor-specific kinetics, and NMDA channel voltage-dependent gating were calibrated against detailed multicompartmental models through automatic tuning procedures. Incorporating these realistic biological properties allowed the network model to simulate key features observed in recordings from acute cerebellar slices. The neuronal discharge and local field potentials elicited by mossy fiber stimulation faithfully reproduced the natural patterns with millisecond precision. Then, selective receptor switch-off revealed the contribution of NMDA, GABA, and AMPA receptors to the frequency-dependent input-output function of the granular layer and Purkinje cells, linking previous empirical findings to specific synaptic mechanisms. This model combines high computational performance with biological realism and offers a computationally efficient framework to investigate neurophysiological phenomena and the neural correlates of behavior in large-scale long-lasting simulations, such as those needed to address the neural underpinnings of learning and of cerebellar pathologies.

Coronaviruses invade human cells within dynamic mechanical environments through endocytosis and membrane fusion, both mediated by the class I fusion protein spike. In SARS-CoV and SARS-CoV-2, the spike engages the human ACE2 receptor through a catch bond--an interaction whose lifetime increases under tensile force. Concurrently, mechanical pulling facilitates disruption of the S1/S2 subunits of spike, a critical step for membrane fusion. To elucidate how mechanical cues coordinate these processes, we developed a unified elastic-stochastic model that integrates theoretical analysis and computational simulations to trace viral entry. Our results identify the force-regulated catch bond between spike and ACE2 as a key determinant of successful invasion. This catch bond not only enhances receptor-mediated endocytosis but also increases the probability of S1/S2 disengagement, thereby promoting membrane fusion. Importantly, under conditions of strong catch bonding, the force-accelerated separation of S1 and S2 fine-tunes the balance between entry pathways. These findings uncover a potential mechanobiological mechanism that mediates viral cell entry by coupling receptor binding strength with spike disassembly under force. By characterizing these mechanical regulations, this work facilitates the assessment of emerging viral threats and inspires the design of drug delivery systems that leverage catch-bond kinetics for enhanced targeting.

Curvature evolution on a deforming surface is governed by the full change in the surface metric, but on biological surfaces captured by serial three-dimensional imaging, only the local area change is observable. The loss of the shear component leaves prediction of curvature evolution underdetermined from imaging alone. On the thoracic aorta, where curvature change marks disease progression, we derive a closed-form equation that predicts the change in integrated Gaussian curvature from the area dilation and initial geometry. The equation combines a conformal term in the area dilation with a leading anisotropy correction from the initial geometry. These two analytic levels, augmented by multi-scale spatial features at neighboring regions and a graph neural network trained on residuals, form a four-level nested predictor. On a synthetic aortic geometry under prescribed isotropic expansion, the equation recovers the analytic coefficient exactly. Across a continuum from pure expansion to pure shear, it holds R2 [≥] 0.71. On 236 paired thoracic aortic surfaces spanning dissection, aneurysm, traumatic injury, and non-pathologic controls, the equation recovers within-surface curvature change patterns with per-patient median Pearson [Formula] and pooled R2 = +0.238 [+0.225, +0.250], matching the graph neural network on the same inputs. The residual is a direct measurement of how far the observed growth field departs from conformality. HighlightsO_LIClosed-form equation predicts aortic curvature change from paired computed tomography scans. C_LIO_LIRecovers analytic predictions exactly on synthetic aortic geometries. C_LIO_LIAnisotropy proxy holds R2 [≥] 0.71 from pure expansion to pure shear. C_LIO_LICoefficients tie to geometric mechanisms ensuring interpretability. C_LIO_LIAnisotropy term, computable from one CT, is twice as large on diseased aortas. C_LI

1Correlations between cellular variables, such as gene-expression levels, provide insights into regulatory mechanisms. We focus here on correlations between mRNA and protein levels and re-examine previously derived analytical predictions. We test this prediction on single-cell E. coli data and see substantial disagreement. We hypothesize that this discrepancy arises from the assumption of constant cell volume and develop a theoretical framework for mRNA-protein correlations in growing and dividing cells. Within this framework, we derive an analytical expression for mRNA- protein correlations and show that explicit incorporation of growth and division substantially alters these correlations. The resulting relation is invariant to upstream transcriptional dynamics, and we validate it using stochastic simulations across multiple gene-regulatory architectures. Finally, we show that the derived predictions are consistent with the E. coli data.

Time-resolved measurements are central to calibrating mechanistic dynamical models, but current inference frameworks typically assume that reported measurement times are exact. In practice, actual sampling times may deviate from reported times because of sample-handling delays, imper-fect synchronization, or reporting errors. Here, we present a Bayesian framework for parameter inference in ordinary differential equation models that explicitly accounts for uncertainty in measurement times. We formulate latent measurement times as random variables and derive a joint and marginalized posterior. To compute the marginal likelihood efficiently, we augment the original dynamical system with additional state variables that evaluate the required integrals during numerical simulation. This reduces the dimensionality of the estimation problems and allows for efficient and reliable Markov chain Monte Carlo sampling. Across synthetic examples and a published model of carotenoid cleavage in Arabidopsis thaliana, neglecting time uncertainty led to biased estimates and overconfident uncertainty quantification, whereas the proposed marginalized formulation recovered reliable parameter estimates while substantially improving sampling efficiency and scalability. These results identify measurement time uncertainty as an important source of variability in dynamic modeling and establish posterior marginalization as a practical strategy for robust mechanistic inference.