Communications Physics

Protein synthesis in cell-free protein synthesis systems often exhibits non-intuitive input-output relationships. In the PURE system, a reconstituted cell-free system, protein production peaked at low elongation factor Tu (EF-Tu) concentrations and decreased at higher concentrations, resulting in a characteristic bell-shaped profile. Here, we investigated the origin of this behavior using a detailed mechanistic model of translation in the PURE system, designated as ePURE, which describes reaction dynamics of hundreds of molecular species and reactions. Our computational analysis suggested that excess EF-Tu sequesters the initiator tRNA (tRNAfMet) into non-productive EF-Tu{middle dot}GTP{middle dot}Met-tRNAfMet complexes, thereby depleting the pool of initiator tRNA available for translation initiation. This suppression arises from competition for a limited molecular resource rather than from direct inhibition. Based on this mechanism, we predicted that increasing the concentrations of tRNAfMet and methionyl-tRNA formyl-transferase would eliminate the bell-shaped dependence, and experimentally confirmed this prediction. Under these modified conditions, the bell-shaped response disappeared and protein production was enhanced. These findings demonstrate how mechanistic computational models can reveal hidden constraints underlying non-intuitive input-output relationships in complex biochemical networks and guide the rational optimization of cell-free protein synthesis systems.

Understanding why specific metabolic states become stable in cancer has remained a fundamental challenge, as current pathway-centric frameworks lack a unifying physical principle governing global metabolic organization. We introduce the Metabolic Spin-Glass (MSG) model, which recasts cellular metabolism as a frustrated many-body system governed by a Hamiltonian that integrates reaction free energies, cofactor-mediated thermodynamic couplings, and patient-specific transcriptomic fields. The Hamiltonian is formulated as a binary optimization problem and solved using hybrid quantum annealing. Embedding gastric cancer transcriptomes (n=497) reveals that malignant phenotypes correspond to thermodynamically distinct ground states rather than isolated pathway perturbations. The Warburg effect emerges intrinsically as a thermodynamic phase transition, and stem-like tumors occupy the deepest attractor basin reflecting high energetic stability. A thermodynamic order parameter stratifies patients into prognostically distinct subtypes independently of transcriptomic classification, suggesting clinically applicable non-redundant biomarkers. This work establishes a spin-glass energy landscape framework for physically principled, patient-specific cancer metabolic stratification.

We investigate the target search process by proteins locating specific target sites along DNA - a phenomenon fundamental to biological functions such as gene regulation, transcription, replication, recombination, and gene-editing technologies. This process proceeds through a repetitive sequence of stochastic motions: consisting of one-dimensional (1D) sliding along the DNA contour interspersed with detachment and three-dimensional (3D) excursions in the bulk, and then reattachment to a random location on DNA. Recognizing this sequence of random events as analogous to the resetting processes widely studied in statistical physics, we employ a first-passage-renewal framework and derive general expressions for both the mean and fluctuations of the total search time. Our results are completely generic and do not depend on the detailed microscopic dynamics of either the 1D or 3D phases. Quite interestingly, we find that intermittent detachment can not only accelerate the mean search but can also regulate fluctuations around it. Our analysis reveals a universal fluctuation inequality that links the variability and mean of the sliding time to the mean excursion time, thereby identifying the fundamental conditions under which target search process becomes efficient. Notably, we find that broad distributions of sliding times emerge as a universal characteristic for optimal search efficiency--a feature emanating from the slow dynamics along the DNA. Using the facilitated diffusion mechanism as a representative example, we validate the generality of our results. These findings provide a unified theoretical framework connecting stochastic search, resetting dynamics, and biological efficiency, while also highlighting the crucial role of DNA structure such as its contour length in modulating search performance.

Emerging evidence suggest that gene expression is controlled though the modulation of transcriptional bursting across species. However, the underlying regulatory mechanisms remain largely uncertain. Recent live-imaging studies have reported that transcription factors (TFs) form a cluster at enhancers just prior to gene activation, thereby locally concentrating the active transcription machinery. This process is thought to be mediated by multivalent interaction between Mediator recruited by TFs. Conversely, transcription itself is also suggested that to influence the assembly of the TF clustering, implicating the presence of a feedback mechanism. To understand the theoretical framework underlying the interplay between TF clustering and transcription, we here develop a polymer micelle model of transcriptional bursting. With this model, multiple RNA polymerase II (Pol II) molecules loaded to the promoter, together with enhancer-bound Mediator, assemble a micelle-like structure due to their connectivity via DNA when the chromatin fiber connecting enhancer and promoter adopts closed conformation, analogous to polysoap micelle. This assembly further recruits freely diffusing Pol II and Mediator in the nucleoplasm even at low concentration up to the optimal size. Our theoretical framework enables quantitative prediction of how dynamic transitions of enhancer-promoter conformation and the stability of the micelle impact the kinetics of transcriptional bursting.

Quantifying task difficulty remains an open theoretical problem in neuroscience and artificial intelligence. While difficulty is often treated as a scalar property of stimuli or optimization landscapes, neural computation unfolds as a transient reconfiguration of high-dimensional dynamical systems. Here we propose a dynamical manifold theory of difficulty based on heterogeneous, modular FitzHugh-Nagumo networks subjected to structured task demand. Task difficulty is modeled as a conflict-driven control parameter that perturbs competing neural submodules. We define four dynamical metrics: (i) transition action (energetic cost), (ii) peak dispersion entropy, (iii) coherence recovery deficit, and (iv) mean-field trajectory curvature. Across systematic sweeps of task demand, we demonstrate that difficulty does not collapse to a single axis but instead emerges as a multidimensional manifold. Energetic cost and dispersion entropy form a dominant axis, while geometric curvature and integration recovery exhibit partial independence and nontrivial correlations. These results suggest that cognitive difficulty corresponds to structured reorganization in neural state space rather than mere increases in activation amplitude. The proposed framework provides a biophysically interpretable foundation for linking neural dynamics, cognitive effort, and difficulty estimation in artificial systems.

Oscillatory behaviour is important in multiple biological contexts. However, the inherent nonlinearity and high dimensionality of mathematical models in biology makes proving the existence and the localization of limit cycle oscillations challenging. Here, we provided an elementary proof for the existence and a method for rigorously localizing the oscillatory solutions in a class of benchmark biomolecular oscillators. To construct the proof, we used a geometric approach based on Brouwers Fixed Point theorem. We constructed a toroidal-like manifold within a positively invariant set by removing the hypervolume containing the fixed point and the trajectories converging to it along its stable manifold. We showed that the vector field describing the system dynamics maps a cross section of the toroidal-like manifold onto itself. The existence of a limit cycle solution in this manifold was guaranteed by Brouwers Fixed Point theorem. For different sets of initial conditions in these cross-sections, we used an interval-based Reachability Analysis to localize the oscillatory behaviour that complements the Brouwers Fixed Point theorem approach. These results add a simple and elegant approach to demonstrating the existence of limit cycles in biomolecular systems as well as a method for rigorous localization of the region of existence.

Epigenetic marks are essential for maintaining cell identity, yet how epigenetic memory is robustly preserved across cell cycles while remaining plastic during cell-state transitions remains unclear. Here, we develop a theory of epigenetic memory that incorporates chromatin compartmentalization and mark modifications, including long-range spreading, writing, and erasing. The spreading-writing-erasing model generates self-sustaining epigenetic mark patterns across multiple cell generations. The model also reveals that to induce or remove a heterochromatic compartment, the writing or erasing strength must exceed a finite threshold, which depends on the long-distance scaling of the contact probability between two chromatin loci. Intriguingly, the scaling exponent for human cells appears to be evolutionarily selected for stability and plasticity in epigenetic memory. We demonstrate that adding noise in parental histone segregation during DNA replication and accelerating cell proliferation significantly enhance reprogramming efficiency in induced pluripotent stem cells. Finally, our theory also predicts cellular senescence arising from chromatin reorganization after many cell generations.

While the regulation of bacterial cell size is widely studied across generations, the stochastic nature of cell volume growth remains elusive within a cell cycle. Here, we investigate the fluctuations of cell volume growth and report a deviation from standard white-noise models: the random growth rate exhibits subdiffusive dynamics. Specifically, the mean square displacement of the growth-rate noise scales as {Delta}t with an anomalous exponent {approx} 0.27. This low exponent implies strong negative temporal correlations in growth rate noise on timescales of minutes, which are significantly faster than those of gene expression dynamics. We attribute this phenomenon to the physical mechanics of the cell wall. By modeling the peptidoglycan network as a complex viscoelastic material with power-law-distributed relaxation times, we successfully recapitulate the observed subdiffusive behavior. Our results suggest that the heterogeneous mechanical constraints of the peptidoglycan network, rather than biological regulatory programs,govern the short-timescale fluctuations of bacterial growth.

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.

The softmax attention mechanism in transformer architectures (Vaswani et al., 2017) is mathematically identical to the Boltzmann distribution governing molecular binding at thermal equilibrium (Boltzmann, 1877). Luces Choice Axiom (1959) establishes this function - which we term the convergence equation - as the unique function satisfying five axioms of competitive selection: positivity, normalization, unrestricted domain, rank preservation, and independence of irrelevant alternatives. We show that five additional architecture conditions - discrete intermolecular contacts, bilinear energy decomposition, finite competitor pools, thermal equilibrium, and stochastic selection - are satisfied by at least ten biological molecular recognition systems and together prescribe a complete neural architecture: dual encoders, cross-attention, InfoNCE contrastive training, symmetric loss, learned temperature, and cross-attentive decoder. We term this architecture a Specificity Foundation Model (SFM) and specify it for antibody-antigen, TCR-peptide-MHC, transcription factor-DNA, microRNA-mRNA, enzyme-substrate, CRISPR guide RNA-DNA, drug-target, peptide-MHC, receptor-ligand, and RNA-binding protein-RNA recognition. The first implementation (CALM; Lee et al., 2026) achieves antibody-antigen retrieval from approximately 4,000 training pairs with [~]100,000-fold greater data efficiency than comparable contrastive architectures trained without the physics derivation. We classify this as Level 3 architecture-physics alignment and derive three further theoretical results: an exponential scaling law for retrieval accuracy as a function of training data diversity (the MRC scaling law), a two-parameter affinity calibration framework connecting contrastive scores to binding free energies, and a hybrid recursive learning framework for cross-modal reinforcement learning with orthogonal verification. The failure conditions of the framework are analyzed in terms of the validity of equilibrium thermodynamics for molecular binding and the convergence properties of gradient-based parameter estimation.

In biological networks, retroactivity describes the feedback from downstream components that can influence and alter the behavior of upstream systems. This effect poses a major challenge to the modular design of synthetic circuits, where upstream modules are expected to function independently of their connections. Beyond disrupting dynamics, retroactivity can also interfere with how information is transmitted through a network, acting as a bottleneck that reduces the fidelity of signal propagation. Here, we combine stochastic biochemical modeling with information-theoretic analysis to quantify how retroactivity constrains upstream signaling, even in strongly amplified feedback architectures, particularly in the presence of molecular noise. At the same time, we identify parameter regimes in which retroactivity can be exploited as a functional mechanism: downstream loading can trigger controllable state transitions, enabling circuits that respond to changes in their environment or interconnections. These findings suggest design principles for harnessing retroactivity for programmable signal processing and decision-making in cellular computation. Finally, we evaluate feedback-gain tuning as a mitigation strategy and demonstrate that increasing gain alone is insufficient under noisy conditions. We therefore propose complementary approaches to reduce retroactivity and delineate the operating regimes in which each strategy is most effective.

Biological rhythms are governed by intricate interactions among oscillatory subsystems, yet how they balance functional demands and energy efficiency remains unclear. We present a bimodal coupling optimization strategy where physiological systems dynamically alternate between synchronized (energy-saving) and desynchronized (function-priority) coupling modes. By employing the water-filling principle developed in communications engineering, we prove synchronized heart rate(HR)-respiration oscillations maximize energy efficiency (oxygen uptake per cardiac work). Then, system modeling confirms task/stress-induced oxygen demands enhance oxygen uptake at the cost of desynchronization and reduced efficiency. Experiments reveal a 70.36% decrease in HR-respiration synchronization during arithmetic versus relaxation, enabling 4.43% higher oxygen uptake but with 11.38% lower energy efficiency. This bimodal coupling optimization strategy is also evident in pancreatic islets, with their insulin/glucagon oscillator alternating between in-phase (energy-saving) and anti-phase (rapid glucose reduction) coupling. This framework, integrating engineering and life sciences, reveals a universal regulatory principle for biological oscillatory systems.

During development, embryos store, transmit, and transform information to generate spatial patterns. Positional information (PI) quantifies how precisely cells form patterns at a given time, but cell motion has limited its application to static tissues. We introduce a framework for PI in dynamic tissues by decomposing mutual information between cells positions and properties over time into information flows contributing to PI preservation, loss and generation. These reveal information-theoretic signatures of ubiquitous developmental processes, including instruction, sorting and mixing, directly from data. Applying this framework to whole-embryo cell trajectories in Drosophila, mouse and zebrafish gastrulation, we provide local and global information-theoretic quantification of cell mixing and derive bounds on PI preservation imposed by tissue dynamics. Analyzing tissue flows as dynamical systems, we further show that morphogenesis structures mixing, preferentially preserving specific patterns. Finally, we derive inequality conditions for tracing generated PI to candidate information sources and distinguishing among alternative pattern-formation mechanisms, from programmed extracellular cues to self-organizing intercellular interactions.

Asymmetric self-organization is a hallmark of cell polarity, yet the diversity of observed polarization patterns is frequently attributed to specialized, complex biochemical mechanisms motifs beyond simple positive feedback. Here, we demonstrate that spatial heterogeneity alone fundamentally reshapes polarization dynamics within minimal stochastic reaction-diffusion processes. We show that weak differences in reaction rates between distinct spatial domains strongly bias polarization timing and determine which region ultimately polarizes. In systems containing two distant favored regions, a "stochastic winner-takes-all" mechanism--driven by long-range competition mediated by a shared cytoplasmic pool--induces stochastic switching that manifests as pole-to-pole oscillations. By relaxing the assumption of a perfectly mixed cytoplasm and incorporating finite cytoplasmic diffusion, we reveal a qualitative shift in this competitive dynamic. Specifically, as the total particle abundance increases, the system transitions from monopolar to bipolar activation, capturing the essence of the New-End Take-Off (NETO) phenomenon during cell growth and provides a physical basis for pole coexistence. These results demonstrate that spatial heterogeneity alone can strongly influence polarization dynamics in minimal models, highlighting the potential importance of quenched spatial variability in biological reaction-diffusion systems. Author summaryCells often need to choose a specific site for growth, division, or shape change. This process, known as cell polarization, is a fundamental organizing principle in biology. The wide variety of polarization patterns seen in living cells is often explained by proposing complex biochemical mechanisms beyond basic positive feedback among signaling molecules. In this work, we asked whether some of this diversity could instead arise from a simpler source: fixed spatial differences within the cell. Using minimal stochastic reaction-diffusion models, we found that even small local differences can strongly influence where polarization appears and how quickly it develops. When two favored sites are present, they can compete for a shared pool of molecules in cytoplasm, so that one site dominates at a time and the polarized state can switch stochastically between them. We also found that this competition changes when the shared molecular pool does not mix instantly: under these conditions, two polarized sites can start to coexist. This behavior offers a simple physical explanation for phenomena such as the appearance of a new growth site during cell development. Our results show that spatial heterogeneity alone can generate behaviors that might otherwise seem to require much more complicated biochemical mechanisms.

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.

Achieving complex multi-species control objectives is essential for engineering advanced autoregulated biomolecular devices. This paper addresses the problem of robust steady-state tracking for outputs defined as multiplicative combinations of biomolecular species concentrations. We first introduce a control architecture realized via chemical reaction networks that steers the product of two target species concentrations in the controlled network to a prescribed value. A robust stability analysis is provided for closed-loop system families with distinct structural characteristics. The proposed framework is also extended to a more general formulation capable of regulating arbitrary monomial outputs involving multiple species. Numerical simulations of representative examples corroborate the theoretical results and illustrate the effectiveness of our approach.

Across adult warm-blooded vertebrates, the product of resting heart rate fH and maximum lifespan L is approximately constant: N[*] = fH L {approx} 109 cardiac cycles. This empirical regularity, noted since Rubner (1908), has lacked a widely accepted thermodynamic interpretation. We derive N[*] {approx} 109 from the non-equilibrium second law by treating the adult organism as a metabolic non-equilibrium steady state (NESS) and introducing the empirical closure[e] p ={sigma} 0f, which links entropy production rate to heart rate via a mass-specific parameter{sigma} 0 {propto} M0. Under this closure, the lifetime entropy budget {sum} ={sigma} 0N[*] is approximately species-independent when{sigma} 0 is approximately constant--a condition whose direct calorimetric verification remains the critical outstanding experimental test. We further show that N[*] is the correct primitive invariant: lifetime energy per unit mass is a derived consequence, valid only when body temperature and the mass-specific entropy cost per cycle are both approximately constant. This framework, which we term the Principle of Biological Time Equivalence (PBTE), is placed on a fully falsifiable footing with explicit assumptions, a domain-of-validity table, and five numerical falsification criteria. We test the framework against a dataset of 230 adult vertebrate species spanning eight taxonomic groups. Ordinary least-squares regression on the n = 43 directly measured non-primate placentals yields slope [Formula] (R2 = 0.863; F -test p = 0.093 against {beta} = -1). Phylogenetically independent contrasts on 112 endotherm species yield a log10 fH-log10 L slope of -0.99 {+/-} 0.04 (p = 0.84 against slope -1), confirming the relation is not a phylogenetic artefact. The WBE kinematic null of zero inter-clade variation is rejected (F = 12.7, p < 0.001). Four warm-blooded clades depart systematically from the mammalian baseline; we derive their longevity deviations from a unified thermodynamic multiplier {Phi}C = {Phi}duty {middle dot} {Phi}thermal {middle dot} {Phi}mito+oxid {middle dot} {Phi}haz, calibrated to independently measured physiology. For primates, the elevated count [&lt;]N[*][&gt;] {approx} (2-3) x 109 follows from a neuro-metabolic entropy model in which greater neural metabolic investment reduces entropy produced per cardiac cycle. For bats, the extreme longevity ({Phi}bat {approx} 7.9) arises from the multiplicative synergy of cardiac suppression during torpor and an Arrhenius thermal factor during hibernation--two mechanisms acting simultaneously whose thermodynamic motivation has not previously been given. For birds, an adverse thermal penalty ({Phi}thermal = 0.73) and adverse flight duty cycle ({Phi}duty = 0.87) are overcome by mitochondrial coupling efficiency and antioxidant robustness. For cetaceans, extreme diving bradycardia ({Phi}duty = 3.08 for bowhead whales) reveals a near-coincidence trap: the raw heartbeat count Nobs {approx} N0 conceals a true thermodynamic budget three times the mammalian baseline. Within this framework, the integral of physiological frequency defines a natural biological proper time, which unifies all longevity mechanisms as Class 1 (time dilation: reduce f ) or Class 2 (budget expansion: reduce{sigma} 0), generating testable predictions for epigenetic aging clocks. The central outstanding experimental requirement is direct calorimetric verification of{sigma} 0 {propto} M0, which would convert PBTE from a statistically supported regularity with thermodynamic motivation into a fully tested conservation law.

The proliferation of primitive life-forms (known as protocells) without sophisticated cell-division molecular machineries has been an intriguing question in evolutionary biology, synthetic biology, and living matter physics. While various modes of protocell proliferation at the individual level have been proposed, the growth dynamics of protocell colonies (i.e., protocolonies) received less attention. Here we chose to study this question in protocolonies consisting of densely packed protocells derived from wall-deficient L-form bacteria. We discovered that protocolonies proliferated robustly under spatial confinement, while isolated protocells failed to divide and eventually experienced membrane rupture due to imbalance of surface and volume growth. Combining results from quantitative imaging and computational modeling, we attributed this unexpected finding to mechanical shearing between densely packed protocells driven by their growth activities; such mechanical shearing enhances cell deformation, thereby enabling cell division and sustaining population growth in a protocolony. Our study reveals a unique role of self-generated mechanical stresses in the lifestyle of primitive life-forms. The findings may help to understand and control the collective growth dynamics of synthetic protocells or active droplets.

AO_SCPLOWBSTRACTC_SCPLOWTransitions between stable states are a defining feature of nonlinear dynamical systems, yet the factors controlling their probabilities and timescales remain poorly understood in non-conservative settings. In many theoretical frameworks, such control is commonly interpreted in terms of potential depth, a concept that becomes ambiguous outside equilibrium. By analyzing a gene regulatory network associated with breast cancer subtypes, we uncover a geometric framework in which the phase-space distance between stationary states, together with the bifurcation structure organizing multistability, provides a robust and well-defined determinant of transition probabilities, times, and variability. Our results show that the coexistence of stable states is only a necessary condition for transitions, while their accessibility is constrained by geometric features of the underlying state space. Within this framework, we find that the HER2+ regime exhibits dynamical robustness to intrinsic parameter variations, whereas the TNBC regime displays strong sensitivity and amplified variability. These differences emerge naturally from the geometric organization of the bistable region and offer a dynamical explanation for the pronounced heterogeneity observed in TNBC. Together, our results establish a general geometric perspective on transitions in non-conservative regulatory networks, with implications for understanding phenotypic plasticity in complex biological systems.

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.