Communications Physics

Cellular adaptation is inherently nonstationary processes with complex stochastic dynamics1-5. Despite remarkable progress in quantitative biology6-11, a quantitative understanding of the cell adaptation dynamics in terms of the underlying cellular network remains elusive. Here, we present the next-generation chemical dynamics model and theory for cellular networks, providing an effective, quantitative description of the adaptive gene expression dynamics in living cells responding to external stimuli. Unlike conventional kinetics, chemical dynamics of cellular network modules are characterized by their reaction-time distributions, rather than by rate coefficients12. For a general model of cell signal transduction and adaptive gene expression, we derive exact analytical expressions for the time-dependent mean and variance of protein numbers produced in response to external stimuli, validated by accurate stochastic simulations. These results provide a unified, quantitative explanation of the stochastic responses of diverse E. coli genes to antibiotic stress and transcriptional induction. Our analysis reveals existence of a general quadratic relationship between the mean and variance of activation times across diverse genes. The gene activation process influences transient dynamics of downstream protein levels, but not their steady-state levels. In contrast, post-translational maturation process affects both transient dynamics and steady-state variability of mature protein levels. This finding indicates that the gene expression variability measured by fluorescent reporter proteins depends on the maturation time of the reporters. This work suggests a new direction for the development of digital twins of living cells.

Biocircuits often realize their functions only within specific parameter regimes, yet identifying those regimes and quantifying how difficult they are to satisfy remain challenging. Powered by the recently developed Reaction Order Polyhedra (ROP) framework enabling a holistic analysis of the behavior in biomolecular networks, we are now able to analyze these questions in a systematic way. In this work, we use ROP to derive the conditions under which Hill-like behaviors and adaptation in enzymatic negative feedback biocircuits can emerge. We also introduce the Realizability Index (R-index), i.e. the volume fraction of valid parameter regions, to quantify how hard it is for a biocircuit to achieve a desired function. We envision ROP theory and the R-index as important components of a new validity-aware conceptual language for studying and designing functional biocircuits.

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.

The analysis of large gene and metabolic networks is often hindered by unknown biochemical parameters and the nonlinear nature of classical S-system models. To address this, we introduce a framework based on combinatorial toric geometry computed with tools such as Normaliz, SageMath, it is worth mentioning this technique in not restrictive to integer vectors, there exists a natural extension to real geometries. Unlike traditional approaches, which rely on parameter dependent fixed points, our method constructs a Topological Environment derived from the dual space of kinetic orders, leading to what we call orthogonal enzyme kinetics. Within this topological setting, fixed points are computed on the algebraic torus, enabling the transformation of nonlinear dynamics into linear forms. Importantly, these fixed points are independent of kinetic parameters and depend only on network topology and interaction signs. Applying this methodology to gene circuits involved in circadian rhythms, we reproduce previously reported oscillatory physiologies.

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.

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.

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.

Micro-calorimetry offers significant potential as a quantitative method for studying the structure and function of biological systems, for instance, by probing the excess heat released by cellular or sub-cellular structures, isothermal or not, when external parameters change. We present the conceptual framework of nonequilibrium calorimetry, and as illustrations, we compute the heat capacity of biophysical models with few degrees of freedom related to ciliar motion (rowing model) and molecular motor motion (flashing ratchets). Our quantitative predictions reveal intriguing dependencies of the (nonequilibrium) heat capacity as a function of relevant biophysical parameters, which can even take negative values as a result of biological activity.

In multi-cellular eukaryotic organisms, cell type and specific functional identity are defined by the epigenetic patterning of chemical modifications to DNA and chromatin that modulate the expression and silencing of specific genes. When a cell divides, histones containing important epigenetic marks are distributed between the two daughter strands leading to a temporary dilution of epigenetic information and cell identity. In this work we introduce a physics-based model of epigenetic memory that explains how cells restore and maintain H3K9me3 and H3K27me3 histone methylation patterning after cell division. We demonstrate that emergence and maintenance of the epigenetic program is driven by an evolved mechanism that makes use of the biophysics of polymers, phase condensates and enzymatic activity. We validate our model via genome-wide epigenetic time-course simulation and comparison to experimental epigenetic data from multiple donors, multiple cell types, and for multiple epigenetic marks. Finally, we use our model as a conceptual framework to understand cellular reprogramming by hypothesizing that these processes first contend with and later utilize somatic epigenetic maintenance programs.

The spatial architecture and mechanical rigidity of polysomes are crucial determinants of translational efficiency and mRNA stability. In this study, we investigate the conformational statistics of an mRNA backbone decorated with high-density ribosomes at varying densities using large-scale, extensive molecular dynamics simulations based on the Kremer-Grest bead-spring model. To address the extreme spatial asymmetry between mRNA monomers and ribosomes, we used an efficient tree-based neighbour list algorithm, enabling the analysis of mRNA chains up to N = 4, 969. Our results demonstrate that the excluded volume of massive ribosomes induces a significant and robust expansion of the scaling exponent v from 0.59 to approximately 0.7. In the conformation of mRNA, this shift translates to a self-induced dimensional reduction from a three-dimensional random coil toward a stretched, a quasi-two-dimensional architecture at biologically relevant scales. Such a transition is further evidenced by a periodic "regain" of the bond-bond correlation function C(n) at ribosome attachment sites, indicating a geometric alignment absent in standard homopolymers. These findings reveal that the geometric crowding of ribosomes itself provides a robust physical prerequisite for the formation of higher-order polysome architectures, bridging the gap between polymer physics and structural properties of mRNA during translation.

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.

Accurate signal processing is essential for proper cell functions, and can be achieved through kinetic proofreading, where an enzyme undergoes sequential state transitions and irreversible deactivation to enable high fidelity. However, synthetically constructing a biological proofreading system has been hindered by the difficulty in engineering single molecular state transitions. Here, we designed a protein circuit that combines diffusion and endocytosis to enable kinetic proofreading at the multimolecular level, without the conservation of total enzymes implicitly assumed in classic kinetic proofreading. Simulations revealed a previously overlooked yet experimentally crucial trade-off between circuit activity and fidelity, and theoretical analysis confirmed it to be fundamental in all kinetic proofreading systems. By integrating self-activation and mutual inhibition mechanisms, the circuit overcomes this activity-fidelity trade-off within biologically plausible parameter regimes. Our results extend proofreading schemes from single enzymes to a multimolecular context, and represent a practical and generalizable strategy for constructing high-fidelity synthetic biological circuits. HIGHLIGHTSO_LIWe design a multimolecular and multicellular proofreading circuit C_LIO_LIA previously overlooked yet practically relevant trade-off arises between circuit activity and fidelity C_LIO_LIThe activity-fidelity trade-off is fundamental in all kinetic proofreading circuits C_LIO_LISelf-activation and mutual inhibition mechanisms collectively overcome the activity-fidelity trade-off C_LI

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.

How large-scale regulatory coordination in biological systems emerges from local signed and directed interactions in sparse gene regulatory networks (GRNs) remains an unanswered fundamental question. We introduce the coherence matrix, a topology-based framework that captures the consistency of regulatory influence between gene pairs by integrating information across all direct and indirect paths. Analysis of synthetic networks reveals that structural coherence - a metric derived from the coherence matrix - dictates global coordination: while highly coherent motifs maintain aligned regulatory coordination across widely varying network sparsity values, motifs with low coherence allow such coordination only at biologically unrealistic sparsity values. Our investigation of six whole-organism GRNs and further analysis of synthetic networks highlighted that hierarchical organization in GRNs a dense middle layer enriched in feedback loops that mediates coordination between input and output layers - serves as a structural buffer to allow regulatory coordination even for sparse networks. Finally, comparison with Escherichia coli transcriptomic modules further shows that the coherence matrix accurately predicts the sign of coordinated gene contribution, emphasizing its biological application, while also serving as a unifying descriptor integrating local interactions and global network architecture to explain the emergent regulatory coordination.

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.

Computational protein design is a foundational challenge in biotechnology, advantageous for engineering novel enzymes and therapeutics, yet its combinatorial complexity remains a bottleneck for classical optimization. We formulate fixed-backbone computational protein design as a quadratic Hamiltonian over rotamer variables to naturally map onto a hybrid photonic entropy computing platform, Dirac-3. To assess solution quality and runtime performance, we benchmark the photonic solver against an exact classical cost function network (CFN) solver, which provides provably optimal baselines. For protein instances ranging from 493 to 943 variables, Dirac-3 attains solutions within 0.16-2.47 % of optimal energies. Empirical scaling analysis reveals a comparatively gentle effective runtime growth for the photonic solver over the measured regime, consistent with near-linear polynomial scaling, in contrast to the sharp super-polynomial growth observed for the classical baseline beyond approximately 1000 variables. These results suggest a near-term crossover regime in which hardware-aligned continuous-variable optimization may offer a practical promise for large computational protein design instances where exact classical methods become time-prohibitive.

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.