Communications Physics

We show that the p53-Mdm2 gene interaction can be understood as a form of antithetic feedback, but with mixed feedback loops. In particular, we show that this viewpoint sheds light on the emergence and robustness properties of p53's oscillatory behaviour, as observed experimentally.

The collective spatial phenomenon of complement protein opsonization on nanoparticle surfaces is a key component of the immune response to viruses, engineered nanoparticles, and diseased cells. Recent work showed this opsonization follows a sharp, percolation-like transition versus the spacing d between surface-bound attachment sites, leaving two open questions: 1) whether the transition exhibits hallmarks of true criticality, such as diverging susceptibility, and 2) whether it can be distinguished from an alternative first-order cooperative (Hill-type) process producing an equally sharp threshold without true criticality. Here, we resolve both questions using a hierarchical statistical-mechanics treatment spanning stochastic, mean-field, and spatial reaction-diffusion models. The variance of two order parameters, peak complement activity and activation lifetime, diverges near threshold and sharpens systematically with system size, the defining signature of a critical point rather than a smooth cooperative response. Extending the analysis across site spacing and intrinsic kinetic rate constants traces a two-dimensional locus of critical points with consistent critical exponents throughout, establishing a single, robust universality class. The mean-field dynamic exponent for activation lifetime agrees quantitatively with the exact value predicted for the general epidemic process. Finally, a reaction-diffusion model of the nanoparticle surface shows the critical locus is set by a diffusion-limited length scale, establishing complement percolation as a fundamentally transport-limited surface reaction. These results place complement activation within the percolation universality class and identify the physical parameters, diffusion, catalysis, and decay, that govern its critical threshold, with direct implications for rational design of complement-evading nanomaterials, immunology, and evolutionary biology.

Maintaining a prescribed composition in engineered microbial consortia is difficult because small fitness differences can drive competitive exclusion. We study a two-strain consortium in continuous culture and develop a feedback architecture that regulates composition by selectively slowing the fast strain as a function of the population ratio. At the population level, we derive an idealized ratio-feedback law with a tunable positive coexistence equilibrium. We then propose a biomolecular realization using orthogonal quorum sensing, an sRNA-based ratiometric controller, and a ppGpp-mediated growth actuator. Exploiting the separation between slow population growth and faster intracellular controller dynamics, we use singular perturbation theory to show that, for sufficiently fast controller dynamics, the full implementation model inherits the coexistence equilibrium and its local stability properties from the reduced model. Numerical simulations validate the reduction and show how weaker timescale separation or loss of the assumed molecular regime degrades performance.

Collective migration is often attributed to complex cell-cell communication, yet coordinated multicellular dynamics can also emerge in organisms lacking social interactions. Continuum descriptions successfully capture such behaviors but generally rely on phenomenological transport coefficients whose microscopic origin remains elusive. Here we show that these coefficients emerge from cell-cell collisions and can be independently determined from experiments. We investigate the aerotactic dispersal of confined colonies of the solitary amoeba Acanthamoeba castellanii, in which oxygen consumption continuously reshapes the local environment to generate self-organized guidance cues. Combining quantitative videomicroscopy, oxygen mapping with phosphorescent sensing films, and oxygen-controlled microfluidics, we directly measure both the oxygen landscape and the aerotactic response governing colony expansion. We then develop a Patlak-Keller-Segel (PKS) -type drift-diffusion model whose transport coefficients are entirely determined from independent experiments and microscopic-to-macroscopic modeling approach, without adjustable parameters. The model quantitatively reproduces the observed dynamics, including the coexistence of a fast ballistic front and a trailing transient accumulation band. We show that both diffusion and aerotactic transport are modulated by the same collision-controlled mechanism through density-dependent changes in cell persistence. More generally, our results establish transport coefficients as measurable emergent properties bridging microscopic cell dynamics and macroscopic collective behavior, providing a predictive framework for oxygen-guided migration in living active matter.

Cells use ATP-driven chaperones to extract clients from biomolecular condensates selectively, yet no closed-form criterion links molecular parameters to condensate quality control. We derive a minimal non-equilibrium sorting reactor model that reduces the reaction-diffusion dynamics to one algebraic equation. In the idealized low-load limit, a concentration-dependent partition coefficient produces a saddle-node bifurcation between functional clearance and pathological storage. The critical Damk\"ohler number is \(\mathrm{Da}_{0c}=e^{-2}\) and is independent of the feedback strength. Corrections shift the value but preserve the topology. The model predicts a Kramers-type functional lifetime and recovery costs that scale as \(R^3\). Critical slowing down near the bifurcation provides early-warning signatures for FCS and FRAP.

Enzymatic reactions in biomolecular condensates are often assumed to be regulated through local enrichment of reactants. However, condensates also reshape molecular transport and reaction kinetics, making it unclear how phase separation controls catalysis in living cells. Here, we develop a quantitative theory of biomolecular catalysis in phase-separated systems and find that liquid condensates can act as tunable catalytic switches, transitioning between regimes of enhanced and suppressed enzymatic activity, exhibiting optimal responses at biologically relevant condensate sizes. We show that condensate-mediated catalysis cannot be understood from reactant enrichment alone, but instead emerges from the coupled interplay of molecular partitioning, diffusive transport, and phase-dependent reaction kinetics. The strongest regulatory effects occur under rapid interphase exchange, where the spatially heterogeneous catalytic network admits a system-level Michaelis-Menten description governed by system-averaged concentrations and reaction kinetics. Our framework predicts that micron-sized condensates can either enhance or suppress enzymatic activity by up to two orders of magnitude, and that optimal catalytic regulation can emerge at condensate sizes comparable to many biomolecular condensates. These results provide experimentally testable predictions for condensate-mediated catalysis and establish quantitative principles for understanding and engineering enzyme-catalysed reactions in biomolecular condensates.

Liquid-liquid phase separation (LLPS) widely organizes the cellular interior, yet how third-party macromolecules modulate LLPS remains a puzzle. While one would expect that macromolecules can either promote or suppress phase separation, empirical observations show that a small dosage of macromolecules virtually always promotes phase separation. To resolve this paradox, we study the linear response of phase separation to macromolecule addition. We prove that for macromolecules significantly larger than the solvent molecule, their addition essentially always promotes phase separation, regardless of how they interact with the scaffold protein. Crucially, in the biologically relevant scenario of dilute condensates, the linear responses, including the saturation volume fraction, scale proportionally to [1-v2(1+{chi}12)2], where v2 is the macromolecule size and {chi}12 is the scaffold-macromolecule interaction parameter. Importantly, this universal behavior extends to multicomponent solutions in which the effective interaction parameter is composition-dependent. Our work shifts macromolecular modulation of LLPS from empirical observation to predictable design.

Radiation-induced DNA double-strand breaks (DSBs) drive cellular mortality, mutagenesis, and severe evolutionary bottlenecks. While classical phenomenological models, such as the Linear-Quadratic (LQ) framework, reliably predict macroscopic population survival, they obscure the intrinsic single-cell stochasticity that governs critical rare events like tumor recurrence or the emergence of radioresistant persisters. To bridge this divide, we develop a mathematically exact stochastic differential equation (SDE) framework that models continuous DSB induction and repair as a Feller square-root process. By deriving exact closed-form expressions for the foci moments, we establish a highly efficient Maximum Likelihood Estimation (MLE) pipeline that circumvents computationally exhaustive Monte Carlo simulations, allowing the direct extraction of deterministic repair velocities and intrinsic molecular noise from empirical single-cell $\gamma$-H2AX data. Integrating this kinetic model with a cumulative damage hazard via the Feynman-Kac formalism, our framework seamlessly recovers the classic macroscopic LQ survival topology from microscopic first principles. Furthermore, systematic sensitivity analysis uncovers a fundamental evolutionary duality: while initial physical damage operates additively, ultimate cellular fate is driven by a nonlinear survival response governed by the trade-off between the damage hazard rate and intrinsic molecular noise strength. Crucially, we demonstrate that this molecular noise inherently enhances population survival. Governed by Jensen's inequality, stochastic variance acts as a non-genetic bet-hedging mechanism that buffers the population by favoring cells with transiently low damage loads. Ultimately, this exact stochastic framework bridges microscopic biophysics and macroscopic demographics, offering deep mechanistic insights into the evolutionary roots of radioresistance.

Structural network representations of metastatic dissemination typically focus on static topology without resolving transport dynamics, relaxation timescales, or steady-state behaviour. Here, we formulate a discrete Markovian transport model on a directed higher-order network with transition rates derived from qualitative clinical affinity classes. By constructing a non-Hermitian row-stochastic transfer operator, we characterise the relaxation dynamics through its spectral decomposition. The system exhibits a fast-mixing regime characterised by a spectral gap of {gamma} {approx} 0.67, corresponding to a characteristic relaxation timescale of {tau} {approx} 1.49 discrete steps, with the influence of the primary tumour origin progressively attenuated during dissemination. Convergence towards a non-equilibrium steady state (NESS) is accompanied by a reduction in Shannon entropy, concentrating probability mass within specific topological sinks. This spectral relaxation delineates two distinct dynamical regimes: early transient dissemination (n < {tau}), dominated by local organ-specific transition probabilities (organotropism), and the asymptotic regime (n > {tau}), determined increasingly by the global transport architecture of the network. Comparison with independent clinical and autopsy observations across 21 primary tumours and 23 target organs indicates that the predicted stationary distribution is consistent with the observed hierarchy of metastatic organ involvement.

The back-and-forth (bidirectional) motion of Endosomes and Phagosomes along microtubules is fundamentally important for nutrient absorption, receptor recycling, pathogen degradation and many other downstream cellular pathways. Bidirectional motion requires opposing force from the kinesin and dynein motors, causing intermittent Tug-of-Wars (ToWs) followed by runs where winning motors drive their cargo until the next ToW. Dynein displays a counter-intuitive behaviour of catch bonding tightly to the microtubule against opposing force, but why such a response is needed remains unknown. Here we force dynein to catch-bond using an optical trap when dynein-teams are transporting phagosomes in-vitro and inside cells. An unexpected form of collective inactivity emerges, where larger dynein-teams remain inactive for longer after they have been catch-bonded. Kinesin exhibits a high probability of reversing the cargo during such periods of inactivity of dyneins. Therefore, the inactivity of dyneins allows cells to auto-regulate the effect of opposing molecular forces for the purpose of achieving bidirectional motion of endosomes/phagosomes. We propose that an inactivating conformational change is induced when dynein detaches against strain from its catch-bonded state. Collective inactivity follows because each inactive dynein exerts an entropic force on the other to delay the entire team from being activated. We capture the dynamics of this process through a statistical model of Entropically Constrained Reactivation, obtaining predictions in excellent agreement with experimental data. The emergent behaviour observed here possibly prevents a runaway dynein situation inside cells, its simple entropic origin suggesting broader relevance to catch-bonded receptor ligand interactions operating under conditions of cellular crowding.

Behavioral variability reflects differences in internal and external parameters and provides a substrate for natural selection. However, uncovering its structure is challenging because behavior evolves nonlinearly across multiple timescales. Our goal is to reconstruct phenotypic variation from finite behavioral observations without prescribing the scales at which individuals should be compared. To achieve this, we introduce a multiscale dissimilarity that compares dynamics across all statistically resolvable resolutions by constructing reduced transfer operators at progressively finer scales and weighting their differences by finite-sampling uncertainty. This dissimilarity defines a geometry of dynamical phenotypes, which we reconstruct using diffusion maps. We show that the resulting phenotypic coordinates locally follow the parameter directions to which dynamics are most sensitive. We validate our approach in a stochastic model and apply it to bacterial and larval zebrafish behavior. In bacteria, we identify run speed as a major component of inter-individual variability, associated with the chemotaxis protein CheB. In zebrafish, we find that prior prey experience reshapes behavioral dynamics and phenotypic variability, with paramecia experience concentrating fish in a prey-capture-associated region of phenotypic space. Together, these results provide a framework for identifying internal and environmental variables that structure dynamical phenotypes across scales.

Kinetic parameters in engineered biomolecular circuits are typically known only within intervals and are not precisely tunable; controller synthesis is therefore naturally posed over sets of gains rather than at a single nominal design. We formulate robust controller tuning under parametric plant uncertainty as a universally quantified set-inversion problem: given a plant-parameter box, compute the controller gains that stabilize every plant in the box. Robust stability is decided by Hurwitz sign conditions, which are bounded over the joint gain-parameter domain using validated range enclosures, yielding machine-checkable certificates of local exponential stability of the deterministic equilibrium. Numerical experiments show that the certified region depends strongly on the range enclosure. For an antithetic integral feedback (AIF) controller acting on a two-species gene-expression cascade, a tensor-product Bernstein enclosure certifies 83.2% of the design plane at bisection tolerance epsilon=0.05 with 324 terminal boxes, whereas four baseline enclosures certify between 50.9% and 58.9% on the same paving. For a fifth-order loop, the certified fraction increases from 34.4% to 73.8%, and the certified and excluded terminal boxes confine the robustly stabilizing area to a window of about 2.1 percentage points. Finally, for a refining variant of the algorithm in which the plant box is refined alongside the design box, the undecided area satisfies |U(epsilon)|=O(epsilon) under a non-degeneracy assumption on the stability boundary.

We develop a general geometrical framework for growth processes in which the growth rate depends exponentially on the number of active growth-supporting components. The framework separates the fraction of active components from the size of the accessible component space, allowing qualitatively different growth laws to arise from the same underlying construction. Bacterial population growth provides an example of a fixed-size component space controlled primarily by activation and deactivation, whereas examples such as human population growth or speciation provide an expanding component space in which interactions between individuals promote further growth. This motivates a Replicative geometrical law, dX/dt= X exp({beta} X^{gamma}), whose exponent characterizes the scaling of the effective growth-supporting component space and is tested against historical human-population regimes and eukaryotic lineage-through-time data. For innovation indicators such as patents and arXiv manuscript submissions, where an existing item need not itself reproduce, the same construction motivates a Direct Geometrical production law without the prefactor X. The framework therefore provides a common description of fixed and expanding component spaces while distinguishing Replicative from Direct Geometrical growth.

Cell density is a fundamental biophysical property of living cells, yet the dynamical architecture underlying density homeostasis remains unknown. Here, we reconstruct the geometry, dynamics, and control structure governing cellular density regulation from single-cell mass-volume measurements acquired during recovery from osmotic perturbation. We identify a persistent anisotropic attractor in mass-volume state space that permits coordinated density-preserving fluctuations while strongly suppressing density-changing deviations. Optimal transport analysis reveals directed recovery trajectories confined to this attractor, enabling inference of an effective density-restoring control law. Density deviations are associated with coordinated changes in biomass accumulation and volume expansion that together generate an effective density-restoring control law. Moreover, density error contains significant predictive information regarding future corrective behavior, revealing an information-rich component of cellular regulation. Together, these findings establish cellular density homeostasis as an emergent dynamical control process and demonstrate how attractor reconstruction, optimal transport, and information theory can be combined to uncover the organizing principles of biological homeostasis.

Protocell communities can support programmable molecular nanonetworks, yet most demonstrations use broadcast diffusion or fixed sender-receiver circuits. We introduce PO_SCPLOWROTOC_SCPLOWNO_SCPLOWETC_SCPLOWSO_SCPLOWTACKC_SCPLOW, a network-layer abstraction in which a logical DNA-encoded packet carries a payload, a processing-address list, and an optional forwarding budget. The list determines where localized molecular services transform the packet, not its bidirectional diffusive trajectory. We formulate a finite-state reaction-transport model whose concentration dynamics and single-copy continuous-time Markov chain use the same generator. Under ideal specificity, positive rates, connected transport, no degradation, and sufficient budget, packet stages advance only in the encoded order and delivery occurs almost surely. All injected concentration is delivered asymptotically. Uniform first-order degradation makes delivery probability the Laplace transform of the lossless delivery-time distribution. A union-bound result separates endpoint delivery from route-faithful delivery under off-target processing. As an application, we develop cancellation-based strict-majority aggregation on rooted protocell trees. Conservation of token imbalance proves asymptotic correctness and yields a finite-time certificate. With one initial token per node, outside-root mass below one guarantees the correct root sign. Direct matrix-exponential calculations show sequential processing, branching addressability, route-length attenuation, and bounded forwarding work. A 16-condition finite-copy benchmark with 20,000 trajectories per condition shows that off-target reactions can increase endpoint arrival while decreasing route-faithful delivery. Adaptive ordinary differential equation simulations on trees up to 511 compartments show decision time increasing approximately with maximum tree depth and quantify bias from asymmetric loss. PO_SCPLOWROTOC_SCPLOWNO_SCPLOWETC_SCPLOWSO_SCPLOWTACKC_SCPLOW is therefore a formally analyzable molecular networking architecture and an experimentally testable blueprint. Sequence-resolved gates and chassis calibration remain future work.

Biological processes, from molecules diffusing to their regulatory destinations to whales pursuing food or mates, are widely exploratory. Such behaviors are effective when some verifiable functional state or outcome can be reached regardless of initial conditions. In these cases, systems repeatedly undergo distinct and abortive trajectories; the process only ends when the system finds 'right' outcomes. This dominance of the terminal condition (and indifference to the initial state) provokes a very different perspective than the conventional 'dynamical systems' framework that has been a centerpiece of the quantitative sciences for centuries. We hypothesize that many of these problems defy the initial-condition driven or gradients on landscapes so useful in problems ranging from mechanics to electrodynamics to chemical kinetics to mass and heat transport. We examine several mathematical frameworks that capture and unify key aspects of exploratory dynamics. One powerful way of thinking of such processes is the geometric distribution, where repeated failures are punctuated by a successful trajectory. We develop intuitions for how random walks with resets accelerate search processes. We highlight fresh and surprising behaviors of search under drift, cues, and checkpoints. Last, appreciating the probability of trajectories conditioned on satisfying macroscopic final outcomes reveals a language for the potency of variation sculpted by selection in their broadest forms. This can give the fictitious appearance of the future making itself known in the present, but we view this as conceptually similar to the way 'fictitious forces' arise in non-inertial reference frames. These approaches stress unity, open questions, and applications across a range of biological phenomena.

The high energy-efficiency of life is hard to understand only with classical physics. Many efforts have been made to study its mechanism based on quantum mechanics; the progress is nevertheless slow due to lack of experimental evidence with living cells. Here, combining experiments on cells, tissues and mitochondria with a theoretical model, we demonstrate a quantum state of mitochondria, which can be employed to modulate ATP production in living cells. We found an anomalous 71.0-THz oscillation mode only in living cells and tissues, which is highly determined by intact structure of mitochondria, and cannot be assigned to any specific molecules. Based on experimental data, a quantum model of light-matter coupling was introduced to trace the origin of this mode. Our calculations suggest a quantum superposition state of functional mitochondrion that forms by the coupling of light and lipid CH2 bonds in functional cristae, and induces a splitting of the intrinsic CH2 vibration mode of 87 THz to two levels at 71 THz and 103 THz, respectively. The former can be observed only in living cells and tissues; whereas the latter falls in the range (90-110 THz) of biomolecular and water vibrations, thus indistinguishable. Additional experiments revealed this mitochondrial quantum state able to serve as an efficient channel to modulate ATP production. Our findings provide a quantum mechanics view for understanding living cells, and it will be interesting to further explore whether such quantum state could act as a channel for energy metabolism, and even information transmission in life.

Single-particle tracking is widely used to probe nanoscale dynamics in biological systems, yet most approaches rely exclusively on translational motion, overlooking rotational dynamics that offer complementary information about the local physical environment. Here, we present a simultaneous rotational and translational single-particle tracking approach using a vortex-engineered point spread function in a single detection channel. We validate this approach with static and freely diffusing nanorods, demonstrating accurate orientation recovery and quantitative agreement with theoretical predictions of rotational diffusion. Using a biomimetic lipid bilayer system, we show that translational and rotational diffusion exhibit distinct sensitivities to environmental perturbations, confirming that these two modalities capture complementary local environment information. Applying this framework to living HeLa cells, we show that combined translational and rotational diffusion signatures define distinct biophysical fingerprints of cytoplasmic and endocytic compartments and reveal compartment-specific responses to metabolic perturbation. Finally, time-resolved analysis of individual endocytic compartments uncovers dynamic changes in the local physical environment that are inaccessible to conventional translational tracking. By coupling translational and rotational readouts, this framework opens a new dimension for probing the physical organization and dynamics of living systems at the nanoscale.

Nanopore sensors have transformed single-molecule analysis, enabling real-time detection of biomolecules with unprecedented resolution. Understanding and modelling noise in nanopore sensing is essential to unlocking their full analytical potential. Although mechanistic models of nanopore noise exist, a rigorous statistical framework that characterises noise structure across diverse experimental conditions is still lacking. Here, we present a comprehensive empirical analysis of nanopore noise using twelve diverse experimental conditions acquired with different nanopores, analytes, and electronic recording systems. By employing multiple, mutually reinforcing statistical methods, we establish that nanopore noise is well described by a composite fractional model comprising multiple fractional Gaussian noise and fractional Brownian motion components. This finding is supported by confirmation of Gaussianity, rigorous interpretation of second-order exponents, multifractal analysis, and evidence that transient deviations are attributable to deterministic or experimental artefacts rather than alternative stochastic mechanisms. We further resolve quasi-deterministic structures, such as baseline trends and structural breaks, and demonstrate their separability from the underlying stochastic profile. Collectively, these results provide the first formal statistical validation of a composite fractional model for nanopore noise and establish a principled basis for noise reconstruction, realistic simulation, and statistically grounded algorithm design for nanopore sensing applications. This study provides the foundation for the creation of high-fidelity performance evaluation datasets for signal processing, and the controlled generation and augmentation of data for machine learning while maintaining statistical fidelity to experimental conditions.

A foundational tenet of modern biophysics dictates that protein-solvent interactions and charge-transport dynamics operate strictly within microscopic, sub-nanometer boundaries where long-range coordination is natively suppressed by rapid room-temperature thermal dephasing. Here, we report an unexpected phenomenon that fundamentally challenges this paradigm: the long-distance, quantum-coherent communication between isolated protein samples in aqueous solution across macroscopic spatial separations. By mapping the distance-dependence of a weak, protein-emitted electromagnetic field on the response dynamics of an adjacent complex, we demonstrate that this inter-protein communication establishes a stable, intermolecular vibronic coupling operating across millimeter-scale distances up to at least 40 mm. This field interference induces a robust quantum coherence that lowers the local potential energy surface, transforming the coupled protein-solvent network into an un-attenuated, low-barrier energy transfer conduit. This stabilized pathway launches a topologically protected, non-dispersive soliton that exhibits exceptional phase stability against room-temperature thermal dephasing. These findings provide definitive empirical evidence of a sophisticated, field-driven quantum infrastructure embedded within a biological macromolecule. More explicitly, they reveal that a protein can possess an inherent capacity to preserve coherent wave propagation over macroscopic scales previously deemed impossible in room-temperature aqueous environments.