Physical Review X

Interactions between bacteriophages and motile bacteria can produce irregular spatial patterns. Here we show that these irregularities arise from stochastic infection dynamics at the single-cell level. We develop a discrete, stochastic model of phage-bacteria co-propagation, which represents bacteria and phage numbers as non-negative integers on a two-dimensional lattice, while nutrients and attractants are treated as real-valued fields. Stochastic rules govern bacterial growth, chemotactic movement, infection, and lysis, allowing spatial heterogeneity to emerge in agreement with experimentally observed asymmetric patterns. Simulations reveal that rare events, in which an infected bacterium migrates ahead of the front before lysis, locally seed new infection centers. The resulting front roughness is controlled by the product of burst size and adsorption rate, and is suppressed when the effective population size per lattice site increases or the variability of latent period decreases. These results link microscopic stochasticity to emergent spatial structure in phage-bacteria populations.

Allostery, in which perturbations at an input protein site tune the activity at a distant output site, allows proteins to serve as molecular logic gates. Often, information is transmitted without altering the structure outside of the input and output sites. This focalized allostery requires correlated motion between protein backbone dihedral angles that are separated by distances many times longer than the scale of electrostatic interactions. What physical properties of folded proteins enable such long-distance information sharing despite thermal noise is unclear. To address this question, we introduce a Variable-Well Dihedral (VWD) model Hamiltonian which removes dependence on chemical details and forces, instead only tuning the degree of nonlinearity of purely local interactions within a densely-packed polymer. We show that tuning the physical parameters of the model gives rise to focalized allostery in so far that doing so increases the discreteness of the internal degrees of freedom, with real proteins occupying the highly discrete regime. These results parallel, at the molecular scale, the superiority of digital compared to analog signal processing for telecommuncations under noisy conditions.

Understanding how group-level dynamics arise from individual interactions re- mains a core challenge in collective behavior research. Traditional models assume that animals follow simple behavioral rules, like explicitly aligning with neighbors, yet experimental support for such interactions is often lacking. Here we consider a model grounded in the neurobiological principles underlying animals navigational circuits, particularly the fact that animals encode their headings, and also bearings to objects (e.g., other individuals) in their environment, via a world-centered--allocentric--neural coding. We compare this to an egocentric representation, where bearings are encoded with respect to the arbitrary heading of the animal. An allocentric framework, as op- posed to an egocentric one, is shown to enable effective tracking of dynamically moving targets. Moreover, we demonstrate that when individuals themselves act as sensory inputs to each other, that sophisticated, coherent collective motion can emerge di- rectly from navigational circuits (and thus, may readily evolve in nature), without requiring explicit alignment, or additional rules of interaction.

We leverage the interplay between microscopic variability and macroscopic order to connect physical descriptions across scales directly from data, without underlying equations. We reconstruct a state space by concatenating measurements in time, building a maximum entropy partition of the resulting sequences, and choosing the sequence length to maximize predictive information. Trading non-linear trajectories for linear, ensemble evolution, we analyze reconstructed dynamics through transfer operators. The evolution is parameterized by a transition time{tau} : capturing the source entropy rate at small{tau} and revealing timescale separation with collective, coherent states through the operator spectrum at larger{tau} . Applicable to both deterministic and stochastic systems, we illustrate our approach through the Langevin dynamics of a particle in a double-well potential and the Lorenz system. Applied to the behavior of the nematode worm C. elegans, we derive a "run-and-pirouette" navigation strategy directly from posture dynamics. We demonstrate how sequences simulated from the ensemble evolution capture both fine scale posture dynamics and large scale effective diffusion in the worms centroid trajectories and introduce a top-down, operator-based clustering which reveals subtle subdivisions of the "run" behavior. POPULAR SUMMARYComplex structure is often composed from a limited set of relatively simple building blocks; such as novels from letters or proteins from amino acids. In musical composition, e.g., sounds and silences combine to form longer time scale structures; motifs form passages which in turn form movements. The challenge we address is how to identify collective variables which distinguish structures across such disparate time scales. We introduce a principled framework for learning effective descriptions directly from observations. Just as a musical piece transitions from one movement to the next, the collective dynamics we infer consists of transitions between macroscopic states, like jumps between metastable states in an effective potential landscape. The statistics of these transitions are captured compactly by transfer operators. These operators play a central role, guiding the construction of maximally-predictive short-time states from incomplete measurements and identifying collective modes via eigenvalue decomposition. We demonstrate our analysis in both stochastic and deterministic systems, and with an application to the movement dynamics of an entire organism, unravelling new insight in long time scale behavioral states directly from measurements of posture dynamics. We can, in principle, also make connections to both longer or shorter timescales. Microscopically, postural dynamics result from the fine scale interactions of actin and myosin in the muscles, and from electrical impulses in the brain and nervous system. Macroscopically, behavioral dynamics may be extended to longer time scales, to moods or dispositions, including changes during aging, or over generations due to ecological or evolutionary adaptation. The generality of our approach provides opportunity for insights on long term dynamics within a wide variety of complex systems.

We show that the COVID-19 pandemic under social distancing exhibits universal dynamics. The cumulative numbers of both infections and deaths quickly cross over from exponential growth at early times to a longer period of power law growth, before eventually slowing. In agreement with a recent statistical forecasting model by the IHME, we show that this dynamics is well described by the erf function. Using this functional form, we perform a data collapse across countries and US states with very different population characteristics and social distancing policies, confirming the universal behavior of the COVID-19 outbreak. We show that the predictive power of statistical models is limited until a few days before curves flatten, forecast deaths and infections assuming current policies continue and compare our predictions to the IHME models. We present simulations showing this universal dynamics is consistent with disease transmission on scale-free networks and random networks with non-Markovian transmission dynamics.

Keeping a memory of evolving stimuli is ubiquitous in biology, an example of which is immune memory for evolving pathogens. However, learning and memory storage for dynamic patterns still pose challenges in machine learning. Here, we introduce an analytical energy-based framework to address this problem. By accounting for the tradeoff between utility in keeping a high-affinity memory and the risk in forgetting some of the diverse stimuli, we show that a moderate tolerance for risk enables a repertoire to robustly classify evolving patterns, without much fine-tuning. Our approach offers a general guideline for learning and memory storage in systems interacting with diverse and evolving stimuli.

We propose an embedding of standard active particle models in terms of two-temperature processes. One temperature refers to an ambient thermal bath, and the other temperature effectively describes "hot spots," i.e., systems with few degrees of freedom showing important population homogenization or even inversion of energy levels as a result of activation. As a result, the effective Carnot efficiency would get much higher than for our standard macroscopic thermal engines, making connection with the recent conundrum of hot mitochondria. Moreover, that setup allows to quantitatively specify the resulting nonequilibrium driving, useful in particular for bringing the notion of heat into play, and making easy contact with thermodynamic features. Finally, we observe that the shape transition in the steady low-temperature behavior of run-and-tumble particles (with the interesting emergence of edge states at high persistence) is stable and occurs for all temperature differences, including close-to-equilibrium.

Metabolic scaling, the relationship between energy use and body size, has long been treated as a universal law of life. However, extensive variation in scaling exponents across species challenges this assumption. Here, we show that such scaling can emerge spontaneously from stochastic cellular growth dynamics, without postulating any fixed relationship between mass and metabolism. In our framework, ontogeny is a nonequilibrium thermodynamic process in which energy is continuously dissipated and redistributed among fluctuating cellular states. When applied across diverse life histories, the model reproduces the observed range of metabolic exponents, revealing that scaling diversity arises naturally from fundamental thermodynamic constraints on stochastic, energy-dissipating growth.

Communal roosting in Bechsteins bat colonies is characterized by the formation of several groups that use different day roosts and that regularly dissolve and re-merge (fission-fusion dynamics). Analyzing data from two colonies of different size over many years, we find that (i) the number of days bats stay in the same roost before changing follows an exponential distribution that is independent of the colony size, and (ii) the number and size of groups bats formed for roosting depend on the size of the colony such that above a critical colony size two to six groups of different sizes are formed. To model these two observations, we propose an agent-based model in which agents make their decisions about roosts based on both random and social influences. For the latter, they copy the roost preference of another agent which models the transfer of the respective information. Our model is able to reproduce both the distribution of stay length in the same roost and the emergence of groups of different sizes dependent on the colony size. Moreover, we are able to predict the critical system size at which the formation of different groups emerges without global coordination. We further comment on dynamics that bridge the roosting decisions on short time scale (less than one day) with the social structures observed at long time scales (more than one year).

Metabolic rate scales with body size, however its universality remains debated and unresolved. We show that such universal scaling may arise from information neutrality in stochastic cell dynamics. Using a stochastic ontogenetic growth model of cellular dynamics, we identify an optimal microscopic noise structure where organism level metabolic fluctuations are least sensitive to the underlying microscopic cellular noise and have maximal dependence on organism size. At this point, the macroscopic scaling exponent collapses to a universal value across species size close to Kleibers law. These results reveal a noncritical RG-like behavior, suggesting that universality emerges here from an information-theoretic optimum of stochastic metabolic fluctuations.

We explore current ideas around the representation of a protein as an amorphous material, in turn represented by an abstract graph [G] with edges weighted by elastic stiffnesses. By embedding this graph in physical space, we can map every graph to a spectrum of conformational fluctuations and responses (as a result of say, ligand-binding). This sets up a "genotype-phenotype" map, which we use to evolve the amorphous material to select for fitness. Using this, we study the emergence of allosteric interaction, hinge joint, crack formation and a slide bolt in functional proteins such as Adenylate kinase, HSP90, Calmodulin and GPCR proteins. We find that these emergent features are associated with specific geometries and mode spectra of floppy or liquid-like regions. Our analysis provides insight into understanding the architectural demands on a protein that enable a prescribed function and its stability to mutations.

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 use an established semi-mechanistic Bayesian hierarchical model of the COVID-19 pandemic [1], driven by European mortality data, to estimate the prevalence of immunity. We allow the infection-fatality ratio (IFR) to vary, adapt the models priors to better reflect emerging information, and re-evaluate the model fitting in the light of current mortality data. The results indicate that the IFR of COVID-19 may be an order of magnitude smaller than the current consensus, with the corollary that the virus is more prevalent than currently believed. These results emerge from a simple model and ought to be treated with caution. They emphasise the value of rapid community-scale antibody testing when this becomes available.

The novel coronavirus disease 2019 (COVID-19) has created a serious threat to global health. We developed a new quantum machine learning (QML) assisted diagnostic method that can provide an accurate diagnosis to aid decision processes of medical providers. One of the key elements in our method was to implement the quantum variational method to efficiently classify data, taking crucial multiple correlations among the features into account. We established and fine-tuned this quantum classifier by using a group of data drawn from publicly available COVID-19 cases. We have shown that QML is capable of processing patient information efficiently and accurately for the diagnosis of COVID-19.

Accurately modelling the potential energy landscapes that govern molecular interactions is a central challenge in computational biophysics. While quantum computers promise to solve such problems with high fidelity, a key bottleneck is the encoding of complex spatial information into low-qubit Hamiltonians suitable for near-term devices. Here, we introduce a generalisable framework for creating quantum surrogate models of 2D biophysical landscapes. Our method translates a discrete, classically-derived potential energy grid into a continuous quantum Hamiltonian by fitting it to a high-degree polynomial, where the polynomials coefficients directly define the potential energy operator. We demonstrate this pipeline on a custom-designed landscape featuring two asymmetric potential wells. By systematically varying a kinetic hopping term in the Hamiltonian, our variational quantum eigensolver simulations, averaged over 100 runs, successfully reproduce the physical transition from a localised ground state to a delocalised state governed by tunnelling. The entire framework is made accessible through the Quantome web application, a pedagogical platform that allows users to both design custom landscapes and explore pre-calculated results on EF-hand protein binding sites, which serve as a simplified real-world test bed for this framework. The web app is freely available at: https://biosig.lab.uq.edu.au/quantumlabs/quantome.

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.

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.

Infectious diseases can cause large disease outbreaks due to their transmission potential from one individual to the next. Vaccination is an effective way of cutting off possible chains of transmission, thereby mitigating the outbreak potential of a disease in a population. From a contact network perspective, vaccination effectively removes nodes from the network, thereby breaking apart the contact network into a much smaller network of susceptible individuals on which the disease can spread. Here, we look at the continuum of small world networks to random networks, and find that vaccination breaks apart networks in ways that can dramatically influence the maximum outbreak size. In particular, after the removal of a constant number of nodes (representing vaccination coverage), the more clustered small world networks more readily fall apart into many disjoint and small susceptible sub-networks, thus preventing large outbreaks, while more random networks remain largely connected even after node removal through vaccination. We further develop a model of social mixing that moves small world networks closer to the random regime, thereby facilitating larger disease outbreaks after vaccination. Our results show that even when vaccination is entirely random, social mixing can lead to contact network structures that strongly influence outbreak sizes. We find the largest effects to be in the regime of relatively high vaccination coverages of around 80%, where despite vaccination being random, outbreak sizes can vary by a factor of 20.

Individual bacterial cells grow and divide stochastically. Yet they maintain their characteristic sizes across generations within a tightly controlled range. What rules ensure intergenerational stochastic homeostasis of individual cell sizes? Valuable clues have emerged from high-precision longterm tracking of individual statistically-identical Caulobacter crescentus cells as reported in [1, 2]: Intergenerational cell size homeostasis is an inherently stochastic phenomenon, follows Markovian or memory-free dynamics, and cells obey an intergenerational scaling law, which governs the stochastic map characterizing generational sequences of cell sizes. These observed emergent simplicities serve as essential building blocks of the data-informed principled theoretical framework we develop here. Our exact analytic fitting-parameter-free results for the predicted intergenerational stochastic map governing the precision kinematics of cell size homeostasis are remarkably well borne out by experimental data, including extant published data on other microorganisms, Escherichia coli and Bacillus subtilis. Furthermore, our framework naturally yields the general exact and analytic condition that is necessary and sufficient to ensure that stochastic homeostasis can be achieved and maintained. Significantly, this condition is more stringent than the known heuristic result from quasi-deterministic frameworks. In turn the fully stochastic treatment we present here extends and updates extant frameworks, and highlights the inherently stochastic behaviors of individual cells in homeostasis.

Bacteria and cancer cells inhabit spatially heterogeneous environments, where migration shapes microhabitat structures critical for colonization and metastasis. The interplay between growth, migration, and spatial structure complicates the prediction of population responses to drug treatment--such as clearance or persistence--even under the same spatially averaged growth rate. Accurately predicting these responses is essential for designing effective treatment strategies. Here, we propose a minimal growth-migration model to study population dynamics on discrete microhabitat structures under spatial drug heterogeneity. By applying a kernel transformation, we map the original structure to an effective fully connected graph and derive a new exact criterion for population response based on a regularized Laplacian kernel reweighted by local growth rates. This criterion connects to forest closeness centrality and yields analytical bounds and sufficient conditions for population growth or decline. We find that higher structural connectivity--like increased migration--generally promotes decline. Our framework also informs optimal spatial drug assignments, which reduce to selecting interconnected subcores in the effective complete graph. For partially controllable microhabitats or unknown drug distributions, we identify strategies that ensure population decline. Overall, our results offer a new theoretical perspective on drug response in spatially structured populations and provide practical guidance for optimizing spatially explicit dosing strategies in heterogeneous environments.