Physical Review X

Accurate propagation of sequence information in nucleic acids is central to the evolutionary dynamics of self-replicating systems. Modern biological systems achieve high fidelity using enzymes that actively correct errors through energy-driven mechanisms. However, such complex machinery was absent under prebiotic conditions. Here, we present a theoretical model of error correction in self-replicating heteropolymers that requires neither enzymes nor an extraneous energy supply. The model relies solely on the free-energy gradient driving strand growth and requires asymmetric cooperativity -- a kinetic asymmetry known to promote unidirectional elongation. Despite its simplicity, we demonstrate that this minimal model facilitates kinetic discrimination between correct and incorrect base pair incorporations, and for specific set of parameters, reproduces the error ratio of [~] 10-4, experimentally observed in passive base selection processes. It replicates key features observed in DNA error correction, including stalling, fraying, next-nucleotide effects, and the speed-accuracy trade-off. Our results provide plausible answers for longstanding questions, such as the energy source for the enhanced base selectivity of passive DNA polymerases and the role of thermodynamics and kinetics of phosphodiester bond formation in error correction. We show that catalysis of the phosphodiester bond plays a central role in error correction, even without explicit enzymatic structural discrimination. This observation points to a plausible pathway for accurate oligomer synthesis under prebiotic conditions, driven solely by the thermodynamic gradient favoring strand elongation. More broadly, the model highlights how persistent molecular order can emerge from non-equilibrium dynamics - a central requirement for emergence of life.

Understanding if pairwise interactions explain the species composition of communities is a central goal in ecology. This question has been challenged by the observation of emergent coexistence, where microbial communities contain species that cannot coexist in pairs, suggesting the presence of non-pairwise mechanisms. Instead, we show that emergent coexistence arises naturally in species-rich models with pairwise interactions. Strikingly, this phenomenon does not require additional mechanisms like intransitive or higher-order interactions; rather, coexistence arises from dense networks of indirect effects. As diversity increases, we show that indirect effects become so intricate that pairwise interactions no longer predict community composition, revealing a fundamental limit to reductionist explanations of coexistence. Like chaos emerging from simple rules, our findings provide theoretical foundations to understand how unexpected species coexistence can emerge from pairwise interactions.

Our ability to predict the properties of a system typically diminishes as the number of its interacting constituents rises. This poses major challenges for understanding natural ecosystems, and humanitys effects on them. How do macroecological patterns emerge from the interplay between species and their environment? What is the impact on complex ecological systems of human interventions, such as extermination of large predators, deforestation, and climate change? The resolution of such questions is hampered in part by the lack of a holistic approach that unifies ecology across temporal and spatial scales. Here we use density functional theory, a computational method for many-body problems in physics, to develop a novel computational framework for ecosystem modelling. Our methods accurately fit experimental and synthetic data of interacting multi-species communities across spatial scales and can project to unseen data. Our mechanistic framework provides a promising new avenue for understanding how ecosystems operate and facilitates quantitative assessment of interventions.

During embryogenesis, as cells proliferate and assemble into tissues, they undergo a sequence of transitions between distinct molecular states eventually giving rise to a cellular population consisting of an appropriate distribution of specific functional cell types. Recent progress on the dynamics underlying decision-making in developmental landscape makes it feasible to start analysing the amount of information involved in constructing such systems. To explore this we introduce the notion of potency of a developmental landscape and attempt to calculate it for two development systems of current interest, in-vitro differentiation of epiblast-like cells into neural and mesodermal progenitors and the worm vulva patterning system. Our approach integrates concepts from developmental biology, information theory and dynamical systems to estimate both the number and identity of signalling regimes that give rise to distinguishable temporal response patterns.

A recurring lesson from random ecological models is that coexistence is hard to come by: in the Generalized Lotka-Volterra (GLV) model with pairwise interactions, the probability that randomly sampled parameters admit a positive (feasible) equilibrium - a necessary condition for coexistence - is exactly 1/2n in n species, vanishing rapidly with diversity. This rarity is often read as evidence that coexistence demands specific ecological mechanisms. Real interactions, however, are rarely strictly pairwise: any nonlinear dependence of one species growth rate on anothers abundance, Taylor-expanded, generates higher-order interactions (HOIs) of increasing degree. Treating the interaction order d as a knob that indexes this nonlinearity, we map the random GLV with HOIs onto the Kostlan-Shub-Smale class of random polynomial systems and approximate the probability of feasibility (Pf ) analytically. We find a phase transition at d = 4: below this threshold, Pf decays with diversity as in the pairwise case; above it, the exponential proliferation of equilibria outpaces the probability that any given equilibrium is feasible, and the probability of feasibility increases with n, approaching one. The transition appears to be universal across symmetric coefficient distributions, but vanishes when sign symmetry of the parameter distribution is broken. This work uncovers a route by which feasibility emerges from nonlinearity alone, with no fine-tuning of parameters and no appeal to specific ecological mechanisms.

Understanding how genetic networks can drive different self-organizing spatial behaviors remains a significant challenge. Here, we use an automated algebraic method to systematically screen for Turing networks capable of generating diverse spatial patterns from noise, including periodic static waves, traveling waves and noise-amplifying patterns. We organize these networks into a topological atlas--a higher-level graph where nodes represent Turing networks linked together when they differ by only one regulatory interaction. In this atlas, Turing networks are arranged into distinct clusters showing a remarkable correspondence between network topology and self-organizing behaviors. Using an analytical approach, we identify the specific regulatory feedbacks that characterize each behavior. Moreover, we discover that different clusters are interconnected by multifunctional networks that can transition between behaviors upon feedback modulation. Among these networks, we find a new class of multiphase Turing networks capable of altering the phase of periodic wave patterns depending on the parameters, and networks that can transition between static and oscillatory Turing behaviors. The atlas further highlights the crucial role of feedback on immobile nodes in regulating pattern formation speed and precision by canalizing system noise. Overall, our study provides a novel framework to study the evolution and development of multicellular self-organization through changes in network topology and feedback modulation. This offers insights into how genetic regulatory networks can be tuned to drive pattern formation in developmental biology and in stem cell systems like embryoids and organoids. Significance StatementBy employing an automated algebraic method, Regueria and Marcon construct a topological atlas that categorizes Turing networks based on their ability to produce periodic patterns, traveling waves, or noise amplifying patterns. The atlas identifies distinct topological clusters linked by multi-functional networks that can transition between behaviors through feedback modulation. Key findings highlight how modulation of regulatory cycle strength in time or space can promote transition between static and oscillatory periodic pattern. The study also reveals the importance of feedback on immobile nodes in managing noise and influencing pattern formation. Overall the topological atlas offers a new framework for examining the evolution and development of multicellular self-organization.

Species interactions--ranging from direct predator-prey relationships to indirect effects mediated by the environment--are central to ecosystem balance and biodiversity. While empirical methods for measuring these interactions exist, their interpretability and limitations remain unclear. Here we examine the empirical matrix of pairwise interactions, a widely used tool, and analyze its temporal variability. We show that apparent fluctuations in interaction strength--and even shifts in interaction signs, often interpreted as transitions between competition and facilitation--can arise intrinsically from population dynamics with fixed ecological roles. Experimental protocols further shape these estimates: the duration of observation and the type of setup in microbial growth studies (e.g., chemostats, batch cultures, or resource conditions) systematically affect measured interactions. Considering interactions across timescales enhances interpretability: short-term measurements primarily capture direct species couplings, whereas long-term observations increasingly reflect indirect community feedback. Taken together, these results establish short-duration inferences, obtained either directly or extrapolated, as a principled way to disentangle direct from indirect interactions. Building on this insight, we propose a model-inference approach that leverages multiple short time series rather than extended longitudinal datasets.

Multiple ecological forces act together to shape the composition of microbial communities. Phyloecology approaches --which combine phylogenetic relationships with community ecology-- have the potential to disentangle such forces, but are often hard to connect with quantitative predictions from theoretical models. On the other hand, macroecology, which focuses on statistical patterns of abundance and diversity, provides natural connections with theoretical models but often neglects inter-speficic correlations and interactions. Here, we propose a unified framework combining both such approaches to analyze microbial communities. In particular, by using both cross-sectional and longitudinal metagenomic data for species abundances, we reveal the existence of a novel empirical macroecological law establishing that correlations in species-abundance fluctuations across communities decay from positive to null values as a function of phylogenetic similarity in a consistent manner across ecologically distinct microbiomes. We formulate three mechanistic models --relying on alternative ecological forces-- that lead to radically different predictions. We conclude that the empirically observed macroecological pattern can be quantitatively explained as a result of shared fluctuating resources, i.e. environmental filtering and not e.g. as a consequence of species competition. Finally, we also show that the macroecological law is also valid for temporal data of a single community, and that the properties of delayed temporal correlations are reproduced by the model with environmental filtering.

Recent work suggests that cross-feeding - the secretion and consumption of metabolic biproducts by microbes - is essential for understanding microbial ecology. Yet how cross-feeding and competition combine to give rise to ecosystem-level properties remains poorly understood. To address this question, we analytically analyze the Microbial Consumer Resource Model (MiCRM), a prominent ecological model commonly used to study microbial communities. Our mean-field solution exploits the fact that unlike replicas, the cavity method does not require the existence of a Lyapunov function. We use our solution to derive new species-packing bounds for diverse ecosystems in the presence of cross-feeding, as well as simple expressions for species richness and the abundance of secreted resources as a function of cross-feeding (metabolic leakage) and competition. Our results show how a complex interplay between competition for resources and cooperation resulting from metabolic exchange combine to shape the properties of microbial ecosystems.

Epidemics generally spread through a succession of waves that reflect factors on multiple time-scales. On short time-scales, superspreading events lead to burstiness and overdispersion, while long-term persistent heterogeneity in susceptibility is expected to lead to a reduction in the infection peak and the herd immunity threshold (HIT). Here, we develop a general approach to encompass both time-scales, including time variations in individual social activity, and demonstrate how to incorporate them phenomenologically into a wide class of epidemiological models through parameterization. We derive a non-linear dependence of the effective reproduction number Re on the susceptible population fraction S. We show that a state of transient collective immunity (TCI) emerges well below the HIT during early, high-paced stages of the epidemic. However, this is a fragile state that wanes over time due to changing levels of social activity, and so the infection peak is not an indication of herd immunity: subsequent waves can and will emerge due to behavioral changes in the population, driven (e.g.) by seasonal factors. Transient and long-term levels of heterogeneity are estimated by using empirical data from the COVID-19 epidemic as well as from real-life face-to-face contact networks. These results suggest that the hardest-hit areas, such as NYC, have achieved TCI following the first wave of the epidemic, but likely remain below the long-term HIT. Thus, in contrast to some previous claims, these reqions can still experience subsequent waves. O_TEXTBOXSignificance Statement Epidemics generally spread through a succession of waves that reflect factors on multiple time-scales. Here, we develop a general approach to encompass super-spreading and population heterogeneity, and demonstrate that a fragile state of transient collective immunity (TCI) emerges well below the HIT during early, high-paced stages of the epidemic. However, this is not an indication of herd immunity: subsequent waves can and will emerge due to behavioral changes in the population, driven (e.g.) by seasonal factors. Analysis of empirical data suggests that even in locations with strong first waves of COVID-19, subsequent waves will still emerge. C_TEXTBOX

To maintain and regenerate adult tissues after injury, the numbers, proliferation, and differentiation rates of tissue-resident stem cells must be precisely regulated. The regulatory strategies preventing exhaustion or overgrowth of the stem cell pool, whether there is coordination between different mechanisms, and how to detect them from snapshots of the cell populations, remains un-resolved. Recent findings in the Drosophila testes show that prior to differentiation, somatic stem cells transition to a state that licenses them to differentiate upon receiving a commitment signal, but remain capable of fully regaining stem cell function. Here, we build stochastic mathematical models for the somatic stem cell population to investigate how licensing contributes to homeostasis and the variability of stem cell numbers. We find that licensing alone is sufficient regulation to maintain a stable homeostatic state and prevent stem cell extinction. Comparison with previous experimental data argues for the likely presence of regulation through competition for niche access. We show that competition for niche access contributes to the reduction of the variability of stem cell numbers but does not prevent extinction. Our results suggest that a combination of both regulation strategies, licensing and competition for niche access, is needed to reduce variability and prevent extinction simultaneously.

Bacteria have evolved many defenses against invading viruses (phage). Typically, each bacterium carries several defense systems, while each phage may carry multiple counter-defense systems. Despite the many bacterial defenses and phage counter-defenses, in most environments, bacteria and phage coexist, with neither driving the other to extinction. How is coexistence realized in the context of the bacteria/phage arms race, and how are the sizes of the bacterial immune and phage counter-immune repertoires determined in conditions of coexistence? Here we develop a simple mathematical model to consider the evolutionary and ecological dynamics of competing bacteria and phage with different immune/counter-immune repertoires. An analysis of our model reveals an ecologically stable fixed point exhibiting coexistence. This fixed point agrees with the experimental observation that each individual bacterium typically carries multiple defense systems, though fewer than the maximum number possible. However, in simulations, the populations typically remain dynamic, exhibiting chaotic fluctuations around this fixed point. We obtain quantitative predictions for the mean, amplitude, and timescale of these dynamics. Our results provide a framework for understanding the evolutionary and ecological dynamics of the bacteria/phage arms race, and demonstrate how bacteria/phage coexistence can stably arise from the coevolution of bacterial defense systems and phage counter-defense systems.

Patients infected with life-threatening multi-drug resistant (MDR) bacteria have been treated with cocktails of bacteriophages. This is a complicated form of personalized medicine as the phages given to a patient have to be selected beforehand on the basis of their lytic capacity of the infecting bacteria. Because bacteria rapidly become resistant, the evolution of resistance to a diverse cocktail of phages is a complicated dynamical process, during which competing bacterial strains replace one another by accumulating several resistance mechanisms, each of which may involve a fitness cost. As a consequence, it is typically not known why a particular phage therapy succeeded or failed, and how one can optimize the composition of the cocktails to maximize the rate of success. To improve upon this, we extend an existing in vivo-calibrated mouse model into a novel mathematical model for the human situation, and include multiple phages infecting multiple bacterial strains, differing in their resistance to each of the phages. We adjust several parameter estimates of the bacterial model to the human situation, and use the model to describe a successful case of phage therapy involving several cocktails, each containing several phages. In the model, treatment success crucially depended on pretreatment resistance levels, and on the diversity and the timing of the cocktails. Once an appropriate cocktail is found, it is less important to further optimize the infection rates of the phages. Resistant bacterial strains expand rapidly when sensitive strains decline, and the higher the infectivity of the phages, the faster resistant strains expand. Because resistance evolves rapidly, it is best to provide a diverse set of phages right from the start of therapy, i.e., to hit hard and early, and create a high genetic barrier to bacterial resistance.

The effective reproduction number R is a predominant statistic for tracking the transmissibility of infectious diseases and informing public health policies. An estimated R=1 is universally interpreted as indicating epidemic stability and is a critical threshold for deciding whether infections will grow (R>1) or fall (R<1). We demonstrate that this threshold, which is typically computed over coarse spatial scales, seldom signifies stability because those scales frequently average stochastic infections from groups with heterogeneous transmission characteristics. Groups with falling and rising infections counteract and early-warning signals from resurging groups are obscured by noisy fluctuations from stable groups with larger infections. We prove that an estimated R=1 is consistent with a vast space of epidemiologically diverse scenarios, often leading to false-positive stability signals that diminish its predictive and policymaking value. In contrast, we show that a popular, alternative definition of transmissibility, relating to the next-generation matrix of the groups, overcorrects for this issue and yields false-negative stability signals by maximising sensitivity to stochasticity. We find a recently developed statistic, E, derived from R using experimental design theory, rigorously constrains the space of scenarios corresponding to stability, while limiting noise sensitivity. We establish that E=1 is a more practical and meaningful stability threshold.

Small molecule modifiers whence bound, allosterically, will alter the binding of a macromolecule to one- or more-cognate substrates/partners via conformational and non-conformational changes. Although allostery is inferred directly from empirical data, the mathematical basis of these models, constraints deployed and choice of parameter(s) are not clear. Here, we present and characterize a discrete-to-continuous mathematical model for ensemble distributions of a ligand-interacting macromolecular species across milieux-dependent conformational states and examine its role in the genesis and progression of cooperative binding. The premise, of our model, is a set of occupancy matrices (sparse, binary, strictly delocalized) which can be partitioned by a probability-based hyperparameter into mutually exclusive proper subsets of occupancy matrices with identical multinomial probabilities. Since each subset is canonical with a constituent occupancy matrix, it is characterized by a unique multinomial probability. The inner product of combinatorial pairs of all mutually exclusive subsets of occupancy matrices, with an expression for the summed transitional probabilities (finite differences between unique multinomial probabilities), is the differentiable matrix of strictly positive real-valued numbers for the system of ensemble distributions. Whilst the harmonic mean is presented as a generic solution for a system of ensemble distributions, the row-wise definite integral for each column is the finite union of open intervals (contiguous, strictly monotone) which in tandem with a set of interval-specific and bounded transitional probabilities constitutes a piecewise smooth curve (path-connected-, closed- and compact-set). Our discrete-to-continuous model is phenomenological and able to recapitulate the basic tenets of cooperative binding whilst offering insights into the genesis and progression of the same.

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.

Antagonistic interactions are critical determinants of microbial community stability and composition, offering host benefits such as pathogen protection and providing avenues for antimicrobial control. While the ability to eliminate competitors confers an advantage to antagonistic microbes, it often incurs a fitness cost. Consequently, many microbes only produce toxins or engage in antagonistic behavior in response to specific cues like quorum sensing molecules or environmental stress. In laboratory settings, antagonistic microbes typically dominate over sensitive ones, raising the question of why both antagonistic and non-antagonistic microbes are found in natural environments and host microbiomes. Here, using both theoretical models and experiments with killer strains of Saccharomyces cerevisiae, we show that boom-and-bust dynamics caused by temporal environmental fluctuations can favor non-antagonistic microbes that do not incur the growth rate cost of toxin production. Additionally, using control theory, we derive bounds on the competitive performance and identify optimal regulatory toxin-production strategies in various boom- and-bust environments where population dilutions occur either deterministically or stochastically over time. Our findings offer a new perspective on how both antagonistic and non-antagonistic microbes can thrive under varying environmental conditions.

Tumor growth occurs within a complex tumor microenvironment (TME) composed of many interacting cell types. The immune cell types in TME tend to organize into two functional communities: a pro-tumor team and an anti-tumor team, each internally cooperative but mutually antagonistic forming a two-team ecosystem. Quantitatively predicting the ecological outcomes of such interactions remains challenging due to cellular diversity and interaction variability, and the exact dynamical regimes accessible to such a two-team ecosystem remain unknown. Here, we model tumor-immune interactions as a structured ecosystem with two competing teams using a generalized Lotka-Volterra framework and analyze it using the cavity method. We derive phase diagrams that delineate when these two communities coexist, when one dominates, and how these outcomes depend on intra-team cooperation, cross-team inhibition, and ecological heterogeneity. Our work provides a foundation for understanding tumor-immune dynamics from a community ecology perspective.

Bacteria evolving in natural and clinical settings experience spatial fluctuations of multiple factors and this heterogeneity is expected to affect bacterial adaptation. Notably, spatial heterogeneity in antibiotic concentrations is believed to accelerate the evolution of antibiotic resistance. However, current literature overlooks the role of cell motility, which is key for bacterial survival and reproduction. Here, we consider a quantitative model for bacterial evolution in antibiotic gradients, where bacteria evolve under the stochastic processes of proliferation, death, mutation and migration. Numerical and analytical results show that cell motility has major effects on bacterial adaptation. If migration is relatively rare, it accelerates adaptation because resistant mutants can colonize neighbouring patches of increasing antibiotic concentration avoiding competition with wild-type cells; but if migration is common throughout the lifespan of bacteria, it decelerates adaptation by promoting genotypic mixing and ecological competition. If migration is sufficiently high, it can limit bacterial survival, and we derive conditions for such a regime. Similar patterns are observed in more complex scenarios, namely where bacteria can bias their motion or switch between motility phenotypes either stochastically or in a density-dependent manner. Overall, our work reveals limits to bacterial adaptation in antibiotic landscapes that are set by cell motility.

Species-rich ecosystems often exhibit multiple stable states with distinct species compositions. Yet, the factors determining the likelihood of each states occurrence remain poorly understood. Here, we characterize and explain the landscape of stable states in the random Generalized Lotka-Volterra (GLV) model, in which multistability is widespread. We find that the same pool of species with random initial abundances can result in different stable states, whose likelihoods typically differ by orders of magnitude. A states likelihood increases sharply with its total biomass, or inverse self-inhibition. We develop a simplified model to predict and explain this behavior, by coarse-graining ecological interactions so that each stable state behaves as a unit. In this setting, we can accurately predict the entire landscape of stable states using only two macroscopic properties: the biomass of each state and species diversity. Our theory also provides insight into the biomass-likelihood relationship: High-biomass states have low self-inhibition and thus grow faster, outcompete others, and become much more likely. These results reveal emergent self-inhibition as a fundamental organizing principle for the attractor landscape of complex ecosystems--and provide a path to predict ecosystem outcomes without knowing microscopic interactions.