Physica A: Statistical Mechanics and its Applications

Habitat destruction leads to a severe decline in biodiversity. Ascertaining effects of habitat loss afterwards is regularly done, whereas predicting the effects of different habitat loss scenarios on biodiversity beforehand is much preferred but as of yet rarely possible. Such predictions would help inform management decisions to prevent biodiversity loss in the first place, or at least mitigate effects if necessary, by providing handles to set priorities in making trade-offs. To this end, we developed and applied an adapted version of the information-theoretical framework of Maximum Entropy Theory in Ecology (METE) to predict species-area relationships in tropical forest landscapes undergoing habitat loss and fragmentation. Species-area relationships provide information about biodiversity and can, in undisturbed systems, be predicted using METE, based on state variables such as the total number of individuals, the total number of species, and the total area size. In disturbed systems, however, it is established that METEs predictions are off. Using an individual-based model, we explore how METEs state variables should be adjusted, based on the landscape characteristics habitat cover and degree of habitat fragmentation, to restore its accuracy of species-area relationship predictions in disturbed environments. We validate our adjusted METE predictions with empirical data. Our adjusted METE predictions demonstrate the severity of fragmentations impact on biodiversity, relative to what could be expected in a pristine, continuous environment. With this new method, we can estimate the immediate effects of habitat loss on biodiversity, as well as its long-term effects.

Biological populations have been evolving in multi-dimensional trait spaces. Ecological interactions can induce the evolutionary diversification of a biological population into distinct multiple populations, which is called evolutionary branching in adaptive dynamics theory. If possible mutations are restricted to certain directions due to developmental, physiological, or physical constraints, the resulting evolutionary dynamics may be restricted to subspaces with fewer dimensions than the original trait spaces. In general, such constraints are also evolving slowly, due to rare and slight mutational deviations from the constraint subspaces. In this sense, constraints are not strict. However, the method for describing non-strict constraints that is globally consistent has yet to be developed. This study proposes a general and flexible method for constructing a non-strict constraint subspace from the corresponding strict constraint subspace. This method enables efficient analysis of adaptive evolution including evolutionary branching under non-strict constraints in the framework of adaptive dynamics theory. Applying this method to a resource competition model shows that the shape of the carrying capacity distribution can be treated as a non-strict constraint curve, and that the likelihood of evolutionary branching is affected not only by the shape of the constraint curve but also by its slow evolution.

In many natural dynamical systems, tipping points emerge where slowly changing external factors induce shifts from one state to another, known as critical transitions or bifurcations. In epidemic systems, detecting these transitions is important for outbreak preparedness. Various statistical indicators like lag-1 autocorrelation and variance have been employed as early warning signals (EWS) of critical transitions by showing how the dynamics of the system exhibit critical slowing down (CSD) near the transition. More recently, deep learning-based algorithms have been developed that attempt to more accurately detect and classify bifurcations; however, they are limited by the systems simulated in the training dataset, the length of the time series, and have not been rigorously evaluated on real-world epidemic data spanning multiple geographic regions. In this paper, we evaluate existing deep learning-based bifurcation prediction models, on a CDC-curated dataset containing weekly influenza hospital admissions across all fifty U.S. states and the nation as a whole. We develop a pipeline for data preparation, reproduction number (Rt) estimation using the EpyEstim package (a Python implementation of the EpiEstim framework [4]), and bifurcation point identification. We systematically evaluate the models under several windowing strategies, including rolling, expanding, and fixed-length windows, and report accuracy, precision, recall, F1 score, and specificity. Our best-performing configuration (expanding window, length 100) achieves an accuracy of 90.09%, precision of 72.86%, recall of 96.23%, and F1 score of 82.93%. We additionally discuss Markov Regime Switching models as an alternative framework for detecting epidemic transitions. Our findings indicate that these models can generalize to real-world, state-level influenza data and are capable of online/real-time prediction.

Buruli ulcer (BU) is a neglected tropical skin disease caused by infection with Mycobacterium ulcerans. The mode of its transmission into the skin has not been fully clarified, but it is believed to involve mechanical transfer, perhaps by insect bites. M. ulcerans secretes a toxin called mycolactone which causes necrosis of the skin and formation of large skin lesions. Understanding the development of these skin lesions over time is crucial to understand the pathogenesis of BU. We formulate a mathematical model to describe the space-time dynamics of M. ulcerans bacteria, mycolactone and skin cell densities as well as fibrin deposition. We investigate the relative contributions to ulcer formation of direct cytotoxicity of mycolactone and ischaemia following the loss of coagulation control. Our results are consistent with existing biological evidence that higher mycolactone concentrations accelerate cell death. Furthermore, the model indicates that the rate of wound expansion is primarily controlled by the diffusion and net birth rate of bacteria, which sets the overall scaling for the speed of wound expansion, along with two dimensionless constants that define the shape of the trajectory of wound edge position against time, namely the ratio of the mycolactone diffusion coefficient to the bacterial diffusion coefficient, and the ratio of the mycolactone degradation rate to the bacterial net birth rate. When mycolactone diffuses significantly faster than bacteria spread or when mycolactone degrades more slowly than bacteria reproduce, the initial development of the wound is faster. In contrast, the long-term wound expansion speed appears to be relatively unchanged across a wide range of the dimensionless parameters.

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.

In this study, we develop a mathematical model of the hypothalamic pituitary adrenal (HPA) axis and systematically investigate the model complexity required to reproduce observed hormone dynamics. The model is fitted to ACTH and cortisol measurements from five healthy volunteers reported in the literature. We show that simultaneous reproduction of both hormone profiles requires a delay differential equation model with at least five state variables among the model architectures considered. Following fitting the volunteer data, we investigate the response of the model to sustained stress using bifurcation analysis. The coupled system exhibits bifurcations over a range of stress intensities. This analysis reveals bifurcations whose critical stress thresholds depend strongly on the modulatory state of the system. These results provide a mathematical framework for investigating transitions between physiological and dysregulated HPA axis dynamics, which may be related to states of health and disease.

It is important to determine whether native state dynamics drive the misfolding and oligomerization of the prion protein, which are important events in prion disease, and how they are modulated by conformational conversion. Native (N) mouse prion protein (moPrP) is known to form small (OS) and large (OL) oligomers rich in {beta}-sheet, and in this study, photoinduced electron transfer-fluorescence correlation spectroscopy (PET-FCS) has been used to characterize intramolecular dynamics within individual monomeric units in both isolated OS and OL, as well as the diffusion properties of the oligomers. It is estimated that OS and OL comprise of about 15 and 55 monomeric units, respectively. Microsecond dynamics at each of the two regions that are the 1-3 and 2-3 interfaces of native protein are distinct in N, OS and OL, although they occur on very similar timescales. Analysis of the evolution of the distribution of diffusion times, determined using the maximum entropy method, indicates heterogeneity in the oligomerization reaction. Analysis of the change in the fluctuations which occur in two different timescales in the native state ensemble shows that they are damped more at the erstwhile 1-3 interface than the erstwhile 2-3 interface. The difference in the extent of damping at the erstwhile 1-3 and 2-3 interfaces can be explained on the basis of the structural changes known to occur across each region. The changes in dynamics occur concurrently in both regions, indicating that the structural changes accompanying conformational conversion also occur simultaneously during the oligomerization of moPrP.

Phase separating biopolymers are often described by the sticker-spacer model, which accounts for non-attractive linkers that connect discrete attractive moieties. "Associative polymer" theories describe these systems as two coexisting fluids of stickers and spacers, respectively. In such theories the stickers and spacers are decoupled in the sense that sticker binding does not affect spacer conformations or vice versa. Informed by coarse-grained simulations, we develop a phenomenological mean-field theory to determine the microscopic coupling between the sticker and spacer degrees of freedom. Accounting for linkers connecting adjacent spacers introduces free energy contributions due to conformational entropy of the spacer and the binding combinatorics of the stickers. These contributions have opposite dependencies on spacer length because longer spacers allow a greater volume to search for binding partners but incur a greater entropy cost upon bond formation. The length dependent terms from these contributions cancel leaving a length-independent elastic term arising from the fact that a small amount of spacer stretching lowers the free energy by increasing the number of possible binding partners. The cancellation of spacer length from the theory justifies the decoupling approximation and supports mean-field treatments of heterogeneous spacers.

Protein evolution requires sequence changes to alter molecular properties without disrupting the dynamic organization necessary for function. How residue-level networks of correlated motions accommodate such mutations remains poorly understood. Here, we investigate the evolution of correlated conformational dynamics in nonstructural protein 1 (NS1) variants of influenza A viruses that emerged between 1918 and 2004. From molecular dynamics (MD) simulations we built residue networks in which edge weights reflect generalized correlations of conformational motion. The network of correlated dynamics is characterized using centrality analysis. Overall network properties are well-conserved across NS1 variants, indicating evolutionary robustness of the dynamical network. Residues ranked highly across multiple centrality measures form a predominantly hydrophobic cluster in the protein core. These residues exhibited low conformational entropy and high sequence conservation, consistent with rigid, coordinated motions. In contrast, residues exhibiting large differences in betweenness and closeness centrality ranks occupied flexible, solvent-exposed regions surrounding the core network. These residues also showed lower evolutionary conservation. These findings reveal a core-periphery structure in which a rigid hydrophobic network enables long-range dynamic connectivity while more adaptable peripheral regions accommodate evolutionary sequence variation. This architecture provides a mechanistic framework for long-range epistatic interactions without compromising the underlying structural framework.

Forecasting and causal inference in complex, non-linear dynamical systems are fundamentally challenging due to noisy and high-dimensional time-series data. While Empirical Dynamic Modeling addresses this via state-space reconstruction in Euclidean space, it suffers from the "curse of dimensionality," distorting distance measurements as dimensions increase. This study proposes Forest-Weighted S-map (FORWS) and Forest-Weighted Causal Inference (FORWC), utilizing adaptive "forest weights" derived from random forest ensembles instead of Euclidean metrics. Using simulated and empirical ecological datasets, I demonstrate that these methods exhibit comparable or improved forecasting skill relative to conventional tools, while offering substantial resilience against dynamic process noise and mitigating the curse of dimensionality. Notably, FORWC enables multimodal causal inference, successfully extracting directed interactions between high-dimensional acoustic vectors and scalar temperature data monitored in a honeybee hive. By bridging chaotic physics with machine learning, this framework accurately extracts intrinsic manifold topology, providing a robust paradigm for uncovering causal networks in complex real-world environments.

We investigate the dynamics of the spread of the infection due to a phage- during the range expansion of an E coli colony. We find a rich panoply of spatio-temporal dynamics at large colony-level length scales, arising due to the interplay of mechanical forces, growth and viral infection dynamics at smaller cellular length scales. Strikingly, the phages "surf" the front of the growing bacterial colony by hitchhiking on E coli that are advected due to the growth of bacteria in the colony, resulting in an anisotropic spread of the phages. We identify microscopic processes - of the phage release during lysis (occurring on short millisecond timescales at length scales close to that of a single bacterium) and local nematic alignment of the rod-like E coli bacteria (occurring on timescales comparable to the bacterial growth rate and the length scales of a few bacterial cells) - that enhance the advective effects driving the hitchhiking behavior. Combining our experiments with a mathematical model, we explain the multiple spatio-temporal dynamical regimes - from the coexistence of uninfected bacteria, resistant (lysogenic) cells and phages, to fixed points where the entire population turns resistant or remains uninfected. Our work broaches a new frontier in the investigation of eco-evolutionary processes arising from the mechanical and ecological forces due to the interactions between viruses and their hosts.

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.

Species at the highest trophic levels are generally the least resilient to perturbations, yet the factors that determine their persistence remain poorly understood. We ask how the intrinsic self-regulation of a basal host governs the persistence of the trophic levels above it. To address this question, we use a minimal discrete-time model of a host-parasitoid-hyperparasitoid system motivated by the biology of trigonalid wasps, obligate hyperparasitoids that complete development only when their caterpillar host is also attacked by a primary parasitoid. We compare two forms of host self-regulation in the absence of natural enemies: scramble (Ricker) fecundity, appropriate when the parasitoid is the host's principal enemy and which recovers the classical model of Beddington and Hammond as a special case; and contest (Beverton-Holt) fecundity, appropriate when the host is held in check by many additional enemies. Using numerical continuation, Lyapunov exponents, and direct computation of the model's trajectories, we find that the form of host regulation is decisive for persistence at the top trophic level. Under scramble host dynamics, coexistence is extremely fragile with respect to both parameter values and initial conditions. Under contest host dynamics, coexistence is robust across broad parameter ranges and loses stability only gradually, through a supercritical Neimark--Sacker bifurcation and a subsequent torus-doubling route to chaos. Therefore, in at least some trophic networks, the resilience of the highest levels can be determined at the base of the network.

Regular environmental cycles such as day and night or the lunar cycle are ubiquitous and drive many biological processes. Many organisms have evolved endogenous time-keeping mechanisms to anticipate these cycles to accurately time their behavior or synchronize physiological processes. The evolution of such synchronization to environmental cycles and their variability is not very well understood. As an example, we use the marine insect Clunio (Diptera, Chironomidae), which synchronize adult emergence and reproduction with the lunar cycle, and show different emergence patterns across populations. We use a model constructed with replicator-mutator dynamics to provide a novel outlook at the evolution of these emergence patterns. In particular, we investigate the effect of two traits of individual phenotypic variability of emergence, the spread and shape, on population-wide emergence patterns. We find that the semilunar and lunar emergence patterns are alternatively stable and occur when the phenotypic distribution has a narrow and is roughly flat. Arrhythmic emergence occurs when the phenotypic distribution is wide and nearly flat. The semi-lunar pattern can only be observed when the parameter of rhythmicity is changed. With our model, we introduce the concepts of frequency-dependent selection and individual phenotypic variability into the theory of chronobiology, which gives us insights into the evolution of rhythmicity in these organisms.

Evolution has given rise to the diversity of life on Earth, but it can also cause species extinctions. While major extinction events are usually associated with external drivers, in this study, we show mechanistically how evolution can trigger abrupt extinction avalanches in ecological networks without any environmental change. In particular, we investigate an eco-evolutionary simulation model of a tripartite mutualistic-antagonistic network, such as a plant-pollinator-herbivore network, with additional intraguild competition. The prevalence of self-organised extinction avalanches depends on a subtle balance of the different interaction types, where antagonism and similarity-based competition are needed for initial diversification while mutualism and trait-independent competition foster evolutionarily driven extinction events. Extinction avalanches are triggered by a mutualist evolving to interact with plants that are not subject to sufficient antagonistic control. Subsequently, the mutualist, its plant partners and their main antagonist potentially outcompete the rest of the community. Our findings point out that evolutionary murder may claim many victims simultaneously and highlight the need to take different interaction types into account to gain a comprehensive understanding of the links between evolution and biodiversity in ecological communities.

Oncogenic mutations are known to occur at non-random rates and specific hotspots, yet the structural and thermodynamic factors underlying these hotspots remain poorly understood. This study presents molecular dynamics simulations of 22 cancer hotspots across 10 oncogene families, simulated as histone-DNA complexes. Across 18 of 22 mutations, thermodynamic effects were predominantly localized to within 6 [A] of the DNA-histone interface (mean capture 104%), with van der Waals interactions driving the effect at the thermodynamic extremes, indicating that oncogenic mutations alter nucleosome binding through precise local contact changes rather than global structural rearrangements. Further, analysis revealed a gene-family correlated pattern in thermodynamic stability. RAS family mutations showed a consistent trend toward nucleosome stabilization (mean {Delta}{Delta}G = -4.82 kcal mol-1), while kinase domain mutations trended toward destabilization (mean {Delta}{Delta}G = +40.12 kcal mol-1), a difference reaching statistical significance in this exploratory analysis (Mann-Whitney U, p = 0.008). This interface-specific mechanism, combined with the gene-family-correlated thermodynamic pattern, provides a biophysical framework for understanding nucleosome-level contributions to cancer hotspot mutation biology.

Healing of the gastrointestinal (GI) tract following surgical interventions is governed by coupled mechanobiological processes and may lead to severe complications such as perforation or stricture formation. A first comprehensive mechanobiological modeling framework of GI healing is herein proposed. The framework addresses two clinically relevant applications of bioprinting: endoscopic treatment of GI tissue defects and bioprinting-assisted surgical anastomosis. Tissue remodeling is based upon a hyperelastic material model with fiber dispersion coupling the spatiotemporal reaction diffusion dynamics of fibroblasts and cytokines with collagen deposition, reorientation, and plastic deformation. An active stress formulation drives fibroblasts and myofibroblast contraction while a multiplicative decomposition approach is adopted for collagen remodeling as a permanent change. The governing equations are discretised in time with an implicit Euler scheme, finite element in space and solved by a staggered algorithm implemented in the open-source platform FEniCS. Numerical simulations show that the initial collagen fibers content and orientation strongly influence fibroblast infiltration and scar contracture formation. The study quantifies the advantage of having a collagen bioprinted architecture aligned with tissue fibers, to reduce structural remodeling distortion. The model also predicts a strong correlation between collagen deposition and luminal burst pressure during the recovery of mechanical integrity in GI anastomosis.

We propose a minimal mathematical framework to describe the go-or-grow dynamics of tumor cells comprising two phenotypically distinct populations. One population is migratory and undergoes constant diffusion, while the other proliferates in an oxygen-dependent manner. The local oxygen concentration governs transitions between these phenotypes. We then ask whether the time scale of cyclic hypoxia, where oxygen is spatially homogeneous but fluctuates between normoxic and hypoxic levels over time, alters the dynamics of the reduced generalist model in the fast phenotype-switching regime compared with the full go-or-grow model. We observe that the reduced generalist phenotype model fails to capture the go-or-grow dynamics under rapid oxygen fluctuations. Our results predict that the tumor growth rate increases in the generalist-phenotype model under rapid oxygen fluctuations compared with tumors of the proposed go-or-grow model. We then explore whether oxygen consumption, which leads to spatial heterogeneity in oxygen concentration, plays a role in distinguishing the dynamics of the reduced model from the proposed go-or-grow model. We demonstrate that the tumor in the proposed go-or-grow model exhibits a higher growth rate than the tumor in the reduced generalist-phenotype model under a slow oxygen consumption rate.

Simulations have emerged as a pillar in biophysics to understand behavior at the molecular scale, in particular for proteins such as intrinsically disordered proteins. These often show transient folding with long-lived states that are challenging to efficiently sample using conventional simulations. Here, we show that Hamiltonian replica-exchange at the level of hydrogen bonds can be used to systematically explore the conformational landscape of proteins. Investigating the IM30 protein, a partially alpha helical protein, under the PLUM coarse-grain force-field, we show that this approach straightforwardly allows characterization of local helix stability, which would be otherwise hard to obtain. For instance, we show that some regions of the conserved coiled-coil structure are less stable than others. By combining the different replicas with principal component analysis, we are able to dissect the conformational landscape of the IM30 protein. Taken together, this indicates that enhanced sampling remains an important part of simulations, allowing insights that cannot be easily obtained in traditional simulations.

Carbohydrates are essential molecules involved in a wide range of biological processes. While their structural representation in the Protein Data Bank (PDB) has been hindered due to their highly diverse and flexible nature, advancements on X-ray crystallography and CryoEM are accelerating the obtaining of their experimental structures, which in turn supports improved analyses of their structural properties, such as the role of their non-chair conformations on biological processes. In this context, the current work provides a comprehensive and up to date overview of carbohydrate structures within the PDB through classification, quantification, and characterization of monosaccharides and glycan chains, incorporating Cremer-Pople puckering coordinates to evaluate pyranose conformations. Our findings show that, even with a steep increase in CryoEM structures including more complex oligosaccharides, carbohydrate data remains concentrate dinsmallglycanchains, with a about 4% of non-chair conformation sintopresolution structures. Free energy landscapes for the pyranose ring in the presence and absence of nine different binding proteins, including both enzymes and non-enzymes, reinforce the preferred stability of chairs and the rarity of conformational induction upon binding.