Physica A: Statistical Mechanics and its Applications

Biomolecular condensates are widespread cellular self-assembled structures with essential functions. There are suggestions of condensates formed by different proteins being near criticality. However, systematic investigation of the criticality of condensates is absent, and critical exponents defining their universality class have not been found. Here, using long-time simulations, we show that condensates exhibit typical critical phenomena, including scale-free spatiotemporal correlations, critical slowing down, divergence of correlation length and dynamic scaling. From these scaling behaviors, a set of critical exponents is determined. Based on dynamic critical exponent, diverse condensates can be divided into two distinct universality classes, arising from differences in their molecular components and interaction types.

Patients suffering from sepsis need to be treated with an effective antibiotic therapy within the first hour after sepsis onset to decrease their risk of death. Microbiological data that provide information about the suitability of antibiotic therapies, however, is usually available only after 72 hours. Consequently, the treating physicians need to judge a therapy's effectiveness based on the patients' measured health records and their general health condition. This medical assessment is complex and requires years of experience. In our study, we investigate how statistical modeling can contribute to assessing the effectiveness of antibiotic therapies. To that purpose, we describe the effectiveness of antibiotic therapies by modeling sepsis patients' health conditions using a three-state continuous-time hidden Markov model (ctHMM). In literature, procalcitonin (PCT) and lactate have proven to be helpful for deriving the health condition in this context. The state probabilities obtained by the ctHMM are subsequently used to quantify the effectiveness of antibiotic therapies. To this end, we apply two different approaches, namely (i) averaging of the state probabilities and (ii) a logistic regression model. For (i), we calculate the average of the state probabilities for the state indicating a sepsis-free condition over an antibiotic administration period of 48 hours. For (ii), we use the information about antibiotic susceptibility testings as dependent variable in the logistic regression model; as independent variables, we calculate the difference between state probabilities at the start of antibiotic administration and 48 hours later. With this work, we are able to better understand the relationship between laboratory values, in particular PCT and lactate, and the patients' health condition. We further provide approaches for quantifying the effectiveness. Therefore, our work contributes to developing a clinical decision support system which helps physicians assess the effectiveness of antibiotic therapies in patients with sepsis. Supported by such a system, a physician is able to quickly adjust an ineffective therapy which avoids antibiotic resistances and increases a patient's chance to survive a sepsis.

A priori assessment of target proteins' druggability remains an unsolved problem in the field of drug development. The empirical approaches widely used to solve this problem demonstrate low efficiency. In this work, we investigated the factor of hydration of a representative set of 65 evolutionarily and structurally unrelated human enzymes in a water environment. This factor depends only on the structure of the proteins, and not on the physical and chemical properties of any potential ligands. The results show that, unlike the widely used approaches based on calculations of the accessible surface area (ASA), the content of low-entropy water molecules (LEW) in the active sites of human enzymes is systematically higher than that in other areas of their surface, including inactive cavities. Optimal criteria and a step-by-step procedure for identifying protein ligand binding sites are proposed. The proposed approach, based on the calculation of the LEW content in the first hydration layer of potentially interesting target proteins, makes it possible to evaluate their medicinal suitability even before the development of any ligands. The article also presents the results of a comparative analysis of experimental Raman spectroscopy data and the results of molecular dynamics simulations of water hydrogen bonds using three widely used water models (TIP3P, OPC3, and TIP5P) and standard algorithms for calculating hydrogen bond networks.

Microbes exhibit complex dynamic behavior as the result of a large number of biochemical processes, spatial and temporal interactions, environmental variations, and evolutionary pressure. Although significant progress has been achieved in understanding microbial ecological dynamics, multiple open questions remain, including the microscopic mechanisms of growth and the roles of nutrients and stochasticity. In this work, we present a minimal theoretical approach to clarify the link between consumption of resources by microbes and their growth. A stochastic model that accounts for a single microbial species consuming a single type of resource while growing via cell division is studied analytically and via Monte Carlo computer simulations. We identify three distinct dynamical regimes of microbial growth determined by the relative magnitudes of resource uptake and division rates and initial conditions. We also show that stochasticity influences the dynamic behavior when the amounts of microbes or resources are low. The model recovers Monod growth kinetics and provides a mechanistic interpretation of the Monod constant and maximal growth rate. The theoretical framework presented captures a wide spectrum of dynamic behaviors in microbial systems, providing a clearer microscopic picture to explain their underlying complex mechanisms.

In order to feed a growing global population without silencing nature, conceiving agricultural management strategies reconciling yield and conservation goals is key. Using numerical simulations of a metacommunity model, we explore the possibilities for compromise offered by spatial management strategies of farmed areas. Each strategy is characterized by its farming intensity, the proportion of farmed lands and their spatial aggregation. We show that achieving equitable yield-biodiversity compromise is difficult. While conciliatory strategies offering top yield and biodiversity are typically not possible, accepting slightly lower yields (ie, "Pretty Good Yield strategies") allows to recover substantial biodiversity. Such reconciliation possibilities are limited for species with small dispersal. Yield increases mainly through farmland expansion, whereas farming intensity strongly influences biodiversity, increasing it at low intensity before decreasing with further intensification. Finally, we demonstrate that reconciliation is easier if agricultural production relies on biodiversity through ecosystem services.

What drove nucleic acids (NA) to associate with proteins (PR) at the Origins of Life? We reason from polymer physics and the Central Dogma (CD) that the fitness value of cooperating through a division of labor - NA for replication fidelity and PR for functional fitness - is much higher than for either polymer alone. Our model shows a Pareto Front, where NA and PR can bootstrap each other to achieve autocatalytic cooperativity towards biology.

Protected areas cannot halt biodiversity loss in isolation; integrating them with surrounding human-dominated landscapes is critical. However, this integration is challenged by substantial landscape heterogeneity at their borders, hindering our understanding of cross-border changes in ecosystem service provision. We introduce a novel framework for characterizing these dynamics by analyzing ecosystem service gradients along protected area borders. For 16 protected areas in the French Alps, we assessed 12 ecosystem services using a mix of established biophysical models and novel connectivity-based models for mobile species. These were aggregated into three stakeholder-driven domains reflecting respectively rural, cultural, and urban management priorities. Automated polynomial regression analysis classified borders into five gradient types. The most common were 'Decreasing Gradients', representing a decline in ecosystem services outside the protected area, and 'Increasing Gradients', with the opposite pattern. Our analysis reveals these patterns are driven by specific landscape configurations, uncovering frequent trade-offs between the three management priorities, where, for instance, landscapes supporting rural priorities often degrade cultural and urban ones. We also identify key opportunities for synergies, by identifying areas where ecosystem services for all three priority domains increase simultaneously outside the protected area. This spatially explicit typology provides a powerful diagnostic tool for designing targeted interventions, such as prioritizing habitat restoration where ecosystem services decline or managing agricultural landscapes to mitigate conflicts across management priorities, supporting a more effective integration of protected areas into the wider landscape.

Diffuse gliomas are deadly because the individual tumor cells invade - they travel far from the imageable mass, so it is impossible to remove the tumor completely. On the cellular level, glioma cells seem to be in either a "go" state (in which they do not divide) or a "grow" state (in which they do not migrate). We investigate what this tiny choice has to say about the large-scale speed of the invasion front and whether the implication is sufficiently strong to rule out the classical description of the Fisher-Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) type, in which a single phenotype migrates and proliferates. We derive a two-phenotype reaction-diffusion model with density-dependent switching, and we prove the cooperative (quasi-monotone) structure and the associated comparison principle and study travelling-wave solutions of the model. A leading-edge linearization gives minimal front speed as minimizer of an explicit dispersion relation, and direct simulation verifies the predicted speed. In the experimentally relevant fast switching limit, we find a closed-form expression for the speed, that is, we obtain an effective Fisher-KPP equation with rescaled diffusivity and growth rate, with the fractions of the phenotypes. The "go-or-grow" (GoG) front can move at a maximum speed of half the Fisher speed for the same single-cell motility $D$ and proliferation rate $r$, which occurs only when the cells divide their time equally between the two phenotypes. This bound is directly testable: measurement of the front speed, plus independent determination of $D$ and $r$, discriminates the two hypotheses, and in the GoG case, yields recovery of the phenotype balance. We then extend the result to anisotropic (DTI-informed) invasion along white-matter tracts and discuss implications for understanding clinical measurements of growth rate.

Cells communicate with their environment by integrating signals, often chemical in nature, triggered by specific molecules bind to specific membrane-bound receptors, resulting in a downstream signaling cascade. Arguably, G-protein-coupled receptors (GPCRs) constitute the most pharmacologically important family of such receptors, binding small molecules, peptides, lipids, and hormones with high specificity. However, despite a highly conserved fold and sequence similarity, GPCRs are still mostly studied on a case-by-case basis. Here, we infer a general, evolutionarily conserved mechanism of class A GPCR activation. By leveraging coevolution and machine learning methods applied to all class A GPCRs structures, we derive a mathematical description (a so-called collective variable - CV) of the receptor's activation state which is independent of its sequence. Then, we bias molecular dynamics simulations along this CV to obtain transitions between activation states of a diverse set of class A GPCR family members. To demonstrate that our model generalizes beyond GPCRs in our training set, we obtain conformational transitions of an orphan receptor, GPR183. Finally, we show that we can model ligand effect on the receptors by converging Free Energy Surfaces of activation of the {beta}2-adrenergic receptor within this common mechanism framework. These results, to our knowledge, prove for the first time the existence of a mechanism uniting all class A GPCRs. Our approach thus facilitates direct comparisons between receptors and opens up the possibility of structural and dynamical studies of many orphan and understudied GPCRs. It also serves as a blueprint for inferring family-wide protein mechanisms.

The mosquito Aedes albopictus is a competent vector for the transmission of several arboviruses and is currently spreading across many continents. Since conventional control methods, like insecticides, often lead to environmental problems and the emergence of resistance, scientists developed alternative mosquito control strategies. One of the most used is the Sterile Insect Technique (SIT), which involves the mass release of males sterilized through irradiation. The Toxic Male Technique (TMT) is instead based on the release of genetically modified males expressing toxic proteins that kill females when they mate. Control strategies are often intended as methods to eradicate mosquito populations, yet a less ambitious and more cost-effective task is to reduce them such that the probability of transmission of viruses to humans becomes negligible. To compare the efficacy of these control strategies, we develop a mathematical model with two communicating compartments: a mosquito population and epidemiological model coupled with a human epidemiological model. As a proof-of-concept, we test the model using meteorological and entomological data for the Emilia-Romagna region. Our results indicate that the TMT strategy is more effective in lowering the probability of transmission and provides indication for the deployment of control strategies.

Molecular dynamics simulations of nucleic acids are performed using a solvent-buffer distance of 10 [A] between the solute surface and the simulation box boundary. Although this cell size has been extensively explored in protein simulations, its implications for nucleic acid dynamics are not well understood. Nucleic acids are elongated, highly charged, and flexible structures with hydration and dynamical properties distinct from those of proteins and therefore, they may require different solvent-layer considerations in simulations. In this study, we investigated the effect of simulation cell size on nucleic acid dynamics by simulating a 30-base-pair double-helical nucleic acid structure and its two single-stranded forms using solvent-buffer distances of 3, 5, 10, 15, and 20 [A]. Smaller cells may impose restricted hydration, molecular crowding, and periodic image interactions. However, larger cells provide solvent space for conformational relaxation. A total of 45 s of molecular dynamics simulations were performed (3 structures x 5 cell sizes x 3 replicates x 1 s). Our results show that while the commonly used 10 [A] buffer may be sufficient to maintain the stability of the double-stranded nucleic acid, larger cells are required to capture the conformational dynamics of single-stranded structures. In both, increasing the cell size to 15 or 20 [A] enables broader conformational sampling. The first hydration shell exhibits reduced crowding in the 20 [A] cell, consistent with more relaxed conformations. At larger cell sizes, single-stranded nucleic acids adopt compact, self-associated conformations for stability. Together, this study presents physical insight into how simulation cell size and solvent environment influence nucleic acid dynamics.

We develop a mathematical model of Rift Valley Fever integrating mosquito vectors, ruminants, and humans, based on an SEIR-type structure with vertical transmission in vectors. Local data from the Sudanian and especially the Sahelian zones are used to capture the impact of climatic variations on mosquito population dynamics. The mathematical analysis establishes the models positivity, determines the basic reproduction number R0, and demonstrates the local and global stability of the disease-free equilibrium. Sensitivity analysis (PRCC) highlights the most influential parameters, while the stochastic approach using a continuous-time Markov chain confirms the major role of seasonal rainfall. Numerical simulations reveal a peak in animal and human infections around the 9th month, correlating with periods of heavy rainfall. This model provides a relevant tool for surveillance and prevention within a "One Health" approach in Chad.

There is a vast literature on the voltage gating of ion channels, with a fairly large fraction concerned with potassium channels, especially of the KV1 family, including Shaker. Experimental evidence derived from protein structure has been interpreted to give gating mechanisms that largely disregard water. We propose that the K+ ion, in order to pass through the gating region and enter the cavity pore, must be largely dehydrated. Competitive interactions of each single hydration shell water at the gate, with counterions, protein, or other water molecules, can remove one water at a time. There are several such interactions for the ion hydration shell; for the ion to pass through the gating region, there must be enough such interactions to leave the ion with at most two hydrating water molecules, in which case the gate is open. Protein conformational changes are secondary, small, and mostly unimportant. The hypothesis has a second part: protons, previously shown to be candidate carriers of the gating current (Kariev and Green, JPC B, 2019, Membranes, 2022, 2024) are capable of reaching the gate; adding four protons to the gate prevents dehydration, leaving the ion with at least three hydrating water molecules, enough to block passage. Quantum calculations presented here support the dehydration part of the hypothesis; they also mostly support the second part, concerning the protons, but further work will be required to fully confirm this. The hypothesis explains the experimental finding that the P475D mutant is essentially constitutively open, while the P475S mutant, with a wider gate opening, is closed at all relevant potentials; the computations presented here show the mechanism for this in detail, further confirming the first part of the hypothesis, and largely but not completely confirming the second part, concerning protons, while showing where further work is needed. This mechanism can also qualitatively account for flicker noise and fluctuations, and their consequences.

Protein folding is the process by which a polypeptide chain organizes into its three-dimensional structure through a balance of stabilizing and destabilizing interactions encoded by the sequence. A central question in protein biophysics is how thermodynamic factors guide a polypeptide toward its native folded state despite the rugged energy landscape and the competing influence of nonnative interactions. In many biomolecular processes, cooperativity provides a mechanism by which multiple weak interactions act collectively to generate a robust response. In the context of protein folding, such cooperative effects may arise when the formation of one native contact enhances the stability or likelihood of nearby native contacts, thereby promoting collective organization toward the folded state. At the same time, folding is opposed by the much larger number of non-native interactions, whose heterogeneity can introduce frustration and destabilize folding even when the average native bias favors the folded phase. The interplay of these competing effects in determining foldability remains unclear in statistical-mechanical models. Here, we address this problem using a one-dimensional spin-glass model of protein folding with explicit shared-residue cooperative interactions encoded through wedge-based motifs. We show that modest cooperative bias can stabilize folding even where the noncooperative system remains unfolded, whereas non-native energetic fluctuation suppresses folding and shifts the transition to higher cooperative strengths. We further find that partial cooperative coverage is sufficient to lower the folding threshold. Therefore, the model provides a mean-field framework for incorporating cooperative interaction strength into the native one-dimensional model of protein folding and for describing how local cooperativity reshapes the folding transition.

Environmental variability can strongly alter coexistence among competing species and their extinction risk, particularly when population dynamics are shaped by behavioral interactions, such as fear. In this work, we develop a novel stochastic differential equation competition model that incorporates both non-consumptive fear effects and environmental variability to investigate how behavioral interactions influence species coexistence under random fluctuations. Our result reveals that environmental stochasticity can drive species to extinction even when the corresponding deterministic system admits coexistence. In particular, under an explicit stability condition on the fear and competition parameters and sufficiently strong averaged noise intensities, we prove that both competing species become extinct exponentially almost surely. Conversely, we derive a stochastic persistence criterion in terms of fear, competition, and noise-induced suppression parameters for the fearful species. We further demonstrate that environmental noise may reverse classical competition-exclusion outcomes, leading to qualitatively different long-term dynamics from those predicted deterministically. These results provide rigorous thresholds separating stochastic extinction from persistence and highlight the critical role of environmental variability in fear-mediated competitive ecosystems. From an applied perspective, these results provide insight into how behavioral interactions and environmental variability influence species survival, with potential applications in ecological management and conservation.

Numerous advances in quantum and computational chemistry over the last decades, well as the development of computer science, allowed utilisation of more precise and complex models, which can be now applied to much bigger systems than in the past. The authors used Gaussian, coupled with theoretical methods, to predict a new way of peptide bond formation, which could have taken place in prebiotic conditions. To better tackle this difficult task, the properties of substrates (glycine-derived radicals) were extensively analysed, using the aforementioned tool - Gaussian, paired with taking resonance and hybridisation into account, to better understand the stereochemistry and the very nature of processes taking place. The result is a series of reactions, which without any sophisticated catalysts and with relatively low energy thresholds ({inverted exclamation}20 kcal/mol) can lead to formation of dipeptides (and further, oligopeptides). The authors also hope, the other predicted properties of the investigated molecules can be of use to any researcher, who would like to utilise them in their experiments. Author summaryOur goal was to investigate a way first peptide bonds in prebiotic conditions could have been formed. This is an extremely important step in research into the beginning of life on Earth. We found a very promising series of reactions, which uses atomic hydrogen as its only catalyst and confirmed our expectations with theoretical calculations, using Gaussian. There are two radicals derived from glycine, which perform major roles in the process, so we investigated their properties with Gaussian and verified that the results are in agreement with our own theoretical considerations. This involved checking for possible geometric isomers and conformers and creating models which could explain their properties. We are well aware that such calculations have limitations and there is no model, which is 100% accurate, so our results should be further confirmed by empirical data in the future. However, we still to be as thorough as possible in how we approached the subject.

The aim of this paper is to model homeless accommodation settings to investigate how vaccination mitigates the outbreaks, highlighting the importance of vaccination in vulnerable settings. We estimate the daily per capita contact rate with wider community, the internal transmission rate, and the achieved vaccine coverage. We present stochastic simulation of the final size of disease outbreaks given choices of internal and external transmission. We conclude that vaccine that has effect in reducing transmission will mitigate the outbreak in homeless hostels but it will have better results when the household population has large vaccination coverage, which may lead to more cost from the health economic perspective.

Systems-level immune profiling data arising from longitudinal studies of vaccination or infection has an inherent multi-index array structure. While tensor decomposition of such datasets has gained popularity, choosing a rank and trial for a decomposition is not straightforward. We show that taking into account the experimental data model can inspire the development of new metrics to assess the quality of a Non-negative CANDECOMP/PARAFAC (NCPD) decomposition, and can thus be used to choose a rank and trial for the decomposition. Moreover, we show how framing the results via a dictionary learning framework can better enable interpretation of the components of the decomposition.

Cells adjust their internal circuits in response to changes in their environment. Hence, exposing cells to changing conditions provides a way to probe the intrinsic dynamics of cellular internal circuits. Metabolic networks are examples of such circuits since metabolic fluxes dynamically adjust when environmental conditions are transiently altered. Most existing theoretical frameworks focus on cellular metabolic steady states and do not consider the dynamics of changes in metabolic fluxes. In this work, we applied transfer function analysis from control theory to analyze the changes of NADH oxidative fluxes in the mitochondria and cytoplasm in mouse oocytes in response to dynamical perturbations of oxygen depletion and recovery. We observed an overshoot of NADH oxidative flux in the cytoplasm upon oxygen recovery which is absent in the mitochondrial NADH oxidative flux. Metabolic perturbation experiments and transfer function analysis indicate that this cytoplasmic NADH overshoot results from the coupling of the mitochondrial and cytoplasmic NADH cycles. The degree of overshoot is determined by competing timescales associated with the exchange rates of lactate and pyruvate with the media and their interconversion rates catalyzed by lactate dehydrogenase. Applying control theory to the data enables the inference of the exchange and conversion rates of pyruvate and lactate, allowing predictions of the contribution of lactate to mitochondrial respiration. Our work indicates that the oocytes maintain a homeostatic respiration rate across nutrient conditions by modulating the contribution of lactate to mitochondrial respiration.

The Protein Data Bank (PDB) is an ever-growing, open-access repository of structural data of biological molecules. This international database has been instrumental in the development of artificial intelligence and deep learning models for protein structure prediction and design. The PDB growth is a crucially important factor influencing further development of these models. Therefore, after analyzing the growth trend in PDB depositions since the archive's launch, we found that it is well fitted by the Gompertz function, a growth curve used across various disciplines. Furthermore, we observed that the function captures the "discovery of novel folds", i.e., the cumulative number of distinct folds among protein domains that constitute most of the PDB. Consequently, based on the fitting results, we estimated the likely numbers of PDB entries and protein folds. These findings provide insights into deceleration of growth in recent years and enable us to assess anticipated trends.