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Many proteins undergo a process of phase separation that leads to the formation of biomolecular condensates. It has been observed that some of these proteins form dense droplets of sizeable dimensions already below their critical concentration for phase separation. To understand this phenomenon, which is not readily compatible with classical nucleation theory, we investigated the properties of the droplet size distributions as a function of protein concentration. We found that these distributions can be described by a scale-invariant log-normal function with an average that increases progressively as the concentration approaches the critical value from below. These results suggest the existence of a universal behaviour independent from the sequences and structures of the proteins undergoing phase separation, which is typically observed for second-order transitions. By determining the parameters of the scale-invariant distribution, we show that it is possible to use it to estimate the critical concentration for phase separation.

Between 2019 and 2020, during the country's hottest and driest year on record, Australia experienced a dramatic bushfire season, with catastrophic ecological and environmental consequences. Several studies highlighted how such abrupt changes in fire regimes may have been in large part a consequence of climate change and other anthropogenic transformations. Here, we analyze the monthly evolution of the burned area in Australia from 2000 to 2020, obtained via satellite imaging through the MODIS platform. We find that the 2019-2020 peak is associated with signatures typically found near critical points. We introduce a modeling framework based on forest-fire models to study the properties of these emergent fire outbreaks, showing that the behavior observed during the 2019-2020 fire season matches the one of a percolation transition, where system-size outbreaks appear. Our model also highlights the existence of an absorbing phase transition that might be eventually crossed, after which the vegetation cannot recover.

Microbial communities are ubiquitous and play crucial roles in many natural processes. Despite their importance for the environment, industry and human health, there are still many aspects of microbial community dynamics that we do not understand quantitatively. Recent experiments have shown that the structure and composition of microbial communities are intertwined with the metabolism of the species that inhabit them, suggesting that properties at the intracellular level such as the allocation of cellular proteomic resources must be taken into account when describing microbial communities with a population dynamics approach. In this work, we reconsider one of the theoretical frameworks most commonly used to model population dynamics in competitive ecosystems, MacArthur’s consumer-resource model, in light of experimental evidence showing how proteome allocation affects microbial growth. This new framework allows us to describe community dynamics at an intermediate level of complexity between classical consumer-resource models and biochemical models of microbial metabolism, accounting for temporally-varying proteome allocation subject to constraints on growth and protein synthesis in the presence of multiple resources, while preserving analytical insight into the dynamics of the system. We first show with a simple experiment that proteome allocation needs to be accounted for to properly understand the dynamics of even the simplest microbial community, i.e. two bacterial strains competing for one common resource. Then, we study our consumer-proteome-resource model analytically and numerically to determine the conditions that allow multiple species to coexist in systems with arbitrary numbers of species and resources.

Low-dimensional representations of underdamped systems often provide useful insights and analytical tractability. Here, we build such representations via information projections, obtaining an optimal model that captures the most information on observed spatial trajectories. We show that, in paradigmatic systems, the minimization of the information loss drives the appearance of a discontinuous transition in the optimal model parameters. Our results raise serious warnings for general inference approaches, and they unravel fundamental properties of effective dynamical representations impacting several fields, from biophysics to dimensionality reduction.

The common intuition among the ecologists of the midtwentieth century was that large ecosystems should be more stable than those with a smaller number of species. This view was challenged by Robert May, who found a stability bound for randomly assembled ecosystems; they become unstable for a sufficiently large number of species. In the present work, we show that May’s bound greatly changes when the past population densities of a species affect its own current density. This is a common feature in real systems, where the effects of species’ interactions may appear after a time lag rather than instantaneously. The local stability of these models with self-interaction is described by bounds, which we characterize in the parameter space. We find a critical delay curve that separates the region of stability from that of instability, and correspondingly, we identify a critical frequency curve that provides the characteristic frequencies of a system at the instability threshold. Finally, we calculate analytically the distributions of eigenvalues that generalize Wigner’s as well as Girko’s laws. Interestingly, we find that, for sufficiently large delays, the eigenvalues of a randomly coupled system are complex even when the interactions are symmetric.

Out-of-equilibrium systems continuously generate entropy, with its rate of production being a fingerprint of non-equilibrium conditions. In small-scale dissipative systems subject to thermal noise, fluctuations of entropy production are significant. Hitherto, mean and variance have been abundantly studied, even if higher moments might be important to fully characterize the system of interest. Here, we introduce a graphical method to compute any moment of entropy production for a generic discrete-state system. Then, we focus on a paradigmatic model of active particles, i.e., run-and-tumble dynamics, which resembles the motion observed in several microorganisms. Employing our framework, we compute the first three cumulants of the entropy production for a discrete version of this model. We also compare our analytical results with numerical simulations. We find that as the number of states increases, the distribution of entropy production deviates from a Gaussian. Finally, we extend our framework to a continuous state-space run-and-tumble model, using an appropriate scaling of the transition rates. The approach here presented might help uncover the features of non-equilibrium fluctuations of any current in biological systems operating out-of-equilibrium., Comment: 13 pages, 6 figures

Proteins are the common constituents of all living cells. They are molecular machines that interact with each other as well as with other cell products and carry out a dizzying array of functions with distinction. These interactions follow from their native state structures and therefore understanding sequence-structure relationships is of fundamental importance. What is quite remarkable about proteins is that their understanding necessarily straddles several disciplines. The importance of geometry in defining protein native state structure, the constraints placed on protein behavior by mathematics and physics, the need for proteins to obey the laws of quantum chemistry, and the rich role of evolution and biology all come together in defining protein science. Here we review ideas from the literature and present an interdisciplinary framework that aims to marry ideas from Plato and Darwin and demonstrates an astonishing consilience between disciplines in describing proteins. We discuss the consequences of this framework on protein behavior., 18 pages; 1 table; 6 figures

Understanding the conditions of feasibility and stability in ecological systems is a major challenge in theoretical ecology. The seminal work of May in 1972 and recent developments based on the theory of random matrices have shown the existence of emergent universal patterns of both stability and feasibility in ecological dynamics. However, only a few studies have investigated the role of delay coupled with population dynamics in the emergence of feasible and stable states. In this work, we study the effects of delay on generalized Loka–Volterra population dynamics of several interacting species in closed ecological environments. First, we investigate the relation between feasibility and stability of the modelled ecological community in the absence of delay and find a simple analytical relation when intra-species interactions are dominant. We then show how, by increasing the time delay, there is a transition in the stability phases of the population dynamics: from an equilibrium state to a stable non-point attractor phase. We calculate analytically the critical delay of that transition and show that it is in excellent agreement with numerical simulations. Finally, following a similar approach to characterizing stability in empirical studies, we investigate the coefficient of variation, which quantifies the magnitude of population fluctuations. We show that in the oscillatory regime induced by the delay, the variability at community level decreases for increasing diversity. This article is part of the theme issue ‘Emergent phenomena in complex physical and socio-technical systems: from cells to societies’.

Significance Allometric scaling has many applications, from the prediction of pharmacokinetics in animals and humans to the probing of ecosystem dynamics. Most studies have neglected to account for variations and fluctuations, although they are intrinsic features of all biological systems. To understand how metabolic scaling emerges in the presence of variations, we developed computer-generated models of cell-laden spheroids to define the experimental size range of cell cultures with quantifiable similitudes in terms of fluctuations and metabolic scaling with living organisms. We show that the estimates of scaling exponents may change with increasing variability in both mass and metabolic rate. The computational pipeline described underpins the sound design of statistically meaningful cell-based models, with impacts in both biomedical science and ecology., Variations and fluctuations are characteristic features of biological systems and are also manifested in cell cultures. Here, we describe a computational pipeline for identifying the range of three-dimensional (3D) cell-aggregate sizes in which nonisometric scaling emerges in the presence of joint mass and metabolic rate fluctuations. The 3D cell-laden spheroids with size and single-cell metabolic rates described by probability density functions were randomly generated in silico. The distributions of the resulting metabolic rates of the spheroids were computed by modeling oxygen diffusion and reaction. Then, a method for estimating scaling exponents of correlated variables through statistically significant data collapse of joint probability distributions was developed. The method was used to identify a physiologically relevant range of spheroid sizes, where both nonisometric scaling and a minimum oxygen concentration (0.04 mol⋅m−3) is maintained. The in silico pipeline described enables the prediction of the number of experiments needed for an acceptable collapse and, thus, a consistent estimate of scaling parameters. Using the pipeline, we also show that scaling exponents may be significantly different in the presence of joint mass and metabolic-rate variations typically found in cells. Our study highlights the importance of incorporating fluctuations and variability in size and metabolic rates when estimating scaling exponents. It also suggests the need for taking into account their covariations for better understanding and interpreting experimental observations both in vitro and in vivo and brings insights for the design of more predictive and physiologically relevant in vitro models.

We present the results of a quantitative study of the phase behavior of a model polymer chain with side spheres using two independent computer simulation techniques. We find that the mere addition of side spheres results in key modifications of standard polymer behavior. One obtains a novel marginally compact phase at low temperatures, the structures in this phase are reduced in dimensionality and are ordered, they include strands assembled into sheets and a variety of helices, and at least one of the transitions on lowering the temperature to access these ordered states is found to be first order. Our model serves to partially bridge conventional polymer phases with biomolecular phases., 15 pages; 5 figures

Chain molecules play a key role in the polymer field and in living cells. Our focus is on a new homopolymer model of a linear chain molecule subject to an attractive self-interaction promoting compactness. We analyze the model using simple analytic arguments complemented by extensive computer simulations. We find several striking results: there is a first order transition from a high temperature random coil phase to a highly unusual low temperature phase; the modular ground states exhibit significant degeneracy; the ground state structures exhibit spontaneous dimensional reduction and have a two-layer structure; and the ground states are assembled from secondary motifs of helices and strands connected by tight loops. We discuss the similarities and notable differences between the ground state structures (we call these PoSSuM -- Planar Structures with Secondary Motifs) in the novel phase and protein native state structures., 14 pages, 5 figures

Significance Empirical laws predicting metabolic rates of a species by its average body mass neglect intraspecies variability arising from the range of physiologically feasible rates and phenotypic heterogeneity. We describe an exploratory experimental test of a theory that explicitly accounts for such variations. We show, by single-cell joint measurements of mass and uptake rates, how marginal distributions of mass and rates collapse onto a common master distribution for species spanning 3 orders of magnitude in cell volume. These results demonstrate the potential of a generalized scaling theory that goes beyond population averages to incorporate within-species variation., Kleiber’s law describes the scaling of metabolic rate with body size across several orders of magnitude in size and across taxa and is widely regarded as a fundamental law in biology. The physiological origins of Kleiber’s law are still debated and generalizations of the law accounting for deviations from the scaling behavior have been proposed. Most theoretical and experimental studies of Kleiber’s law, however, have focused on the relationship between the average body size of a species and its mean metabolic rate, neglecting intraspecific variation of these 2 traits. Here, we propose a theoretical characterization of such variation and report on proof-of-concept experiments with freshwater phytoplankton supporting such framework. We performed joint measurements at the single-cell level of cell volume and nitrogen/carbon uptake rates, as proxies of metabolic rates, of 3 phytoplankton species using nanoscale secondary ion mass spectrometry (NanoSIMS) and stable isotope labeling. Common scaling features of the distribution of nutrient uptake rates and cell volume are found to hold across 3 orders of magnitude in cell size. Once individual measurements of cell volume and nutrient uptake rate within a species are appropriately rescaled by a function of the average cell volume within each species, we find that intraspecific distributions of cell volume and metabolic rates collapse onto a universal curve. Based on the experimental results, this work provides the building blocks for a generalized form of Kleiber’s law incorporating intraspecific, correlated variations of nutrient-uptake rates and body sizes.

Biodiversity provides support for life, vital provisions, regulating services and has positive cultural impacts. It is therefore important to have accurate methods to measure biodiversity, in order to safeguard it when we discover it to be threatened. For practical reasons, biodiversity is usually measured at fine scales whereas diversity issues (e.g. conservation) interest regional or global scales. Moreover, biodiversity may change across spatial scales. It is therefore a key challenge to be able to translate local information on biodiversity into global patterns. Many databases give no information about the abundances of a species within an area, but only its occurrence in each of the surveyed plots. In this paper, we introduce an analytical framework (implemented in a ready‐to‐use R code) to infer species richness and abundances at large spatial scales in biodiversity‐rich ecosystems when species presence/absence information is available on various scattered samples (i.e. upscaling). This framework is based on the scale‐invariance property of the negative binomial. Our approach allows to infer and link within a unique framework important and well‐known biodiversity patterns of ecological theory, such as the species accumulation curve (SAC) and the relative species abundance (RSA) as well as a new emergent pattern, which is the relative species occupancy (RSO). Our estimates are robust and accurate, as confirmed by tests performed on both in silico‐generated and real forests. We demonstrate the accuracy of our predictions using data from two well‐studied forest stands. Moreover, we compared our results with other popular methods proposed in the literature to infer species richness from presence to absence data and we showed that our framework gives better estimates. It has thus important applications to biodiversity research and conservation practice.

Empirical observations show that ecological communities can have a huge number of coexisting species, also with few or limited number of resources. These ecosystems are characterized by multiple type of interactions, in particular displaying cooperative behaviors. However, standard modeling of population dynamics based on Lotka-Volterra type of equations predicts that ecosystem stability should decrease as the number of species in the community increases and that cooperative systems are less stable than communities with only competitive and/or exploitative interactions. Here we propose a stochastic model of population dynamics, which includes exploitative interactions as well as cooperative interactions induced by cross-feeding. The model is exactly solved and we obtain results for relevant macro-ecological patterns, such as species abundance distributions and correlation functions. In the large system size limit, any number of species can coexist for a very general class of interaction networks and stability increases as the number of species grows. For pure mutualistic/commensalistic interactions we determine the topological properties of the network that guarantee species coexistence. We also show that the stationary state is globally stable and that inferring species interactions through species abundance correlation analysis may be misleading. Our theoretical approach thus show that appropriate models of cooperation naturally leads to a solution of the long-standing question about complexity-stability paradox and on how highly biodiverse communities can coexist., 25 pages, 10 figures

The Species-Area Relation (SAR), which describes the increase in the number of species S with increasing area A, is under intense scrutiny in contemporary ecology, in particular to probe its reliability in predicting the number of species going extinct as a direct result of habitat loss. Here, we focus on the island SAR, which is measured across a set of disjoint habitat patches, and we argue that the SAR portrays an average trend around which fluctuations are to be expected due to the stochasticity of community dynamics within the patches, external perturbations, and habitat heterogeneity across different patches. This probabilistic interpretation of the SAR, though already implicit in the theory of island biogeography and manifest in the scatter of data points in plots of empirical SAR curves, has not been investigated systematically from the theoretical point of view. Here, we show that the two main contributions to SAR fluctuations, which are due to community dynamics within the patches and to habitat heterogeneity between different patches, can be decoupled and analyzed independently. To investigate the community dynamics contribution to SAR fluctuations, we explore a suite of theoretical models of community dynamics where the number of species S inhabiting a patch emerges from diverse ecological and evolutionary processes, and we compare stationary predictions for the coefficient of variation of S, i.e. the fluctuations of S with respect to the mean. We find that different community dynamics models diverge radically in their predictions. In island biogeography and in neutral frameworks, where fluctuations are only driven by the stochasticity of diversification and extinction events, relative fluctuations decay when the mean increases. Computational evidence suggests that this result is robust in the presence of competition for space or resources. When species compete for finite resources, and mass is introduced as a trait determining species' birth, death and resource consumption rates based on empirical allometric scalings, relative fluctuations do not decay with increasing mean S due to the occasional introduction of new species with large resource demands causing mass extinctions in the community. Given this observation, we also investigate the contribution of external disturbance events to fluctuations of S in neutral community dynamics models and compare this scenario with the community dynamics in undisturbed non-neutral models. Habitat heterogeneity within a single patch, in the context of metapopulation models, causes variability in the number of coexisting species which proves negligible with respect to that caused by the stochasticity of the community dynamics. The second contribution to SAR fluctuations, which is due to habitat heterogeneity among different patches, introduces corrections to the coefficient of variation of S. Most importantly, inter-patches heterogeneity introduces a constant, lower bound on the relative fluctuations of S equal to the coefficient of variation of a habitat variable describing the heterogeneity among patches. Because heterogeneity across patches is inevitably present in natural ecosystems, we expect that the relative fluctuations of S always tend to a constant in the limit of large mean S or large patch area A, with contributions from community dynamics, inter-patches heterogeneity or both. We provide a theoretical framework for modelling these two contributions and we show that both can affect significantly the fluctuations of the SAR. (C) 2018 The Authors. Published by Elsevier Ltd.

Chain molecules play a key role in the polymer field and in living cells. Our focus is on a new homopolymer model of a linear chain molecule subject to an attractive self-interaction promoting compactness. We analyze the model using simple analytic arguments complemented by extensive computer simulations. We find several striking results: there is a first order transition from a high temperature random coil phase to a highly unusual low temperature phase; the modular ground states exhibit significant degeneracy; the ground state structures exhibit spontaneous dimensional reduction and have a two-layer structure; and the ground states are assembled from secondary motifs of helices and strands connected by tight loops. We discuss the similarities and notable differences between the ground state structures (we call these PoSSuM - Planar Structures with Secondary Motifs) in the novel phase and protein native state structures.

Significance For most of its path through plant bodies, water moves in conduits in the wood. Plant water conduction is crucial for Earth’s biogeochemical cycles, making it important to understand how natural selection shapes conduit diameters along the entire lengths of plant stems. Can mathematical modeling and global sampling explain how wood conduits ought to widen from the tip of a plant to its trunk base? This question is evolutionarily important because xylem conduits should widen in a way that keeps water supply constant to the leaves as a plant grows taller. Moreover, selection should act on economy of construction costs of the conducting system. This issue is ecologically important because it helps suggest why climate change alters vegetation height worldwide., Shaping global water and carbon cycles, plants lift water from roots to leaves through xylem conduits. The importance of xylem water conduction makes it crucial to understand how natural selection deploys conduit diameters within and across plants. Wider conduits transport more water but are likely more vulnerable to conduction-blocking gas embolisms and cost more for a plant to build, a tension necessarily shaping xylem conduit diameters along plant stems. We build on this expectation to present the Widened Pipe Model (WPM) of plant hydraulic evolution, testing it against a global dataset. The WPM predicts that xylem conduits should be narrowest at the stem tips, widening quickly before plateauing toward the stem base. This universal profile emerges from Pareto modeling of a trade-off between just two competing vectors of natural selection: one favoring rapid widening of conduits tip to base, minimizing hydraulic resistance, and another favoring slow widening of conduits, minimizing carbon cost and embolism risk. Our data spanning terrestrial plant orders, life forms, habitats, and sizes conform closely to WPM predictions. The WPM highlights carbon economy as a powerful vector of natural selection shaping plant function. It further implies that factors that cause resistance in plant conductive systems, such as conduit pit membrane resistance, should scale in exact harmony with tip-to-base conduit widening. Furthermore, the WPM implies that alterations in the environments of individual plants should lead to changes in plant height, for example, shedding terminal branches and resprouting at lower height under drier climates, thus achieving narrower and potentially more embolism-resistant conduits.

A hot Markovian system can cool down faster than a colder one: this is known as the Mpemba effect. Here, we show that a non-equilibrium driving via stochastic reset can induce this phenomenon, when absent. Moreover, we derive an optimal driving protocol simultaneously optimizing the appearance time of the Mpemba effect, and the total energy dissipation into the environment, revealing the existence of a Pareto front. Building upon previous experimental results, our findings open up the avenue of possible experimental realizations of optimal cooling protocols in Markovian systems., Comment: Accepted Manuscript in New Journal of Physics (in press, 2021)

Big data require new techniques to handle the information they come with. Here we consider four datasets (email communication, Twitter posts, Wikipedia articles and Gutenberg books) and propose a novel statistical framework to predict global statistics from random samples. More precisely, we infer the number of senders, hashtags and words of the whole dataset and how their abundances (i.e. the popularity of a hashtag) change through scales from a small sample of sent emails per sender, posts per hashtag and word occurrences. Our approach is grounded on statistical ecology as we map inference of human activities into the unseen species problem in biodiversity. Our findings may have applications to resource management in emails, collective attention monitoring in Twitter and language learning process in word databases.

Local coexistence of species in large ecosystems is traditionally explained within the broad framework of niche theory. However, its rationale hardly justifies rich biodiversity observed in nearly homogeneous environments. Here we consider a consumer-resource model in which a coarse-graining procedure accounts for a variety of ecological mechanisms and leads to effective spatial effects which favour species coexistence. Herein, we provide conditions for several species to live in an environment with very few resources. In fact, the model displays two different phases depending on whether the number of surviving species is larger or smaller than the number of resources. We obtain conditions whereby a species can successfully colonize a pool of coexisting species. Finally, we analytically compute the distribution of the population sizes of coexisting species. Numerical simulations as well as empirical distributions of population sizes support our analytical findings., 5 pages + 4 figures, Major revision

The native state structures of globular proteins are stable and well-packed indicating that self-interactions are favored over protein-solvent interactions under folding conditions. We use this as a guiding principle to derive the geometry of the building blocks of protein structures, alpha-helices and strands assembled into beta-sheets, with no adjustable parameters, no amino acid sequence information, and no chemistry. There is an almost perfect fit between the dictates of mathematics and physics and the rules of quantum chemistry. Our theory establishes an energy landscape that channels protein evolution by providing sequence-independent platforms for elaborating sequence-dependent functional diversity. Our work highlights the vital role of discreteness in life and has implications for the creation of artificial life and on the nature of life elsewhere in the cosmos., 32 pages, 6 figures, 2 tables; Added key sentence about the important role of amino acid side chains in providing steric constraints

Deoxyribonucleic acid (DNA) hybridization is at the heart of countless biological and biotechnological processes. Its theoretical modeling played a crucial role, since it has enabled extracting the relevant thermodynamic parameters from systematic measurements of DNA melting curves. In this article, we propose a framework based on statistical physics to describe DNA hybridization and melting in an arbitrary mixture of DNA strands. In particular, we are able to analytically derive closed expressions of the system partition functions for any number $N$ of strings and explicitly calculate them in two paradigmatic situations: (i) a system made of self-complementary sequences and (ii) a system comprising two mutually complementary sequences. We derive the melting curve in the thermodynamic limit ($N\ensuremath{\rightarrow}\ensuremath{\infty}$) of our description, which provides a full justification for the extra entropic contribution that in classic hybridization modeling was required to correctly describe within the same framework the melting of sequences either self-complementary or not. We thus provide a thorough study comprising limit cases and alternative approaches showing how our framework can give a comprehensive view of hybridization and melting phenomena.

DNA hybridization is at the heart of countless biological and biotechnological processes. Its theoretical modeling played a crucial role, since it has enabled extracting the relevant thermodynamic parameters from systematic measurements of DNA melting curves. However, in its current state, hybridization modelling requires introducing an extra entropic contribution in self-complementary sequences that lacks any biophysical meaning. In this article, we propose a framework based on statistical physics to describe DNA hybridization and melting in an arbitrary mixture of DNA strands. In particular, we are able to analytically derive closed expressions of the system partition functions for any numberNof strings, and explicitly calculate them in two paradigmatic situations: (i) a system made of self-complementary sequences and (ii) a system comprising two mutually complementary sequences. We derive the melting curve in the thermodynamic limit (N→ ∞) of our description, which differs from the expression commonly used to evaluate the melting of self-complementary systems in that it does not require correcting terms. We provide a thorough study comprising limit cases and alternative approaches showing how our framework can give a comprehensive view of hybridization and melting phenomena.SIGNIFICANCEIn this study, we provide a transparent derivation of the melting curves of DNA duplexes using basic tools of statistical mechanics. We find that in the case of self-complementary sequences, our expression differs from the one used in literature, which is generally amended by the introduction of a phenomenological correction which in our approach becomes unnecessary. By offering a clean formal description of DNA hybridization, our approach sharpens our understanding of DNA interactions and opens the way to study the pairing of DNA oligomers away from any thermodynamic limit.