arXiv subjects

Amos Maritan

Publications and source records attributed to Amos Maritan.

At least 37 records · Page 2Linked to original sources

arXiv2024

Theory of polymers in binary solvent solutions: mean-field free energy and phase behavior

We present a lattice model for polymer solutions, explicitly incorporating interactions with a bath of solvent and cosolvent molecules. By exploiting the well-known analogy between polymer systems and the $O(n)$-vector spin model in the limit $n \to 0$, we derive an exact field-theoretic expression for the partition function of the system. The latter is then evaluated at the saddle point, providing a mean-field estimate of the free energy. The resulting expression, which conforms to the Flory-Huggins type, is then used to analyze the system's stability with respect to phase separation, complemented by a numerical approach based on convex hull evaluation. We demonstrate that this simple lattice model can effectively explain the behavior of a variety of seemingly unrelated polymer systems, which have been predominantly investigated in the past only through numerical simulations. This includes both, single-chain and multi-chain, solutions. Our findings emphasize the fundamental, mutually competing, roles of solvent and cosolvent in polymer systems.

cond-mat.soft↗

arXiv2024

Phase behaviour and self-assembly of semiflexible polymers in poor-solvent solutions

Using Langevin dynamics complemented by Wang-Landau Monte Carlo simulations, we study the phase behavior of single and multiple semiflexible polymer chains in solution under poor-solvent conditions. In the case of a single chain, we obtain the full phase diagram in the temperature-bending rigidity (stiffness) plane and we provide connections with a classical mean field result on a lattice as well as with past results on the same model. At low bending rigidity and upon cooling, we find a second order coil-globule transition, followed by a subsequent first order globule-crystal transition at lower temperatures. The obtained crystals have the shape of a twisted rod whose length increases with the increase of the stiffness of the chain. Above a critical value of the stiffness, we also find a direct first order globule-crystal transition, with the crystal having the form of a twisted toroid. Close to the triple point, we find a region with isoenergetic structures with frequent switching from rods to toroids, with the toroid eventually becoming the only observed stable phase at higher stiffness. The model is then extended to many thermally equilibrated chains in a box and the analogous phase diagram is deduced where the chains are observed to first fold into a globule bundle at low stiffness upon cooling, and then rearrange into a nematic bundle via a nucleation process involving an isotropic-nematic transition. As in the single chain counterpart, above a critical stiffness the chains are observed to undergo a direct transition from a gas of isotropically distributed chains to a nematic bundle as the temperature decreases in agreement with recent suggestions from mean field theory. The consequences of these findings for self-assembly of biopolymers in solutions are discussed.

cond-mat.soft↗

arXiv2024

Exact solution of Dynamical Mean-Field Theory for a linear system with annealed disorder

We investigate a disordered multi-dimensional linear system in which the interaction parameters vary stochastically in time with defined temporal correlations. We refer to this type of disorder as "annealed", in contrast to quenched disorder in which couplings are fixed in time. We extend Dynamical Mean-Field Theory to accommodate annealed disorder and employ it to find the exact solution of the linear model in the limit of a large number of degrees of freedom. Our analysis yields analytical results for the non-stationary auto-correlation, the stationary variance, the power spectral density, and the phase diagram of the model. Interestingly, some unexpected features emerge upon changing the correlation time of the interactions. The stationary variance of the system and the critical variance of the disorder are generally found to be a non-monotonic function of the correlation time of the interactions. We also find that in some cases a re-entrant phase transition takes place when this correlation time is varied.

cond-mat.dis-nn↗

arXiv2024

Generalized Lotka-Volterra Systems with Time Correlated Stochastic Interactions

In this work, we explore the dynamics of species abundances within ecological communities using the Generalized Lotka-Volterra (GLV) model. At variance with previous approaches, we present an analysis of stochastic GLV dynamics with temporal fluctuations in interaction strengths between species. We develop a dynamical mean field theory (DMFT) tailored for scenarios with annealed colored noise and simple functional responses. We show that time-dependent interactions can be effectively modeled as environmental noise in the DMFT and we obtain analytical predictions for the species abundance distribution that well matches empirical observations. Our results suggest that environmental noise favors species coexistence and allows to overcome the complexity-stability paradox, especially in comparison to dynamics with quenched disorder. This study offers new insights not only into the modeling of large ecosystem dynamics, but also proposes novel methodologies for examining ecological systems.

q-bio.PE↗

arXiv2024

Spatially disordered environments stabilize competitive metacommunities

Metapopulation models have been instrumental in demonstrating the ecological impact of landscape structure on the survival of a focal species in complex environments. However, extensions to multiple species with arbitrary dispersal networks often rely on phenomenological assumptions limiting their scope. Here, we develop a multilayer network model of competitive dispersing metacommunities to investigate how spatially structured environments impact species coexistence and ecosystem stability. We show that homogeneous environments always lead to monodominance unless all species' fitness parameters are in an exact trade-off. However, this precise fine-tuning does not guarantee coexistence in generic heterogeneous environments. By introducing general spatial disorder in the model, we solve it exactly in the mean-field limit, finding that stable coexistence becomes possible in the presence of strong disorder. Crucially, coexistence is supported by the spontaneous localization of species through the emergence of ecological niches. Our results remain qualitatively valid in arbitrary dispersal networks, where topological features can improve species coexistence. Finally, we employ our model to study how correlated disorder promotes spatial ecological patterns in realistic terrestrial and riverine landscapes. Our work provides a novel framework to understand how landscape structure enables coexistence in metacommunities by acting as the substrate for ecological interactions.

q-bio.PE↗

arXiv2024

Amino acid characteristics in protein native state structures

We present a geometrical analysis of the protrusion statistics of side chains in more than 4,000 high-resolution protein structures. We employ a coarse-grained representation of the protein backbone viewed as a linear chain of Cα atoms and consider just the heavy atoms of the side chains. We study the large variety of behaviors of the amino acids based on both rudimentary structural chemistry as well as geometry. Our geometrical analysis uses a backbone Frenet coordinate system for the common study of all amino acids. Our analysis underscores the richness of the repertoire of amino acids that is available to nature to design protein sequences that fit within the putative native state folds.

cond-mat.soft↗

arXiv2023

III. Geometrical framework for thinking about globular proteins: turns in proteins

We have shown recently that the notion of poking pairwise interactions along a chain provides a unifying framework for understanding the formation of both secondary and the tertiary protein structure based on symmetry and geometry. $α$-helices and $β$-sheets are found to be special geometries that have systematic poking contacts in a repetitive manner with the contacts being local along the $α$-helix and non-local along a pair of adjacent strands within a $β$-sheet. Pairwise poking interactions also govern tertiary structure formation, but they are weaker and there are no special geometrical constraints as in secondary structure formation. Here we demonstrate that protein turns, the most prevalent non-repetitive structural element in proteins, are instances of local (as in $α$-helices) and isolated (non-repetitive) poking pairwise contacts for which the geometrical constraints are partially relaxed. This simple and purely geometrical definition of protein turns (also sometimes known as reverse turns, $β$-turns, $β$-bends, hairpin bends, $3_{10}$ bends, kinks, widgets, ...) provides a simple framework for unifying them. We present the results of a systematic analysis and identify their structural classes as well as their respective amino acid preferences.

cond-mat.soft↗

arXiv2023

Generalization of Fluctuation-Dissipation Theorem to Systems with Absorbing States

Systems that evolve towards a state from which they cannot depart are common in nature. But the fluctuation-dissipation theorem, a fundamental result in statistical mechanics, is mainly restricted to systems near-stationarity. In processes with absorbing states, the total probability decays with time, eventually reaching zero and rendering the predictions from the standard response theory invalid. In this article, we investigate how such processes respond to external perturbations and develop a new theory that extends the framework of the fluctuation-dissipation theorem. We apply our theory to two paradigmatic examples that span vastly different fields - a birth-death process in forest ecosystems and a targeted search on DNA by proteins. These systems can be affected by perturbations which increase their rate of extinction/absorption, even though the average or the variance of population sizes are left unmodified. These effects, which are not captured by the standard response theory, are exactly predicted by our framework. Our theoretical approach is general and applicable to any system with absorbing states. It can unveil important features of the path to extinction masked by standard approaches.

cond-mat.stat-mech↗

arXiv2023

Phase behaviour of semiflexible lattice polymers in poor-solvent solution: mean-field theory and Monte Carlo simulations

We study a solution of interacting semiflexible polymers with curvature energy in poor-solvent conditions on the d-dimensional cubic lattice using mean-field theory and Monte Carlo computer simulations. Building upon past studies on a single chain, we construct a field-theory representation of the system and solve it within a mean-field approximation supported by Monte Carlo simulations in d=3. A gas-liquid transition is found in the temperature-density plane that is then interpreted in terms of real systems. Interestingly, we find this transition to be independent of the bending rigidity. Past classical Flory-Huggins and Flory mean-field results are shown to be particular cases of this more general framework. Perspectives in terms of guiding experimental results towards optimal conditions are also proposed.

cond-mat.soft↗

arXiv2023

Large system population dynamics with non-Gaussian interactions

We investigate the Generalized Lotka-Volterra (GLV) equations, a central model in theoretical ecology, where species interactions are assumed to be fixed over time and heterogeneous (quenched noise). Recent studies have suggested that the stability properties and abundance distributions of large disordered GLV systems depend, in the simplest scenario, solely on the mean and variance of the distribution of species interactions. However, empirical communities deviate from this level of universality. In this article, we present a generalized version of the dynamical mean field theory for non-Gaussian interactions that can be applied to various models, including the GLV equations. Our results show that the generalized mean field equations have solutions which depend on all cumulants of the distribution of species interactions, leading to a breakdown of universality. We leverage on this informative breakdown to extract microscopic interaction details from the macroscopic distribution of densities which are in agreement with empirical data. Specifically, in the case of sparse interactions, which we analytically investigate, we establish a simple relationship between the distribution of interactions and the distribution of species population densities.

q-bio.PE↗

arXiv2023

A geometrical framework for thinking about proteins

We present a model, based on symmetry and geometry, for proteins. Using elementary ideas from mathematics and physics, we derive the geometries of discrete helices and sheets. We postulate a compatible solvent-mediated emergent pairwise attraction that assembles these building blocks, while respecting their individual symmetries. Instead of seeking to mimic the complexity of proteins, we look for a simple abstraction of reality that yet captures the essence of proteins. We employ analytic calculations and detailed Monte Carlo simulations to explore some consequences of our theory. The predictions of our approach are in accord with experimental data. Our framework provides a rationalization for understanding the common characteristics of proteins. Our results show that the free energy landscape of a globular protein is pre-sculpted at the backbone level, sequences and functionalities evolve in the fixed backdrop of the folds determined by geometry and symmetry, and that protein structures are unique in being simultaneously characterized by stability, diversity, and sensitivity.

cond-mat.soft↗

arXiv2023

II. Geometrical framework for thinking about globular proteins: the power of poking

Recently, we presented a framework for understanding protein structure based on the idea that simple constructs of holding hands or touching of objects can be used to rationalize the common characteristics of globular proteins. We developed a consistent approach for understanding the formation of the two key common building blocks of helices and sheets as well as the compatible assembly of secondary structures into the tertiary structure through the notion of poking pairwise interactions. Here we benchmark our predictions with a detailed analysis of structural data of over 4000 proteins from the Protein Data Bank. We also present the results of detailed computer simulations of a simplified model demonstrating a pre-sculpted free energy landscape, determined by geometry and symmetry, comprising numerous minima corresponding to putative native state structures. We explore the consequences of our model. Our results suggest that symmetry and geometry are a powerful guide to capture the simplicity underlying protein complexity.

cond-mat.soft↗

arXiv2023

The emergence of scale-free fires in Australia

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.

cond-mat.stat-mech↗

arXiv2023

Fluctuations of entropy production of a run-and-tumble particle

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.

cond-mat.stat-mech↗

arXiv2022

Information-driven transitions in projections of underdamped dynamics

Low-dimensional representations of underdamped systems often provide insightful grasps 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 unravel fundamental properties of effective dynamical representations, impacting several fields, from biophysics to dimensionality reduction.

cond-mat.stat-mech↗

arXiv2021

Proteins -- a celebration of consilience

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.

q-bio.BM↗

arXiv2021

Effect of delay on the emergent stability patterns in Generalized Lotka-Volterra ecological dynamics

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 modeled 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, we introduce a measure of stability that holds for out of equilibrium dynamics and we show that in the oscillatory regime induced by the delay stability increases for increasing ecosystem diversity.

q-bio.PE↗

arXiv2021

Effective Resource-Competition Model for Species Coexistence

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.

q-bio.PE↗