arXiv subjects

Amos Maritan

Publications and source records attributed to Amos Maritan.

At least 109 records · Page 6Linked to original sources

arXiv2012

Absence of Detailed Balance in Ecology

Living systems are typically characterized by irreversible processes. A condition equivalent to the reversibility is the detailed balance, whose absence is an obstacle for analytically solving ecological models. We revisit a promising model with an elegant field-theoretic analytic solution and show that the theoretical analysis is invalid because of an implicit assumption of detailed balance. A signature of the difficulties is evident in the inconsistencies appearing in the many-point correlation functions and in the analytical formula for the species area relationship.

cond-mat.stat-mech↗

arXiv2012

Spatial aggregation and the species-area relationship across scales

There has been a considerable effort to understand and quantify the spatial distribution of species across different ecosystems. Relative species abundance (RSA), beta diversity and species area relationship (SAR) are among the most used macroecological measures to characterize plants communities in forests. In this article we introduce a simple phenomenological model based on Poisson cluster processes which allows us to exactly link RSA and beta diversity to SAR. The framework is spatially explicit and accounts for the spatial aggregation of conspecific individuals. Under the simplifying assumption of neutral theory, we derive an analytical expression for the SAR which reproduces tri-phasic behavior as sample area increases from local to continental scales, explaining how the tri-phasic behavior can be understood in terms of simple geometric arguments. We also find an expression for the endemic area relationship (EAR) and for the scaling of the RSA.

q-bio.PE↗

arXiv2012

Spontaneously Broken Neutral Symmetry in an Ecological System

Spontaneous symmetry breaking plays a fundamental role in many areas of condensed matter and particle physics. A fundamental problem in ecology is the elucidation of the mechanisms responsible for biodiversity and stability. Neutral theory, which makes the simplifying assumption that all individuals (such as trees in a tropical forest) --regardless of the species they belong to-- have the same prospect of reproduction, death, etc., yields gross patterns that are in accord with empirical data. We explore the possibility of birth and death rates that depend on the population density of species while treating the dynamics in a species-symmetric manner. We demonstrate that the dynamical evolution can lead to a stationary state characterized simultaneously by both biodiversity and spontaneously broken neutral symmetry.

q-bio.PE↗

arXiv2012

An exactly solvable coarse-grained model for species diversity

We present novel analytical results about ecosystem species diversity that stem from a proposed coarse grained neutral model based on birth-death processes. The relevance of the problem lies in the urgency for understanding and synthesizing both theoretical results of ecological neutral theory and empirical evidence on species diversity preservation. Neutral model of biodiversity deals with ecosystems in the same trophic level where per-capita vital rates are assumed to be species-independent. Close-form analytical solutions for neutral theory are obtained within a coarse-grained model, where the only input is the species persistence time distribution. Our results pertain: the probability distribution function of the number of species in the ecosystem both in transient and stationary states; the n-points connected time correlation function; and the survival probability, definned as the distribution of time-spans to local extinction for a species randomly sampled from the community. Analytical predictions are also tested on empirical data from a estuarine fish ecosystem. We find that emerging properties of the ecosystem are very robust and do not depend on specific details of the model, with implications on biodiversity and conservation biology.

q-bio.PE↗

arXiv2012

Shapes of hydrophobic thick membranes

We introduce and study the behavior of a tethered membrane of non-zero thickness embedded in three dimensions subject to an effective self-attraction induced by hydrophobicity arising from the tendency to minimize the area exposed to a solvent. The phase behavior and the nature of the folded conformations are found to be quite distinct in the small and large solvent size regimes. We demonstrate spontaneous symmetry-breaking with the membrane folding along a preferential axis, when the solvent molecules are small compared to the membrane thickness. For large solvent molecule size, a local crinkling mechanism effectively shields the membrane from the solvent, even in relatively flat conformations. We discuss the binding/unbinding transition of a membrane to a wall that serves to shield the membrane from the solvent.

cond-mat.soft↗

arXiv2012

A universal model for mobility and migration patterns

Introduced in its contemporary form by George Kingsley Zipf in 1946, but with roots that go back to the work of Gaspard Monge in the 18th century, the gravity law is the prevailing framework to predict population movement, cargo shipping volume, inter-city phone calls, as well as bilateral trade flows between nations. Despite its widespread use, it relies on adjustable parameters that vary from region to region and suffers from known analytic inconsistencies. Here we introduce a stochastic process capturing local mobility decisions that helps us analytically derive commuting and mobility fluxes that require as input only information on the population distribution. The resulting radiation model predicts mobility patterns in good agreement with mobility and transport patterns observed in a wide range of phenomena, from long-term migration patterns to communication volume between different regions. Given its parameter-free nature, the model can be applied in areas where we lack previous mobility measurements, significantly improving the predictive accuracy of most of phenomena affected by mobility and transport processes.

physics.soc-ph↗

arXiv2012

Protein sequence and structure: Is one more fundamental than the other?

We argue that protein native state structures reside in a novel "phase" of matter which confers on proteins their many amazing characteristics. This phase arises from the common features of all globular proteins and is characterized by a sequence-independent free energy landscape with relatively few low energy minima with funnel-like character. The choice of a sequence that fits well into one of these predetermined structures facilitates rapid and cooperative folding. Our model calculations show that this novel phase facilitates the formation of an efficient route for sequence design starting from random peptides.

q-bio.BM↗

arXiv2011

Spatial effects on species persistence and implications for biodiversity

Natural ecosystems are characterized by striking diversity of form and functions and yet exhibit deep symmetries emerging across scales of space, time and organizational complexity. Species-area relationships and species-abundance distributions are examples of emerging patterns irrespective of the details of the underlying ecosystem functions. Here we present empirical and theoretical evidence for a new macroecological pattern related to the distributions of local species persistence times, defined as the timespans between local colonizations and extinctions in a given geographic region. Empirical distributions pertaining to two different taxa, breeding birds and herbaceous plants, analyzed in a new framework that accounts for the finiteness of the observational period, exhibit power-law scaling limited by a cut-off determined by the rate of emergence of new species. In spite of the differences between taxa and spatial scales of analysis, the scaling exponents are statistically indistinguishable from each other and significantly different from those predicted by existing models. We theoretically investigate how the scaling features depend on the structure of the spatial interaction network and show that the empirical scaling exponents are reproduced once a two-dimensional isotropic texture is used, regardless of the details of the ecological interactions. The framework developed here also allows to link the cut-off timescale with the spatial scale of analysis, and the persistence-time distribution to the species-area relationship. We conclude that the inherent coherence obtained between spatial and temporal macroecological patterns points at a seemingly general feature of the dynamical evolution of ecosystems.

physics.bio-ph↗

arXiv2011

Analysis of noise-induced bistability in Michaelis Menten single-step enzymatic cycle

In this paper we study noise-induced bistability in a specific circuit with many biological implications, namely a single-step enzymatic cycle described by Michaelis Menten equations with quasi-steady state assumption. We study the system both with a Master Equation formalism, and with the Fokker-Planck continuous approximation, characterizing the conditions in which the continuous approach is a good approximation of the exact discrete model. An analysis of the stationary distribution in both cases shows that bimodality can not occur in such a system. We discuss which additional requirements can generate stochastic bimodality, by coupling the system with a chemical reaction involving enzyme production and turnover. This extended system shows a bistable behaviour only in specific parameter windows depending on the number of molecules involved, providing hints about which should be a feasible system size in order that such a phenomenon could be exploited in real biological systems.

physics.bio-ph↗

arXiv2011

The second law, maximum entropy production and Liouville's theorem

In 1965 Jaynes provided an intuitively simple proof of the 2nd law of thermodynamics as a general requirement for any macroscopic transition to be experimentally reproducible. His proof was based on Boltzmann's formula S = klnW and the dynamical invariance of the phase volume W for isolated systems (Liouville's theorem). Here Jaynes' proof is extended to show that Liouville's theorem also implies maximum entropy production (MaxEP) for the stationary states of open, non-equilibrium systems. According to this proof, MaxEP stationary states are selected because they can exist within a greater number of environments than any other stationary states. Liouville's theorem applied to isolated systems also gives an intuitive derivation of the fluctuation theorem in a form consistent with an earlier conjecture by Jaynes on the probability of violations of the 2nd law. The present proof of MaxEP, while largely heuristic, suggests an approach to establishing a more fundamental basis for MaxEP using Jaynes' maximum entropy formulation of statistical mechanics.

cond-mat.stat-mech↗

arXiv2011

Prescription-induced jump distributions in multiplicative Poisson processes

Generalized Langevin equations (GLE) with multiplicative white Poisson noise pose the usual prescription dilemma leading to different evolution equations (master equations) for the probability distribution. Contrary to the case of multiplicative gaussian white noise, the Stratonovich prescription does not correspond to the well known mid-point (or any other intermediate) prescription. By introducing an inertial term in the GLE we show that the Ito and Stratonovich prescriptions naturally arise depending on two time scales, the one induced by the inertial term and the other determined by the jump event. We also show that when the multiplicative noise is linear in the random variable one prescription can be made equivalent to the other by a suitable transformation in the jump probability distribution. We apply these results to a recently proposed stochastic model describing the dynamics of primary soil salinization, in which the salt mass balance within the soil root zone requires the analysis of different prescriptions arising from the resulting stochastic differential equation forced by multiplicative white Poisson noise whose features are tailored to the characters of the daily precipitation. A method is finally suggested to infer the most appropriate prescription from the data.

cond-mat.stat-mech↗

arXiv2010

System size expansion for systems with an absorbing state

The well known van Kampen system size expansion, while of rather general applicability, is shown to fail to reproduce some qualitative features of the time evolution for systems with an absorbing state, apart from a transient initial time interval. We generalize the van Kampen ansatz by introducing a new prescription leading to non-Gaussian fluctuations around the absorbing state. The two expansion predictions are explicitly compared for the infinite range voter model with speciation as a paradigmatic model with an absorbing state. The new expansion, both for a finite size system in the large time limit and at finite time in the large size limit, converges to to the exact solution as obtained in a numerical implementation using the Gillespie algorithm. Furthermore, the predicted lifetime distribution is shown to have the correct asymptotic behavior.

cond-mat.stat-mech↗

arXiv2010

A simplified exactly solvable model for beta-amyloid aggregation

We propose an exactly solvable simplified statistical mechanical model for the thermodynamics of beta-amyloid aggregation, generalizing a well-studied model for protein folding. The monomer concentration is explicitly taken into account as well as a non trivial dependence on the microscopic degrees of freedom of the single peptide chain, both in the alpha-helix folded isolated state and in the fibrillar one. The phase diagram of the model is studied and compared to the outcome of fibril formation experiments which is qualitatively reproduced.

q-bio.BM↗

arXiv2010

Self-Similarity and Scaling in Forest Communities

Ecological communities exhibit pervasive patterns and inter-relationships between size, abundance, and the availability of resources. We use scaling ideas to develop a unified, model-independent framework for understanding the distribution of tree sizes, their energy use and spatial distribution in tropical forests. We demonstrate that the scaling of the tree crown at the individual level drives the forest structure when resources are fully used. Our predictions match perfectly with the scaling behaviour of an exactly solvable self-similar model of a forest and are in good accord with empirical data. The range, over which pure power law behaviour is observed, depends on the available amount of resources. The scaling framework can be used for assessing the effects of natural and anthropogenic disturbances on ecosystem structure and functionality.

cond-mat.stat-mech↗

arXiv2009

Universal Scaling of Optimal Current Distribution in Transportation Networks

Transportation networks are inevitably selected with reference to their global cost which depends on the strengths and the distribution of the embedded currents. We prove that optimal current distributions for a uniformly injected d-dimensional network exhibit robust scale-invariance properties, independently of the particular cost function considered, as long as it is convex. We find that, in the limit of large currents, the distribution decays as a power law with an exponent equal to (2d-1)/(d-1). The current distribution can be exactly calculated in d=2 for all values of the current. Numerical simulations further suggest that the scaling properties remain unchanged for both random injections and by randomizing the convex cost functions.

cond-mat.stat-mech↗

arXiv2009

First-principles design of nanomachines

Learning from nature's amazing molecular machines, globular proteins, we present a framework for the predictive design of nano-machines. We show that the crucial ingredients for a chain molecule to behave as a machine are its inherent anisotropy and the coupling between the local Frenet coordinate reference frames of nearby monomers. We demonstrate that, even in the absence of heterogeneity, protein-like behavior is obtained for a simple chain molecule made up of just thirty hard spheres. This chain spontaneously switches between two distinct geometries, a single helix and a dual helix, merely due to thermal fluctuations.

cond-mat.soft↗

arXiv2009

Probing Noise in Gene Expression and Protein Production

We derive exact solutions of simplified models for the temporal evolution of the protein concentration within a cell population arbitrarily far from the stationary state. We show that monitoring the dynamics can assist in modeling and understanding the nature of the noise and its role in gene expression and protein production. We introduce a new measure, the cell turnover distribution, which can be used to probe the phase of transcription of DNA into messenger RNA.

q-bio.BM↗

arXiv2009

Self-Templated Nucleation in Peptide and Protein aggregation

Peptides and proteins exhibit a common tendency to assemble into highly ordered fibrillar aggregates, whose formation proceeds in a nucleation-dependent manner that is often preceded by the formation of disordered oligomeric assemblies. This process has received much attention because disordered oligomeric aggregates have been associated with neurodegenerative disorders such as Alzheimer's and Parkinson's diseases. Here we describe a self-templated nucleation mechanism that determines the transition between the initial condensation of polypeptide chains into disordered assemblies and their reordering into fibrillar structures. The results that we present show that at the molecular level this transition is due to the ability of polypeptide chains to reorder within oligomers into fibrillar assemblies whose surfaces act as templates that stabilise the disordered assemblies.

q-bio.BM↗