152 research outputs found
Chain stiffness bridges conventional polymer and bio-molecular phases
No full textChain molecules play important roles in industry and in living cells. Our focus here is on distinct ways of modeling the stiffness inherent in a chain molecule. We consider three types of stiffnesses—one yielding an energy penalty for local bends (energetic stiffness) and the other two forbidding certain classes of chain conformations (entropic stiffness). Using detailed Wang-Landau microcanonical Monte Carlo simulations, we study the interplay between the nature of the stiffness and the ground state conformation of a self-attracting chain. We find a wide range of ground state conformations, including a coil, a globule, a toroid, rods, helices, and zig-zag strands resembling β-sheets, as well as knotted conformations allowing us to bridge conventional polymer phases and biomolecular phases. An analytical mapping is derived between the persistence lengths stemming from energetic and entropic stiffness. Our study shows unambiguously that different stiffnesses play different physical roles and have very distinct effects on the nature of the ground state of the conformation of a chain, even if they lead to identical persistence lengths
Optimal transport from a point-like source
No full textWe present a dynamical interpretation of the Monge-Kanto-rovich theory in a stationary regime. This new principle, akin to the Fermat principle of geometrical optics, captures the geodesic character of many distribution networks such as plant roots, river basins and the physiological transportation network of metabolites in living systems. Our general continuum framework allows us to map a previously proposed phenomenological principle into a stationary Monge optimization principle in the Kantorovich relaxed format
A non-equilibrium percolation transition in random Ising ferromagnets
No full textWe study the geometrical properties of the domain structure that results when a random Ising ferromagnet is quenched to zero temperature. We define a novel connectivity transition between like spins in the frozen configuration, and show that it is in a new universality class, distinct from that of random percolation. The scaling is robust and independent of model details. The relevance of this transition to spinodal decomposition is discussed
Local sequence‐structure relationships in proteins
No full textWe seek to understand the interplay between amino acid sequence and local structure in proteins. Are some amino acids unique in their ability to fit harmoniously into certain local structures? What is the role of sequence in sculpting the putative native state folds from myriad possible conformations? In order to address these questions, we represent the local structure of each C-alpha atom of a protein by just two angles, theta and mu, and we analyze a set of more than 4,000 protein structures from the PDB. We use a hierarchical clustering scheme to divide the 20 amino acids into six distinct groups based on their similarity to each other in fitting local structural space. We present the results of a detailed analysis of patterns of amino acid specificity in adopting local structural conformations and show that the sequence-structure correlation is not very strong compared with a random assignment of sequence to structure. Yet, our analysis may be useful to determine an effective scoring rubric for quantifying the match of an amino acid to its putative local structure
Seeing the forest for the trees through metabolic scaling
No full text8 pagesWe demonstrate that when power scaling occurs for an individual tree and in a forest, there is great resulting simplicity notwithstanding the underlying complexity characterizing the system over many size scales. Our scaling framework unifies seemingly distinct trends in a forest and provides a simple yet promising approach to quantitatively understand a bewilderingly complex many-body system with imperfectly known interactions. We show that the effective dimension, Dtree, of a tree is close to 3, whereas a mature forest has Dforest approaching 1. We discuss the energy equivalence rule and show that the metabolic rate–mass relationship is a power law with an exponent D/(D + 1) in both cases leading to a Kleiber’s exponent of 3/4 for a tree and 1/2 for a forest. Our work has implications for understanding carbon sequestration and for climate science
Shapes of hydrophobic thick membranes
No full textWe 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
Maximum entropy approach for deducing amino Acid interactions in proteins
No full textWe present a maximum entropy approach for inferring amino acid interactions in proteins subject to constraints pertaining to the mean numbers of various types of equilibrium contacts for a given sequence or a set of sequences. We have carried out several kinds of tests for a two-dimensional lattice model with just two types of amino acids with very promising results. We also show that the method works very well even when the mean numbers of contacts are not known and therefore can be applied to real proteins
Inverse problem for multivariate time series using dynamical latent variables
No full textFactor analysis is a well known statistical method to describe the variability among observed variables in terms of a smaller number of unobserved latent variables called factors. While dealing with multivariate time series, the temporal correlation structure of data may be modeled by including correlations in latent factors, but a crucial choice is the covariance function to be implemented. We show that analyzing multivariate time series in terms of latent Gaussian processes, which are mutually independent but with each of them being characterized by exponentially decaying temporal correlations, leads to an efficient implementation of the expectation-maximization algorithm for the maximum likelihood estimation of parameters, due to the properties of block-tridiagonal matrices. The proposed approach solves an ambiguity known as the identifiability problem, which renders the solution of factor analysis determined only up to an orthogonal transformation. Samples with just two temporal points are sufficient for the parameter estimation: hence the proposed approach may be applied even in the absence of prior information about the correlation structure of latent variables by fitting the model to pairs of points with varying time delay. Our modeling allows one to make predictions of the future values of time series and we illustrate our method by applying it to an analysis of published gene expression data from cell culture HeLa
Emergence of structural and dynamical properties of ecological mutualistic networks
No full textMutualistic networks are formed when the interactions between two classes of species are mutually beneficial. They are important examples of cooperation shaped by evolution. Mutualism between animals and plants has a key role in the organization of ecological communities. Such networks in ecology have generally evolved a nested architecture independent of species composition and latitude; specialist species, with only few mutualistic links, tend to interact with a proper subset of the many mutualistic partners of any of the generalist species. Despite sustained efforts to explain observed network structure on the basis of community-level stability or persistence, such correlative studies have reached minimal consensus. Here we show that nested interaction networks could emerge as a consequence of an optimization principle aimed at maximizing the species abundance in mutualistic communities. Using analytical and numerical approaches, we show that because of the mutualistic interactions, an increase in abundance of a given species results in a corresponding increase in the total number of individuals in the community, and also an increase in the nestedness of the interaction matrix. Indeed, the species abundances and the nestedness of the interaction matrix are correlated by a factor that depends on the strength of the mutualistic interactions. Nestedness and the observed spontaneous emergence of generalist and specialist species occur for several dynamical implementations of the variational principle under stationary conditions. Optimized networks, although remaining stable, tend to be less resilient than their counterparts with randomly assigned interactions. In particular, we show analytically that the abundance of the rarest species is linked directly to the resilience of the community. Our work provides a unifying framework for studying the emergent structural and dynamical properties of ecological mutualistic networks
Spatial aggregation and the species-area relationship across scales
No full textThere 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 paper 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
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