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Amos Maritan

Publications and source records attributed to Amos Maritan.

At least 127 records · Page 7Linked to original sources
arXiv2008

Emergence of Secondary Motifs in Tube-Like Polymers in a Solvent

We study the effects of two kinds of interactions in tube-like polymers and demonstrate that they result in the formation of secondary motifs. The first has an entropic origin and is a measure of the effective space available to the solvent. The second arises from solvophobic interactions of the solvent with the polymers and leads to an energy proportional to the contact surface between the tube and solvent particles. The solvent molecules are modeled as hard spheres and the two interactions are considered separately with the solvent density affecting their relative strength. In addition to analytical calculations, we present the results of numerical simulations in order to understand the role played by the finite length of short polymers and the discrete versus continuum descriptions of the system in determining the preferred conformation.

cond-mat.stat-mech↗
arXiv2007

Symmetry, shape, and order

Packing problems have been of great interest in many diverse contexts for many centuries. The optimal packing of identical objects has been often invoked to understand the nature of low temperature phases of matter. In celebrated work, Kepler conjectured that the densest packing of spheres is realized by stacking variants of the face-centered cubic lattice and has a packing fraction of $π/(3\sqrt{2}) \sim 0.7405$. Much more recently, an unusually high density packing of approximately 0.770732 was achieved for congruent ellipsoids. Such studies are relevant for understanding the structure of crystals, glasses, the storage and jamming of granular materials, ceramics, and the assembly of viral capsid structures. Here we carry out analytical studies of the stacking of close-packed planar layers of systems made up of truncated cones possessing uniaxial symmetry. We present examples of high density packing whose order is characterized by a {\em broken symmetry} arising from the shape of the constituent objects. We find a biaxial arrangement of solid cones with a packing fraction of $π/4$. For truncated cones, there are two distinct regimes, characterized by different packing arrangements, depending on the ratio $c$ of the base radii of the truncated cones with a transition at $c^*=\sqrt{2}-1$.

cond-mat.stat-mech↗
arXiv2007

Structural motifs of biomolecules

Biomolecular structures are assemblies of emergent anisotropic building modules such as uniaxial helices or biaxial strands. We provide an approach to understanding a marginally compact phase of matter that is occupied by proteins and DNA. This phase, which is in some respects analogous to the liquid crystal phase for chain molecules, stabilizes a range of shapes that can be obtained by sequence-independent interactions occurring intra- and intermolecularly between polymeric molecules. We present a singularityfree self-interaction for a tube in the continuum limit and show that this results in the tube being positioned in the marginally compact phase. Our work provides a unified framework for understanding the building blocks of biomolecules.

q-bio.BM↗
arXiv2007

The maximum relative entropy principle

We show that the naive application of the maximum entropy principle can yield answers which depend on the level of description, i.e. the result is not invariant under coarse-graining. We demonstrate that the correct approach, even for discrete systems, requires maximization of the relative entropy with a suitable reference probability, which in some instances can be deduced from the symmetry properties of the dynamics. We present simple illustrations of this crucial yet surprising feature in examples of classical and quantum statistical mechanics, as well as in the field of ecology.

cond-mat.stat-mech↗
arXiv2006

Geometry of proteins: hydrogen bonding, sterics and marginally compact tubes

The functionality of proteins is related to their structure in the native state. Protein structures are made up of emergent building blocks of helices and almost planar sheets. A simple coarse-grained geometrical model of a flexible tube barely subject to compaction provides a unified framework for understanding the common character of globular proteins.We argue that a recent critique of the tube idea is not well founded.

q-bio.BM↗
arXiv2005

Spatial Scaling in Model Plant Communities

We present an analytically tractable variant of the voter model that provides a quantitatively accurate description of beta-diversity (two-point correlation function) in two tropical forests. The model exhibits novel scaling behavior that leads to links between ecological measures such as relative species abundance and the species area relationship.

q-bio.PE↗
arXiv2005

Proteins and polymers

Proteins, chain molecules of amino acids, behave in ways which are similar to each other yet quite distinct from standard compact polymers. We demonstrate that the Flory theorem, derived for polymer melts, holds for compact protein native state structures and is not incompatible with the existence of structured building blocks such as $α$-helices and $β$-strands. We present a discussion on how the notion of the thickness of a polymer chain, besides being useful in describing a chain molecule in the continuum limit, plays a vital role in interpolating between conventional polymer physics and the phase of matter associated with protein structures.

q-bio.BM↗
arXiv2005

Geometrical model for the native-state folds of proteins

We recently introduced a physical model [Hoang et al., P. Natl. Acad. Sci. USA (2004), Banavar et al., Phys. Rev. E (2004)] for proteins which incorporates, in an approximate manner, several key features such as the inherent anisotropy of a chain molecule, the geometrical and energetic constraints placed by the hydrogen bonds and sterics, and the role played by hydrophobicity. Within this framework, marginally compact conformations resembling the native state folds of proteins emerge as broad competing minima in the free energy landscape even for a homopolymer. Here we show how the introduction of sequence heterogeneity using a simple scheme of just two types of amino acids, hydrophobic (H) and polar (P), and sequence design allows a selected putative native fold to become the free energy minimum at low temperature. The folding transition exhibits thermodynamic cooperativity, if one neglects the degeneracy between two different low energy conformations sharing the same fold topology.

q-bio.BM↗
arXiv2005

Neutral Theory and Relative Species Abundance in Ecology

The theory of island biogeography[1] asserts that an island or a local community approaches an equilibrium species richness as a result of the interplay between the immigration of species from the much larger metacommunity source area and local extinction of species on the island (local community). Hubbell[2] generalized this neutral theory to explore the expected steady-state distribution of relative species abundance (RSA) in the local community under restricted immigration. Here we present a theoretical framework for the unified neutral theory of biodiversity[2] and an analytical solution for the distribution of the RSA both in the metacommunity (Fisher's logseries) and in the local community, where there are fewer rare species. Rare species are more extinction-prone, and once they go locally extinct, they take longer to re-immigrate than do common species. Contrary to recent assertions[3], we show that the analytical solution provides a better fit, with fewer free parameters, to the RSA distribution of tree species on Barro Colorado Island (BCI)[4] than the lognormal distribution[5,6].

q-bio.PE↗
arXiv2005

Pretransitional behavior in a water-DDAB-5CB microemulsion close to the demixing transition. Evidence for intermicellar attraction mediated by paranematic fluctuations

We present a study of a water-in-oil microemulsion in which surfactant coated water nanodroplets are dispersed in the isotropic phase of the thermotropic liquid crystal 5CB. As the temperature is lowered below the isotropic to nematic phase transition of pure 5CB, the system displays a demixing transition leading to a coexistence of a droplet rich isotropic phase with a droplet poor nematic. The transition is anticipated, in the high T side, by increasing pretransitional fluctuations in 5CB molecular orientation and in the nanodroplet concentration. The observed phase behavior supports the notion that the nanosized droplets, while large enough for their statistical behavior to be probed via light scattering, are also small enough to act as impurities, disturbing the local orientational ordering of the liquid crystal and thus experiencing pretransitional attractive interaction mediated by paranematic fluctuations. The pretransitional behavior, together with the topology of the phase diagram, can be understood on the basis of a diluted Lebwohl-Lasher model which describes the nanodroplets simply as holes in the liquid crystal.

cond-mat.soft↗
arXiv2004

Lattice tube model of proteins

We present a new lattice model for proteins that incorporates a tube-like anisotropy by introducing a preference for mutually parallel alignments in the conformations. The model is demonstrated to capture many aspects of real proteins.

q-bio.BM↗
arXiv2004

Unified perspective on proteins: A physics approach

We study a physical system which, while devoid of the complexity one usually associates with proteins, nevertheless displays a remarkable array of protein-like properties. The constructive hypothesis that this striking resemblance is not accidental leads not only to a unified framework for understanding protein folding, amyloid formation and protein interactions but also has implications for natural selection.

cond-mat.stat-mech↗
arXiv2004

Network Structures from Selection Principles

We present an analysis of the topologies of a class of networks which are optimal in terms of the requirements of having as short a route as possible between any two nodes while yet keeping the congestion in the network as low as possible. Strikingly, we find a variety of distinct topologies and novel phase transitions between them on varying the number of links per node. Our results suggest that the emergence of the topologies observed in nature may arise both from growth mechanisms and the interplay of dynamical mechanisms with a selection process.

cond-mat.stat-mech↗
arXiv2004

Geometry and symmetry presculpt the free-energy landscape of proteins

We present a simple physical model which demonstrates that the native state folds of proteins can emerge on the basis of considerations of geometry and symmetry. We show that the inherent anisotropy of a chain molecule, the geometrical and energetic constraints placed by the hydrogen bonds and sterics, and hydrophobicity are sufficient to yield a free energy landscape with broad minima even for a homopolymer. These minima correspond to marginally compact structures comprising the menu of folds that proteins choose from to house their native-states in. Our results provide a general framework for understanding the common characteristics of globular proteins.

q-bio.BM↗
arXiv2004

What one can learn from experiments about the elusive transition state?

We present the results of an exact analysis of a model energy landscape of a protein to clarify the notion of the transition state and the physical meaning of the $ϕ$ values determined in protein engineering experiments. We benchmark our findings to various theoretical approaches proposed in the literature for the identification and characterization of the transition state.

q-bio.BM↗
arXiv2004

Accurate and efficient description of protein vibrational dynamics: comparing molecular dynamics and Gaussian models

Current all-atom potential based molecular dynamics (MD) allow the identification of a protein's functional motions on a wide-range of time-scales, up to few tens of ns. However, functional large scale motions of proteins may occur on a time-scale currently not accessible by all-atom potential based molecular dynamics. To avoid the massive computational effort required by this approach several simplified schemes have been introduced. One of the most satisfactory is the Gaussian Network approach based on the energy expansion in terms of the deviation of the protein backbone from its native configuration. Here we consider an extension of this model which captures in a more realistic way the distribution of native interactions due to the introduction of effective sidechain centroids. Since their location is entirely determined by the protein backbone, the model is amenable to the same exact and computationally efficient treatment as previous simpler models. The ability of the model to describe the correlated motion of protein residues in thermodynamic equilibrium is established through a series of successful comparisons with an extensive (14 ns) MD simulation based on the AMBER potential of HIV-1 protease in complex with a peptide substrate. Thus, the model presented here emerges as a powerful tool to provide preliminary, fast yet accurate characterizations of proteins near-native motion.

cond-mat.stat-mech↗
arXiv2004

A Stochastic Model for the Species Abundance Problem in an Ecological Community

We propose a model based on coupled multiplicative stochastic processes to understand the dynamics of competing species in an ecosystem. This process can be conveniently described by a Fokker-Planck equation. We provide an analytical expression for the marginalized stationary distribution. Our solution is found in excellent agreement with numerical simulations and compares rather well with observational data from tropical forests.

q-bio.PE↗