1,721,089 research outputs found
Universality for interacting oriented self-avoiding walk: A transfer matrix calculation
No full textIn this paper we perform transfer matrix calculations to study the two-dimensional problem of oriented self-avoiding walks on a square lattice where nearest neighbor interactions depend on the relative orientation (parallel or antiparallel) between different parts of the path. Our main purpose is to verify a conformal field theory conjecture that the entropic exponent gamma, which is related to the number of such walks, varies continuously with the energy of the parallel interaction. We find no evidence of this behavior, but see many unexpected features for the model, such as the existence of a line of a points belonging to the universality class of polymer collapse on a Manhattan lattice. Finally we study the phase diagram in the parallel and antiparallel interaction planes and we conjecture a crucial role for the standard a point
Simple model to study insertion of a protein into a membrane
No full textA simple coarse grained model on a two-dimensional lattice is presented to elucidate the main effects ruling the insertion of a protein into a polar environment such as a lipidic membrane. The amino acids are divided into two classes (hydrophobic or polar), and they behave differently according to their surroundings. In aqueous solution the hydrophobic amino acids are forced to minimize contacts with water, whereas in the apolar environment all the amino acids try to aggregate regardless to their specificity. The lattice is employed in order to perform exact calculations and to generate a fictitious protein data bank. Despite the simplicity of the model, some morphological features of the proteinlike lattice structures obtained by our model are compatible with the observed phenomenology of transmembrane proteins. These results seem to corroborate the hypothesis that the number of classes into which the amino acids can be divided that correctly describe the phenomena may be extremely low
Minireview: The compact phase in polymers and proteins
No full textProteins are linear molecules. However, the simple model of a polymer viewed as spheres tethered together does not account for many of the observed characteristics of protein structures. Here we review some recent works tackling this problem. In particular, we will show that there is a growing evidence suggesting that the compact structures of folded proteins are selected in their gross topological features based on geometry and symmetry rather than on sequence consideration. They are poised at the edge of compaction, thus accounting for their flexibility, Different aspects of protein behavior can be rationalized by studying how the energy landscape of a single chain in the marginally compact phase can be modified
Phase diagram of branched polymer collapse
No full textThe phase diagram of the collapse of a two-dimensional infinite branched polymer interacting with the solvent and with itself through contact interactions is studied from the q --> 1 limit of an extension of the q-state Potts model. Exact solution on the Bethe lattice and Migdal-Kadanoff renormalization group calculations shows that there is a line of theta transitions from the extended to a single compact phase. The theta line, governed by three different fixed points, consists of two lines of extended-compact transitions which are in different universality classes and meet in a multicritical point. On the other hand, directed branched polymers are shown to be completely determined by the strongly embedded case and there is a single theta transition which is in the directed percolation universality class
Surface Exponents For A Linear Polymer At the D = 2 Phi-point
No full textBy extending a previous analysis of bulk properties, accurate Monte Carlo enumerations of SAW with attractive n.n. interactions on the square lattice are used to obtain γ1t = 0.57 ± 0.09 and γ11t = -0.53 ± 0.10 for the entropic boundary exponents at the Θ-point. This gives new indications concerning the possible validity of recent conjectures about the Θ-point universality class. In particular, under plausible assumptions, these results appear compatible with a field-theoretic description in terms of a nonunitary superconformal field theory with central charge c = 1/2, for which γ1t = 15/28 and γ11t = -4/7 should be expected
Simulations of deposition growth models in various dimensions: The possible importance of overhangs
No full textWe present simulation results of deposition growth of surfaces in two, three, and four dimensions for ballistic deposition where overhangs are present, and for restricted solid on solid deposition where there are no overhangs. The values of the scaling exponents for the two models are found to be different, suggesting that they belong to different universality classes
Conduction and Connection Properties of Self-avoiding Walks With Bridges
No full textThe voltage drop distribution in the random-resistor networks constituted by all nearest-neighbor bonds connecting points visited by a lattice self-avoiding walk (SAW) is studied by accurate numerical techniques in d=2. An analysis of the moments of the distribution allows one to establish the value ζ=1.333±0.007 for the resistance exponent and to exclude the possibility of multifractal behavior. These results are also consistent with a topological investigation of the connection properties of SAW, which independently yields ζ=1.33±0.01. This clearly supports ζ=(4/3 and a spectral dimension d̃=1 for these walks, solving an old controversy. A possible extension of such an analysis to SAW at the FTHETA point is also discussed
Nonuniversality In the Collapse of 2-dimensional Branched Polymers
No full textIn this paper we study the complete phase diagram of a model of interacting branched polymers. The model we consider is a lattice animal one, where the collapse transition can be driven both by a contact fugacity between two occupied nearest neighbours and by a fugacity related to each occupied edge. Using a Potts model formulation of the problem we conjecture the existence of two different universality classes for the theta transitions (with thermal exponents, nu and phi, equal to (1/2, 2/3) and (8/15, 8/15)), separated by a higher-order percolation point. We also present convincing numerical evidence for these exponent values using a transfer-matrix approach. We discuss the possibility of a collapse-collapse transition and we predict the behaviour of our model when an adsorbing surface is included
A new perspective on analysis of helix-helix packing preferences in globular proteins
No full textFor many years, statistical analysis of protein databanks has led to the belief that the steric compatibility of helix interfaces may be the source of observed preferences for particular angles between neighboring helices. Several elegant models describing how side chains on helices can interdigitate without steric clashes were able to account quite reasonably for the observed distributions. However, it was later recognized that the 'bare' measured angle distribution should be corrected to avoid statistical bias.(1,2) Disappointingly, the resealed distributions dramatically lost their similarity with theoretical predictions, casting doubts on the validity of the geometrical assumptions and models. In this article, we elucidate a few points concerning the proper choice of a random reference distribution. In particular we demonstrate the need for corrections induced by unavoidable uncertainties in determining whether two helices are in face-to-face contact or not and their relative orientations. By using this new resealing, we show that 'true' packing angle preferences are well described by regular packing models, thus proving that preferential angles between contacting helices do exist
Two dimensional self-avoiding walk with hydrogen-like bonding: phase diagram and critical behaviour
No full textThe phase diagram for a two-dimensional self-avoiding walk model on the square lattice incorporating attractive short-ranged interactions between parallel sections of walk is derived using numerical transfer matrix techniques. The model displays a collapse transition. In contrast to the standard θ-point model, the transition is first order. The phase diagram in the full fugacity–temperature plane displays an additional transition line, when compared to the θ-point model, as well as a critical transition at finite temperature in the Hamiltonian walk limit
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