Thermodynamic origin of cooperativity in actomyosin interactions: The coupling of short-range interactions with actin bending stiffness in an Ising-like model

We present Monte Carlo simulations for a molecular motor system found in virtually all eukaryotic cells, the acto-myosin motor system, composed of a group of organic macromolecules. Cell motors were mapped to an Ising-like model, where the interaction field is transmitted through a tropomyosin polymer chain. The presence of Ca(2+) induces tropomyosin to block or unblock binding sites of the myosin motor leading to its activation or deactivation. We used the Metropolis algorithm to find the transient and the equilibrium states of the acto-myosin system composed of solvent, actin, tropomyosin, troponin, Ca(2+), and myosin-S1 at a given temperature, including the spatial configuration of tropomyosin on the actin filament surface. Our model describes the short- and long-range cooperativity during actin-myosin binding which emerges from the bending stiffness of the tropomyosin complex. We found all transition rates between the states only using the interaction energy of the constituents. The agreement between our model and experimental data also supports the recent theory of flexible tropomyosin.

Integrability and exact solution of an electronic model with long range interactions

We present an electronic model with long range interactions. Through the quantum inverse scattering method, integrability of the model is established using a one-parameter family of typical irreducible representations of gl(211). The eigenvalues of the conserved operators are derived in terms of the Bethe ansatz, from which the energy eigenvalues of the Hamiltonian are obtained.

T-Cell Receptors Binding Orientation over Peptide/MHC Class I Is Driven by Long-Range Interactions.

Crystallographic data about T-Cell Receptor - peptide - major histocompatibility complex class I (TCRpMHC) interaction have revealed extremely diverse TCR binding modes triggering antigen recognition. Understanding the molecular basis that governs TCR orientation over pMHC is still a considerable challenge. We present a simplified rigid approach applied on all non-redundant TCRpMHC crystal structures available. The CHARMM force field in combination with the FACTS implicit solvation model is used to study the role of long-distance interactions between the TCR and pMHC. We demonstrate that the sum of the coulomb interactions and the electrostatic solvation energies is sufficient to identify two orientations corresponding to energetic minima at 0° and 180° from the native orientation. Interestingly, these results are shown to be robust upon small structural variations of the TCR such as changes induced by Molecular Dynamics simulations, suggesting that shape complementarity is not required to obtain a reliable signal. Accurate energy minima are also identified by confronting unbound TCR crystal structures to pMHC. Furthermore, we decompose the electrostatic energy into residue contributions to estimate their role in the overall orientation. Results show that most of the driving force leading to the formation of the complex is defined by CDR1,2/MHC interactions. This long-distance contribution appears to be independent from the binding process itself, since it is reliably identified without considering neither short-range energy terms nor CDR induced fit upon binding. Ultimately, we present an attempt to predict the TCR/pMHC binding mode for a TCR structure obtained by homology modeling. The simplicity of the approach and the absence of any fitted parameters make it also easily applicable to other types of macromolecular protein complexes.

Long-range-interactions induced ordered structures in deposition processes

We present a new model of sequential adsorption in which the adsorbing particles experience dipolar interactions. We show that in the presence of these long-range interactions, highly ordered structures in the adsorbed layer may be induced at low temperatures. The new phenomenology is manifest through significant variations of the pair correlation function and the jamming limit, with respect to the case of noninteracting particles. Our study could be relevant in understanding the adsorption of magnetic colloidal particles in the presence of a magnetic field.

Local thermodynamics and the generalized Gibbs-Duhem equation in systems with long-range interactions

The local thermodynamics of a system with long-range interactions in d dimensions is studied using the mean-field approximation. Long-range interactions are introduced through pair interaction potentials that decay as a power law in the interparticle distance. We compute the local entropy, Helmholtz free energy, and grand potential per particle in the microcanonical, canonical, and grand canonical ensembles, respectively. From the local entropy per particle we obtain the local equation of state of the system by using the condition of local thermodynamic equilibrium. This local equation of state has the form of the ideal gas equation of state, but with the density depending on the potential characterizing long-range interactions. By volume integration of the relation between the different thermodynamic potentials at the local level, we find the corresponding equation satisfied by the potentials at the global level. It is shown that the potential energy enters as a thermodynamic variable that modifies the global thermodynamic potentials. As a result, we find a generalized Gibbs-Duhem equation that relates the potential energy to the temperature, pressure, and chemical potential. For the marginal case where the power of the decaying interaction potential is equal to the dimension of the space, the usual Gibbs-Duhem equation is recovered. As examples of the application of this equation, we consider spatially uniform interaction potentials and the self-gravitating gas. We also point out a close relationship with the thermodynamics of small systems.

Bright solitons in a quasi-one-dimensional reduced model of a dipolar Bose-Einstein condensate with repulsive short-range interactions

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Thermodynamics of Ising model with infinite-range interactions by generalized canonical ensemble

In this work we present the idea of how generalized ensembles can be used to simplify the operational study of non-additive physical systems. As alternative of the usual methods of direct integration or mean-field theory, we show how the solution of the Ising model with infinite-range interactions is obtained by using a generalized canonical ensemble. We describe how the thermodynamical properties of this model in the presence of an external magnetic field are founded by simple parametric equations. Without impairing the usual interpretation, we obtain an identical critical behaviour as observed in traditional approaches.

Critical behavior of su(1|1) supersymmetric spin chains with long-range interactions

We introduce a general class of su(1|1) supersymmetric spin chains with long-range interactions which includes as particular cases the su(1|1) Inozemtsev (elliptic) and Haldane-Shastry chains, as well as the XX model. We show that this class of models can be fermionized with the help of the algebraic properties of the su(1|1) permutation operator and take advantage of this fact to analyze their quantum criticality when a chemical potential term is present in the Hamiltonian. We first study the low-energy excitations and the low-temperature behavior of the free energy, which coincides with that of a (1+1)-dimensional conformal field theory (CFT) with central charge c=1 when the chemical potential lies in the critical interval (0,E(π)), E(p) being the dispersion relation. We also analyze the von Neumann and Rényi ground state entanglement entropies, showing that they exhibit the logarithmic scaling with the size of the block of spins characteristic of a one-boson (1+1)-dimensional CFT. Our results thus show that the models under study are quantum critical when the chemical potential belongs to the critical interval, with central charge c=1. From the analysis of the fermion density at zero temperature, we also conclude that there is a quantum phase transition at both ends of the critical interval. This is further confirmed by the behavior of the fermion density at finite temperature, which is studied analytically (at low temperature), as well as numerically for the su(1|1) elliptic chain.

Detecting long-range chromatin interactions using the chromosome conformation capture sequencing (4C-seq) method.

Eukaryotic transcription is tightly regulated by transcriptional regulatory elements, even though these elements may be located far away from their target genes. It is now widely recognized that these regulatory elements can be brought in close proximity through the formation of chromatin loops, and that these loops are crucial for transcriptional regulation of their target genes. The chromosome conformation capture (3C) technique presents a snapshot of long-range interactions, by fixing physically interacting elements with formaldehyde, digestion of the DNA, and ligation to obtain a library of unique ligation products. Recently, several large-scale modifications to the 3C technique have been presented. Here, we describe chromosome conformation capture sequencing (4C-seq), a high-throughput version of the 3C technique that combines the 3C-on-chip (4C) protocol with next-generation Illumina sequencing. The method is presented for use in mammalian cell lines, but can be adapted to use in mammalian tissues and any other eukaryotic genome.

Classical simulation of deposition of thiophene oligomers on TiO(2)-anatase: Relevance of long-range electrostatic interactions

We performed classical molecular dynamics simulations of the vapor-deposition of alpha-T4 oligomers on the TiO(2)-anatase (101) surface, comparing different sets of charges associated with the atoms of the model. The potential energy surfaces for alpha-T4 and TiO(2) were described by re-parametrizations of the Universal force field with charges given by the charge equilibration (QEq) scheme, or with fixed charges obtained by an ab initio method using the Hirshfeld partition. The two sets of charges lead to completely different results for the interface formation, and for the characteristics of the organic film, with a clearly defined alpha-T4 contact layer in the QEq case, and a more homogeneous molecular distribution when using Hirshfeld charges. The main reason for the discrepancy was found to be the incorrect charge assignment given by QEq to the sulfur and alpha-carbon atoms in thiophenes, and highlight the relevance of long-range interactions in the organization of molecular films. (C) 2009 Elsevier B.V. All rights reserved.

Simulation of the Barkhausen Noise using random field Ising model with long-range interaction

We present a method to simulate the Magnetic Barkhausen Noise using the Random Field Ising Model with magnetic long-range interaction. The method allows calculating the magnetic flux density behavior in particular sections of the lattice reticule. The results show an internal demagnetizing effect that proceeds from the magnetic long-range interactions. This demagnetizing effect induces the appearing of a magnetic pattern in the region of magnetic avalanches. When compared with the traditional method, the proposed numerical procedure neatly reduces computational costs of simulation. (c) 2008 Published by Elsevier B.V.

Long-range automaton models of earthquakes: Power-law accelerations, correlation evolution, and mode-switching

We introduce a conceptual model for the in-plane physics of an earthquake fault. The model employs cellular automaton techniques to simulate tectonic loading, earthquake rupture, and strain redistribution. The impact of a hypothetical crustal elastodynamic Green's function is approximated by a long-range strain redistribution law with a r(-p) dependance. We investigate the influence of the effective elastodynamic interaction range upon the dynamical behaviour of the model by conducting experiments with different values of the exponent (p). The results indicate that this model has two distinct, stable modes of behaviour. The first mode produces a characteristic earthquake distribution with moderate to large events preceeded by an interval of time in which the rate of energy release accelerates. A correlation function analysis reveals that accelerating sequences are associated with a systematic, global evolution of strain energy correlations within the system. The second stable mode produces Gutenberg-Richter statistics, with near-linear energy release and no significant global correlation evolution. A model with effectively short-range interactions preferentially displays Gutenberg-Richter behaviour. However, models with long-range interactions appear to switch between the characteristic and GR modes. As the range of elastodynamic interactions is increased, characteristic behaviour begins to dominate GR behaviour. These models demonstrate that evolution of strain energy correlations may occur within systems with a fixed elastodynamic interaction range. Supposing that similar mode-switching dynamical behaviour occurs within earthquake faults then intermediate-term forecasting of large earthquakes may be feasible for some earthquakes but not for others, in alignment with certain empirical seismological observations. Further numerical investigation of dynamical models of this type may lead to advances in earthquake forecasting research and theoretical seismology.

Correspondence between long-range and short-range spin glasses

We compare the critical behavior of the short-range Ising spin glass with a spin glass with long-range interactions which fall off as a power σ of the distance. We show that there is a value of σ of the long-range model for which the critical behavior is very similar to that of the short range model in four dimensions. We also study a value of σ for which we find the critical behavior to be compatible with that of the three-dimensional model, although we have much less precision than in the four-dimensional case.

Copy number variation and chromatin structure

The functional consequences of structural variation in the human genome range from adaptation, to phenotypic variation, to predisposition to diseases. Copy number variation (CNV) was shown to influence the phenotype by modifying, in a somewhat dose-dependent manner, the expression of genes that map within them, as well as that of genes located on their flanks. To assess the possible mechanism(s) behind this neighboring effect, we compared histone modification status of cell lines from patients affected by Williams-Beuren, Williams-Beuren region duplication, Smith-Magenis or DiGeorge Syndrome and control individuals using a high-throughput version of chromatin immuno-precipitation method (ChIP), called ChlP-seq. We monitored monomethylation of lysine K20 on histone H4 and trimethylation of lysine K27 on histone H3, as proxies for open and condensed chromatin, respectively. Consistent with the changes in expression levels observed for multiple genes mapping on the entire length of chromosomes affected by structural variants, we also detected regions with modified histone status between samples, up- and downstream from the critical regions, up to the end of the rearranged chromosome. We also gauged the intrachromosomal interactions of these cell lines utilizing chromosome conformation capture (4C-seq) technique. We observed that a set of genes flanking the Williams-Beuren Syndrome critical region (WBSCR) were often looping together, possibly forming an interacting cluster with each other and the WBSCR. Deletion of the WBSCR disrupts the expression of this group of flanking genes, as well as long-range interactions between them and the rearranged interval. We conclude, that large genomic rearrangements can lead to changes in the state of the chromatin spreading far away from the critical region, thus possibly affecting expression globally and as a result modifying the phenotype of the patients. - Les conséquences fonctionnelles des variations structurelles dans le génome humain sont vastes, allant de l'adaptation, en passant par les variations phénotypiques, aux prédispositions à certaines maladies. Il a été démontré que les variations du nombre de copies (CNV) influencent le phénotype en modifiant, d'une manière plus ou moins dose-dépendante, l'expression des gènes se situant à l'intérieur de ces régions, mais également celle des gènes se trouvant dans les régions flanquantes. Afin d'étudier les mécanismes possibles sous-jacents à cet effet de voisinage, nous avons comparé les états de modification des histones dans des lignées cellulaires dérivées de patients atteints du syndrome de Williams-Beuren, de la duplication de la région Williams-Beuren, du syndrome de Smith-Magenis ou du syndrome de Di- George et d'individus contrôles en utilisant une version haut-débit de la méthode d'immunoprécipitation de la chromatine (ChIP), appelée ChIP-seq. Nous avons suivi la mono-méthylation de la lysine K20 sur l'histone H4 et la tri-méthylation de la lysine K27 sur l'histone H3, marqueurs respectifs de la chromatine ouverte et fermée. En accord avec les changements de niveaux d'expression observés pour de multiples gènes tout le long des chromosomes affectés par les CNVs, nous avons aussi détecté des régions présentant des modifications d'histones entre les échantillons, situées de part et d'autre des régions critiques, jusqu'aux extrémités du chromosome réarrangé. Nous avons aussi évalué les interactions intra-chromosomiques ayant lieu dans ces cellules par l'utilisation de la technique de capture de conformation des chromosomes (4C-seq). Nous avons observé qu'un groupe de gènes flanquants la région critique du syndrome de Williams-Beuren (WBSCR) forment souvent une boucle, constituant un groupe d'interactions privilégiées entre ces gènes et la WBSCR. La délétion de la WBSCR perturbe l'expression de ce groupe de gènes flanquants, mais également les interactions à grande échelle entre eux et la région réarrangée. Nous en concluons que les larges réarrangements génomiques peuvent aboutir à des changements de l'état de la chromatine pouvant s'étendre bien plus loin que la région critique, affectant donc potentiellement l'expression de manière globale et ainsi modifiant le phénotype des patients.

Structural variation-associated expression changes are paralleled by chromatin architecture modifications.

Copy number variants (CNVs) influence the expression of genes that map not only within the rearrangement, but also to its flanks. To assess the possible mechanism(s) underlying this "neighboring effect", we compared intrachromosomal interactions and histone modifications in cell lines of patients affected by genomic disorders and control individuals. Using chromosome conformation capture (4C-seq), we observed that a set of genes flanking the Williams-Beuren Syndrome critical region (WBSCR) were often looping together. The newly identified interacting genes include AUTS2, mutations of which are associated with autism and intellectual disabilities. Deletion of the WBSCR disrupts the expression of this group of flanking genes, as well as long-range interactions between them and the rearranged interval. We also pinpointed concomitant changes in histone modifications between samples. We conclude that large genomic rearrangements can lead to chromatin conformation changes that extend far away from the structural variant, thereby possibly modulating expression globally and modifying the phenotype. GEO SERIES ACCESSION NUMBER: GSE33784, GSE33867.