scholarly journals Phase transitions in a 3 dimensional lattice loop gas

2010 ◽  
Vol 81 (11) ◽  
Author(s):  
Richard MacKenzie ◽  
F. Nebia-Rahal ◽  
M. B. Paranjape
Keyword(s):  
Phase Transitions ◽  
Dimensional Lattice ◽  
3 Dimensional

scholarly journals LASSI: A lattice model for simulating phase transitions of multivalent proteins

2019 ◽  
Author(s):  
Jeong-Mo Choi ◽  
Furqan Dar ◽  
Rohit V. Pappu
Keyword(s):  
Monte Carlo ◽  
Phase Transitions ◽  
Phase Diagrams ◽  
Multicomponent Systems ◽  
Dimensional Lattice ◽  
3 Dimensional ◽  
Associative Polymers ◽  
Condensate Formation ◽  
Combine Phase ◽  
Specific Phase

AbstractBiomolecular condensates form via phase transitions that combine phase separation or demixing and networking of key protein and RNA molecules. Proteins that drive condensate formation are either linear or branched multivalent proteins where multivalence refers to the presence of multiple protein-protein or protein-nucleic acid interaction domains or motifs within a protein. Recent work has shown that multivalent protein drivers of phase transitions are in fact biological instantiations of associative polymers. Such systems can be characterized by stickers-and-spacers architectures where stickers contribute to system-specific spatial hierarchies of directional interactions and spacers control the concentration-dependent inhomogeneities in densities of stickers around one another. The collective effects of interactions among stickers and spacers lead to the emergence of dense droplet phases wherein the stickers form percolated networks of polymers. To enable the calculation of system-specific phase diagrams of multivalent proteins, we have developed LASSI (LAttice simulations of Sticker and Spacer Interactions), which is an efficient open source computational engine for lattice-based polymer simulations built on the stickers and spacers framework. In LASSI, a specific multivalent protein architecture is mapped into a set of beads on the 3-dimensional lattice space with proper coarse-graining, and specific sticker-sticker interactions are modeled as pairwise anisotropic interactions. For efficient and broad search of the conformational ensemble, LASSI uses Monte Carlo methods, and we optimized the move set so that LASSI can handle both dilute and dense systems. Also, we developed quantitative measures to extract phase boundaries from LASSI simulations, using known and hidden collective parameters. We demonstrate the application of LASSI to two known archetypes of linear and branched multivalent proteins. The simulations recapitulate observations from experiments and importantly, they generate novel quantitative insights that augment what can be gleaned from experiments alone. We conclude with a discussion of the advantages of lattice-based approaches such as LASSI and highlight the types of systems across which this engine can be deployed, either to make predictions or to enable the design of novel condensates.Author SummarySpatial and temporal organization of molecular matter is a defining hallmark of cellular ultrastructure and recent attention has focused intensely on organization afforded by membraneless organelles, which are referred to as biomolecular condensates. These condensates form via phase transitions that combine phase separation and networking of condensate-specific protein and nucleic acid molecules. Several questions remain unanswered regarding the driving forces for condensate formation encoded in the architectures of multivalent proteins, the molecular determinants of material properties of condensates, and the determinants of compositional specificity of condensates. Building on recently recognized analogies between associative polymers and multivalent proteins, we have developed and deployed LASSI, an open source computational engine that enables the calculation of system-specific phase diagrams for multivalent proteins. LASSI relies on a priori identification of stickers and spacers within a multivalent protein and mapping the stickers onto a 3-dimensional lattice. A Monte Carlo engine that incorporates a suite of novel and established move sets enables simulations that track density inhomogeneities and changes to the extent of networking among stickers as a function of protein concentration and interaction strengths. Calculation of distribution functions and other nonconserved order parameters allow us to compute full phase diagrams for multivalent proteins modeled using a stickers-and-spacers representation on simple cubic lattices. These predictions are shown to be system-specific and allow us to rationalize experimental observations while also enabling the design of systems with bespoke phase behavior. LASSI can be deployed to study the phase behavior of multicomponent systems, which allows us to make direct contact with cellular biomolecular condensates that are in fact multicomponent systems.

Deviations from Ideal Decagonal Symmetry in Electron Diffraction Patterns of the “Decagonal” Phase in the Al-Co-Cu Alloy System

1991 ◽  
Vol 49 ◽  
pp. 914-915
Author(s):  
Atul S. Ramani ◽  
Earle R. Ryba ◽  
Paul R. Howell
Keyword(s):  
Electron Microscope ◽  
Alloy System ◽  
Nominal Composition ◽  
Dimensional Lattice ◽  
3 Dimensional ◽  
Decagonal Phase ◽  
Cu Alloy ◽  
Transmission Electron ◽  
Lattice Periodicity ◽  
Diffraction Patterns

The “decagonal” phase in the Al-Co-Cu system of nominal composition Al65CO15Cu20 first discovered by He et al. is especially suitable as a topic of investigation since it has been claimed that it is thermodynamically stable and is reported to be periodic in the dimension perpendicular to the plane of quasiperiodic 10-fold symmetry. It can thus be expected that it is an important link between fully periodic and fully quasiperiodic phases. In the present paper, we report important findings of our transmission electron microscope (TEM) study that concern deviations from ideal decagonal symmetry of selected area diffraction patterns (SADPs) obtained from several “decagonal” phase crystals and also observation of a lattice of main reflections on the 10-fold and 2-fold SADPs that implies complete 3-dimensional lattice periodicity and the fundamentally incommensurate nature of the “decagonal” phase. We also present diffraction evidence for a new transition phase that can be classified as being one-dimensionally quasiperiodic if the lattice of main reflections is ignored.

Finite-order Integration Weights Can be Dangerous

2007 ◽  
Vol 7 (3) ◽  
pp. 239-254 ◽  
Author(s):  
I.H. Sloan
Keyword(s):  
Function Space ◽  
Finite Order ◽  
Small Subset ◽  
Worst Case ◽  
Integration Rule ◽  
Dimensional Lattice ◽  
3 Dimensional ◽  
Sum Of Functions ◽  
Integration Rules

Abstract Finite-order weights have been introduced in recent years to describe the often occurring situation that multivariate integrands can be approximated by a sum of functions each depending only on a small subset of the variables. The aim of this paper is to demonstrate the danger of relying on this structure when designing lattice integration rules, if the true integrand has components lying outside the assumed finiteorder function space. It does this by proving, for weights of order two, the existence of 3-dimensional lattice integration rules for which the worst case error is of order O(N¯½), where N is the number of points, yet for which there exists a smooth 3- dimensional integrand for which the integration rule does not converge.

scholarly journals A MATHEMATICAL APPROACH TO STRUCTURAL TRANSITIONS IN VIRAL CAPSIDS

2012 ◽  
Vol 09 ◽  
pp. 11-23
Author(s):  
GIULIANA INDELICATO ◽  
REIDUN TWAROCK
Keyword(s):  
Phase Transitions ◽  
Icosahedral Symmetry ◽  
Mathematical Approach ◽  
Structural Transitions ◽  
Viral Capsids ◽  
3 Dimensional ◽  
Crystallographic Theory

The majority of viruses have protein containers, called capsids, in which proteins are arranged with icosahedral symmetry. The capsids of these viruses follow structural blueprints that can be modelled as subsets of 3-dimensional aperiodic lattices called quasicrystals. These, in turn, can be obained by projection from 6-dimensional Bravais lattices. In this work we apply the crystallographic theory of phase transitions to these 6D lattices, and via projection of these results derive information on the structural transitions of viruses important for infection.

Influence of Post-Deposition Annealing on Lattice Strain, Electrical Transport and Magnetic Properties in Epitaxial La0.8Ca0.2MnO3 CMR Films

1999 ◽  
Vol 574 ◽  
Author(s):  
T. K. Nath ◽  
R. A. Rao ◽  
D. Lavric ◽  
C. B. Eom
Keyword(s):  
Cell Volume ◽  
Annealing Time ◽  
Unit Cell Volume ◽  
Lattice Strain ◽  
Unit Cell ◽  
Clear Correlation ◽  
Dimensional Lattice ◽  
X Ray ◽  
3 Dimensional ◽  
Perovskite Unit Cell

AbstractThe effect of annealing on 3-dimensional lattice strain, crystallographic domain structure, magnetic and electrical properties of both 250 Å and 4000 Å thick epitaxial La0.8Ca0.2MnO3 (LCMO(x=0.2)) thin films grown on (001) LaAlO3 substrates have been studied. While short annealing time (∼2hrs. at 950 °C in oxygen of 1 atm. pressure) leads to anomalous increase of the peak temperature (Tp) and Curie temperature (Tc) above room temperature and that of the bulk material, longer annealing time (∼10 hrs.) restores the Tp and Tc to almost the same values as that of the as-grown films. Furthermore, as the annealing time is increased, the lattice strain relaxes with film's lattice parameter approaching the bulk value. In-plane and out-of-plane lattice parameters and strain states of the as-grown and annealed films were measured directly using normal and grazing incidence x-ray diffraction. A clear correlation is observed between Tp and perovskite unit cell volume for both the films. Tp is found to increase with the decrease of perovskite unit cell volume. This is attributed to the enhancement of overlap between Mn d orbitals and oxygen p orbitals leading to increased bandwidth and conductivity. Crystalline quality of the films as determined by the full width at half maximum (FWHM) of the x-ray rocking curves, improves with the annealing time. This work highlights the importance of controlling the 3-dimensional lattice strain for optimizing the properties of CMR films.

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