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Since the 1920s, packing arguments have been used to rationalize crystal structures in systems ranging from atomic mixtures to colloidal crystals. Packing arguments have recently been applied to complex nanoparticle structures, where they…
Protein structure is generally conceptualized as the global arrangement or of smaller, local motifs of helices, sheets, and loops. These regular, recurring secondary structural elements have well-understood and standardized definitions in…
Despite the recognized importance of the multi-scale spatio-temporal organization of proteins, most computational tools can only access a limited spectrum of time and spatial scales, thereby ignoring the effects on protein behavior of the…
Determining the structure of a protein has been a decades-long open question. A protein's three-dimensional structure often poses nontrivial computation costs, when classical simulation algorithms are utilized. Advances in the transformer…
We examine the structure of the percolating cluster (PC) formed by site percolation on a random clustered network (RCN) model. Using the generating functions, we formulate the clustering coefficient and assortative coefficient of the PC. We…
Proteins are composed of chains of amino acids that fold into complex three-dimensional structures. Several key features, such as the radius of gyration, fraction of core amino acids $f_{\rm core}$, packing fraction $\langle \phi\rangle$ of…
Single-stranded RNA viruses co-assemble their capsid with the genome and variations in capsid structures can have significant functional relevance. In particular, viruses need to respond to a dehydrating environment to prevent genomic…
Geometric and structural constraints greatly restrict the selection of folds adapted by protein backbones, and yet, folded proteins show an astounding diversity in functionality. For structure to have any bearing on function, it is thus…
In both nature and engineering, loosely packed granular materials are often compacted inside confined geometries. Here, we explore such behaviour in a quasi-two dimensional geometry, where parallel rigid walls provide the confinement. We…
The developing structure in systems of compacting ductile grains were studied experimentally in two and three dimensions. In both dimensions, the peaks of the radial distribution function were reduced, broadened, and shifted compared with…
Confined thin structures are ubiquitous in nature. Spatial and length constraints have led to a number of novel packing strategies at both the micro-scale, as when DNA packages inside a capsid, and the macro-scale, seen in plant root…
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…
Elucidating the interplay of stress and geometry is a fundamental scientific question arising in multiple fields. In this work, we investigate the geometric frustration of crystalline caps confined on the sphere in both elastic and plastic…
Percolation theory from statistical physics has been applied to several aspects of tumor progression. Tumor growth on percolation clusters has been used to model spatial expansion, vascular percolation to describe nutrient supply and…
Clustering of proteins is of interest in cancer cell biology. This article proposes a hierarchical Bayesian model for protein (variable) clustering hinging on correlation structure. Starting from a multivariate normal likelihood, we enforce…
In this study, the distributions of protein structure classes (or folding types) of experimentally determined structures from a legacy dataset and a comprehensive database (SCOP) are modeled precisely with geometric constructs such as…
The beautiful structures of single and multi-domain proteins are clearly ordered in some fashion but cannot be readily classified using group theory methods that are successfully used to describe periodic crystals. For this reason, protein…
Proteins form a very important class of polymers. In spite of major advances in the understanding of polymer science, the protein problem has remained largely unsolved. Here, we show that a polymer chain viewed as a tube not only captures…
We review the recent progress in computational approaches to protein design which builds on advances in statistical-mechanical protein folding theory. In particular, we evaluate the degeneracy of the protein code (i.e. how many sequences…
A nutrient-limited model for avascular cancer growth including cell proliferation, motility and death is presented. The model qualitatively reproduces commonly observed morphologies for primary tumors, and the simulated patterns are…