Related papers: The Ramachandran number: an order parameter for pr…
Recently, we presented a framework for understanding protein structure based on the idea that simple constructs of holding hands or touching of objects can be used to rationalize the common characteristics of globular proteins. We developed…
The primary structure of a ribonucleic acid (RNA) molecule can be represented as a sequence of nucleotides (bases) over the alphabet {A, C, G, U}. The secondary or tertiary structure of an RNA is a set of base pairs which form bonds between…
H-bonds are known to play an important role in the folding of proteins into three-dimensional structures, which in turn determine their diverse functions. The conformations around H-bonds are important, in that they can be non-local along…
We investigate the fine structure of the sp3 hybridized covalent bond geometry that governs the tetrahedral architecture around the central C$_\alpha$ carbon of a protein backbone, and for this we develop new visualization techniques to…
The GOR program for predicting protein secondary structure is extended to include triple correlation. A score system for a residue pair to be at certain conformation state is derived from the conditional weight matrix describing amino acid…
Protein structures are a very special class among all possible structures. It was suggested that a ``designability principle'' plays a crucial role in nature's selection of protein sequences and structures. Here we provide a theoretical…
Changes in the extent of local concavity along with changes in surface roughness of binding sites of proteins have long been considered as useful markers to identify functional sites of proteins. However, an algorithm that describes the…
In biology, predicting RNA secondary structures plays a vital role in determining its physical and chemical properties. Although we have powerful energy models to predict them as well as parametric analysis to understand the models…
This work reports a new methodology aimed at describing characteristics of protein structural shapes, and suggests a framework in which to resolve or classify automatically such structures into known families. This new approach to protein…
The Ramachandran plot is a potent way to understand structures of biomolecules, however, the original formulation of the Ramachandran plot only considers backbone conformations. We formulate a new interpretation of the original Ramachandran…
The presence of low dimensional chaos in the protein secondary structures, using the binary coded $\alpha$-helices and $\beta$-sheet motifs, has been investigated. In order to analyse symbolic DNA/RNA sequences the assignment, based on the…
Microproteins are a newly recognized and rapidly growing class of small proteins, typically encoded by fewer than 100 to 150 codons and translated from small open reading frames (smORFs). Although research has shown that smORFs and their…
The evolutionary trajectory of a protein through sequence space is constrained by function and three-dimensional (3D) structure. Residues in spatial proximity tend to co-evolve, yet attempts to invert the evolutionary record to identify…
Some natural proteins display recurrent structural patterns. Despite being highly similar at the tertiary structure level, repetitions within a single repeat protein can be extremely variable at the sequence level. We propose a mathematical…
In this paper, we develop a quantitative comparison method for two arbitrary protein structures. This method uses a root-mean-square deviation (RMSD) characterization and employs a series expansion of the protein's shape function in terms…
Computational protein design has the potential to deliver novel molecular structures, binders, and catalysts for myriad applications. Recent neural graph-based models that use backbone coordinate-derived features show exceptional…
Despite recent breakthroughs in understanding how protein sequence relates to structure and function, considerably less attention has been paid to the general features of protein surfaces beyond those regions involved in binding and…
We introduce a new, simplified model of proteins, which we call protein metastructure. The metastructure of a protein carries information about its secondary structure and $\beta$-strand conformations. Furthermore, protein metastructure…
An RNA molecule is structured on several layers. The primary and most obvious structure is its sequence of bases, i.e. a word over the alphabet {A,C,G,U}. The higher structure is a set of one-to-one base-pairings resulting in a…
Determining the 3D structures of proteins is essential in understanding their behavior in the cellular environment. Computational methods of predicting protein structures have advanced, but assessing prediction accuracy remains a challenge.…