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Much scientific enquiry across disciplines is founded upon a mechanistic treatment of dynamic systems that ties form to function. A highly visible instance of this is in molecular biology, where an important goal is to determine…
Aligning multiple protein structures can yield valuable information about structural similarities among related proteins, as well as provide insight into evolutionary relationships between proteins in a family. We have developed an…
Most of the current understanding of structure-property relations at the molecular and the supramolecular scales can be formulated in terms of the stability of and the interactions between a limited number of recurring structural motifs…
We modify and extend the recently developed statistical mechanical model for predicting the thermodynamic properties of chain molecules having noncovalent double-stranded conformations, as in RNA or ssDNA, and $\beta-$sheets in protein, by…
Proteins constitute a large group of macromolecules with a multitude of functions for all living organisms. Proteins achieve this by adopting distinct three-dimensional structures encoded by the sequence of their constituent amino acids in…
An RNA sequence is a word over an alphabet on four elements $\{A,C,G,U\}$ called bases. RNA sequences fold into secondary structures where some bases match one another while others remain unpaired. Pseudoknot-free secondary structures can…
Background: One-dimensional protein structures such as secondary structures or contact numbers are useful for three-dimensional structure prediction and helpful for intuitive understanding of the sequence-structure relationship. Accurate…
Three types of geometric structure---grid triangulations, rectangular subdivisions, and orthogonal polyhedra---can each be described combinatorially by a regular labeling: an assignment of colors and orientations to the edges of an…
We present a statistical approach to protein structure by introducing a representation of protein folds based on simple observables defined as frequencies of oriented cycles in contact graphs. Motivated by the idea that these cycles may…
We argue that protein native state structures reside in a novel "phase" of matter which confers on proteins their many amazing characteristics. This phase arises from the common features of all globular proteins and is characterized by a…
Proteins are macromolecules responsible for essential functions in almost all living organisms. Designing reasonable proteins with desired functions is crucial. A protein's sequence and structure are strongly correlated and they together…
Proteins are biomolecules of life. They fold into a great variety of three-dimensional (3D) shapes. Underlying these folding patterns are many recurrent structural fragments or building blocks (analogous to `LEGO bricks'). This paper…
The mechanisms by which a protein's 3D structure can be determined based on its amino acid sequence have long been one of the key mysteries of biophysics. Often simplistic models, such as those derived from geometric constraints, capture…
Structure fluctuations and conformational changes accompany all biological processes involving macromolecules. The paper presents a classification of protein residues based on the normalized equilibrium fluctuations of the residue centers…
This chapter deals with approaches for protein three-dimensional structure prediction, starting out from a single input sequence with unknown struc- ture, the 'query' or 'target' sequence. Both template based and template free modelling…
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…
Instead of conformation states of single residues, refined conformation states of quintuplets are proposed to reflect conformation correlation. Simple hidden Markov models combining with sliding window scores are used for predicting…
RNA molecules are known to form complex secondary structures including pseudoknots. A systematic framework for the enumeration, classification and prediction of secondary structures is critical to determine the biological significance of…
Learning effective protein representations is critical in a variety of tasks in biology such as predicting protein function or structure. Existing approaches usually pretrain protein language models on a large number of unlabeled amino acid…
Finite mixture models are fitted to spherical data. Kent distributions are used for the components of the mixture because they allow considerable flexibility. Previous work on such mixtures has used an approximate maximum likelihood…