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We have shown recently that the notion of poking pairwise interactions along a chain provides a unifying framework for understanding the formation of both secondary and the tertiary protein structure based on symmetry and geometry.…
These lectures will address two questions. Is there a simple variational principle underlying the existence of secondary motifs in the native state of proteins? Is there a general approach which can qualitatively capture the salient…
Proteins are inherently multiscale physical systems whose functional properties emerge from coordinated structural organization across multiple spatial resolutions, ranging from atomic interactions to global fold topology. However, existing…
Understanding complex biological macromolecules, especially proteins, is vital for grasping their diverse chemical functions with direct impact in biology and pharmacology. While techniques like X-ray crystallography and cryo-electron…
We previously described the representation of protein 3D structures in spherical coordinates (rho, phi, theta) and two of its applications: separation of the outer layer (OL) from the inner core (IC) of proteins, and assessment of protein…
Finding correspondences between 3D shapes is an important and long-standing problem in computer vision, graphics and beyond. A prominent challenge are partial-to-partial shape matching settings, which occur when the shapes to match are only…
We review algorithms for protein design in general. Although these algorithms have a rich combinatorial, geometric, and mathematical structure, they are almost never covered in computer science classes. Furthermore, many of these algorithms…
The precise sequence of aminoacids plays a central role in the tertiary structure of proteins and their functional properties. The Hydrophobic-Polar lattice models have provided valuable insights regarding the energy landscape. We…
The science of fractography revolves around the correlation between topographic characteristics of the fracture surface and the mechanisms and external conditions leading to their creation. While being a topic of investigation for…
Protein structure prediction has been a grand challenge problem in the structure biology over the last few decades. Protein quality assessment plays a very important role in protein structure prediction. In the paper, we propose a new…
The equivalent nature of 3D coordinates has posed long term challenges in protein structure representation learning, alignment, and generation. Can we create a compact and invariant language that equivalently represents protein structures?…
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…
The protein folding problem must ultimately be solved on all length scales from the atomic up through a hierarchy of complicated structures. By analyzing the stability of the folding process using physics and mathematics, this paper shows…
Despite the recent advances in various Structural Genomics Projects, a large gap remains between the number of sequenced and structurally characterized proteins. Some reasons for this discrepancy include technical difficulties, labor, and…
Proteins are essential biological macromolecules that execute life functions. Local structural motifs, such as active sites, are the most critical components for linking structure to function and are key to understanding protein evolution…
Artificial intelligence for scientific discovery has recently generated significant interest within the machine learning and scientific communities, particularly in the domains of chemistry, biology, and material discovery. For these…
Predicting the three-dimensional (3D) functional structures of proteins remains an important computational milestone in molecular biology to be achieved. This feat is hinged on a clear understanding of the mechanism which proteins use to…
Proteins are a matter of dual nature. As a physical object, a protein molecule is a folded chain of amino acids with multifarious biochemistry. But it is also an instantiation along an evolutionary trajectory determined by the function…
The soft condensed matter of biological organisms exhibits atomic motions whose properties depend strongly on temperature and hydration conditions. Due to the superposition of rapidly fluctuating alternative motions at both very low…
Protein structure reconstruction from Nuclear Magnetic Resonance (NMR) experiments largely relies on computational algorithms. Recently, some effective low-rank matrix completion (MC) methods, such as ASD and ScaledASD, have been…