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The recently introduced Physics-Informed Neural Networks (PINNs) have popularized least squares formulations of both forward and inverse problems involving partial differential equations (PDEs) in strong form. We employ both Isogeometric…
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…
Understanding protein dynamics are essential for deciphering protein functional mechanisms and developing molecular therapies. However, the complex high-dimensional dynamics and interatomic interactions of biological processes pose…
How proteins fold remains a central unsolved problem in biology. While the idea of a folding code embedded in the amino acid sequence was introduced more than 6 decades ago, this code remains undefined. While we now have powerful predictive…
Inverse protein folding -- the task of predicting a protein sequence from its backbone atom coordinates -- has surfaced as an important problem in the "top down", de novo design of proteins. Contemporary approaches have cast this problem as…
Computational protein design has a wide variety of applications. Despite its remarkable success, designing a protein for a given structure and function is still a challenging task. On the other hand, the number of solved protein structures…
Peptides play a pivotal role in a wide range of biological activities through participating in up to 40% protein-protein interactions in cellular processes. They also demonstrate remarkable specificity and efficacy, making them promising…
X-ray crystallography, NMR (Nuclear Magnetic Resonance) spectroscopy, and dual polarization interferometry, etc are indeed very powerful tools to determine the 3D structures of proteins (including the membrane proteins), though they are…
Using a coarse-grained model, self-organized assembly of proteins (e.g. CorA and its inner segment iCorA) is studied by examining quantities such as contact profile, radius of gyration, and structure factor as a function of protein…
As protein folding is a NP-complete problem, artificial intelligence tools like neural networks and genetic algorithms are used to attempt to predict the 3D shape of an amino acids sequence. Underlying these attempts, it is supposed that…
Multiple phenotypic protein expressions arising from one genome represent variations in the protein relative abundance and their stoichiometry. A lack of definite compositional parts challenges the modeling of protein megacomplexes and…
RNA molecules are essential cellular machines performing a wide variety of functions for which a specific three-dimensional structure is required. Over the last several years, experimental determination of RNA structures through X-ray…
Physics-informed neural networks (PINNs) have recently become a powerful tool for solving partial differential equations (PDEs). However, finding a set of neural network parameters that lead to fulfilling a PDE can be challenging and…
A comparative classification scheme provides a good basis for several approaches to understand proteins, including prediction of relations between their structure and biological function. But it remains a challenge to combine a…
Predicting the structure of multi-protein complexes is a grand challenge in biochemistry, with major implications for basic science and drug discovery. Computational structure prediction methods generally leverage pre-defined structural…
This paper proposes a new mathematical framework that can be applied to biological problems such as analysis of the structures of proteins and protein complexes. In particular, it gives a new method for encoding the three-dimensional…
The native structures of proteins, except for notable exceptions of intrinsically disordered proteins, in general take their most stable conformation in the physiological condition to maintain their structural framework so that their…
This chapter describes the application of constrained geometric simulations for prediction of antibody structural dynamics. We utilize constrained geometric simulations method FRODAN, which is a low computational complexity alternative to…
Proteins are the major building blocks of life, and actuators of almost all chemical and biophysical events in living organisms. Their native structures in turn enable their biological functions which have a fundamental role in drug design.…
Local protein structure analysis is informative to protein structure analysis and has been used successfully in protein structure prediction and others. Proteins have recurring structural features, such as helix caps and beta turns, which…