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The identification of compound-protein interactions (CPI) plays a critical role in drug screening, drug repurposing, and combination therapy studies. The effectiveness of CPI prediction relies heavily on the features extracted from both…

Protein-protein interaction (PPI) networks, providing a comprehensive landscape of protein interacting patterns, enable us to explore biological processes and cellular components at multiple resolutions. For a biological process, a number…

This paper proposes a new mathematical approach to characterize native protein structures based on the discrete differential geometry of tetrahedron tiles. In the approach, local structure of proteins is classified into finite types…

Accurate identification of protein nucleic-acid-binding residues poses a significant challenge with important implications for various biological processes and drug design. Many typical computational methods for protein analysis rely on a…

A quasi-metric is a distance function which satisfies the triangle inequality but is not symmetric: it can be thought of as an asymmetric metric. The central result of this thesis, developed in Chapter 3, is that a natural correspondence…

Protein-protein interactions are fundamental to many biological processes. Experimental screens have identified tens of thousands of interactions and structural biology has provided detailed functional insight for select 3D protein…

The ability to consistently distinguish real protein structures from computationally generated model decoys is not yet a solved problem. One route to distinguish real protein structures from decoys is to delineate the important physical…

Protein-protein interactions (PPIs) are governed by surface complementarity and hydrophobic interactions at protein interfaces. However, designing diverse and physically realistic protein structure and surfaces that precisely complement…

We present a novel dual-head deep learning architecture for protein-protein interaction modeling that enables simultaneous prediction of binding affinity ($\Delta G$) and mutation-induced affinity changes ($\Delta\Delta G$) using only…

Crystal structure prediction (CSP) for inorganic materials is one of the central and most challenging problems in materials science and computational chemistry. This problem can be formulated as a global optimization problem in which global…

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…

In 1999 Wright and Dyson highlighted the fact that large sections of the proteome of all organisms are comprised of protein sequences that lack globular folded structures under physiological conditions. Since then the biophysics community…

Accurately predicting complex protein-protein interactions (PPIs) is crucial for decoding biological processes, from cellular functioning to disease mechanisms. However, experimental methods for determining PPIs are computationally…

The Automated Protein Structure Analysis (APSA) method is used for the classification of supersecondary structures. Basis for the classification is the encoding of three-dimensional (3D) residue conformations into a 16-letter code (3D-1D…

Protein engineering is experiencing a paradigmatic shift through the integration of geometric deep learning into computational design workflows. While traditional strategies, such as rational design and directed evolution, have enabled…

Molecular structure has important applications in many fields. For example, some studies show that molecular spatial information can be used to achieve better prediction results when predicting molecular properties. However, traditional…

This is a summary of mathematical tools we used in research of analyzing the structure of proteins with amyloid form \cite{xi2024Top}. We defined several geometry indicators on the discrete curve namely the hop distance, the discrete…

AI-based in silico methods have improved protein structure prediction but often struggle with large protein complexes (PCs) involving multiple interacting proteins due to missing 3D spatial cues. Experimental techniques like Cryo-EM are…

Protein-protein interactions (protein functionalities) are mediated by water, which compacts individual proteins and promotes close and temporarily stable large-area protein-protein interfaces. In their classic paper Kyte and Doolittle (KD)…

In materials science, the selection of structural descriptors for machine learning protocols strongly influences predictive performance and the degree of physical interpretability that can be achieved from the derived models. Although more…