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Proteins are the basic building blocks of life. They usually perform functions by folding to a particular structure. Understanding the folding process could help the researchers to understand the functions of proteins and could also help to…
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…
Protein structure tokenization converts 3D structures into discrete or vectorized representations, enabling the integration of structural and sequence data. Despite many recent works on structure tokenization, the properties of the…
Given the amino acid sequence of a protein, researchers often infer its structure and function by finding homologous, or evolutionarily-related, proteins of known structure and function. Since structure is typically more conserved than…
Protein sequence generation via stochastic attention produces plausible family members from small alignments without training, but treats all stored sequences equally and cannot direct generation toward a functional subset of interest. We…
Protein structures are much more conserved than sequences during evolution. Based on this observation, we investigate the consequences of structural conservation on protein evolution. We study seven of the most studied protein folds,…
Recently developed deep learning techniques have significantly improved the accuracy of various speech and image recognition systems. In this paper we adapt some of these techniques for protein secondary structure prediction. We first train…
Molecular phenotypes are important links between genomic information and organismic functions, fitness, and evolution. Complex phenotypes, which are also called quantitative traits, often depend on multiple genomic loci. Their evolution…
Recent years have seen tremendous developments in the use of machine learning models to link amino acid sequence, structure and function of folded proteins. These methods are, however, rarely applicable to the wide range of proteins and…
Understanding the relationships between protein sequence, structure and function is a long-standing biological challenge with manifold implications from drug design to our understanding of evolution. Recently, protein language models have…
Proteins display generic properties that are challenging to explain by direct selection, notably allostery, the capacity to be regulated through long-range effects, and evolvability, the capacity to adapt to new selective pressures. An…
All known terrestrial proteins are coded as continuous strings of ~20 amino acids. The patterns formed by the repetitions of elements in groups of finite sequences describes the natural architectures of protein families. We present a method…
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in various contexts. Here we propose a generative model to capture the dynamics of survival analysis,…
Deep learning is catalyzing a scientific revolution fueled by big data, accessible toolkits, and powerful computational resources, impacting many fields including protein structural modeling. Protein structural modeling, such as predicting…
Proteins exist as a dynamic ensemble of multiple conformations, and these motions are often crucial for their functions. However, current structure prediction methods predominantly yield a single conformation, overlooking the conformational…
Evolutionary dynamics is often viewed as a subtle process of change accumulation that causes a divergence among organisms and their genomes. However, this interpretation is an inheritance of a gradualistic view that has been challenged at…
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…
Network theory-based approaches provide valuable insights into the variations in global structural connectivity between differing dynamical states of proteins. Our objective is to review network-based analyses to elucidate such variations,…
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 this paper we analyze the equilibrium properties of a large class of stochastic processes describing the fundamental biological process within bacterial cells, {\em the production process of proteins}. Stochastic models classically used…