Related papers: Protein Structure and Evolutionary History Determi…
Proteins contain a large fraction of regular, repeating conformations, called secondary structure. A simple, generic definition of secondary structure is presented which consists of measuring local correlations along the protein chain.…
We study the impact of mutations (changes in amino acid sequence) on the thermodynamics of simple protein-like heteropolymers consisting of N monomers, representing the amino acid sequence. The sequence is designed to fold into its native…
Proteins are responsible for the most diverse set of functions in biology. The ability to extract information from protein sequences and to predict the effects of mutations is extremely valuable in many domains of biology and medicine.…
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…
In evolution, the effects of a single deleterious mutation can sometimes be compensated for by a second mutation which recovers the original phenotype. Such epistatic interactions have implications for the structure of genome space -…
In the protein sequence space, natural proteins form clusters of families which are characterized by their unique native folds whereas the great majority of random polypeptides are neither clustered nor foldable to unique structures. Since…
Quantification and classification of protein structures, such as knotted proteins, often requires noise-free and complete data. Here we develop a mathematical pipeline that systematically analyzes protein structures. We showcase this…
Activated processes such as protein unfolding are highly sensitive to heterogeneity in the environment. We study a highly simplified model of a protein in a random heterogeneous environment, a model of the in vivo environment. It is found…
Cooperativity is a hallmark of proteins, many of which show a modular architecture comprising discrete structural domains. Detecting and describing dynamic couplings between structural regions is difficult in view of the many-body nature of…
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…
Supergenes are genomic regions containing sets of tightly linked loci that control multi-trait phenotypic polymorphisms under balancing selection. Recent advances in genomics have uncovered significant variation in both the genomic…
Correlation of gene histories in the human genome determines the patterns of genetic variation (haplotype structure) and is crucial to understanding genetic factors in common diseases. We derive closed analytical expressions for the…
Protein evolution involves mutations occurring across a wide range of time scales. In analogy with disordered systems in statistical physics, this dynamical heterogeneity suggests strong correlations between mutations happening at distinct…
Knotted proteins embed a physical (i.e., open) knot within their native structures. For decades, significant effort has been devoted to elucidating the functional role of knots in proteins, yet no consensus has been reached. Here, using…
The analysis of the three-dimensional structure of proteins is an important topic in molecular biochemistry. Structure plays a critical role in defining the function of proteins and is more strongly conserved than amino acid sequence over…
Evolution of genetic code is studied as the change in the choice of enzymes that are used to synthesize amino acids from the genetic information of nucleic acids. We propose the following theory: the differentiation of physiological states…
The origin and organizing principles of the genetic code remain fundamental puzzles in life science. The vanishingly low probability of the natural codon-to-amino acid mapping arising by chance has spurred the hypothesis that its structure…
The notion of energy landscapes provides conceptual tools for understanding the complexities of protein folding and function. Energy Landscape Theory indicates that it is much easier to find sequences that satisfy the "Principle of Minimal…
We discuss the gauge field theory approach to protein structure study, which allows a natural way to introduce collective degrees of freedom and nonlinear topological structures. Local symmetry of proteins and its breaking in the medium is…
Applying machine learning to biological sequences - DNA, RNA and protein - has enormous potential to advance human health, environmental sustainability, and fundamental biological understanding. However, many existing machine learning…