Related papers: Protein Evolution within a Structural Space
We study the statistical properties of contact vectors, a construct to characterize a protein's structure. The contact vector of an N-residue protein is a list of N integers n_i, representing the number of residues in contact with residue…
Lattice models or structures are geometrical objects with mathematical forms, that are used to represent physical systems. They have been used widely in diverse fields, namely, in condensed matter physics, to study degrees of freedom of…
The remarkable structural diversity of modern proteins reflects millions of years of evolution, during which sequence space has expanded while many structural features remain conserved. This conservation is evident not only among homologous…
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…
We propose a general theory to describe the distribution of protein-folding transition paths. We show that transition paths follow a predictable sequence of high-free-energy transient states that are separated by free-energy barriers. Each…
While many good textbooks are available on Protein Structure, Molecular Simulations, Thermodynamics and Bioinformatics methods in general, there is no good introductory level book for the field of Structural Bioinformatics. This book aims…
Geometric and structural constraints greatly restrict the selection of folds adapted by protein backbones, and yet, folded proteins show an astounding diversity in functionality. For structure to have any bearing on function, it is thus…
Since protein mutations are the main driving force of evolution at the molecular level, a proper analysis of them (and the factors controlling them) will enable us to find a response to several crucial queries in evolutionary biology. Among…
We propose a novel method for the determination of the effective interaction potential between the amino acids of a protein. The strategy is based on the combination of a new optimization procedure and a geometrical argument, which also…
Interacting proteins coevolve at multiple but interconnected scales, from the residue-residue over the protein-protein up to the family-family level. The recent accumulation of enormous amounts of sequence data allows for the development of…
The simulation of a protein's folding process is often done via stochastic local search, which requires a procedure to apply structural changes onto a given conformation. Here, we introduce a constraint-based approach to enumerate lattice…
In the standard approach to lattice proteins the models based on nearest neighbor interaction are used. In this kind of models it is difficult to explain the existence of secondary structures --- special preferred conformations of protein…
The expansion of a population into new habitat is a transient process that leaves its footprints in the genetic composition of the expanding population. How the structure of the environment shapes the population front and the evolutionary…
In this perspective article, we present a multidisciplinary approach for characterizing protein structure networks. We first place our approach in its historical context and describe the manner in which it synthesizes concepts from quantum…
Protein structure prediction is pivotal for understanding the structure-function relationship of proteins, advancing biological research, and facilitating pharmaceutical development and experimental design. While deep learning methods and…
In this letter, the possible dynamic scaling properties of protein molecules in folding are investigated theoretically by assuming that the protein molecules are percolated networks. It is shown that the fractal character and the fractal…
This paper investigates the structure-property relations of thin-walled lattices under dynamic longitudinal compression, characterized by their cross-sections and heights. These relations elucidate the interactions of different geometric…
Characterizing structural and dynamic properties of proteins and large macromolecular assemblies is crucial to understand the molecular mechanisms underlying biological functions. In the field of Structural Biology, no single method…
A structural genetic model incorporating a modern understanding of the genome and common practice in genome-wide association studies is derived mathematically. The model shows the Haldane map distance as a direct consequence of the…
We present results of a long-term team collaboration of mathematicians and biologists. We focus on building a mathematical framework for the shape space constituted by a collection of homologous bones or teeth from many species. The…