Related papers: Understanding hierarchical protein evolution from …

Proteins are the most important biomolecules for living organisms. The understanding of protein structure, function, dynamics and transport is one of most challenging tasks in biological science. In the present work, persistent homology is,…

A representation of the genetic code as a six-dimensional Boolean hypercube is proposed. It is assumed here that this structure is the result of the hierarchical order of the interaction energies of the bases in codon-anticodon recognition.…

We review the development of thermodynamic protein hydropathic scaling theory, starting from backgrounds in mathematics and statistical mechanics, and leading to biomedical applications. Darwinian evolution has organized each protein family…

Intracellular protein patterns govern essential cellular functions by dynamically redistributing proteins between membrane-bound and cytosolic states, conserving their total numbers. This review presents a theoretical framework for…

The Saccharomyces cerevisiae protein-protein interaction map, as well as many natural and man-made networks, shares the scale-free topology. The preferential attachment model was suggested as a generic network evolution model that yields…

Some natural proteins display recurrent structural patterns. Despite being highly similar at the tertiary structure level, repetitions within a single repeat protein can be extremely variable at the sequence level. We propose a mathematical…

Protein sequence generation for engineering requires samples that are biophysically plausible and, when targeting a family/domain, remain recognizable members while exploring within-family diversity. Current discrete generative models…

Proteins are constructed from a limited alphabet of ~20 amino acids, yet the origins and selection of this specific alphabet are unresolved. One largely overlooked aspect is whether elemental composition constrains the range of viable…

We propose a general method for predicting potentially good folders from a given number of amino acid sequences. Our approach is based on the calculation of the rate of convergence of each amino acid chain towards the native structure using…

Here we review the development of protein scaling theory, starting from backgrounds in mathematics and statistical mechanics, and leading to biomedical applications. Evolution has organized each protein family in different ways, but scaling…

The evolution processes of complex systems carry key information in the systems' functional properties. Applying machine learning algorithms, we demonstrate that the historical formation process of various networked complex systems can be…

Natural protein sequences that self-assemble to form globular structures are compact with high packing densities in the folded states. It is known that proteins unfold upon addition of denaturants, adopting random coil structures. The…

The aim of this work is to elucidate how physical principles of protein design are reflected in natural sequences that evolved in response to the thermal conditions of the environment. Using an exactly solvable lattice model, we design…

Time dependence is a universal phenomenon in nature, and a variety of mathematical models in terms of dynamical systems have been developed to understand the time-dependent behavior of real-world problems. Originally constructed to analyze…

Proteins have regular tertiary structures but irregular amino acid sequences. This made it very difficult to decode the structural information in the protein sequences. Here we demonstrate that many small alpha protein domains have hidden…

Current-day genomes bear the mark of the evolutionary processes. One of the strongest indications is the sequence homology among families of proteins that perform similar biological functions in different species. The number of proteins in…

Structural prediction of protein-protein interactions is important to understand the molecular basis of cellular interactions, but it still faces major challenges when significant conformational changes are present. We propose a generative…

Models of protein energetics which neglect interactions between amino acids that are not adjacent in the native state, such as the Go model, encode or underlie many influential ideas on protein folding. Implicit in this simplification is a…

Making use of a simplified model for protein folding, it can be shown that conformations which are particularly stable when their energy is minimized with respect to amino acid sequence (in the sense that they display a large energy gap to…

The time-dependent relaxation of a dynamical system may exhibit a power-law behavior that is superimposed by log-periodic oscillations. Sornette [Phys. Rep. 297, 239 (1998)] showed that this behavior can be explained by a discrete scale…