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The sequence of a protein is not only constrained by its physical and biochemical properties under current selection, but also by features of its past evolutionary history. Understanding the extent and the form that these evolutionary…

Using a fast tree-searching algorithm and a Pentium cluster, we enumerated all the sequences and compact conformations (structures) for a protein folding model on a cubic lattice of size $4\times3\times3$. We used two types of amino acids…

The atomistic characterization of the transition state is a fundamental step to improve the understanding of the folding mechanism and the function of proteins. From a computational point of view, the identification of the conformations…

Protein function does not solely depend on structure but often relies on dynamical transitions between distinct conformations. Despite this fact, our ability to characterize or predict protein dynamics is substantially less developed…

The folding kinetics of a number of sequences for off-lattice continuum model of proteins is studied using Langevin simulations at two values of the friction coefficient. We show that there is a remarkable correlation between folding times,…

Protein function frequently involves conformational changes with large amplitude on timescales which are difficult and computationally expensive to access using molecular dynamics. In this paper, we report on the combination of three…

Paradigmatic model systems, which are used to study the mechanical response of matter, are random networks of point-atoms, random sphere packings, or simple crystal lattices, all of these models assume central-force interactions between…

A minimal off-lattice model for alpha-helical proteins is presented. It is based on hydrophobicity forces and sequence independent local interactions. The latter are chosen so as to favor the formation of alpha-helical structure. They model…

Inverse protein folding -- the task of predicting a protein sequence from its backbone atom coordinates -- has surfaced as an important problem in the "top down", de novo design of proteins. Contemporary approaches have cast this problem as…

In this paper we present a variant of the Calculus of Looping Sequences (CLS for short) with global and local rewrite rules. While global rules, as in CLS, are applied anywhere in a given term, local rules can only be applied in the…

We seek to understand the interplay between amino acid sequence and local structure in proteins. Are some amino acids unique in their ability to fit harmoniously into certain local structures? What is the role of sequence in sculpting the…

Protein design is the inverse approach of the three-dimensional (3D) structure prediction for elucidating the relationship between the 3D structures and amino acid sequences. In general, the computation of the protein design involves a…

This paper provides the theoretical foundation for the construction of lattice algorithms for multivariate $L_2$ approximation in the worst case setting, for functions in a periodic space with general weight parameters. Our construction…

Simple theoretical concepts and models have been helpful to understand the folding rates and routes of single-domain proteins. As reviewed in this article, a physical principle that appears to underly these models is loop closure.

Proteins are complex molecules responsible for different functions in nature. Enhancing the functionality of proteins and cellular fitness can significantly impact various industries. However, protein optimization using computational…

Exploring and understanding the protein-folding problem has been a long-standing challenge in molecular biology. Here, using molecular dynamics simulation, we reveal how parallel distributed adjacent planar peptide groups of unfolded…

Lattice models, for their coarse-grained nature, are best suited for the study of the ``designability problem'', the phenomenon in which most of the about 16,000 proteins of known structure have their native conformations concentrated in a…

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…

Local search is widely used to solve combinatorial optimisation problems and to model biological evolution, but the performance of local search algorithms on different kinds of fitness landscapes is poorly understood. Here we consider how…

The stochastic protein kinetic equations can be stiff for certain parameters, which makes their numerical simulation rely on very small time step sizes, resulting in large computational cost and accumulated round-off errors. For such…