Related papers: Space-filling discrete helices
Proteins populate a manifold in the high-dimensional sequence space whose geometrical structure guides their natural evolution. Leveraging recently-developed structure prediction tools based on transformer models, we first examine the…
Two proteins, one belonging to the mainly alpha class and the other belonging to the alpha/beta class, are selected to test a kinetic mechanism for protein folding. Targeted molecular dynamics is applied to generate folding pathways for…
The intrinsic property of proteins to form structural motifs such as alpha-helices and beta-sheets leads to a complex phase behavior in which proteins can assemble into various types of aggregates including crystals, liquidlike phases of…
Analysis of the geometric properties of a mean-field HP model on a square lattice for protein structure shows that structures with large number of switch backs between surface and core sites are chosen favorably by peptides as unique ground…
$\alpha$-helices stand out as common and relatively invariant secondary structural elements of proteins. However, $\alpha$-helices are not rigid bodies and their deformations can be significant in protein function ({\it e.g.} coiled coils).…
The theory of elastic rods can be used to describe certain geometric and topological properties of the DNA molecules. A similar effective field theory approach was previously suggested to describe the conformations and dynamics of proteins.…
Optimal geometrical arrangements, such as the stacking of atoms, are of relevance in diverse disciplines. A classic problem is the determination of the optimal arrangement of spheres in three dimensions in order to achieve the highest…
A fascinating and open question challenging biochemistry, physics and even geometry is the presence of highly regular motifs such as alpha-helices in the folded state of biopolymers and proteins. Stimulating explanations ranging from…
Native protein folds often have a high degree of symmetry. We study the relationship between the symmetries of native proteins, and their designabilities -- how many different sequences encode a given native structure. Using a…
Proteins, chain molecules of amino acids, behave in ways which are similar to each other yet quite distinct from standard compact polymers. We demonstrate that the Flory theorem, derived for polymer melts, holds for compact protein native…
Globular proteins are expected to assume folds with fixed secondary structures, alpha-helices and beta-sheets. Fold-switching proteins challenge this expectation by remodeling their secondary and/or tertiary structures in response to…
The protein folding problem must ultimately be solved on all length scales from the atomic up through a hierarchy of complicated structures. By analyzing the stability of the folding process using physics and mathematics, this paper shows…
Despite recent breakthroughs in understanding how protein sequence relates to structure and function, considerably less attention has been paid to the general features of protein surfaces beyond those regions involved in binding and…
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…
A reduced model, which can fold both helix and sheet structures, is proposed to study the problem of protein folding. The goal of this model is to find an unbiased effective potential that has included the effects of water and at the same…
Protein folds are built primarily from the packing together of two types of structures: alpha-helices and beta-sheets. Neither structure is rigid, and the flexibility of helices and sheets is often important in determining the final fold…
Proteins are biomolecules of life. They fold into a great variety of three-dimensional (3D) shapes. Underlying these folding patterns are many recurrent structural fragments or building blocks (analogous to `LEGO bricks'). This paper…
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…
A reduced protein model with five to six atoms per amino acid and five amino acid types is developed and tested on a three-helix-bundle protein, a 46-amino acid fragment from staphylococcal protein A. The model does not rely on the widely…
Predicting protein secondary structure using lattice model is one of the most studied computational problem in bioinformatics. Here secondary structure or three dimensional structure of protein is predicted from its amino acid sequence.…