相关论文: III. Geometrical framework for thinking about glob…

Geometric deep learning has recently achieved great success in non-Euclidean domains, and learning on 3D structures of large biomolecules is emerging as a distinct research area. However, its efficacy is largely constrained due to the…

The chain of algebraic geometry constructions permits to transfer from the minimal surface with zero instability index, and from the lattice over the ring of cyclotomic integers to the tetra-block helix. The tetra-block is the 7-vertex…

Protein one-dimensional (1D) structures such as secondary structure and contact number provide intuitive pictures to understand how the native three-dimensional (3D) structure of a protein is encoded in the amino acid sequence. However, it…

Bin/Amphiphysin/Rvs superfamily proteins and other curvature-inducing proteins have anisotropic shapes and anisotropically bend biomembrane. Here, we report how the anisotropic proteins bind the membrane tube and are orientationally ordered…

We review the theoretical analyses and simulations of the interactions between curvature-inducing proteins and biomembranes. Laterally isotropic proteins induce spherical budding, whereas anisotropic proteins, such as Bin/Amphiphysin/Rvs…

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…

We inspect the geometry of proteins by identifying their backbones as framed polygons. We find that the left-handed helix region of the Ramachandran map for non-glycyl residues corresponds to an isolated and highly localized sector in the…

An optimization technique is used to determine the pairwise interactions between amino acids in globular proteins. A numerical strategy is applied to a set of proteins for maximizing the native fold stability with respect to alternative…

Controlling the self-assembly of supramolecular structures is vital for living cells, and a central challenge for engineering at the nano- and microscales. Nevertheless, even particles without optimized shapes can robustly form well-defined…

A 3-parameter family of helical tubular surfaces obtained by screw revolving a circle provides a useful pedagogical example of how to study geodesics on a surface that admits a 1-parameter symmetry group, but is not as simple as a surface…

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…

The biological function of a protein stems from its 3-dimensional structure, which is thermodynamically determined by the energetics of interatomic forces between its amino acid building blocks (the order of amino acids, known as the…

In this study, we tackle the challenging task of predicting secondary structures from protein primary sequences, a pivotal initial stride towards predicting tertiary structures, while yielding crucial insights into protein activity,…

Artificial intelligence for scientific discovery has recently generated significant interest within the machine learning and scientific communities, particularly in the domains of chemistry, biology, and material discovery. For these…

The past decade has witnessed the development and success of coarse-grained network models of proteins for predicting many equilibrium properties related to collective modes of motion. Curiously, the results are usually robust towards the…

We present a series of experiments investigating the local microstructure of cylindrical piles composed of highly concave particles. By systematically varying particle geometry -- from spheres to strongly non-convex polypods -- as well as…

A major issue in biology is the understanding of the interactions between proteins. These interactions can be described by a network, where the proteins are modeled by nodes and the interactions by edges. The origin of these protein…

Segments with the amino acid sequence EKAYLRT appear in natural occurring proteins both in $\alpha$-helices and $\beta$-sheets. For this reason, we have use this peptide to study how secondary structure formation in proteins depends on the…

Proteins need to selectively interact with specific targets among a multitude of similar molecules in the cell. But despite a firm physical understanding of binding interactions, we lack a general theory of how proteins evolve high…

Protein structures can be studied as complex networks of interacting amino acids. We study proteins of different structural classes from the network perspective. Our results indicate that proteins, regardless of their structural class, show…