Related papers: Geometric and physical considerations for realisti…
The protein backbone is described as a smooth curved and twisted line in three-dimensional (3D) space and characterized by its curvature $\kappa(s)$ and torsion $\tau(s)$ both expressed as a function of arc length s. It is shown that the…
The ability to computationally generate novel yet physically foldable protein structures could lead to new biological discoveries and new treatments targeting yet incurable diseases. Despite recent advances in protein structure prediction,…
The notion that the geometry of our space-time is not only a static background but can be physically dynamic is well established in general relativity. Geometry can be described as shaped by the presence of matter, where such shaping…
It is becoming clear that traditional, single-structure models of proteins are insufficient for understanding their biological function. Here, we outline one method for inferring, from experiments, not only the most common structure a…
Protein aggregation in cell membrane is vital for the majority of biological functions. Recent experimental results suggest that transmembrane domains of proteins such as $\alpha$-helices and $\beta$-sheets have different structural…
Revealing the structure of complex biological macromolecules, such as proteins, is an essential step for understanding the chemical mechanisms that determine the diversity of their functions. Synchrotron based x-ray crystallography and…
Understanding the complex self-assembly of biomacromolecules is a major outstanding question. Microtubules are one example of a biopolymer that possesses characteristics quite distinct from standard synthetic polymers that are derived from…
The adhesion of biomembranes is mediated by the binding of membrane-anchored receptor and ligand proteins. The proteins can only bind if the separation between apposing membranes is sufficiently close to the length of the protein complexes,…
The conformation and the phase diagram of a membrane protein are investigated via grand canonical ensemble approach using a homopolymer model. We discuss the nature and pathway of $\alpha$-helix integration into the membrane that results…
This chapter discusses geometric models of biomolecules and geometric constructs, including the union of ball model, the weigthed Voronoi diagram, the weighted Delaunay triangulation, and the alpha shapes. These geometric constructs enable…
Protein structure prediction is a challenging and unsolved problem in computer science. Proteins are the sequence of amino acids connected together by single peptide bond. The combinations of the twenty primary amino acids are the…
A small fraction of all protein structures characterized so far are entangled. The challenge of understanding the properties of these knotted proteins, and the why and the how of their natural folding process, has been taken up in the past…
Experiments have revealed that membrane proteins can form two-dimensional clusters with regular translational and orientational protein arrangements, which may allow cells to modulate protein function. However, the physical mechanisms…
We introduce a simple "patchy particle" model to study the thermodynamics and dynamics of self-assembly of homomeric protein complexes. Our calculations allow us to rationalize recent results for dihedral complexes. Namely, why evolution of…
How proteins fold remains a central unsolved problem in biology. While the idea of a folding code embedded in the amino acid sequence was introduced more than 6 decades ago, this code remains undefined. While we now have powerful predictive…
Deep learning is catalyzing a scientific revolution fueled by big data, accessible toolkits, and powerful computational resources, impacting many fields including protein structural modeling. Protein structural modeling, such as predicting…
Designing novel proteins with desired functions is crucial in biology and chemistry. However, most existing work focus on protein sequence design, leaving protein sequence and structure co-design underexplored. In this paper, we propose…
Protein-protein binding enables orderly and lawful biological self-organization, and is therefore considered a miracle of nature. Protein-protein binding is steered by electrostatic forces, hydrogen bonding, van der Waals force, and…
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…
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…