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Recently, we presented a framework for understanding protein structure based on the idea that simple constructs of holding hands or touching of objects can be used to rationalize the common characteristics of globular proteins. We developed…
Data describing the three-dimensional structure of physical networks is increasingly available, leading to a surge of interest in network science to explore the relationship between the shape and connectivity of physical networks. We…
The adhesion of biological membranes is mediated by the binding of membrane-anchored receptor and ligand proteins. Central questions are how the binding kinetics of these proteins is affected by the membranes and by the membrane anchoring…
The mechanisms by which a protein's 3D structure can be determined based on its amino acid sequence have long been one of the key mysteries of biophysics. Often simplistic models, such as those derived from geometric constraints, capture…
The different quantum phases appearing in strongly correlated systems as well as their transitions are closely related to the entanglement shared between their constituents. In 1D systems, it is well established that the entanglement…
Protein folding and design are major biophysical problems, the solution of which would lead to important applications especially in medicine. Here a novel protein model capable of simultaneously provide quantitative protein design and…
A complex network approach to protein folding is proposed. The graph object is the network of shortcut edges present in a native-state protein (SCN0). Although SCN0s are found via an intuitive message passing algorithm (S. Milgram,…
Among the unsolved problems in computational biology, protein folding is one of the most interesting challenges. To study this folding, tools like neural networks and genetic algorithms have received a lot of attention, mainly due to the…
We study here global and local entanglements of open protein chains by implementing the concept of knotoids. Knotoids have been introduced in 2012 by Vladimir Turaev as a generalization of knots in 3-dimensional space. More precisely,…
Single-filament tracing has been a valuable tool to directly determine geometrical and mechanical properties of entangled polymer networks. However, systematically verifying how the stiffness of the tracer filament or its molecular…
We examine the conformations of a model for a short segment of closed DNA. The molecule is represented as a cylindrically symmetric elastic rod with a constraint corresponding to a specification of the linking number. We obtain analytic…
We study a physical system which, while devoid of the complexity one usually associates with proteins, nevertheless displays a remarkable array of protein-like properties. The constructive hypothesis that this striking resemblance is not…
This paper deals with the relations among structural, topological, and chemical properties of the E.Coli proteome from the vantage point of the solubility/aggregation propensity of proteins. Each E.Coli protein is initially represented…
In this study, the distributions of protein structure classes (or folding types) of experimentally determined structures from a legacy dataset and a comprehensive database (SCOP) are modeled precisely with geometric constructs such as…
Since proteins carry out biological processes by interacting with other proteins, analyzing the structure of protein-protein interaction (PPI) networks could explain complex biological mechanisms, evolution, and disease. Similarly, studying…
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…
A microscopic theory of the free energy barriers and folding routes for minimally frustrated proteins is presented, greatly expanding on the presentation of the variational approach outlined previously [J. J. Portman, S. Takada, P. G.…
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…
Proteins created by combinatorial methods in vitro are an important source of information for understanding sequence-structure-function relationships. Alignments of folded proteins from combinatorial libraries can be analyzed using methods…
We introduce a lattice model of protein conformations which is able to reproduce second structures of proteins (alpha--helices and beta--sheets). This model is based on the following two main ideas. First, we model backbone parts of amino…