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Despite many advances in computational modeling of protein structures, these methods have not been widely utilized by experimental structural biologists. Two major obstacles are preventing the transition from a purely-experimental to a…
Simple hidden Markov models are proposed for predicting secondary structure of a protein from its amino acid sequence. Since the length of protein conformation segments varies in a narrow range, we ignore the duration effect of length…
The behavior of a system of two-dimensional elongated particles (discorectangles) packed into a slit between two parallel walls was analyzed using a simulation approach. The packings were produced using the random sequential adsorption…
In this letter, the possible dynamic scaling properties of protein molecules in folding are investigated theoretically by assuming that the protein molecules are percolated networks. It is shown that the fractal character and the fractal…
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.…
The remarkable structural diversity of modern proteins reflects millions of years of evolution, during which sequence space has expanded while many structural features remain conserved. This conservation is evident not only among homologous…
The precise sequence of aminoacids plays a central role in the tertiary structure of proteins and their functional properties. The Hydrophobic-Polar lattice models have provided valuable insights regarding the energy landscape. We…
We develop the theory of the coupling between in-plane order and out-of-plane geometry in twisted, two-dimensionally ordered filament bundles based on the non-linear continuum elasticity theory of columnar materials. We show that twisted…
We present A-CODE, a fully atomic unified one-stage protein co-design model that simultaneously refines discrete atom types and continuous atom coordinates. Unlike predominant two-stage methods that cascade structure design with amino…
We present structural properties of two-dimensional polymers as far as they can be described by percolation theory. The percolation threshold, critical exponents and fractal dimensions of clusters are determined by computer simulation and…
Thin solids often develop elastic instabilities and subsequently complex, multiscale deformation patterns. Revealing the organizing principles of this spatial complexity has ramifications for our understanding of morphogenetic processes in…
Determining protein structures at an atomic level remains a significant challenge in structural biology. We introduce $\texttt{RecCrysFormer}$, a hybrid model that exploits the strengths of transformers with the aim of integrating…
We use a large $N$-body simulation to study the relation of the structural properties of dark matter halos to their assembly history and environment. The complexity of individual halo assembly histories can be well described by a small…
Most cancers in humans are large, measuring centimeters in diameter, composed of many billions of cells. An equivalent mass of normal cells would be highly heterogeneous as a result of the mutations that occur during each cell division.…
The distribution of inequivalent geometries occurring during self-assembly of the major capsid protein in thermodynamic equilibrium is determined based on a master equation approach. These results are implemented to characterize the…
We study two mechanisms for the formation of protein patterns near membranes of living cells by mathematical modelling. Self-assembly of protein domains by electrostatic lipid-protein interactions is contrasted with self-organization due to…
Volume-fraction expressions are obtained for the systems of an infinite number of parallel planes arranged both regularly and randomly. As a special case of random arrangement, a non-Poissonian point process (the second-order Erlang…
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…
Spatial organization of proteins in cells is important for many biological functions. In general, the nonlinear, spatially coupled models for protein-pattern formation are only accessible to numerical simulations, which has limited insight…
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.…