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A fundamental challenge in protein design is the trade-off between generating structural diversity while preserving motif biological function. Current state-of-the-art methods, such as partial diffusion in RFdiffusion, often fail to resolve…
We propose a general theory to describe the distribution of protein-folding transition paths. We show that transition paths follow a predictable sequence of high-free-energy transient states that are separated by free-energy barriers. Each…
We perform Monte Carlo simulations to study the elastic properties of the helix-coil worm-like chain model of alpha-helical polypeptides. In this model the secondary structure enters as a scalar (Ising like) variable that controls the local…
A protein's function depends critically on its conformational ensemble, a collection of energy weighted structures whose balance depends on temperature and environment. Though recent deep learning (DL) methods have substantially advanced…
Understanding the mechanism of protein secondary structure formation is an essential part of protein-folding puzzle. Here we describe a simple model for the formation of the $\beta$-hairpin, motivated by the fact that folding of a…
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…
Though the problem of sequence-reversed protein folding is largely unexplored, one might speculate that reversed native protein sequences should be significantly more foldable than purely random heteropolymer sequences. In this article, we…
We test a simplified, local version of the helix model on two synthetic and two natural proteins, to study its efficiency in predicting the native secondary structure. The results we obtain are very good for the synthetic sequences, poorer…
Folded proteins have a modular assembly. They are constructed from regular secondary structures like alpha-helices and beta-strands that are joined together by loops. Here we develop a visualization technique that is adapted to describe…
Protein folding, which dictates the protein structure from its amino acid sequence, is half a century old problem of biology. The function of the protein correlates with its structure, emphasizing the need of understanding protein folding…
Understanding how monomeric proteins fold under in vitro conditions is crucial to describing their functions in the cellular context. Significant advances both in theory and experiments have resulted in a conceptual framework for describing…
We use a three dimensional cubic lattice model of proteins to study their properties that determine folding to the native state. The protein chain is modeled as a sequence of $N$ beads. The interactions between beads are taken from a…
Natural protein molecules are exceptional polymers. Encoded in apparently random strings of amino-acids, these objects perform clear physical tasks that are rare to find by simple chance. Accurate folding, specific binding, powerful…
We present a simple physical model which demonstrates that the native state folds of proteins can emerge on the basis of considerations of geometry and symmetry. We show that the inherent anisotropy of a chain molecule, the geometrical and…
The three dimensional structure of a protein is an outcome of the interactions of its constituent amino acids in 3D space. Considering the amino acids as nodes and the interactions among them as edges we have constructed and analyzed…
Amyloid fibrils are stable aggregates of misfolded proteins and polypeptides that are insoluble and resistant to protease activity. Abnormal formation of amyloid fibrils in vivo may lead to neurodegenerative disorders and other systemic…
The presence of low dimensional chaos in the protein secondary structures, using the binary coded $\alpha$-helices and $\beta$-sheet motifs, has been investigated. In order to analyse symbolic DNA/RNA sequences the assignment, based on the…
The Automated Protein Structure Analysis (APSA) method is used for the classification of supersecondary structures. Basis for the classification is the encoding of three-dimensional (3D) residue conformations into a 16-letter code (3D-1D…
We have investigated the potential energy surfaces for alanine chains consisting of three and six amino acids. For these molecules we have calculated potential energy surfaces as a function of the Ramachandran angles Phi and Psi, which are…
Macroscopic mechanical properties of polymers are determined by their microscopic molecular chain distribution. Due to randomness of these molecular chains, probability theory has been used to find their micro-states and energy…