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Simulations of knotting and unknotting in polymers or other filaments rely on random processes to facilitate topological changes. Here we introduce a method of \textit{topological steering} to determine the optimal pathway by which a…
The possibility of deriving the contact potentials between amino acids from their frequencies of occurence in proteins is discussed in evolutionary terms. This approach allows the use of traditional thermodynamics to describe such…
Model off-lattice sequences in two dimensions are constructed so that their native states are close to an on-lattice target. The Hamiltonian involves the Lennard-Jones and harmonic interactions. The native states of these sequences are…
We develop a path-based approach to continuous-time random walks on networks with arbitrarily weighted edges. We describe an efficient numerical algorithm for calculating statistical properties of the stochastic path ensemble. After…
The understanding, and even the description of protein folding is impeded by the complexity of the process. Much of this complexity can be described and understood by taking a statistical approach to the energetics of protein conformation,…
There are several simple criteria of folding to a native state in model proteins. One of them involves crossing of a threshold value of the RMSD distance away from the native state. Another checks whether all native contacts are…
Prediction of ligand binding sites of proteins is a fundamental and important task for understanding the function of proteins and screening potential drugs. Most existing methods require experimentally determined protein holo-structures as…
A simple lattice model for proteins that allows for distinct sizes of the amino acids is presented. The model is found to lead to a significant number of conformations that are the unique ground state of one or more sequences or encodable.…
This paper presents a method of computing free motions of a planar assembly of rigid bodies connected by loose joints. Joints are modeled using local distance constraints, which are then linearized with respect to configuration space…
After the recent ground-breaking advances in protein structure prediction, one of the remaining challenges in protein machine learning is to reliably predict distributions of structural states. Parametric models of fluctuations are…
Many aspects of the study of protein folding and dynamics have been affected by the recent advances in machine learning. Methods for the prediction of protein structures from their sequences are now heavily based on machine learning tools.…
The folding pathway and rate coefficients of the folding of a knotted protein are calculated for a potential energy function with minimal energetic frustration. A kinetic transition network is constructed using the discrete path sampling…
The high computational cost of carrying out molecular dynamics simulations of even small-size proteins is a major obstacle in the study, at atomic detail and in explicit solvent, of the physical mechanism which is at the basis of the…
Using three-dimensional Go lattice models with side chains for proteins, we investigate the dependence of folding times on protein length. In agreement with previous theoretical predictions, we find that the folding time grows as a power…
We introduce a system where an elastic lattice of particles is moved slowly at a constant velocity under the influence of a local external potential, construct a rigid-body model through simplification processes, and show that the two…
We review the recent progress in computational approaches to protein design which builds on advances in statistical-mechanical protein folding theory. In particular, we evaluate the degeneracy of the protein code (i.e. how many sequences…
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…
Growing experimental evidence shows that proteins follow one or a few distinct paths when folding. We propose in this paper a procedure to parametrize these observed pathways, and from this parametrization construct effective Hamiltonians…
Tokenization is a promising path to multi-modal models capable of jointly understanding protein sequences, structure, and function. Existing protein structure tokenizers create tokens by pooling information from local neighborhoods, an…
The classical approach to protein folding inspired by statistical mechanics avoids the high dimensional structure of the conformation space by using effective coordinates. Here we introduce a network approach to capture the statistical…