Related papers: Exact Sequence Analysis for Three-Dimensional HP L…
Hydrophobicity is thought to be one of the primary forces driving the folding of proteins. On average, hydrophobic residues occur preferentially in the core, whereas polar residues tends to occur at the surface of a folded protein. By…
The intricate three-dimensional geometries of protein tertiary structures underlie protein function and emerge through a folding process from one-dimensional chains of amino acids. The exact spatial sequence and configuration of amino…
Linear polymers are represented as chains of hopping reptons and their motion is described as a stochastic process on a lattice. This admittedly crude approximation still catches essential physics of polymer motion, i.e. the universal…
Directed polymers on 1+1 dimensional lattices coupled to a heat bath at temperature $T$ are studied numerically for three ensembles of the site disorder. In particular correlations of the disorder as well as fractal patterning are…
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…
We propose a novel method for the determination of the effective interaction potential between the amino acids of a protein. The strategy is based on the combination of a new optimization procedure and a geometrical argument, which also…
A lattice model of the directed self-avoiding walk is used to estimate the possibility on the formation of an infinitely long linear semi-flexible copolymer chain. The copolymer chain is assumed to composed of four different types of the…
In protein secondary structure prediction, each amino acid in sequence is typically treated as a distinct category and represented by a one-hot vector. In this study, we developed two novel chemical representations for amino acids utilizing…
Chain molecules play a key role in the polymer field and in living cells. Our focus is on a new homopolymer model of a linear chain molecule subject to an attractive self-interaction promoting compactness. We analyze the model using simple…
We propose an off-lattice model for a self-avoiding homopolymer chain with two different competing attractive interactions, mimicking the hydrophobic effect and the hydrogen bond formation respectively. By means of Monte Carlo simulations,…
Proteins inherently possess a consistent sequence-structure duality. The abundance of protein sequence data, which can be readily represented as discrete tokens, has driven fruitful developments in protein language models (pLMs). A key…
We consider the folding of a self-avoiding homopolymer on a lattice, with saturating hydrogen bond interactions. Our goal is to numerically evaluate the statistical distribution of the topological genus of pseudoknotted configurations. The…
We find the exact solution of three interacting friendly directed walks on the square lattice in the bulk, modelling a system of homopolymers that can undergo gelation by introducing two distinct interaction parameters that differentiate…
We address the problem of inverse polymer swelling. This phenomenon, in which a collapsed polymer chain swells upon decreasing temperature, can be observed experimentally in so-called thermoreversible homopolymers in aqueous solution, and…
Models of protein energetics which neglect interactions between amino acids that are not adjacent in the native state, such as the Go model, encode or underlie many influential ideas on protein folding. Implicit in this simplification is a…
We propose a new and effective means for designing stable and fast-folding polypeptide sequences using a cumulant expansion of the molecular partition function. This method is unique in that $T_{Z}$, the ``cumulant design temperature''…
Protein folding is the intricate process by which a linear sequence of amino acids self-assembles into a unique three-dimensional structure. Protein folding kinetics is the study of pathways and time-dependent mechanisms a protein undergoes…
Based on large-scale Monte Carlo simulations on lattice the energy probability distribution functions are investigated for a large set of primary sequences in distinct models of copolymers at low temperatures below transitions to compacted…
Protein sequence generation via stochastic attention produces plausible family members from small alignments without training, but treats all stored sequences equally and cannot direct generation toward a functional subset of interest. We…
Physical mechanisms underlying the empirical correlation between relative contact order (CO) and folding rate among naturally-occurring small single-domain proteins are investigated by evaluating postulated interaction schemes for a set of…