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We present a statistical mechanics approach to the protein folding problem. We first review some of the basic properties of proteins, and introduce some physical models to describe their thermodynamics. These models rely on a random…
The kinetic behavior of a three-dimensional off-lattice heteropolymer model is studied in terms of the time dependence of the average mean-square displacement between configurations. It is found that at short time-scales similar behavior is…
The conformational kinetics of enzymes can be reliably revealed when they are governed by Markovian dynamics. Hidden Markov Models (HMMs) are appropriate especially in the case of conformational states that are hardly distinguishable.…
Isomorphs are curves in the thermodynamic phase diagram of invariant excess entropy, structure, and dynamics, while pseudoisomorphs are curves of invariant structure and dynamics, but not of the excess entropy. The latter curves have been…
A reduced protein model with five to six atoms per amino acid and five amino acid types is developed and tested on a three-helix-bundle protein, a 46-amino acid fragment from staphylococcal protein A. The model does not rely on the widely…
Proteins fold using a two-state or multi-state kinetic mechanisms, but up to now there isn't a first-principle model to explain this different behaviour. We exploit the network properties of protein structures by introducing novel…
In the present paper we give a brief summary of some recent theoretical advances in the treatment of inhomogeneous fluids and methods which have applications in the study of dynamical properties of liquids in situations of extreme…
The bond graph approach to modelling biochemical networks is extended to allow hierarchical construction of complex models from simpler components. This is made possible by representing the simpler components as thermodynamically open…
Enzyme-based systems have been shown to undergo directional motion in response to their substrate gradient. Here, we formulate a kinetic model to analyze the directional movement of an ensemble of protein molecules in response to a gradient…
A kinetic model for granular mixtures is considered to study three different non-equilibrium situations. The model is based on the equivalence between a gas of elastic hard spheres subjected to a drag force proportional to the particle…
We present a statistical approach to protein structure by introducing a representation of protein folds based on simple observables defined as frequencies of oriented cycles in contact graphs. Motivated by the idea that these cycles may…
We present a unified framework for folding kinetics of proteins and RNA. The basis for this framework relies on the notion of topological frustration, which gives rise to several competing basins of attraction (CBA) in addition to the…
With the formal construction of a thermodynamic spring, I describe the mechanics, energetics, entropy, and kinetics of a binary mechanical model system. A protein that transitions between two metastable structural states behaves as a…
Empirical scoring functions based on either molecular force fields or cheminformatics descriptors are widely used, in conjunction with molecular docking, during the early stages of drug discovery to predict potency and binding affinity of a…
Neither of the two prevalent theories, namely thermodynamic stability and kinetic stability, provides a comprehensive understanding of protein folding. The thermodynamic theory is misleading because it assumes that free energy is the…
Kinetic models of solid thermal decomposition are traditionally used for individual fit of isothermal decomposition experimental data. However, this methodology can provide unacceptable errors in some cases. To solve this problem, a neural…
The ability of a protein to recognise multiple independent target conformations was demonstrated in [1]. Here we consider the recognition of correlated configurations, which we apply to funnel design for a single conformation. The maximum…
The protein folding problem must ultimately be solved on all length scales from the atomic up through a hierarchy of complicated structures. By analyzing the stability of the folding process using physics and mathematics, this paper shows…
Predicting protein-ligand binding affinity remains intractable for multi-domain proteins, where inter-domain dynamics govern molecular recognition. Existing geometric deep learning methods typically treat proteins as monolithic static…
Protein structure prediction and folding are fundamental to understanding biology, with recent deep learning advances reshaping the field. Diffusion-based generative models have revolutionized protein design, enabling the creation of novel…