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The effective free energy of globular protein chain is considered to be a functional defined on smooth curves in three dimensional Euclidean space. From the requirement of geometrical invariance, together with basic facts on conformation of…
The free energy landscape of a protein-like chain in a fluid was studied by combining discontinuous molecular dynamics and parallel tempering. The model protein is a repeating sequence of four different beads, with interactions mimicking…
The extensive application of surfactants motivates comprehensive and predictive theoretical studies that improve our understanding of the behaviour of these complex systems. In this study, an expression for the elastic free-energy density…
We use a free energy functional theory to elucidate general properties of heterogeneously ordering, fast folding proteins, and we test our conclusions with lattice simulations. We find that both structural and energetic heterogeneity can…
We show how to localize and quantify the functional evolutionary constraints on natural proteins. The method compares the perturbations caused by local sequence variants to the energetics of the protein folding process and to the…
We investigate relations between spatial properties of the free energy and the radius of Gaussian curvature of the underlying curved lattice geometries. For this purpose we derive recurrence relations for the analysis of the free energy…
The molecular distributions obtained from canonical Monte Carlo simulations can be used to find an approximate interaction energy. This serves as the basis of a method for estimating the binding free energy for a ligand to a protein which…
In this article the configurational space of two simple protein models consisting of polymers composed of a periodic sequence of four different kinds of monomers is studied as a function of temperature. In the protein models, hydrogen bond…
Proteins are linear chain molecules that play a central role in life and health. Protein native state folds are modular assemblies of space-filling building blocks of {\alpha}-helices, \{beta}-sheets and tight turns. Here we deduce the…
This letter aims to derive the exact relativistic orbital-free kinetic energy density functional for one-particle nuclear systems in one-dimensional case. The kinetic energy is expressed as a functional of both vector and scalar densities.…
Metadynamics is a powerful computational tool to obtain the free energy landscape of complex systems. The Monte Carlo algorithm has proven useful to calculate thermodynamic quantities associated with simplified models of proteins, and thus…
Optimal structure of proteins is described by linear stochastic differential equation with mean decrease of free energy and volatility. Structure determining strategy is given by a twin of stochastic variables for which empirical conditions…
A general theoretical framework is developed using free energy functional methods to understand the effects of heterogeneity in the folding of a well-designed protein. Native energetic heterogeneity arising from non-uniformity in native…
The Debye-H\"uckel approximation to the free-energy of a simple fluid is written as a functional of the pair correlation function. This functional can be seen as the Debye-H\"uckel equivalent to the functional derived in the hyper-netted…
Current theories of heteropolymers are inherently macrpscopic, but are applied to folding proteins which are only mesoscopic. In these theories, one computes the averaged free energy over sequences, always assuming that it is self-averaging…
We present a model, based on symmetry and geometry, for proteins. Using elementary ideas from mathematics and physics, we derive the geometries of discrete helices and sheets. We postulate a compatible solvent-mediated emergent pairwise…
In this work we show that there is a direct relationship between a graph's topology and the free energy of a spin system on the graph. We develop a method of separating topological and enthalpic contributions to the free energy, and find…
In this work we introduce an energy function in order to study finite scale free graphs generated with different models. The energy distribution has a fractal pattern and presents log periodic oscillations for high energies. This…
We study the free energy landscape of the small peptide Met-enkephalin. Our data were obtained from a generalized-ensemble Monte Carlo simulation taking the interactions among all atoms into account. We show that the free energy landscape…
A theoretical framework is developed to study the dynamics of protein folding. The key insight is that the search for the native protein conformation is influenced by the rate r at which external parameters, such as temperature, chemical…