Quantitative Protein Dynamics from Dominant Folding Pathways

We develop a theoretical approach to the protein folding problem based on out-of-equilibrium stochastic dynamics. Within this framework, the computational difficulties related to the existence of large time scale gaps in the protein folding problem are removed and simulating the entire reaction in atomistic details using existing computers becomes feasible. In addition, this formalism provides a natural framework to investigate the relationships between thermodynamical and kinetic aspects of the folding. For example, it is possible to show that, in order to have a large probability to remain unchanged under Langevin diffusion, the native state has to be characterized by a small conformational entropy. We discuss how to determine the most probable folding pathway, to identify configurations representative of the transition state and to compute the most probable transition time. We perform an illustrative application of these ideas, studying the conformational evolution of alanine di-peptide, within an all-atom model based on the empiric GROMOS96 force field.Comment: 4 pages, 1 figur

Statistical Mechanics of Quantum-Classical Systems with Holonomic Constraints

The statistical mechanics of quantum-classical systems with holonomic constraints is formulated rigorously by unifying the classical Dirac bracket and the quantum-classical bracket in matrix form. The resulting Dirac quantum-classical theory, which conserves the holonomic constraints exactly, is then used to formulate time evolution and statistical mechanics. The correct momentum-jump approximation for constrained system arises naturally from this formalism. Finally, in analogy with what was found in the classical case, it is shown that the rigorous linear response function of constrained quantum-classical systems contains non-trivial additional terms which are absent in the response of unconstrained systems.Comment: Submitted to Journal of Chemical Physic

Molecular dynamics simulation of the transport of small molecules across a polymer membrane

The transport of small molecules through a polymer membrane is modeled using the computer simulation technique of molecular dynamics (MD). The transport coefficient is derived from a combination of the excess free energy and the diffusion constant. Both properties are derived from MD simulations, applied to helium and methane in polydimethylsiloxane (PDMS). The diffusional process appears to have the character of a jump diffusion for methane and less so for helium. Jumps are allowed by fluctuations of the size and shape of holes. Experimental diffusion constants are well reproduced. The excess free energies, determined by a particle insertion method, are lower by 5-7 kJ/mol than experimental values. It is shown that, as a result of a higher solubility, methane has a higher permeability constant than helium, despite its lower diffusion constant

Design and Experimental Validation of a Ducted Counter-rotating Axial-flow Fans System

An experimental study on the design of counter-rotating axial-flow fans was carried out. The fans were designed using an inverse method. In particular, the system is designed to have a pure axial discharge flow. The counter-rotating fans operate in a ducted-flow configuration and the overall performances are measured in a normalized test bench. The rotation rate of each fan is independently controlled. The relative axial spacing between fans can vary from 17% to 310%. The results show that the efficiency is strongly increased compared to a conventional rotor or to a rotor-stator stage. The effects of varying the rotation rates ratio on the overall performances are studied and show that the system has a very flexible use, with a large patch of high efficient operating points in the parameter space. The increase of axial spacing causes only a small decrease of the efficiencyComment: accepted in Journal of Fluid Engineerin

Molecular dynamics with coupling to an external bath

In molecular dynamics (MD) simulations the need often arises to maintain such parameters as temperature or pressure rather than energy and volume, or to impose gradients for studying transport properties in nonequilibrium MD. A method is described to realize coupling to an external bath with constant temperature or pressure with adjustable time constants for the coupling. The method is easily extendable to other variables and to gradients, and can be applied also to polyatomic molecules involving internal constraints. The influence of coupling time constants on dynamical variables is evaluated. A leap‐frog algorithm is presented for the general case involving constraints with coupling to both a constant temperature and a constant pressure bath

Exploring the Levinthal limit in protein folding

According to the thermodynamic hypothesis, the native state of proteins is uniquely defined by their amino acid sequence. On the other hand, according to Levinthal, the native state is just a local minimum of the free energy and a given amino acid sequence, in the same thermodynamic conditions, can assume many, very different structures that are as thermodynamically stable as the native state. This is the Levinthal limit explored in this work. Using computer simulations, we compare the interactions that stabilize the native state of four different proteins with those that stabilize three non-native states of each protein and find that the nature of the interactions is very similar for all such 16 conformers. Furthermore, an enhancement of the degree of fluctuation of the non-native conformers can be explained by an insufficient relaxation to their local free energy minimum. These results favor Levinthal's hypothesis that protein folding is a kinetic non-equilibrium process.FCT - Foundation for Science and Technology, Portugal [UID/Multi/04326/2013]; Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP); Conselho Nacional de Desenvolvimento Cientia co e Tecnologico (CNPq

Estimating entropies from molecular dynamics simulations

The methods to compute the excess entropy and the entropy of solvation using liquid water as a test system were studied. The accuracy and convergence behavior of five methods based on thermodynamic integration and perturbation techniques was evaluated. Through the thermodynamic integration accurate entropy differences were obtained in which many copies of a solute were desolvated. Only two methods yield useful results, the calculation of solute-solvent entropy through thermodynamic integration and the calculation of solvation entropy through the temperature derivative of the corresponding free-energy difference, when one solute molecule is involved

Recurrence quantification analysis as a tool for the characterization of molecular dynamics simulations

A molecular dynamics simulation of a Lennard-Jones fluid, and a trajectory of the B1 immunoglobulin G-binding domain of streptococcal protein G (B1-IgG) simulated in water are analyzed by recurrence quantification, which is noteworthy for its independence from stationarity constraints, as well as its ability to detect transients, and both linear and nonlinear state changes. The results demonstrate the sensitivity of the technique for the discrimination of phase sensitive dynamics. Physical interpretation of the recurrence measures is also discussed.Comment: 7 pages, 8 figures, revtex; revised for review for Phys. Rev. E (clarifications and expansion of discussion)-- addition of the 8 postscript figures previously omitted, but unchanged from version