Efficient equilibrium sampling of all-atom peptides using library-based Monte Carlo

We applied our previously developed library-based Monte Carlo (LBMC) to equilibrium sampling of several implicitly solvated all-atom peptides. LBMC can perform equilibrium sampling of molecules using the pre-calculated statistical libraries of molecular-fragment configurations and energies. For this study, we employed residue-based fragments distributed according to the Boltzmann factor of the OPLS-AA forcefield describing the individual fragments. Two solvent models were employed: a simple uniform dielectric and the Generalized Born/Surface Area (GBSA) model. The efficiency of LBMC was compared to standard Langevin dynamics (LD) using three different statistical tools. The statistical analyses indicate that LBMC is more than 100 times faster than LD not only for the simple solvent model but also for GBSA.Comment: 5 figure

Extending fragment-based free energy calculations with library Monte Carlo simulation: Annealing in interaction space

Pre-calculated libraries of molecular fragment configurations have previously been used as a basis for both equilibrium sampling (via "library-based Monte Carlo") and for obtaining absolute free energies using a polymer-growth formalism. Here, we combine the two approaches to extend the size of systems for which free energies can be calculated. We study a series of all-atom poly-alanine systems in a simple dielectric "solvent" and find that precise free energies can be obtained rapidly. For instance, for 12 residues, less than an hour of single-processor is required. The combined approach is formally equivalent to the "annealed importance sampling" algorithm; instead of annealing by decreasing temperature, however, interactions among fragments are gradually added as the molecule is "grown." We discuss implications for future binding affinity calculations in which a ligand is grown into a binding site

Modeling ion and water permeation through narrow biological channels

Standard Poisson-Nernst-Planck (PNP) theory is modified by adding contributions due the Dielectric Self Energy and dynamic relaxation of a protein channel in response to ion permeation. This approach is utilized to predict ionic currents through the Gramicidin A (GA) channel, in which the applicability of conventional continuum theories is questionable. The Potential of Mean Force for K+ and Cl- ions in GA are obtained by combining an equilibrium molecular dynamics (MD) simulation that samples dynamic protein configurations with a continuum electrostatic calculation of the free energy. The results of our study show that the channel response to the permeating ion produces significant electrostatic stabilization of K+ inside the channel.The local diffusion constant of K+ inside the GA channel has been calculated using four different computational methods based on MD simulations: Mean Square Displacement (MSD), Velocity Autocorrelation Function (FACF), Second Fluctuation Dissipation Theorem (SFDT) and analysis of the Generalized Langevin Equation for a Harmonic Oscillator (GLE-HO). All methods were tested and compared in bulk water and all predicted the correct diffusion constant. Inside GA, MSD and VACF methods were found to be unreliable because they are biased by the systematic force exerted by the channel system. SFDT and GLE-HO methods properly unbias the influence of systematic force and predicted a similar diffusion constant of K+ inside GA, namely, ca. 10 times smaller than in the bulk.A simplified three-dimensional model of ClC chloride channel was constructed to couple the ion permeation to the motion of a glutamate side chain which acts as the putative fast gate. Dynamic Monte Carlo (DMC) simulations were carried out using this model channel to investigate the dependence of the gate closing rate on internal and external chloride concentration as well as the gate charge. Our simulation results were in qualitative agreement with experimental observations and consistent with the "foot-in-the-door" mechanism.Osmotic and diffusion permeabilities of H2O and D2O in Aquaporin 1 (AQP1) were calculated using MD simulations and, subsequently, osmotic permeabilities were measured experimentally. The combined computational and experimental results suggest that D2O permeability through AQP1 is similar to that of water

The Role of the Dielectric Barrier in Narrow Biological Channels: a Novel Composite Approach to Modeling Single-channel Currents

A composite continuum theory for calculating ion current through a protein channel of known structure is proposed, which incorporates information about the channel dynamics. The approach is utilized to predict current through the Gramicidin A ion channel, a narrow pore in which the applicability of conventional continuum theories is questionable. The proposed approach utilizes a modified version of Poisson-Nernst-Planck (PNP) theory, termed Potential-of-Mean-Force-Poisson-Nernst-Planck theory (PMFPNP), to compute ion currents. As in standard PNP, ion permeation is modeled as a continuum drift-diffusion process in a self-consistent electrostatic potential. In PMFPNP, however, information about the dynamic relaxation of the protein and the surrounding medium is incorporated into the model of ion permeation by including the free energy of inserting a single ion into the channel, i.e., the potential of mean force along the permeation pathway. In this way the dynamic flexibility of the channel environment is approximately accounted for. The PMF profile of the ion along the Gramicidin A channel is obtained by combining an equilibrium molecular dynamics (MD) simulation that samples dynamic protein configurations when an ion resides at a particular location in the channel with a continuum electrostatics calculation of the free energy. The diffusion coefficient of a potassium ion within the channel is also calculated using the MD trajectory. Therefore, except for a reasonable choice of dielectric constants, no direct fitting parameters enter into this model. The results of our study reveal that the channel response to the permeating ion produces significant electrostatic stabilization of the ion inside the channel. The dielectric self-energy of the ion remains essentially unchanged in the course of the MD simulation, indicating that no substantial changes in the protein geometry occur as the ion passes through it. Also, the model accounts for the experimentally observed saturation of ion current with increase of the electrolyte concentration, in contrast to the predictions of standard PNP theory

Thermal Motions of the E. Coli Glucose-Galactose Binding Protein Studied Using Well-Sampled Semi-Atomistic Simulations

The E. coli glucose-galactose chemosensory receptor is a 309 residue, 32 kDa protein consisting of two distinct structural domains. In this computational study, we studied the protein's thermal fluctuations, including both the large scale interdomain movements that contribute to the receptor's mechanism of action, as well as smaller scale motions, using two different computational methods. We employ extremely fast, "semi-atomistic" Library-Based Monte Carlo (LBMC) simulations, which include all backbone atoms but "implicit" side chains. Our results were compared with previous experiments and an all-atom Langevin dynamics simulation. Both LBMC and Langevin dynamics simulations were performed using both the apo and glucose-bound form of the protein, with LBMC exhibiting significantly larger fluctuations. The LBMC simulations are also in general agreement with the disulfide trapping experiments of Careaga & Falke (JMB, 1992; Biophys. J., 1992), which indicate that distant residues in the crystal structure (i.e. beta carbons separated by 10 to 20 angstroms) form spontaneous transient contacts in solution. Our simulations illustrate several possible "mechanisms" (configurational pathways) for these fluctuations. We also observe several discrepancies between our calculations and experiment. Nevertheless, we believe that our semi-atomistic approach could be used to study the fluctuations in other proteins, perhaps for ensemble docking, or other analyses of protein flexibility in virtual screening studies.Comment: 23 pages, 4 figures, 2 table

Water and Deuterium Oxide Permeability through Aquaporin 1: MD Predictions and Experimental Verification

Determining the mechanisms of flux through protein channels requires a combination of structural data, permeability measurement, and molecular dynamics (MD) simulations. To further clarify the mechanism of flux through aquaporin 1 (AQP1), osmotic pf (cm3/s/pore) and diffusion pd (cm3/s/pore) permeability coefficients per pore of H2O and D2O in AQP1 were calculated using MD simulations. We then compared the simulation results with experimental measurements of the osmotic AQP1 permeabilities of H2O and D2O. In this manner we evaluated the ability of MD simulations to predict actual flux results. For the MD simulations, the force field parameters of the D2O model were reparameterized from the TIP3P water model to reproduce the experimentally observed difference in the bulk self diffusion constants of H2O vs. D2O. Two MD systems (one for each solvent) were constructed, each containing explicit palmitoyl-oleoyl-phosphatidyl-ethanolamine (POPE) phospholipid molecules, solvent, and AQP1. It was found that the calculated value of pf for D2O is ∼15% smaller than for H2O. Bovine AQP1 was reconstituted into palmitoyl-oleoyl-phosphatidylcholine (POPC) liposomes, and it was found that the measured macroscopic osmotic permeability coefficient Pf (cm/s) of D2O is ∼21% lower than for H2O. The combined computational and experimental results suggest that deuterium oxide permeability through AQP1 is similar to that of water. The slightly lower observed osmotic permeability of D2O compared to H2O in AQP1 is most likely due to the lower self diffusion constant of D2O

Centrality evolution of the charged-particle pseudorapidity density over a broad pseudorapidity range in Pb-Pb collisions at root s(NN)=2.76TeV

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