Artem B. Mamonov

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.

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.

Absolute free energies estimated by combining precalculated molecular fragment libraries

The absolute free energy—or partition function, equivalently—of a molecule can be estimated computationally using a suitable reference system. Here, we demonstrate a practical method for staging such calculations by growing a molecule based on a series of fragments. Significant computer time is saved by precalculating fragment configurations and interactions for reuse in a variety of molecules. We use such fragment libraries and interaction tables for amino acids and capping groups to estimate free energies for small peptides. Equilibrium ensembles for the molecules are generated at no additional computational cost and are used to check our results by comparison to standard dynamics simulation. We explain how our work can be extended to estimate relative binding affinities.

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 precalculated statistical libraries of molecular-fragment configurations and energies. For this study, we employed residue-based fragments distributed according to the Boltzmann factor of the optimized potential for liquid simulations all-atom (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.

Rapid sampling of all‐atom peptides using a library‐based polymer‐growth approach

We adapted existing polymer growth strategies for equilibrium sampling of peptides described by modern atomistic forcefields with a simple uniform dielectric solvent. The main novel feature of our approach is the use of precalculated statistical libraries of molecular fragments. A molecule is sampled by combining fragment configurations—of single residues in this study—which are stored in the libraries. Ensembles generated from the independent libraries are reweighted to conform with the Boltzmann‐factor distribution of the forcefield describing the full molecule. In this way, high‐quality equilibrium sampling of small peptides (4–8 residues) typically requires less than one hour of single‐processor wallclock time and can be significantly faster than Langevin simulations. Furthermore, approximate, clash‐free ensembles can be generated for larger peptides (up to 32 residues in this study) in less than a minute of single‐processor computing. We discuss possible applications of our growth procedure to free energy calculation, fragment assembly protein‐structure prediction protocols, and to “multi‐resolution” sampling.

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 time 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.

Extending Fragment Based Free Energy Calculations with Library Based 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 librarybased Monte Carlo) and for obtaining absolute free energies using a polymergrowth 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.

Improved Library-Based Monte Carlo, Applied to Multi-Level Sampling

We describe further advances in our previously developed library-based Monte Carlo (LBMC) simulation. LBMC is a memory-intensive molecular simulation strategy which uses pre-calculated configurations of molecular fragments, such as amino acids or side-chains. We showed previously that LBMC using whole-residue fragments could lead to dramatic efficiency gains for sampling flexible peptides; however, such fragments are not ideal for simulating folded systems because trial moves are highly non-local. We therefore have developed a new implementation of LBMC, by separating the backbone from side-chain libraries, which allows for exactly local moves perturbing only a small part of a protein. Because the positions of all atoms are carried in memory at minimal run-time cost, LBMC readily permits the use of hybrid protein models mixing full and reduced interactions. Hybrid models are useful in themselves - e.g., to simulate an atomistic binding site allosterically coupled to a reduced description of the remainder of the protein. Here, however, we explore the use of hybrid models in multi-level equilibrium sampling algorithms based on Hamiltonian and resolution exchange. Higher ladder levels are built to allow cheaper energy calls and smoother potential energy landscapes to facilitate sampling of low levels.

Library-Based Monte Carlo as a Convenient Platform for Variable-Resolution Protein Models

We recently developed the library-based Monte Carlo (LBMC) which exploits pre-calculated libraries of molecular fragments, such as amino acids. We now use LBMC as the foundation for a variable-resolution platform for protein modeling. The unique feature of this platform is the capability to track coordinates of all atoms at no run-time cost, while turning on only desired interactions. More accurate interactions can be used in some parts of the protein (e.g., a binding site) and more approximate in others, depending on the problem. This strategy permits model tuning/simplification to the point where good statistical sampling can be achieved. We hope our platform will prove useful for estimating protein-ligand binding affinities.