The Partial Infinite Swapping Algorithm

Performance and Free Energy Estimation for
Solvated Polypeptides and Proteins Using Partial
Infinite Swapping

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The method is more extensively detailed in my PhD thesis, Chapter 3

Partial infinite swapping (PINS) is a powerful enhanced sampling method for complex systems. In the present work thermodynamic observables are determined from reweighting at the post-processing stage for folding of (Ala)_10 in implicit and explicit solvent and for Xenon migration in myoglobin.

In every case free energy surfaces are determined using PINS with an accuracy comparable to Molecular Dynamics and Parallel Tempering simulations but at considerably reduced computational cost. Round trip times through the ensemble of temperature space are shown to be almost one order of magnitude shorter for PINS compared to PT simulations for (Ala)_10 in implicit solvent which suggests that PINS is more efficient for sampling diverse structures. Consistent with NMR experiments on shorter (Ala)_7 poly-alanine peptides, simulations of (Ala)_10 in explicit solvent highlight the essential role played by the environment in stabilizing extended conformations which are unfavourable in implicit solvent. Additional low-energy regions are beta-hairpins, 1 to 2 kcal/mol above the minimum energy structure.

(Ala10): extended starting structure (blue), and folded structure (red) obtained after 100 ns of MD with GENBORN implicit solvent. In cyan and orange, the carbonyl carbon atoms define the end-to-end distance ξ in Å, used for following compactification and building ∆F surfaces. The extended structure has ξ = 31.04 Å, and the α-helical structure is characterised by a ξ = 14.13 Å.
Free Energy as a function of ξ for Ala10 in explicit TIP3P water from 4 μs MD simulation. The red vertical line marks the point where ∆F = 0 kcal/mol for ξ = 22.75 Å, i.e. the most sampled extended (non-helical) state. The 4 displayed configurations are examples of structures for which ∆F ≤ 1 kcal/mol.

For Xenon migration in Myoglobin, PINS finds stabilization energies of the experimentally known Xenon-pockets to range from -4.6 to -6.2 kcal/mol, in accord with experiment. Furthermore, the barrier heights between neighboring pockets have been determined to be ~ 4 kcal/mol.

Left: Myoglobin with its heme functional group. Color code for the protein secondary structure is purple and blue for α and 3-10 helices, cyan and white for turn and coil, respectively. Right: Isosurface of normalised probabilities (ρ = 10−5 ) to find the Xe atom at a given grid point, and definition of the 4 Xe pockets. Blue surface for MD, red for PINS. Built using the 100 ns and 96 ns long simulations. For simulations starting in pocket Xe4. PINS samples pocket Xe3 not explored with conventional MD. The transition channels Xe4 ↔Xe2 and Xe1↔Xe2 are also more widely sampled when using PINS than with standard MD.

By starting simulations from individual pockets, PINS finds sampling of the entire pocket network on the time scale of 3 ns using 32 replicas whereas with MD, 100 ns are not sufficient to access all pockets. Hence, PINS with reweighting is found to be both, a quantitatively accurate and computationally efficient method for studying complex biological molecules in solution.

See the page “Contributions to CHARMM” for details concerning the CHARMM implementation.