| Abstract
| - The energetic consequences of amino acid substitutions were investigated using molecular dynamics freeenergy simulations (MD/FES). A focus of the present study is how one can treat some of the intrinsic problemsassociated with the use of dummy atoms, which are introduced in standard MD/FES procedures workingwith a constant number of particles. Specifically, we show how one can introduce dummy atoms, whichretain all the covalent interactions, in a “hybrid residue”, in such a way that the influence of the bondedinteractions with dummy atoms do not influence the final free energy change. The simulations thus can bedone using a transformation protocol in which all covalent bond contributions are maintained invariantthroughout the calculations; only the nonbonded interactions are varied. That is, the number of atoms ismaintained constant by introducing dummy atoms, which are covalently linked to the protein in question, butwhich have no nonbonded interactions at one or the other of the two end point reference states. The potentialenergy function describing the transformation was constructed such that all internal energy terms are invariantwith respect to the thermodynamic coupling parameter λ (0 ≤ λ ≤ 1). This simulation procedure thereforehas similarities with both the “single topology” and “dual topology” methods, which have been used in otherinvestigations. This transformation and MD/FES strategy was evaluated using three different systems, inwhich an Ala is transformed into a Val (the italicized residues were transformed): formyl-Ala-ethanolamine;formyl-(Ala)3-Ala-Ala-Ala-(Ala)3-ethanolamine (as an α-helix); and formyl-(Ala)3-Val-Ala-Val-(Ala)3-ethanolamine (as an α-helix). The calculations examined how the free energy difference associated with anAla-to-Val transformation depends on the choice of transformation path, the equilibration time, and the numberwindows used in the calculation. The results show that MD/FES provides for stable energy estimates for anyintermediate state, as defined by the coupling parameter λ, including the end point reference states: λ = 0and λ = 1. With an appropriate choice of sigmoid transformation path, free energy changes with minimalvariability and good reversibility were obtained for all three systems using MD/FES lasting longer than 2.4ns.
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