In dual topology approaches, (8,12) in which both states are present simultaneously, the problem seems avoided, but at each of the endpoints, one of the groups has no nonbonded interactions with the remainder of the system, yet remains connected to the physical system. If dummy atoms are attached to the physical part of the system through bonded energy terms, the question arises whether they alter the properties of the physical system. (9−11) Typically, some or all of the bonded force field terms present for the native atom are kept for the corresponding dummy atom. However, they must remain connected to the physical system, either through bonded energy terms or suitable restraints. Figure 1ĭummy atoms do not participate in any nonbonded interactions. In most practical calculations, one really computes ΔΔA ′ = A 2 ′ – A 1 ′ as shown in Figure 1(b), relying on that ΔΔA′ equals ΔΔA from the idealized cycle Figure 1(a). This is made explicit in Figure 1(b), where the presence of dummy atoms is indicated by the superscripts D. Especially in the so-called single topology paradigm, (8) these placeholders are usually referred to as dummy atoms. Since the number of particles in simulations in the canonical ensemble must not change, one needs to add “placeholders” at one or both end states to formally maintain the overall number of particles. In most practical applications, however, the number of atoms in the initial and final chemical moiety (the parts which are different in, for example, two ligands of interest) is not the same.
Thus, one needs to transform only a small part of the system, i.e., such as changing a functional group into another.
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(7) Rather than computing the double free energy difference of interest according to ΔΔA = ΔA 4 – ΔA 3, as would be done in an experiment, it is obtained along the “alchemical” paths, ΔΔA = ΔA 2 – ΔA 1. While our analysis focuses on the so-called single topology approach to set up alchemical transformations, similar considerations apply to dual topology, at least many widely used variants thereof.Ĭalculations of relative free energy differences rely on a thermodynamic cycle as shown in Figure 1(a). We find that a naive (but often practiced) treatment of dummy atoms results in errors of up to k BT when calculating the relative solvation free energy difference between two small solutes, such as methane and ammonia. Cycle closure (or lack thereof) was used as a sensitive indicator to probing the effects of dummy atom treatment on the resulting free energy differences. A detailed theoretical analysis of both aspects is provided, illustrated by 24 calculations of relative solvation free energy differences, for which all four legs of the underlying thermodynamic cycle were computed. On the other hand, the bonded terms used to attach a dummy atom (or group of dummy atoms) to the physical system have to maintain it in a well-defined position and orientation relative to the physical system. On the one hand, one has to ensure that dummy atoms only give a multiplicative contribution to the partition function so that their contribution cancels from double-free energy differences. We investigate the conditions necessary so that the presence of dummy atoms does not influence the result of a relative free energy calculation. These placeholders interact with the physical system only by bonded energy terms. This necessitates the introduction of dummy atoms.
In calculations of relative free energy differences, the number of atoms of the initial and final states is rarely the same.
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