Alchemical Transfer Method (ATM): Tried and Tested

As one of the gold standards for alchemical calculations of absolute binding free energy, the Double Decoupling Method (DDM)1 is a well-employed alchemical concept that obtains binding free energy (BFE) by process of decoupling the ligand from the unbound and bound states of a complex to the intermediate vacuum state, and then taking the difference between the two. What allows one to obtain the BFE depends on the existence of the thermodynamically linked intermediate vacuum state.

In our recent arXiv submission (, also announced on Twitter (, we present our new Alchemical Transfer Method (ATM). A noteworthy development to the broadly recognized Double Decoupling Method (DDM) in explicit solvent, ATM involves a coordinate displacement perturbation of the ligand between the receptor binding site and explicit solvent bulk, ultimately linking the two states at lambda = 1/2 and eliminating the need to transfer the ligand to vacuum. By allowing the ligand to interact at half strength each with solvent bulk (unbound) and the binding region of the receptor (bound) all within one solvent box, we also eliminate employing soft-core pair potentials, alchemical topologies, and the need to separately couple electrostatic and non-electrostatic steps, while also enabling its broad applicability to a slew of numerous many-body potentials that includes but is not limited to polarizable, QM/MM, and neural network forcefields.

Figure 1. Illustration of the bound and unbound states of the CB8-G3 complex. The CB8 host, with multiple colors, is situated at the center of the solvent box. The two states of the G3 guest are shown in green, linked by a green translation vector from the host binding site to the solvent bulk. The guest situated inside of the host is bound, while the guest located on the bottom right corner of the solvent box is unbound. Both guests exist in the same solvent box, with each representation of the guest exhibiting the λ = 1/2 state. The scattered red spheres represent the oxygen atoms of the water molecules.

To test the accuracy and precision of ATM, we applied the method to a vigorous benchmarking dataset developed by Rizzi et al.3 (, where we consistently yielded a BFE estimate much closer to experimental values than those displayed by established methods that utilized similar or greater computational expense. One of the sample host-guest systems that we tested on, as shown in Figure 1 above, consisted of the host, cucurbit[8]uril (CB8), and its guest, quinine (G3). The other two complexes (not shown) consisted of an octa-acid (OA) host and its two guests, 5-hexenoic acid (G3) and 4-methylpentanoic acid (G6).

Experimental data collected for the host-guest complexes yielded BFE of -5.18 ± 0.02 kcal/mol for OA-G3, -4.97 ± 0.02 for OA-G6, and -6.45 ± 0.06 kcal/mol for CB8-G3. Well-converged computational results, on average, overestimated (more negatively) BFE estimates by -1.2 kcal/mol, -2.1 kcal/mol, and -4.4 kcal/mol, respectively. In comparison, ATM predicted BFE estimates of -5.89 ± 0.33 kcal/mol, -6.32 ± 0.21 kcal/mol, and -8.53 ± 0.64 kcal/mol, respectively; which differed by -0.71 kcal/mol, -1.35 kcal/mol, and -2.08 kcal/mol from the experimental values. ATM, compared to the other well-converged computational methods, had a significantly closer estimate with respect to the experimental values. Equilibration analysis of each complex’s five conformations also converged at 5 ns equilibration time with BFE estimates consistent with ATM.

Considering the relatively low computational cost compared to other methods, ATM’s statistical uncertainties indicate that comparable levels of reproducibility and computational efficiency could be achieved. As such, we would like to validate ATM’s method and implementation on the SAMPL6 benchmark host-guest dataset.

While ATM is an alchemical method, its implementation is very straightforward and achieves results akin to physical pathway methodologies. ATM does not require splitting the alchemical transformations in electrostatic and non-electrostatic steps, alchemical topologies, and soft-core pair potentials, and is potential-function agnostic, with functionality that can be extended to other more advanced many-body potentials. Additionally, ATM does not require any modification of the OpenMM core energy routines, and is freely available via a plugin of the OpenMM molecular simulation package.

(1) Gilson, M. K.; Given, J. A.; Bush, B. L.; McCammon, J. A. The Statistical Thermodynamic Basis for Computation of Binding Affinities: A Critical Review. Biophys. J. 1997, 72, 1047–1069.(2) Wu, J. Z.; Azimi, S.; Khuttan, S.; Deng, N.; Gallicchio, E. Alchemical Transfer Approach to Absolute Binding Free Energy Estimation. arXiv preprint, 2021, 2101.07894.(3) Rizzi, A. et al. The SAMPL6 SAMPLing challenge: Assessing the reliability and efficiency of binding free energy calculations. J. Comp. Aid. Mol. Des. 2020, 1–33.