The Good, the Bad, and the Ugly: “HiPen”, a New Dataset for Validating (S)QM/MM Free Energy Simulations

Abstract

Indirect (S)QM/MM free energy simulations (FES) are vital to efficiently incorporating sufficient sampling and accurate (QM) energetic evaluations when estimating free energies of practical/experimental interest. Connecting between levels of theory, i.e., calculating Δ A l o w → h i g h , remains to be the most challenging step within an indirect FES protocol. To improve calculations of Δ A l o w → h i g h , we must: (1) compare the performance of all FES methods currently available; and (2) compile and maintain datasets of Δ A l o w → h i g h calculated for a wide-variety of molecules so that future practitioners may replicate or improve upon the current state-of-the-art. Towards these two aims, we introduce a new dataset, “HiPen”, which tabulates Δ A g a s M M → 3 o b (the free energy associated with switching from an M M to an S C C − D F T B molecular description using the 3ob parameter set in gas phase), calculated for 22 drug-like small molecules. We compare the calculation of this value using free energy perturbation, Bennett’s acceptance ratio, Jarzynski’s equation, and Crooks’ equation. We also predict the reliability of each calculated Δ A g a s M M → 3 o b by evaluating several convergence criteria including sample size hysteresis, overlap statistics, and bias metric ( Π ). Within the total dataset, three distinct categories of molecules emerge: the “good” molecules, for which we can obtain converged Δ A g a s M M → 3 o b using Jarzynski’s equation; “bad” molecules which require Crooks’ equation to obtain a converged Δ A g a s M M → 3 o b ; and “ugly” molecules for which we cannot obtain reliably converged Δ A g a s M M → 3 o b with either Jarzynski’s or Crooks’ equations. We discuss, in depth, results from several example molecules in each of these categories and describe how dihedral discrepancies between levels of theory cause convergence failures even for these gas phase free energy simulations.

Optimizing the Calculation of Free Energy Differences in Nonequilibrium Work SQM/MM Switching Simulations

“… 28 − 31 We showed in previous work that the use of nonequilibrium work simulations (NEW) 32 leads to converged values for the correction free energies Δ A low→high where other approaches fail. 33 − 35 Since NEW calculations connecting two levels of theory can easily become computationally impractical, it is imperative to keep the cost of such calculations manageable to make real world applications feasible. A related challenge is to find reliable indicators whether a particular NEW switching protocol has resulted in converged results.. 27 In the context of classical mechanical interactions, a large body of work 36 − 39 is concerned with optimizing calculations using Jarzinsky’s and Crooks’ 40 relations.…”

“…In a recent work, 35 we introduced the “HiPen” test set, a collection of 22 molecules for which we analyzed the convergence of Δ A low→high . The compounds were selected from the Maybridge Hitfinder library of drug-like compounds 45 based on several criteria.…”

Development of a Robust Indirect Approach for MM → QM Free Energy Calculations That Combines Force-Matched Reference Potential and Bennett’s Acceptance Ratio Methods

“…The reference potential approach was pioneered by Gao 14,15 and Warshel, 16 and advanced recently by Woodcock, Boresch, König, Brooks and others. 17-26…”

“…They developed a dataset for validating QM/MM free energy corrections consisting of 22 drug-like small molecules, and gas-phase QM corrections are obtained for a self-consistent charge density functional tight-binding (SCC-DFTB) semiempirical Hamiltonian. 17 The authors obtain accurate free energy estimates and compare several analysis methods (Zwanzig’s relation, BAR, Jarzynski’s equation). Our present work differs in several ways: we use the PBE0/6-31G* ab initio Hamiltonian and obtain accurate estimates in both condensed- and gas-phases (for solvation free energies), and bound- and unbound-states (for ligand-binding free energies).…”

“…The reference potential approach was pioneered by Gao 14,15 and Warshel, 16 and advanced recently by Woodcock, Boresch, König, Brooks and others. [17][18][19][20][21][22][23][24][25][26] The high cost of quantum mechanical (QM) calculations has led to the exploration of various methods to reduce the number of energy (and force) evaluations necessary to converge the free energy estimate. These include the use of frozen density functional approximations, 27,28 orthogonal space random walk strategies, 29 integrated Hamiltonian sampling, 30 paradynamics, 31,32 and trajectory reweighting.…”