Unbiased free energy estimates in fast nonequilibrium transformations using Gaussian mixtures

SAMPL9 blind predictions using nonequilibrium alchemical approaches

We present our blind predictions for the Statistical Assessment of the Modeling of Proteins and Ligands (SAMPL), ninth challenge, focusing on the binding of WP6 (carboxy-pillar[6]arene) with ammonium/diammonium cationic guests. Host-guest binding free energies have been calculated using the recently developed virtual double system single box approach, based on the enhanced sampling of the bound and unbound end-states followed by fast switching nonequilibrium alchemical simulations [M. Macchiagodena et al., J. Chem. Theory Comput. 16, 7160 (2020)]. As far as Pearson and Kendall coefficients are concerned, performances were acceptable and, in general, better than those we submitted for calixarenes, cucurbituril-like open cavitand, and beta-cyclodextrines in previous SAMPL host-guest challenges, confirming the reliability of nonequilibrium approaches for absolute binding free energy calculations. In comparison with previous submissions, we found a rather large mean signed error that we attribute to the way the finite charge correction was addressed through the assumption of a neutralizing background plasma.

Seeding the multi-dimensional nonequilibrium pulling for Hamiltonian variation: indirect nonequilibrium free energy simulations at QM levels

The combination of free energy simulations in the alchemical and configurational spaces provides a feasible route to access the thermodynamic profiles under a computationally demanding target Hamiltonian. Normally, due to the significant differences between the computational cost of ab initio quantum mechanics (QM) calculations and those of semi-empirical quantum mechanics (SQM) and molecular mechanics (MM), this indirect method could be used to obtain the QM thermodynamics by combining the SQM or MM results and the SQM-to-QM or MM-to-QM corrections. In our previous work, a multi-dimensional nonequilibrium pulling framework for Hamiltonian variations was introduced based on bidirectional pulling and bidirectional reweighting. The method performs nonequilibrium free energy simulations in the configurational space to obtain the thermodynamic profile along the conformational change pathway under a selected computationally efficient Hamiltonian, and uses the nonequilibrium alchemical method to correct or perturb the thermodynamic profile to that under the target Hamiltonian. The BAR-based method is designed to achieve the best generality and transferability and thus leads to modest (∼20 fold) speedup. In this work, we explore the possibility of further accelerating the nonequilibrium free energy simulation by employing unidirectional pulling and using the selection criterion to obtain the initial configurations used to initiate nonequilibrium trajectories following the idea of adaptive steered molecular dynamics (ASMD). A single initial condition is used to seed the whole multi-dimensional nonequilibrium free energy simulation and the sampling is performed fully in the nonequilibrium ensemble. Introducing very short ps-length equilibrium sampling to grab more initial seeds could also be helpful. The ASMD scheme estimates the free energy difference with the unidirectional exponential average (EXP), but it does not follow exactly the requirements of the EXP estimator. Another deficiency of the seeding simulation is the inherently sequential or serial pulling due to the inter-segment dependency, which triggers some problems in the parallelizability of the simulation. Numerical tests are performed to grasp some insights and guidelines for using this selection-criterion-based ASMD scheme. The presented selection-criterion-based multi-dimensional ASMD scheme follows the same perturbation network of the BAR-based method, and thus could be used in various Hamiltonian-variation cases.

On the NS-DSSB unidirectional estimates in the SAMPL6 SAMPLing challenge

In the context of the recent SAMPL6 SAMPLing challenge (Rizzi et al. 2020 in J Comput Aided Mol Des 34:601–633) aimed at assessing convergence properties and reproducibility of molecular dynamics binding free energy methodologies, we propose a simple explanation of the severe errors observed in the nonequilibrium switch double-system-single-box (NS-DSSB) approach when using unidirectional estimates. At the same time, we suggest a straightforward and minimal modification of the NS-DSSB protocol for obtaining reliable unidirectional estimates for the process where the ligand is decoupled in the bound state and recoupled in the bulk.

On the calculation of free energies over Hamiltonian and order parameters via perturbation and thermodynamic integration

In this work, complementary formulas are presented to compute free-energy differences via perturbation (FEP) methods and thermodynamic integration (TI). These formulas are derived by selecting only the most statistically significant data from the information extractable from the simulated points involved. On the one hand, commonly used FEP techniques based on overlap sampling leverage the full information contained in the overlapping macrostate probability distributions. On the other hand, conventional TI methods only use information on the first moments of those distributions, as embodied by the first derivatives of the free energy. Since the accuracy of simulation data degrades considerably for high-order moments (for FEP) or free-energy derivatives (for TI), it is proposed to consider, consistently for both methods, data up to second-order moments/derivatives. This provides a compromise between the limiting strategies embodied by common FEP and TI and leads to simple, optimized expressions to evaluate free-energy differences. The proposed formulas are validated with an analytically solvable harmonic Hamiltonian (for assessing systematic errors), an atomistic system (for computing the potential of mean force with coordinate-dependent order parameters), and a binary-component coarse-grained model (for tracing a solid-liquid phase diagram in an ensemble sampled through alchemical transformations). It is shown that the proposed FEP and TI formulas are straightforward to implement, perform similarly well, and allow robust estimation of free-energy differences even when the spacing of successive points does not guarantee them to have proper overlapping in phase space.

SAMPL7 blind predictions using nonequilibrium alchemical approaches

In the context of the SAMPL7 challenge, we computed, employing a non-equilibrium (NE) alchemical technique, the standard binding free energy of two series of host-guest systems, involving as a host the Isaac's TrimerTrip, a Cucurbituril-like open cavitand, and the Gilson's Cyclodextrin derivatives. The adopted NE alchemy combines enhanced sampling molecular dynamics simulations with driven fast out-of-equilibrium alchemical trajectories to recover the free energy via the Jarzynski and Crooks NE theorems. The GAFF2 non-polarizable force field was used for the parametrization. Performances were acceptable and similar in accuracy to those we submitted for Gibb's Deep Cavity Cavitands in the previous SAMPL6 host-guest challenge, confirming the reliability of the computational approach and exposing, in some cases, some important deficiencies of the GAFF2 non-polarizable force field.

Methodological uncertainties in drug-receptor binding free energy predictions based on classical molecular dynamics

Computational approaches are becoming an essential tool in modern drug design and discovery, with fast compound triaging using a combination of machine learning and docking techniques followed by molecular dynamics binding free energies assessment using alchemical techniques. The traditional MD-based alchemical free energy perturbation (FEP) method faces severe sampling issues that may limits its reliability in automated workflows. Here we review the major sources of uncertainty in FEP protocols for drug discovery, showing how the sampling problem can be effectively tackled by switching to nonequilibrium alchemical techniques.

Virtual Double-System Single-Box: A Nonequilibrium Alchemical Technique for Absolute Binding Free Energy Calculations: Application to Ligands of the SARS-CoV-2 Main Protease

In the context of drug-receptor binding affinity calculations using molecular dynamics techniques, we implemented a combination of Hamiltonian replica exchange (HREM) and a novel nonequilibrium alchemical methodology, called virtual double-system single-box, with increased accuracy, precision, and efficiency with respect to the standard nonequilibrium approaches. The method has been applied for the determination of absolute binding free energies of 16 newly designed noncovalent ligands of the main protease (3CL^pro) of SARS-CoV-2. The core structures of 3CL^pro ligands were previously identified using a multimodal structure-based ligand design in combination with docking techniques. The calculated binding free energies for four additional ligands with known activity (either for SARS-CoV or SARS-CoV-2 main protease) are also reported. The nature of binding in the 3CL^pro active site and the involved residues besides the CYS-HYS catalytic dyad have been thoroughly characterized by enhanced sampling simulations of the bound state. We have identified several noncongeneric compounds with predicted low micromolar activity for 3CL^pro inhibition, which may constitute possible lead compounds for the development of antiviral agents in Covid-19 treatment.

Best Practices for Alchemical Free Energy Calculations [Article v1.0]

Alchemical free energy calculations are a useful tool for predicting free energy differences associated with the transfer of molecules from one environment to another. The hallmark of these methods is the use of "bridging" potential energy functions representing alchemical intermediate states that cannot exist as real chemical species. The data collected from these bridging alchemical thermodynamic states allows the efficient computation of transfer free energies (or differences in transfer free energies) with orders of magnitude less simulation time than simulating the transfer process directly. While these methods are highly flexible, care must be taken in avoiding common pitfalls to ensure that computed free energy differences can be robust and reproducible for the chosen force field, and that appropriate corrections are included to permit direct comparison with experimental data. In this paper, we review current best practices for several popular application domains of alchemical free energy calculations performed with equilibrium simulations, in particular relative and absolute small molecule binding free energy calculations to biomolecular targets.

Solvation free energies via alchemical simulations: let's get honest about sampling, once more

Free energy perturbation (FEP) approaches with stratification have seen widespread and increasing use in computational studies of biologically relevant molecules. However, when the molecular systems are characterized by a complex conformational free energy landscape, the assessment of convergence remains a concern for many practitioners. The sampling problem in FEP has been authoritatively addressed in a recent perspective paper [D. Mobley, J. Comput.-Aided Mol. Des., 2012, 26, 93], incisively entitled "Let's get honest about sampling". Here, I return to the issue of sampling in the determination of the octanol-water partition coefficient for a synthetic precursor of kinase inhibitors that has been included in the recent extension of the SAMPL6 blind challenge of log P coefficients. I will show that even for this simple compound, whose conformational space is essentially dictated by two sp₃ rotable bonds connecting rigid planar units, canonical sampling using standard techniques can be surprisingly hard to achieve. I will also show how the conformational sampling problem can be effectively bypassed using unidirectional and bidirectional nonequilibrium work methods, reliably recovering the solvation energy with minimal methodological uncertainty.

Extensive Assessment of Various Computational Methods for Aspartate's pKa Shift

A series of computational methods for pK_a shift prediction are extensively tested on a set of benchmark protein systems, aiming at identifying pitfalls and evaluating their performance on high variants. Including 19 ASP residues in 10 protein systems, the benchmark set consists of both residues with highly shifted pK_a values as well as those varying little from the reference value, with an experimental RMS free energy differences of 2.49 kcal/mol with respect to blocked amino acid, namely the RMS pK_a shift being 1.82 pK_a units. The constant pH molecular dynamics (MD), alchemical methods, PROPKA3.1, and multiconformation continuum electrostatics give RMSDs of 1.52, 2.58, 1.37, and 3.52 pK_a units, respectively, on the benchmark set. The empirical scoring method is the most accurate one with extremely low computational cost, and the pH-dependent model is also able to provide accurate results, while the accuracy of MD sampling incorporating alchemical free energy simulation is prohibited by convergence achievement and the performance of conformational search incorporating multiconformation continuum electrostatics is bad. Former research works did not define statistical uncertainty with care and yielded the questionable conclusion that alchemical methods perform well in most benchmarks. In this work the traditional alchemical methods are thoroughly tested for high variants. We also performed the first application of nonequilibrium alchemical methods to the pK_a cases.

Hybrid MPI/OpenMP Implementation of the ORAC Molecular Dynamics Program for Generalized Ensemble and Fast Switching Alchemical Simulations

We present a new release (6.0β) of the ORAC program [Marsili et al. J. Comput. Chem. 2010, 31, 1106-1116] with a hybrid OpenMP/MPI (open multiprocessing message passing interface) multilevel parallelism tailored for generalized ensemble (GE) and fast switching double annihilation (FS-DAM) nonequilibrium technology aimed at evaluating the binding free energy in drug-receptor system on high performance computing platforms. The production of the GE or FS-DAM trajectories is handled using a weak scaling parallel approach on the MPI level only, while a strong scaling force decomposition scheme is implemented for intranode computations with shared memory access at the OpenMP level. The efficiency, simplicity, and inherent parallel nature of the ORAC implementation of the FS-DAM algorithm, project the code as a possible effective tool for a second generation high throughput virtual screening in drug discovery and design. The code, along with documentation, testing, and ancillary tools, is distributed under the provisions of the General Public License and can be freely downloaded at www.chim.unifi.it/orac .

A comment on the reweighting method for accelerated molecular dynamics simulations

Accelerated molecular dynamics (aMD) is a popular method for biomolecular simulations. The estimator to recover the true free energy profile, termed "reweighting", constitutes a critical part of aMD. Recently the second order cumulant expansion has been recommended as an improved reweighting method. Here we examine the validity of this reweighting method and provide an insight into the need for selecting appropriate boost potentials.

II. Dissociation free energies in drug–receptor systems via nonequilibrium alchemical simulations: application to the FK506-related immunophilin ligands

The fast switch double annihilation method (FS-DAM) provides an effective mean to the compute the binding free energies in drug-receptor systems. Here we present an application to the FK506-related ligands of the FKBP12 protein.

I. Dissociation free energies of drug–receptor systems via non-equilibrium alchemical simulations: a theoretical framework

In this contribution I critically discuss the alchemical approach for evaluating binding free energies in drug–receptor systems, placing this methodology into the broader context of non-equilibrium thermodynamics.