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1. What to Make of Zero: Resolving the Statistical Noise from Conformational Reorganization in Alchemical Binding Free Energy Estimates with Metadynamics Sampling

   Khuttan, Sheenam; Gallicchio, Emilio (October 2023, arXivorg)

   We introduce the self-Relative Binding Free Energy (self-RBFE) approach to evaluate the intrinsic statistical variance of dual-topology alchemical binding free energy estimators. The self-RBFE is the relative binding free energy between a ligand and a copy of the same ligand, and its true value is zero. Nevertheless, because the two copies of the ligand move independently, the self-RBFE value produced by a finite-length simulation fluctuates and can be used to measure the variance of the model. The results of this validation provide evidence that a significant fraction of the errors observed in benchmark studies reflect the statistical fluctuations of unconverged estimates rather than the models' accuracy. Furthermore, we find that ligand reorganization is a significant contributing factor to the statistical variance of binding free energy estimates and that metadynamics-accelerated conformational sampling of torsional degrees of freedom of the ligand can drastically reduce the time to convergence. 

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2. GPU-Enhanced DFTB Metadynamics for Efficiently Predicting Free Energies of Biochemical Systems

   https://doi.org/10.3390/molecules28031277  

   Kumar, Anshuman; Arantes, Pablo R.; Saha, Aakash; Palermo, Giulia; Wong, Bryan M. (February 2023, Molecules)

   Metadynamics calculations of large chemical systems with ab initio methods are computationally prohibitive due to the extensive sampling required to simulate the large degrees of freedom in these systems. To address this computational bottleneck, we utilized a GPU-enhanced density functional tight binding (DFTB) approach on a massively parallelized cloud computing platform to efficiently calculate the thermodynamics and metadynamics of biochemical systems. To first validate our approach, we calculated the free-energy surfaces of alanine dipeptide and showed that our GPU-enhanced DFTB calculations qualitatively agree with computationally-intensive hybrid DFT benchmarks, whereas classical force fields give significant errors. Most importantly, we show that our GPU-accelerated DFTB calculations are significantly faster than previous approaches by up to two orders of magnitude. To further extend our GPU-enhanced DFTB approach, we also carried out a 10 ns metadynamics simulation of remdesivir, which is prohibitively out of reach for routine DFT-based metadynamics calculations. We find that the free-energy surfaces of remdesivir obtained from DFTB and classical force fields differ significantly, where the latter overestimates the internal energy contribution of high free-energy states. Taken together, our benchmark tests, analyses, and extensions to large biochemical systems highlight the use of GPU-enhanced DFTB simulations for efficiently predicting the free-energy surfaces/thermodynamics of large biochemical systems. 

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3. Taming multiple binding poses in alchemical binding free energy prediction: the β-cyclodextrin host–guest SAMPL9 blinded challenge

   https://doi.org/10.1039/D3CP02125D  

   Khuttan, Sheenam; Azimi, Solmaz; Wu, Joe Z.; Dick, Sebastian; Wu, Chuanjie; Xu, Huafeng; Gallicchio, Emilio (September 2023, Physical Chemistry Chemical Physics)

   We apply the Alchemical Transfer Method (ATM) and a bespoke fixed partial charge force field to the SAMPL9 bCD host-guest binding free energy prediction challenge that comprises a combination of complexes formed between five phenothiazine guests and two cyclodextrin hosts. Multiple chemical forms, competing binding poses, and computational modeling challenges pose significant obstacles to obtaining reliable computational predictions for these systems. The phenothiazine guests exist in solution as racemic mixtures of enantiomers related by nitrogen inversions that bind the hosts in various binding poses, each requiring an individual free energy analysis. Due to the large size of the guests and the conformational reorganization of the hosts, which prevent a direct absolute binding free energy route, binding free energies are obtained by a series of absolute and relative binding alchemical steps for each chemical species in each binding pose. Metadynamics-accelerated conformational sampling was found to be necessary to address the poor convergence of some numerical estimates affected by conformational trapping. Despite these challenges, our blinded predictions quantitatively reproduced the experimental affinities for the beta-cyclodextrin host and, to a lesser extent, those with a methylated derivative. The work illustrates the challenges of obtaining reliable free energy data in in-silico drug design for even seemingly simple systems and introduces some of the technologies available to tackle them. 

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4. Molecular Latent Space Simulators

   https://doi.org/10.1039/D0SC03635H  

   Sidky, Hythem; Chen, Wei; Ferguson, Andrew L (January 2020, Chemical Science)

   Small integration time steps limit molecular dynamics (MD) simulations to millisecond time scales. Markov state models (MSMs) and equation-free approaches learn low-dimensional kinetic models from MD simulation data by performing configurational or dynamical coarse-graining of the state space. The learned kinetic models enable the efficient generation of dynamical trajectories over vastly longer time scales than are accessible by MD, but the discretization of configurational space and/or absence of a means to reconstruct molecular configurations precludes the generation of continuous all-atom molecular trajectories. We propose latent space simulators (LSS) to learn kinetic models for continuous all-atom simulation trajectories by training three deep learning networks to (i) learn the slow collective variables of the molecular system, (ii) propagate the system dynamics within this slow latent space, and (iii) generatively reconstruct molecular configurations. We demonstrate the approach in an application to Trp-cage miniprotein to produce novel ultra-long synthetic folding trajectories that accurately reproduce all-atom molecular structure, thermodynamics, and kinetics at six orders of magnitude lower cost than MD. The dramatically lower cost of trajectory generation enables greatly improved sampling and greatly reduced statistical uncertainties in estimated thermodynamic averages and kinetic rates. 

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5. Implementing and Assessing an Alchemical Method for Calculating Protein–Protein Binding Free Energy

   https://doi.org/doi: 10.1021/acs.jctc.0c01045  

   Patel, Dharmeshkumar; Patel, Jagdish S.; Ytreberg, F. Marty (March 2021, Journal of chemical theory and computation)

   null (Ed.)

   Protein–protein binding is fundamental to most biological processes. It is important to be able to use computation to accurately estimate the change in protein–protein binding free energy due to mutations in order to answer biological questions that would be experimentally challenging, laborious, or time-consuming. Although nonrigorous free-energy methods are faster, rigorous alchemical molecular dynamics-based methods are considerably more accurate and are becoming more feasible with the advancement of computer hardware and molecular simulation software. Even with sufficient computational resources, there are still major challenges to using alchemical free-energy methods for protein–protein complexes, such as generating hybrid structures and topologies, maintaining a neutral net charge of the system when there is a charge-changing mutation, and setting up the simulation. In the current study, we have used the pmx package to generate hybrid structures and topologies, and a double-system/single-box approach to maintain the net charge of the system. To test the approach, we predicted relative binding affinities for two protein–protein complexes using a nonequilibrium alchemical method based on the Crooks fluctuation theorem and compared the results with experimental values. The method correctly identified stabilizing from destabilizing mutations for a small protein–protein complex, and a larger, more challenging antibody complex. Strong correlations were obtained between predicted and experimental relative binding affinities for both protein–protein systems. 

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