Towards fast and accurate binding affinity. prediction with pmemdgti: an efficient. implementation of GPU-accelerated. Thermodynamic Integration

Transcription

1 Towards fast and accurate binding affinity prediction with pmemdgti: an efficient implementation of GPU-accelerated Thermodynamic Integration Tai-Sung Lee,, Yuan Hu, Brad Sherborne, Zhuyan Guo, and Darrin M. York, Laboratory for Biomolecular Simulation Research, Center for Integrative Proteomics Research and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854, USA Department of Chemistry, Modeling and Informatics, Merck Research Laboratories, 2000 Galloping Hill Road, Kenilworth, NJ

2 Supporting Information 1 Ligand structures and experimental binding affinities Figure S1: Structures, experimental K i and converted binding affinities, G, of the Factor Xa inhibitors. a L51bt is the tautomer structure of L51b. b Experimentally measured K i (unit: nm) are taken from Ref. 1. c Binding affinities (unit: kcal/mol) are calculated by G = RT ln K i with T=300 K. 2

3 2 Simulation Setup Initial structures and simulation parameters The initial structures of the FXa protein receptor (PDB code: 2RA0) and ten FXa inhibitors were directly taken from previously prepared protonated structures, as described in details elsewhere. 2 Disulfide bonds were automatically built by including additional disulfide bond list, and ligands and complexes were neutralized by adding ions (Cl or Na + if necessary; one Na + and two Cl ions in the simulations reported here) and then solvated in a water box extending at least 11 Å in each direction from the solute. All the topology files and structures were visually inspected. Atom types of the inhibitors were assigned from General AMBER Force Field (GAFF), 3 Atomic partial charges were prepared using the AM1-BCC approach. The AMBER ff12sb force field 4 was used for the rest of the system. There are different methodological approaches to the implementation of free energy methods with respect to how topologies are handled. Traditionally, both single and dual topology approaches have been utilized. 5 In the present work, a hybrid topology scheme 6 was utilized: both ends of the perturbed regions have separate topology descriptions within one single topology file. In the other words, the non-perturbed region is treated by the single-topology approach and the perturbed region is treated by the dual-topology approach. This commonly used hybrid scheme 6 is employed in AMBER, 4 GROMACS, 7 and CHARMM 8 packages. The input format of the TI regions are kept exactly the same as the CPU version of AMBER pmemd module. Simulation protocols As suggested, 4 a time step of 1 fs was used for the integration of the equations of motion, since SHAKE is not employed in those mutation simulations involving deleting/adding hydrogens. The translational center-of-mass motion was removed every 1000 steps. Long-range electrostatic interactions were treated by the particle-mesh Ewald method (PME) 9 with a direct-space sum cutoff of 9 Å, consistent with the minimal requirement of 8 Å 4 and our previously published work. 2 The Ewald error tolerance is set to The Ewald coefficient is set to The FFT grid sizes 3

4 are determined automatically by the program and are 80, 84, and 72 for complex simulations, and 36, 40, and 40 for ligand simulations. Setup/pre-equilibration for TI calculations FESetup (release 1.2) 10 was used to automatically prepare the topology files for TI calculations by setting free energy type as pmemd/softcore. The system for each mutation was first minimized and relaxed at 300 K in the NVT ensemble, then the initial conformations for each λ window were sequentially generated with 1.4 ns pre-equilibration for each λ-value from 0.0 to 1.0 with λ = 0.1, where the pre-equilibrated conformation of the current λ window was used as the starting conformation of the next λ window for production. All TI calculations, both with and without softcore potentials, were done as one-step perturbation without decoupling electrostatic and van der Wall interactions. Production simulations 5-ns TI simulations were performed for each λ window for every mutation. Only the last 4-ns data were collected for data analysis at a sampling frequency of 10 fs. Simulations were performed for both solvated ligands and complexes to calculate the relative binding affinities. Each simulation was repeated 10 times to calculate the ensemble-averaged values. 4

5 3 Binding free energy results for all runs Figure S2: The calculated free energies of all runs along, with the average values and the associated standard deviations, from both pmemdgti (GPU, in light gray background) and pmemd (CPU, in yellow background). a bt* is done without softcore potential. The entries of exp= are the corresponding experimental G values, 1 also listed in Figure S1. The unpaired t-test p-values at 95 % of confidence level, with the null hypothesis GPU and CPU results are from the same distribution, are also listed. As the p-values are in the range of 0.11 to 0.92, we conclude that there is no statistically significant difference between the GPU and CPU results. 5

6 4 Extra binding free energy results Figure S3: The free energy results of additional simulations: a bt and a bt* are the same as shown in Figure S2, both with 5-ns simulations and 1-fs steps; the a bt* (20ns) is a set of ten 20-ns long simulations (1-ns equilibration followed by 20 ns data collection); a bt (2fs-step) and a bt* (2fs-step) are the same simulations as a bt and a bt*, except 2-fs time steps are utilized. p-values has the same meaning as in Figure S2. As described in the main text, the a bt* (20ns) results, both the averaged G and the standard deviations, are essentially identical to a bt*, where 5-ns simulations were performed. When softcore potentials are not used, 1-fs (a bt*) and 2-fs (a bt* 2fs-step) steps lead to the same results; while when softcore potential are employed, the results of 2-fs step (a bt 2fs-step) might be problematic, showing much larger standard deviations in the ligand calculations. 6

7 5 TI add-on modules As described in the main text, TI modules are implemented as derived classes. The MD modules were re-packaged as base classes and no additional modification was made to the original MD GPU modules, i.e., when running TI calculations, the MD GPU modules runs as if it is a plain MD simulation. All original MD CUDA kernels are kept unmodified. There are two types of TI interactions: the long-range electrostatic interaction PME part, and other local interaction parts: PME execution flow: In order to perform TI calculations, the contribution from two end-point states needs to be evaluated. In our implementation, the original modules are kept untouched when possible. Figure S4 demonstrates the work-flow of the PME modules: the original PME engine is kept and it in fact does not know if it is in the TI mode or MD mode. The TI modification is the creation of the input charge grids of both end points of perpetuated regions Figure S4: The work-flow of the the particle mesh Ewald (PME 11 ) modules: pmemd (left) vs. pmemdgti (right). The original PME engine is kept untouched and it does not know if it is in the TI mode or MD mode. The TI modification mainly is the creation of the input charge grids and the calculations of resulting PME contributions. and feeding the info into the original PME modules, as well as collecting the resulting PME contributions. 7

8 Other local interactions: CUDA multiple stream execution The TI add-ons to handle other local interactions besides long-range PME interactions are implemented in the way totally independent to the non-ti parts (Figure S5). Similar to the long-range PME part, the original MD parts are kept untouched and do not have any knowledge of the TI add-ons, except are now packaged into base classes (colored green in Figure S5). Other the local bonded and non-bonding TI add-on modules in pmemdgti are packaged into derived classes and the newly added TI CUDA kernels are responsible of handling TI-only calculations and run independently (colored orange in Figure S5). The mulit-stream concept of CUDA is utilized and the TI modules and the original non-ti modules run on separate CUDA streams. A snapshot from a performance monitoring program (Nsight) is shown in Figure S6. Figure S5: The addition of TI non-bound modules (in orange) to the original pmemd non-bound modules (in light green). The non-bonding TI modules in pmemdgti are totally independent to the non-ti parts. The mulit-stream concept of CUDA is utilized and the TI modules and the original non-ti modules run on separate CUDA streams. 8

9 Figure S6: An example screen snapshot from Nsight output showing the multiple stream execution of pmemdgti program. Steam 1 in the figure is the default stream mentioned in the text and in Figure S5, Steam 2 is the MD stream, and Stream 3 is the TI stream. 9

10 6 Examples of dh dλ λ results from CPU and GPU dh Figure S7: The 5-ns time series plots (left panels) and the distribution plots (right panels) of dλ λ for the a bt mutation (Figure S1) in complex at λ = 0 (upper) λ = 1 (lower), from pmemdgti (GPU, in black) and pmemd.mpi (CPU, in red), with data sampled at the frequency of 10 fs. The results shown are from one simulation and demonstrate that pmemdgti and pmemd.mpi essentially give the identical dynamical behaviors of TI simulations. 10

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