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Title: Efficient force field and energy emulation through partition of permutationally equivalent atoms
Gaussian process (GP) emulator has been used as a surrogate model for predicting force field and molecular potential, to overcome the computational bottleneck of ab initio molecular dynamics simulation. Integrating both atomic force and energy in predictions was found to be more accurate than using energy alone, yet it requires O(( NM) 3 ) computational operations for computing the likelihood function and making predictions, where N is the number of atoms and M is the number of simulated configurations in the training sample due to the inversion of a large covariance matrix. The high computational cost limits its applications to the simulation of small molecules. The computational challenge of using both gradient information and function values in GPs was recently noticed in machine learning communities, whereas conventional approximation methods may not work well. Here, we introduce a new approach, the atomized force field model, that integrates both force and energy in the emulator with many fewer computational operations. The drastic reduction in computation is achieved by utilizing the naturally sparse covariance structure that satisfies the constraints of the energy conservation and permutation symmetry of atoms. The efficient machine learning algorithm extends the limits of its applications on larger molecules under the same computational budget, with nearly no loss of predictive accuracy. Furthermore, our approach contains an uncertainty assessment of predictions of atomic forces and energies, useful for developing a sequential design over the chemical input space.  more » « less
Award ID(s):
1940118 2053423
NSF-PAR ID:
10337855
Author(s) / Creator(s):
; ; ; ;
Date Published:
Journal Name:
The Journal of Chemical Physics
Volume:
156
Issue:
18
ISSN:
0021-9606
Page Range / eLocation ID:
184304
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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  1. ; ; ; ( , Zenodo)

    This data set for the manuscript entitled "Design of Peptides that Fold and Self-Assemble on Graphite" includes all files needed to run and analyze the simulations described in the this manuscript in the molecular dynamics software NAMD, as well as the output of the simulations. The files are organized into directories corresponding to the figures of the main text and supporting information. They include molecular model structure files (NAMD psf or Amber prmtop format), force field parameter files (in CHARMM format), initial atomic coordinates (pdb format), NAMD configuration files, Colvars configuration files, NAMD log files, and NAMD output including restart files (in binary NAMD format) and trajectories in dcd format (downsampled to 10 ns per frame). Analysis is controlled by shell scripts (Bash-compatible) that call VMD Tcl scripts or python scripts. These scripts and their output are also included.

    Version: 2.0

    Changes versus version 1.0 are the addition of the free energy of folding, adsorption, and pairing calculations (Sim_Figure-7) and shifting of the figure numbers to accommodate this addition.


    Conventions Used in These Files
    ===============================

    Structure Files
    ----------------
    - graph_*.psf or sol_*.psf (original NAMD (XPLOR?) format psf file including atom details (type, charge, mass), as well as definitions of bonds, angles, dihedrals, and impropers for each dipeptide.)

    - graph_*.pdb or sol_*.pdb (initial coordinates before equilibration)
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    - amber_*.prmtop (combined topology and parameter files for Amber force field simulations)
    - repart_amber_*.prmtop (same as the above prmtop files, but the masses of non-water hydrogen atoms have been repartitioned by ParmEd)

    Force Field Parameters
    ----------------------
    CHARMM format parameter files:
    - par_all36m_prot.prm (CHARMM36m FF for proteins)
    - par_all36_cgenff_no_nbfix.prm (CGenFF v4.4 for graphene) The NBFIX parameters are commented out since they are only needed for aromatic halogens and we use only the CG2R61 type for graphene.
    - toppar_water_ions_prot_cgenff.str (CHARMM water and ions with NBFIX parameters needed for protein and CGenFF included and others commented out)

    Template NAMD Configuration Files
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    These contain the most commonly used simulation parameters. They are called by the other NAMD configuration files (which are in the namd/ subdirectory):
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    - template_eq.namd (NPT equilibration with lower graphene fixed)
    - template_abf.namd (for adaptive biasing force)

    Minimization
    -------------
    - namd/min_*.0.namd

    Equilibration
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    - namd/eq_*.0.namd

    Adaptive biasing force calculations
    -----------------------------------
    - namd/eabfZRest7_graph_chp1404.0.namd
    - namd/eabfZRest7_graph_chp1404.1.namd (continuation of eabfZRest7_graph_chp1404.0.namd)

    Log Files
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    For each NAMD configuration file given in the last two sections, there is a log file with the same prefix, which gives the text output of NAMD. For instance, the output of namd/eabfZRest7_graph_chp1404.0.namd is eabfZRest7_graph_chp1404.0.log.

    Simulation Output
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    The simulation output files (which match the names of the NAMD configuration files) are in the output/ directory. Files with the extensions .coor, .vel, and .xsc are coordinates in NAMD binary format, velocities in NAMD binary format, and extended system information (including cell size) in text format. Files with the extension .dcd give the trajectory of the atomic coorinates over time (and also include system cell information). Due to storage limitations, large DCD files have been omitted or replaced with new DCD files having the prefix stride50_ including only every 50 frames. The time between frames in these files is 50 * 50000 steps/frame * 4 fs/step = 10 ns. The system cell trajectory is also included for the NPT runs are output/eq_*.xst.

    Scripts
    -------
    Files with the .sh extension can be found throughout. These usually provide the highest level control for submission of simulations and analysis. Look to these as a guide to what is happening. If there are scripts with step1_*.sh and step2_*.sh, they are intended to be run in order, with step1_*.sh first.


    CONTENTS
    ========

    The directory contents are as follows. The directories Sim_Figure-1 and Sim_Figure-8 include README.txt files that describe the files and naming conventions used throughout this data set.

    Sim_Figure-1: Simulations of N-acetylated C-amidated amino acids (Ac-X-NHMe) at the graphite–water interface.

    Sim_Figure-2: Simulations of different peptide designs (including acyclic, disulfide cyclized, and N-to-C cyclized) at the graphite–water interface.

    Sim_Figure-3: MM-GBSA calculations of different peptide sequences for a folded conformation and 5 misfolded/unfolded conformations.

    Sim_Figure-4: Simulation of four peptide molecules with the sequence cyc(GTGSGTG-GPGG-GCGTGTG-SGPG) at the graphite–water interface at 370 K.

    Sim_Figure-5: Simulation of four peptide molecules with the sequence cyc(GTGSGTG-GPGG-GCGTGTG-SGPG) at the graphite–water interface at 295 K.

    Sim_Figure-5_replica: Temperature replica exchange molecular dynamics simulations for the peptide cyc(GTGSGTG-GPGG-GCGTGTG-SGPG) with 20 replicas for temperatures from 295 to 454 K.

    Sim_Figure-6: Simulation of the peptide molecule cyc(GTGSGTG-GPGG-GCGTGTG-SGPG) in free solution (no graphite).

    Sim_Figure-7: Free energy calculations for folding, adsorption, and pairing for the peptide CHP1404 (sequence: cyc(GTGSGTG-GPGG-GCGTGTG-SGPG)). For folding, we calculate the PMF as function of RMSD by replica-exchange umbrella sampling (in the subdirectory Folding_CHP1404_Graphene/). We make the same calculation in solution, which required 3 seperate replica-exchange umbrella sampling calculations (in the subdirectory Folding_CHP1404_Solution/). Both PMF of RMSD calculations for the scrambled peptide are in Folding_scram1404/. For adsorption, calculation of the PMF for the orientational restraints and the calculation of the PMF along z (the distance between the graphene sheet and the center of mass of the peptide) are in Adsorption_CHP1404/ and Adsorption_scram1404/. The actual calculation of the free energy is done by a shell script ("doRestraintEnergyError.sh") in the 1_free_energy/ subsubdirectory. Processing of the PMFs must be done first in the 0_pmf/ subsubdirectory. Finally, files for free energy calculations of pair formation for CHP1404 are found in the Pair/ subdirectory.

    Sim_Figure-8: Simulation of four peptide molecules with the sequence cyc(GTGSGTG-GPGG-GCGTGTG-SGPG) where the peptides are far above the graphene–water interface in the initial configuration.

    Sim_Figure-9: Two replicates of a simulation of nine peptide molecules with the sequence cyc(GTGSGTG-GPGG-GCGTGTG-SGPG) at the graphite–water interface at 370 K.

    Sim_Figure-9_scrambled: Two replicates of a simulation of nine peptide molecules with the control sequence cyc(GGTPTTGGGGGGSGGPSGTGGC) at the graphite–water interface at 370 K.

    Sim_Figure-10: Adaptive biasing for calculation of the free energy of the folded peptide as a function of the angle between its long axis and the zigzag directions of the underlying graphene sheet.

     

    This material is based upon work supported by the US National Science Foundation under grant no. DMR-1945589. A majority of the computing for this project was performed on the Beocat Research Cluster at Kansas State University, which is funded in part by NSF grants CHE-1726332, CNS-1006860, EPS-1006860, and EPS-0919443. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1548562, through allocation BIO200030. 
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