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+ + + + +Journal of Open Source Software +JOSS + +2475-9066 + +Open Journals + + + +6970 +10.21105/joss.06970 + +MoSDeF-dihedral-fit: A lightweight software for fitting +dihedrals within MoSDeF + + + +https://orcid.org/0000-0003-0638-7333 + +Crawford +Brad + + + + + +https://orcid.org/0000-0002-1255-4161 + +Quach +Co D. + + + + + +https://orcid.org/0000-0002-4607-4377 + +Craven +Nicholas C. + + + + + +https://orcid.org/0000-0003-0557-0427 + +Iacovella +Christopher R. + + + + + + +https://orcid.org/0000-0002-8552-9135 + +McCabe +Clare + + + + + + +https://orcid.org/0000-0002-9766-2216 + +Cummings +Peter T. + + + + + + +https://orcid.org/0000-0002-4421-8787 + +Potoff +Jeffrey J. + + + + + +Atomfold, PA, United States of America + + + + +Department of Chemical Engineering and Materials Science, +Wayne State University, Detroit, MI 48202-4050, United States of +America + + + + +Department of Chemical and Biomolecular Engineering, +Vanderbilt University, Nashville, TN 37235-1604, United States of +America + + + + +Multiscale Modeling and Simulation (MuMS) Center, +Vanderbilt University, Nashville, TN 37212, United States of +America + + + + +Interdisciplinary Material Science Program, Vanderbilt +University, Nashville, TN 37235-0106, United States of +America + + + + +School of Engineering and Physical Sciences, Heriot-Watt +University, Edinburgh EH14 4AS, United Kingdom + + + + +6 +12 +2024 + +9 +104 +6970 + +Authors of papers retain copyright and release the +work under a Creative Commons Attribution 4.0 International License (CC +BY 4.0) +2024 +The article authors + +Authors of papers retain copyright and release the work under +a Creative Commons Attribution 4.0 International License (CC BY +4.0) + + + +Python +Molecular simulations +Molecular mechanics +Molecular dynamics +Monte Carlo +Quantum mechanics +dihedral fitting +torsion fitting +force field +MoSDeF +GOMC +MoSDeF-GOMC + + + + + + Summary +

Molecular Mechanics (MM) simulations (e.g., molecular dynamics and + Monte Carlo) provide a third method of scientific discovery, adding to + the traditional theoretical and experimental scientific methods + (Mielke + et al., 2019; + Siegfried, + 2014). Experimental methods measure the data under set + conditions (e.g., temperature and pressure), whereas the traditional + theoretical methods are based on analytical equations, and sometimes + their constants are fitted to experimental data. The MM simulations + are deterministic and stochastic, and their models, commonly known as + “force fields”, can be optimized to match experimental data, similar + to analytical theory-based methods + (Allen + & Tildesley, 2017; + Errington + & Panagiotopoulos, 1999; + Frenkel + & Smit, 2002; + Hemmen + & Gross, 2015; + Jorgensen + et al., 1996; + Martin + & Siepmann, 1998; + Potoff + & Bernard-Brunel, 2009; + Scott + J. Weiner et al., 1984; + S. + J. Weiner et al., 1986). In larger, more complex systems, the + stochastic simulation’s molecules can jump large energy barriers that + deterministic simulations may not be able to overcome in a reasonable + timeframe, even with modern computing capabilities + (Allen + & Tildesley, 2017; + Frenkel + & Smit, 2002). However, deterministic and stochastic + systems that provide adequate sampling for calculating a given + property can provide critical insights into the system’s phase space, + which are not obtainable via traditional theoretical and experimental + methods. Additionally, molecular simulations provide critical insights + from visualizations and by obtaining chemical or material properties + that do not currently exist, are not easily attainable (e.g., too + expensive or dangerous) by traditional theoretical and experimental + methods + (Hirst + et al., 2014; + Hollingsworth + & Dror, 2018), or require hard-to-achieve conditions, such + as very high pressures and temperatures + (Koneru + et al., 2022; + Kumar + et al., 2022; + Louie + et al., 2021; + Swai, + 2020; + Yu + & Pahl, 2023). However, the force field parameters are + ideally determined from Quantum Mechanics (QM) simulations or other + methods, including the vibrational spectrum and machine learning + methods + (Friederich + et al., 2018; + Kania + et al., 2021; + Mayne + et al., 2013; + Schmid + et al., 2011; + Kenno + Vanommeslaeghe et al., 2014; + Vermeyen + et al., 2023). The MM proper dihedrals (i.e., dihedrals) are + challenging to obtain if they do not currently exist for the chosen + force field, inaccurately scale-up in larger molecules, or misbehave + with other moiety combinations, provided some were separately derived + using small molecules + (Kania + et al., 2021; + Mayne + et al., 2013). While the same QM simulations can fit the + dihedrals in most force field types, these dihedrals are not easily + transferable between force fields due to the different parameters and + formulas, including the combining rules and 1-4 scaling factors. + (Chen + et al., 2015; + Huang + & Roux, 2013; + K. + Vanommeslaeghe et al., 2010; + Kenno + Vanommeslaeghe et al., 2014).

+

The MoSDeF-Dihedral-Fit + (Crawford, + Quach, et al., 2023) library allows users to quickly calculate + the MM dihedrals directly from the QM simulations for several force + fields (OPLS, TraPPE, AMBER, Mie, and Exp6) + (Errington + & Panagiotopoulos, 1999; + Hemmen + & Gross, 2015; + Jorgensen + et al., 1996; + Martin + & Siepmann, 1998; + Potoff + & Bernard-Brunel, 2009; + Scott + J. Weiner et al., 1984; + S. + J. Weiner et al., 1986). The user simply has to generate or use + an existing Molecular Simulation Design Framework (MoSDeF) force field + .xml file + (Cummings + et al., 2021; + GMSO, + 2019; + Summers + et al., 2020; + Timalsina, + 2022), provide Gaussian 16 .log or + Gaussian-style QM simulation files that cover the dihedral rotation + (typically between 0-360 degrees), and provide the molecular structure + information in a .mol2 format + (Frisch + et al., 2016). The MoSDeF-Dihedral-Fit + software uses the QM and MM data to produce the dihedral for the + specific force field, fitting the constants for the OPLS dihedral form + (equation 1)

+

+ + UOPLS=k02 + + + +k12*(1+cos(θ))+k22*(1−cos(2*θ)) + + + +k32*(1+cos(3*θ))+k42*(1−cos(4*θ))

+

and then analytically converting them to the Ryckaert-Bellemans + torsion (equation 2)

+

+ + URyckaert-Bellemans=C0 + + + +C1*cos(ψ)+C2*cos(ψ)2 + + + +C3*cos(ψ)3+C4*cos(ψ)4 + + + where: ψ=θ−180o

+

and the periodic dihedral forms (equation + 3).

+

+ + UPeriodic=K0*(1+cos(n0*θ−d0)) + + + +K1*(1+cos(n1*θ−d1))+K2*(1+cos(n2*θ−d2)) + + + +K3*(1+cos(n3*θ−d3))+K4*(1+cos(n4*θ)−d4) + + + where: n0=0;n1=1;n2=2;n3=3;n4=4 + + + d0=90o;d1=180o;d2=0o;d3=180o;d4=0o

+

This analytical conversion from the OPLS dihedral form requires + setting the specified parameters in the Ryckaert-Bellemans torsion and + periodic dihedral forms (see equations + 2 and + 3). The software + outputs the calculated MM dihedral points, enabling users to fit + unsupported dihedral forms, provided the force fields are supported by + the MoSDeF, GPU Optimized Monte Carlo (GOMC), MoSDeF-GOMC + (Crawford + et al., 2022; + Crawford, + Timalsina, et al., 2023; + Crawford, + Quach, et al., 2023; + Nejahi + et al., 2019, + 2021), + and vmd-python + (Betz, + 2016) software (a derivative of the VMD software + (Humphrey + et al., 1996; + Stone + et al., 2001)).

+ + + Statement of need +

While many of these MM force field parameters can be transferred + between force fields, such as bonds, angles, and improper dihedrals + (often referred to as “impropers”), the proper dihedrals (dihedrals) + can not be easily transferred due to the different combining rules + (arithmetic and geometric) and 1-4 scaling factors (i.e., between the + 1st and 4th bonded atoms) that were used in the development of the + original parameters + (Berthelot, + 1898; + Good + & Hope, 1970; + Lorentz, + 1881). The accuracy of these dihedral parameters is critical in + obtaining the correct molecular conformations and configurations, + which are required for understanding and analyzing the system’s + microstructure and physical properties (e.g., free energies, + viscosities, adsorption loading, diffusion constants, and many + more).

+

Some integrated dihedral fitting software currently exists for + AMBER + (Horton + et al., 2022) or CHARMM-style force fields + (Mayne + et al., 2013), and other software will fit the dihedral + constants to the final MM and QM energies, which need to be calculated + by other means + (Guvench + & MacKerell, 1998). However, there is a need for a simple, + generalized software package that supports multiple potential + functions, imports QM and MM files, automatically reads and organizes + the QM data, calculates the MM energies, auto-corrects the dihedral + fit to account for multiple instances of the dihedral, and + automatically removes the unusable cosine power series combinations + due to this symmetry. The MoSDeF-dihedral-fit + software accomplishes all this and automatically accounts for any of + the common combining rules and the 1-4 scaling factors specified via + the MoSDeF .xml (i.e., force field) files + (Cummings + et al., 2021; + GMSO, + 2019; + Summers + et al., 2020; + Timalsina, + 2022). By allowing the user to set any other dihedral in the + molecule to zero, this software avoids forcing one dihedral fit to + correct the inaccurate forces of another dihedral, resulting in a + problematic or bad cosine series fit; thus, providing a more flexible + and accurate fit by combining multiple dihedral conformational + energies in a single dihedral, a strategy used in the original and + modern OPLS force fields + (Jorgensen + et al., 1996; + Lu + et al., 2021). For example, a carboxylic acid with an alkyl + tail has two dihedrals in the same rotation cycle; the C-C-C-O: (O: = + oxygen without hydrogen) dihedral is set to zero while the C-C-O-H + dihedral is fit + (Jorgensen + et al., 1996; + Kamath + et al., 2004; + Lu + et al., 2021). The MoSDeF-dihedral-fit + (Crawford, + Quach, et al., 2023) API fills the missing gap by providing a + generalized and easy solution to fitting dihedrals in their commonly + used forms and outputting the MM dihedral data points so users can fit + other custom dihedral forms.

+ + + Acknowledgements +

This research was partially supported by the National Science + Foundation (grants OAC-1835713, OAC-1835874, and CBET 2052438). + Atomfold LLC also donated research and development time and + computational resources for this research and software. Wayne State + University Grid provided some of the computational resources used in + this work.

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