Journal of Biomolecular NMR (2021) 75:143–149 https://doi.org/10.1007/s10858-021-00363-z ARTICLE NMR refnement and peptide folding using the GROMACS software Anna Sinelnikova1 · David van der Spoel2 Received: 10 September 2020 / Accepted: 18 March 2021 / Published online: 28 March 2021 © The Author(s) 2021 Abstract Nuclear magnetic resonance spectroscopy is used routinely for studying the three-dimensional structures and dynamics of proteins and nucleic acids. Structure determination is usually done by adding restraints based upon NMR data to a classi- cal energy function and performing restrained molecular simulations. Here we report on the implementation of a script to extract NMR restraints from a NMR-STAR fle and export it to the GROMACS software. With this package it is possible to model distance restraints, dihedral restraints and orientation restraints. The output from the script is validated by performing simulations with and without restraints, including the ab initio refnement of one peptide. Keywords Python · NMR-STAR · Force Field · Amber · Charmm Introduction Determination of biomolecular structures is to a large extent automated these days (Wrz et al. 2017). Neverthe- Nuclear Magnetic Resonance spectroscopy is a power- less, it may be advantageous to both the NMR and the simu- ful technique to study structure and dynamics of biologi- lations communities to have a variety of tools to analyze cally relevant molecules in solution (Palmer 2004; Kay biomolecules using NMR data. Therefore we have imple- 2016). Due to steady methodological progress, membrane mented a script to include restraints from NMR into the proteins (Opella and Marassi 2017) as well as disordered GROMACS software suite for classical molecular dynamics proteins (Gibbs et al. 2017) and even macromolecules in simulations(Berendsen et al. 1995; Lindahl et al. 2001; van vivo (Inomata et al. 2009; Sakakibara et al. 2009; Luchi- der Spoel et al. 2005; Hess et al. 2008; Pronk et al. 2013; Páll nat and Banci 2017) can now be studied using NMR spec- et al. 2015). The script is validated by performing restrained troscopy techniques. Molecular dynamics simulations have as well as unrestrained molecular dynamics simulations of been used for over thirty years as a tool to supplement the peptides from the Protein Data Bank (Westbrook et al. 2002) sometimes limited amounts of data, and to allow determina- and by performing ab initio refnement of a short peptide. tion and refnement of structures or aid the interpretation of experimental data (Torda and Van Gunsteren 1991; Torda et al. 1993). In addition, NMR data can be used to validate Theory simulation results giving detailed insights when simulated structures deviate from experimental data (van der Spoel Background and Lindahl 2003; Lange et al. 2010) or to validate force felds (Hornak et al. 2006; Huang and MacKerell 2013). Here, we briefy recap relevant equations that are imple- mented in the GROMACS software suite. Within classical molecular simulation software packages, trajectories of mol- * David van der Spoel ecules can be simulated by numerically solving of Newton’s [email protected] equations of motion (Allen and Tildesley 1987). To do so, Anna Sinelnikova the force at every atom is calculated as the negative gradient [email protected] of the potential function. The potential functions in turn, are 1 Department of Physics and Astronomy, Uppsala University, divided into three diferent categories: Uppsala, Sweden 2 Department of Cell and Molecular Biology, Uppsala University, Uppsala, Sweden Vol.:(0123456789)1 3 144 Journal of Biomolecular NMR (2021) 75:143–149 – bonded forces, including chemical bonds, angles and number of software packages and is the standard for storing dihedrals, processed NMR data. For the purpose of this project it is – Van der Waals and Coulomb forces, important to note that there is a Python library that can be – diferent kind of restraints. used to read and process the content of the fles (Wedell and Baskaran 2020). In this paper we are interested in the last group, using the The scripts use two layers of conversion of inputs. First, restraint information that can be obtained from NMR exper- from NMR notation for degenerate groups to actual atoms, iments. We consider the three types of restraints that are and second, to convert to atom names matching the force implemented in GROMACS: distance, dihedral and orienta- felds. The latter is needed since, unfortunately, at least tion restraints. three diferent naming schemes for hydrogen atoms are in Distance restraints introduce a lower and upper limit for use today despite that standard nomenclature (IUPAC-IUB the distance for a particular atom pair. In GROMACS this is 1970) predates biomolecular force felds. Table 1 lists the implemented as a fat-bottom harmonic oscillator potential: efective translations. The script expands, for instance, the interaction between an Ala MB and an Ile MD to 9 distances 6 1 k (r − r )2, for r < r r− 2 dr ij 0 ij 0 that are however treated as one restraint using averag- 0, for r ≤ r < r ing of the distances. Logical OR statements in the input V (r )=⎧ 0 ij 1 dr ij ⎪ 1 k (r − r )2, for r ≤ r < r for distance restraints are honored. Both dihedral restraints 2 dr ij 1 1 ij 2 ⎪ 1 k (r − r )(2r − r − r ), for r ≤ r and orientation restraints apply the renaming conventions ⎨ 2 dr 2 1 ij 2 1 2 ij ⎪ in Table 1. In the case of dihedral restraints, the lower and ⎪ (1) upper bounds are extracted from the data and the average ⎩ where rij is a distance between atoms i and j, kdr is a dis- angle is computed, taking periodicity into account. A har- tance restraint force constant, r0 is a lower bound of the monic potential is applied starting from the bounds (Eqn. 2). restraint and r1 and r2 are two upper bounds. The second For orientation restraints the chemical shift anisotropy is upper bound is introduced to prevent extremely large forces read from the NMR data and output to GROMACS for- in case an atom pair is far from the target distance. In addi- mat (Lindahl et al. 2020). Multiple chains are supported as tion, GROMACS implements time averaging (Torda et al. well. More documentation for the script is at the GitHub 1989) as well as ensemble averaging of distance restraints. repository (Sinelnikova et al. 2020). Dihedral angles can be restrained using a similar fat- bottom potential: Methods 1 k (�� − � − ��)2, for �� > �� V (��)= 2 dihr 0 dihr 0, for �� ≤ �� (2) Technical validation where A test set is part of the package. In short, 44 PDB entries � are downloaded and processed and the resulting output fles =( − 0) MOD 2 (3) compared to reference tables (that is, the GROMACS input with 0 the reference angle, typically derived from J-cou- fles). If input fles are indeed correct, a GROMACS energy pling constants using a Karplus relation (Karplus 1959). minimization is run and the output structure compared to the Time averaging can be applied for dihedral restraints (Torda PDB structure. Since the energy minimization is performed et al. 1993) in GROMACS as well (Lindahl et al. 2020). in vacuo some conformational changes does occur but in all Orientation restraints can be obtained from e.g. resid- cases the root mean square deviation remains within 0.02 ual dipolar couplings. They have been implemented in nm. By applying the scripts to a few dozen diferent entries, GROMACS previously, including time and ensemble aver- it was possible to detect potential errors. If the script is aging (Hess and Scheek 2003). We refer to that paper or the updated or extended in the future the test set can be used to GROMACS manual (Lindahl et al. 2020) for more informa- make sure functionality remains intact. The test set includes tion because the mathematics is rather extensive. systems containing proteins, RNA and DNA and those bio- molecules supported by the Amber force feld should work with the script as well. In systems where GROMACS does Implementation details not recognize e.g. the protonation state of Histidine resi- dues, a warning is printed and one or more restraints may Here we briefy describe the script “nmr2gmx.py” used to be skipped. convert a NMR-STAR fle (Ulrich et al. 2019) to GROMACS inputs. The NMR-STAR file format is supported by a 1 3 Journal of Biomolecular NMR (2021) 75:143–149 145 Table 1 Atom and identifer Residue Identifer Amber Charmm name translations applied in the script for amino acids and Backbone H H HN nucleobases Ala MB HB1,2,3 HB1,2,3 Thr MG HG1,2,3 HG1,2,3 Ile MG HG21,2,3 HG21,2,3 Ile HG12 HG11 HG11 Ile HG13 HG12 HG12 Ile MD HD1,2,3 HD1,2,3 Ile CD1 CD CD Ile HD1x HDx HDx Gly HA2 HA1 HA1 Gly HA3 HA2 HA2 Ser, Thr, Cys HG HG HG1 Lys, Asn, Ser, Asp, Glu, Pro, Gln, Arg, Met, Trp, Tyr, Phe, His, Leu HB2 HB1 HB1 Lys, Asn, Ser, Asp, Glu, Pro, Gln, Arg, Met, Trp, Tyr, Phe, His, Leu HB3 HB2 HB2 Lys, Asn, Ser, Asp, Glu, Pro, Gln, Arg, Met, Val HG3 HG2 HG2 Lys, Asn, Ser, Asp, Glu, Pro, Gln, Arg, Met, Val HG3 HG2 HG2 Lys, Asn, Ser, Asp, Glu, Pro, Gln, Arg, Met HD3 HD2 HD2 Lys, Asn, Ser, Asp, Glu, Pro, Gln, Arg, Met HD3 HD2 HD2 Lys, Asn, Ser, Asp, Glu, Pro, Gln, Arg, Met HE3 HE2 HE2 Lys, Asn, Ser, Asp, Glu, Pro, Gln, Arg, Met HE3 HE2 HE2 Met ME HE1,2,3 HE1,2,3 Lys QZ HZ1,2,3 HZ1,2,3 Arg QH1 HH11,2 HH11,2 Arg QH2 HH21,2 HH21,2 Leu MD1 HD11,2,3 HD11,2,3 Leu MD2 HD21,2,3 HD21,2,3 Tyr, Phe QD HD1,2 HD1,2 Tyr, Phe QE HE1,2 HE1,2 G, A, U, C, DG, DA, DT, DC HO2’ HO’2 HO’2 G, A, U, C, DG, DA, DT, DC H5’ H5’1 H5’1 G, A, U, C, DG, DA, DT, DC H5” H5’2 H5’2 G, A, U, C, DG, DA, DT, DC H2’ H2’1 H2’1 G, A, U, C, DG, DA, DT, DC H2” H2’2 H2’2 DT M7 H71,2,3 H71,2,3 Simulation details dispersion (Allen and Tildesley 1987).