SANDRO BOTTARO, PAVEL BANÁŠ, JIŘÍ ŠPONER, AND GIOVANNI BUSSI

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1 FREE ENERGY LANDSCAPE OF GAGA AND UUCG RNA TETRALOOPS. SANDRO BOTTARO, PAVEL BANÁŠ, JIŘÍ ŠPONER, AND GIOVANNI BUSSI Contents 1. Supplementary Text 1 2 Sample PLUMED input file. 2. Supplementary Figure 1 3 Definition of ermsd and comparison with RMSD. 3. Supplementary Figure 2 4 ermsd from native of demultiplexed trajectories. 4. Supplementary Figure 3 5 Comparison between experimental and calculated NOE distances for GAGA tetraloop. 5. Supplementary Figure 4 7 Comparison between experimental and calculated NOE distances for UUCG tetraloop. 6. Supplementary Figure 5 9 Free energy surfaces projected onto the ermsd from native and onto the end-to-e nd distance at 300.9K for cgagag and cuucgg. 7. Supplementary Figure 6 10 Change in folding free energy upon addition of a local Gaussian penalty on different torsion potential. 8. Supplementary Figure 7 11 Potential energy and free energy profiles upon the addition of cosine modifications on α and ζ angles. 9. Supplementary Figure 8 13 Free energy surfaces upon the addition of cosine corrections on α and ζ angles. 10. Supplementary Figure 9 16 Comparison between potential energies calculated using the classical AMBER force field and high-level quantum mechanical calculations. References 17 1

2 2 SANDRO BOTTARO, PAVEL BANÁŠ, JIŘÍ ŠPONER, AND GIOVANNI BUSSI 1. Supplementary Text 1 # PDB that provides information on the molecules that are present in your system. MOLINFO STRUCTURE=NATIVE.pdb # ermsd with augmented cutoff, used for biasing. # The value of the cutoff determines at which distance a pair of nucleobases is counted # as a contact. An augmented value here allows forces to drive # the system towards and away from native even when nucleobases are far from # each other DIST0... ERMSD ATOMS=@lcs-1,@lcs-2,@lcs-3,@lcs-4,@lcs-5,@lcs-6,@lcs-7,@lcs-8 REFERENCE=NATIVE.pdb CUTOFF= DIST0 # ermsd with standard cutoff (2.4), used for monitoring only. # The cutoff employed here is the same used in the original paper # describing the ermsd metric. This value allows only proper contact to # be included in the assessment of the structures. DIST1... ERMSD ATOMS=@lcs-1,@lcs-2,@lcs-3,@lcs-4,@lcs-5,@lcs-6,@lcs-7,@lcs-8 REFERENCE=NATIVE.pdb... DIST1 # metadynamics metad: METAD ARG=DIST0 PACE=500 TAU=70 SIGMA=0.1 FILE=HILLS TEMP=300.9 BIASFACTOR=15 # print colvar file PRINT ARG=DIST0,DIST1,metad.bias FILE=colvar STRIDE=1000

3 FREE ENERGY LANDSCAPE OF GAGA AND UUCG RNA TETRALOOPS Supplementary Figure 1 ermsd is a metric for measuring distances between RNA 3D structures [1]. In essence, the ermsd is the difference in the contact maps between two RNA structures. This contact map is constructed considering only the relative position and orientation of the nucleobases, while it does not contain any explicit information on the backbone. In the figures above are shown the ermsd versus heavy-atom RMSD calculated on the UUCG and GAGA trajectories at 300.9K. The red line represents the average and standard deviation RMSD at a given ermsd value. The plots are useful to establish a correspondence between ermsd and RMSD at small distances. More precisely, it can be seen that to ermsd of 0.8 or lower correspond structures with average RMSD from native of 2Å.

4 4 SANDRO BOTTARO, PAVEL BANÁŠ, JIŘÍ ŠPONER, AND GIOVANNI BUSSI 3. Supplementary Figure 2 ermsd from native of each replica for each system, as labeled. Each bin is colored according to the average value calculated over 10ns. Demultiplexed trajectories were obtained using the demux script available at

5 FREE ENERGY LANDSCAPE OF GAGA AND UUCG RNA TETRALOOPS Supplementary Figure 3 Comparison between experimental and calculated NOE distances for GAGA tetraloop. Blue points indicate the calculated average NOE distance, the gray area indicates the experimental range. Violations larger than 0.5Å are labeled. Here we consider 4 different datasets: 1. the native NMR models (PDB code 1ZIG), 2. the MD samples with ermsd <0.8 from native 3. the MD samples with ermsd <0.7 from native, considering the stem only and 4. a mock ensemble with ermsd from native > 1.0. Weighted averages were computed considering the bias from the well-tempered Metadynamics using the software BARNABA [1]. Only data relative to the 4 tetraloop residues and the first closing base pair were calculated. The statistics for the different ensembles (shown in Table 1) show that the least violations are observed when considering the ensemble ermsd stem <0.7. Surprisingly, the mock ensemble, which is obviously wrong, performs similarly to the native ensemble. These results indicate that: i) the native fold of the GAGA loop is highly dynamic and ii) the available NOE distances are too sparse for a proper evaluation of the different ensembles. Ensemble number of violations RMSE from boundary (nm) Native ermsd < ermsd stem < ermsd >

6 6 SANDRO BOTTARO, PAVEL BANÁŠ, JIŘÍ ŠPONER, AND GIOVANNI BUSSI Figure 1. Random samples from each MD ensemble for GAGA tetraloop are shown as grey 3d structures and superimposed onto the native NMR model (PDB 1ZIG).

7 FREE ENERGY LANDSCAPE OF GAGA AND UUCG RNA TETRALOOPS Supplementary Figure 4 Comparison between experimental and calculated NOE distances for UUCG tetraloop. Blue points indicate the calculated average NOE distance, the gray area indicates the experimental range. Violations larger than 0.5Å are labeled. Here we consider 4 different datasets: 1. the native NMR models (PDB code 2KOC), 2. the MD samples with ermsd <0.72 from native 3. the MD samples with ermsd <0.7 from native, considering the stem only and 4. a mock ensemble with ermsd from native > 1.0. Weighted averages were computed considering the bias from the well-tempered Metadynamics using the software BARNABA [1]. Only data relative to the 4 tetraloop residues and the first closing base pair were calculated. The statistics for the different ensembles (shown in Table 2) show that the least violations are observed when considering the ensemble ermsd <0.72. Ensemble Number of violations RMSE from boundary (nm) Native ermsd < ermsd stem < ermsd >

8 8 SANDRO BOTTARO, PAVEL BANÁŠ, JIŘÍ ŠPONER, AND GIOVANNI BUSSI Figure 2. Random samples from each MD ensemble for UUCG tetraloop are shown as grey 3d structures and superimposed onto the native NMR model (PDB 2KOC).

9 FREE ENERGY LANDSCAPE OF GAGA AND UUCG RNA TETRALOOPS Supplementary Figure 5 Free energy surfaces projected onto the ermsd from native and onto the C1 -C1 endto-end distance at 300.9K for cgagag and cuucgg hexamers. Gray shades indicate statistical error.

10 10 SANDRO BOTTARO, PAVEL BANÁŠ, JIŘÍ ŠPONER, AND GIOVANNI BUSSI 7. Supplementary Figure 6 Change in folding free energy upon addition of a local Gaussian penalty on different torsion potential. G shown in the color bar are expressed in kj/mol.

11 FREE ENERGY LANDSCAPE OF GAGA AND UUCG RNA TETRALOOPS Supplementary Figure 7 Comparison between AMBERχ OL force field and modified α (A) and ζ (B) torsion potential energy. The gauche region is not perturbed, while gauche + is destabilized. The effect of

12 12 SANDRO BOTTARO, PAVEL BANÁŠ, JIŘÍ ŠPONER, AND GIOVANNI BUSSI these modifications on the free energy surfaces projected onto α torsion angle are shown in panel C (G3 in GAGA 8) and panel E (G6 in UUCG 8). Equivalent profiles projected on to ζ are shown in panels D and F. Note that the modification on α affects the free energy surface along ζ and vice-versa. Small differences can be also observed to the free energy profiles projected onto χ (panels G,H)

13 FREE ENERGY LANDSCAPE OF GAGA AND UUCG RNA TETRALOOPS Supplementary Figure 8 Free energy surfaces at K projected onto the ermsd from native for GAGA and UUCG tetraloops with and without backbone modifications. Gray shades represent statistical error. The vertical line indicate the treshold used for calculating free energy differences between folded and unfolded.

14 14 SANDRO BOTTARO, PAVEL BANÁŠ, JIŘÍ ŠPONER, AND GIOVANNI BUSSI Free energy surfaces at K projected onto the C1 -C1 end-to-end distance for AAAA, CAAU, CCCC, GACCC and UUUU tetranucleotides with and without backbone modifications. Gray shades represent statistical error, while red dots indicate infinite error. The vertical line indicate the treshold used for calculating free energy differences between compact/extended. In all cases the backbone modifications stabilize extended conformations.

15 FREE ENERGY LANDSCAPE OF GAGA AND UUCG RNA TETRALOOPS. 15 Free energy surfaces at K projected onto the ermsd from ideal A-form helix for AAAA, CAAU, CCCC, GACCC and UUUU tetranucleotides with and without backbone modifications. Gray shades represent statistical error.

16 16 SANDRO BOTTARO, PAVEL BANÁŠ, JIŘÍ ŠPONER, AND GIOVANNI BUSSI 10. Supplementary Figure 9 Comparison between potential energies calculated using the classical AMBER force field and DLPNO-CCSD(T)/CBS* calculations on 46 UpU dinucleotides (see ref. [2]. The quantum-chemical calculations presented in ref. 2 derive a set of 46 benchmark structures of RNA UpU dinucleotides representing all 46 known RNA backbone families. These are obtained by using restrained geometry optimizations targeting the centroids of the Richardson s RNA backbone families [3]. The structures are then used to derive relative electronic structure energies of the 46 backbone families. Such benchmark structure-energy databases are common in QM literature and can be used for verification of other computational methods. The Figures show a correlation of the benchmark QM database with equivalent AMBER force field calculations, with the canonical A-RNA 1a family set to have energy 0 with both methods. The Figure shows that none of the suggested modifications of the backbone dihedrals leads to an improvement of the agreement between the QM and MM potential energy surfaces for the UpU dinucleotides.)

17 FREE ENERGY LANDSCAPE OF GAGA AND UUCG RNA TETRALOOPS. 17 References [1] S. Bottaro, F. Di Palma, and G. Bussi, The role of nucleobase interactions in rna structure and dynamics, Nucleic Acids Res., vol. 42, no. 21, pp , [2] H. Kruse, A. Mladek, K. Gkionis, A. Hansen, S. Grimme, and J. Sponer, Quantum chemical benchmark study on 46 rna backbone families using a dinucleotide unit, J. Chem. Theory Comput., vol. 11, no. 10, pp , [3] J. S. Richardson, B. Schneider, L. W. Murray, G. J. Kapral, R. M. Immormino, J. J. Headd, D. C. Richardson, D. Ham, E. Hershkovits, L. D. Williams, et al., Rna backbone: consensus all-angle conformers and modular string nomenclature (an rna ontology consortium contribution), Rna, vol. 14, no. 3, pp , 2008.