Data-informed reparameterization of modified RNA and the effect of explicit water models: application to pseudouridine and derivatives

Pseudouridine is one of the most abundant post-transcriptional modifications in RNA. We have previously shown that the FF99-derived parameters for pseudouridine and some of its naturally occurring derivatives in the AMBER distribution either alone or in combination with the revised γ torsion parameters (parmbsc0) failed to reproduce their conformational characteristics observed experimentally (Deb et al. in J Chem Inf Model 54:1129–1142, 2014; Deb et al. in J Comput Chem 37:1576–1588, 2016; Dutta et al. in J Chem Inf Model 60:4995–5002, 2020). However, the application of the recommended bsc0 correction did lead to an improvement in the description not only of the distribution in the γ torsional space but also of the sugar pucker distributions. In an earlier study, we examined the transferability of the revised glycosidic torsion parameters (χIDRP) for Ψ to its derivatives. We noticed that although these parameters in combination with the AMBER FF99-derived parameters and the revised γ torsional parameters resulted in conformational properties of these residues that were in better agreement with experimental observations, the sugar pucker distributions were still not reproduced accurately. Here we report a new set of partial atomic charges for pseudouridine, 1-methylpseudouridine, 3-methylpseudouridine and 2′-O-methylpseudouridine and a new set of glycosidic torsional parameters (χND) based on chosen glycosidic torsional profiles that most closely corresponded to the NMR data for conformational propensities and studied their effect on the conformational distributions using REMD simulations at the individual nucleoside level. We have also studied the effect of the choice of water model on the conformational characteristics of these modified nucleosides. Our observations suggest that the current revised set of parameters and partial atomic charges describe the sugar pucker distributions for these residues more accurately and that the choice of a suitable water model is important for the accurate description of their conformational properties. We have further validated the revised sets of parameters by studying the effect of substitution of uridine with pseudouridine within single stranded RNA oligonucleotides on their conformational and hydration characteristics. Supplementary Information The online version contains supplementary material available at 10.1007/s10822-022-00447-4.


Introduction
Post-transcriptional modifications have been known to be crucial in the regulation of the structure, stability and function of RNA molecules. The MODOMICS database currently lists 172 such modifications [1]. Pseudouridine (Ψ) was the first post-transcriptional modification discovered [2][3][4] and is one of the most abundant modifications. Pseudouridine, an isomer of uridine (U), was identified as 5-ribosyluracil and was called the fifth nucleoside [5][6][7][8]. This modified residue contains a C-C base-sugar bond, i.e., in the case of pseudouridine, the uracil base is attached to the sugar by a C1′-C5 bond unlike the C1′-N1 glycosidic linkage found in uridine (Fig. 1a). Hence, in contrast to uridine, pseudouridine contains an additional ring nitrogen atom (N1 imino atom) which acts as an additional hydrogen bond donor and is found to be protonated at physiological pH [3,9].
Pseudouridine was reported to be the most commonly observed modification in the stable RNAs, i.e., tRNA, rRNA and snRNA [3]. Further studies involving high-throughput sequencing methods and transcriptome mapping revealed the abundance of pseudouridine as an epigenetic modification, i.e. in mRNA as well as in long noncoding RNA (lncRNA) [10][11][12][13][14]. Several experimental and theoretical studies suggest the important contribution of pseudouridine to the structure, dynamics and thermal stability of RNA [15][16][17][18][19][20][21]. This modification has been found to reduce the motion of the neighbouring bases, stabilize the C3′-endo conformation and enhance the stability and the stacking propensity in a context-dependent manner [15,[20][21][22][23]. Newby and Greenbaum studied the interaction between Ψ and water in the pre-mRNA branch-site helix and reported that a water-ΨHN1 hydrogen bond contributes to the stabilization of the unique observed architectural features of this helix [18].
In 2016, we reported that the reoptimized set of glycosidic torsion parameters (χ IDRP ) for pseudouridine developed by us, were sufficient to improve the description of the conformational distribution of the glycosidic torsion space but the description of the sugar pucker distribution for Ψ was still not accurate [24]. In another study in 2020, we checked the transferability of these parameters (χ IDRP ) to the derivatives of Ψ and observed that the χ IDRP parameters combined with the AMBER FF99-derived parameters [25] and the revised set of γ torsional parameters predicted the conformational properties of these residues which were in general agreement with the experimental (NMR) data but failed to describe the sugar pucker distributions accurately [26].
In the present study we report a new set of partial atomic charges for pseudouridine (Ψ), 1-methylpseudouridine (m 1 Ψ), 3-methylpseudouridine (m 3 Ψ) and 2′-O-methylpseudouridine (Ψm) and a new set of glycosidic torsional parameters (χ ND ) (Fig. 1). We have compared the results obtained with these parameters with those previously obtained with the FF99 parameters and the FF99 parameters in combination with the χ IDRP parameters and bsc0 γ torsional parameters.
In the earlier studies, multiple schemes [27] and/or general schemes [28] were chosen for the quantum mechanical scan and the molecular mechanical energy profiles were fitted with those with the objective that the re-optimized parameters will be able to explore, preferentially, any of the four quadrants (NORTH/syn, NORTH/anti, SOUTH/syn, SOUTH/anti) of the conformational preferences. In the present work, we calculated the quantum mechanical glycosidic torsional energy profiles for five different initial conformations. Then a particular scheme was chosen which outperformed other schemes in reproducing QM profile that was in agreement with the experimentally observed conformational preference. Next, the MM profile was fitted to the chosen QM profile. Additionally, the partial charges were newly generated at the individual modification level before generating the MM profile to incorporate the effect of electrostatic interactions. As a proof of concept, we have chosen pseudouridine and three of its derivatives as a (small) closely related test set that includes molecules with different chemical moieties. For additional validation of our parameter sets, we examined their performance in predicting the conformational and hydration characteristics of the ssRNA trimers and tetramers containing pseudouridine.
Finally, the parameters developed in a targeted approach were further tested in different explicit water models to get insight into the correlation between the solvation model and conformational preferences. It has been reported in recent studies that the choice of water model has a significant impact on the predicted RNA structure and dynamics [29,30]. Kührova et al., based on their study involving the simulation of canonical A-RNA duplexes using explicit water models, i.e. TIP3P [31], TIP4P/2005 [32], TIP5P [33] and SPC/E [34], reported that the TIP5P water model was not found to be optimal for simulating RNA systems [29]. Here, we have investigated the impact of the choice of explicit water models on the conformational characteristics and hydration pattern of Ψ, m 1 Ψ, m 3 Ψ, and Ψm.

Preparation of the initial geometries
For the initial geometries of the modified nucleosides Ψ (PSU), m 1 Ψ (1MP), m 3 Ψ (3MP), and Ψm (MRP), we have used the mean values for bonds, angles and dihedral angles corresponding to the ribose sugar following Gelbin et al. (1996) [35] and considered planar geometries for the bases. The three-letter codes of the modified residues are according to Aduri et al. (2007) [25]. These structures were prepared using the molecular structure editor MOLDEN [36]. The geometries of the modified nucleosides were kept either in the C3′-endo/g + conformation or in the C2′-endo/g + conformation and for that the corresponding torsional angles were fixed at definite values. The value of the γ dihedral angle (O5′-C5′-C4′-C3′) was fixed at 54° (which corresponds to the g + conformation) as observed in the A-form RNA [37]. To compel the nucleoside geometries to stay in the C3′-endo conformation, the values of the δ (C5′-C4′-C3′-O3′) and O4′-C1′-C2′-C3′ dihedral angles were fixed at 81° and − 24°, respectively. To constrain the geometries to the C2′-endo sugar pucker conformation the value of the δ (C5′-C4′-C3′-O3′) and O4′-C1′-C2′-C3′ dihedral angles were set to 140° and 32° respectively. Five initial geometries, i.e., SC1, SC2, SC3, SC4 and SC5 (Table S1) with constrained values of the H5T-O5′-C5′-C4′ and C1′-C2′-O2′-HO2′ torsional angles were prepared for each of the modified nucleosides, to either promote or restrict the base-sugar hydrogen bonding interactions by maintaining the nucleosides either in C3′-endo or in C2′-endo sugar pucker conformation. The schemes SC1-SC4 were chosen following the values of the torsional angles corresponding to the four schemes chosen in Yildirim et al. [27] and SC5 was chosen based on the syn scheme as mentioned in Deb et al. [24]. SC4 also corresponds to the anti scheme as mentioned in Deb et al. [24]. For the SC4 conformational scheme, the H5T-O5′-C5′-C4′ and C1′-C2′-O2′-HO′2 dihedrals were respectively constrained to 174° and 93° and due to that the O5′-H···O4 base-sugar hydrogen bonding interaction is restricted and O2′-H···O4 base-sugar hydrogen bonding interaction is facilitated and hence the geometries corresponding to PSU and its derivatives are compelled towards anti conformation which is not the predominant conformation for these nucleosides. For the SC5 scheme, the values of the H5T-O5′-C5′-C4′ and C1′-C2′-O2′-HO′2 dihedrals were respectively constrained to 60° and − 153° to promote the O5′-H···O4 and restrict the O2′-H···O4 base-sugar hydrogen bonding interactions and hence to force a syn conformation which is predominant for PSU and its derivatives [38]. The SC1 and SC2 conformational schemes were kept in the C2′-endo conformation while SC3-SC5 were kept in the C3′-endo conformation. To prevent any hydrogen bonding interaction between H3T or O2′ and base, so that these interactions cannot affect the glycosidic torsion energy profile, the C4′-C3′-O3′-H3T torsion was fixed at -148° for all the initial geometries. The initial structures corresponding to each of the five conformational schemes are shown in Fig. S1. The geometry which corresponds to the SC5 conformational scheme for each of the modified nucleosides (along with the atom names) is shown in Fig. S2.

Quantum mechanical scan
All the quantum mechanical calculations were performed using the GAUSSIAN09 software suite [39]. For all the five initial geometries for each of the modified nucleosides, a gas phase PES scan was executed around the glycosidic torsion angle (O4′-C1′-C5-C6) with an increase in its value by 5° resulting in 72 conformations for each nucleoside geometry. Optimization of the structures, during the PES scan, was carried out using the HF/6-31G* level of theory. During the geometry optimization step, the dihedral angles mentioned in Table S1, were kept frozen with the objective of obtaining a smooth QM energy profile. The QM energies (E QM ) corresponding to each of the 72 geometry optimized conformations (for each scheme) were calculated using the MP2/6-31G* level of theory. Out of the five quantum mechanical energy (E QM ) profiles around χ, we have chosen one particular conformational scheme, i.e. SC5, because the lowest energy minimum for this scheme corresponded to the syn region of the glycosidic torsional space (Fig. S3) and experimental (NMR) studies for pseudouridine and its derivatives, under study, reported a preference for the syn conformation [54][55][56]. Additionally, the value of energy corresponding to the global minimum of that profile was found to be the least compared to other schemes (Fig. S3).

RESP fitting
The new set of partial atomic charges for each of the modified nucleosides was developed corresponding to the lowest energy conformation of the quantum mechanical energy profile of the chosen scheme, i.e. SC5, by RESP [40,41] fitting (Restrained Electrostatic Potential fitting) method using the R.E.D. version III.52 perl program [42]. The partial atomic charges for the atoms of each of the nucleosides are listed in the supporting information (Table S2).

Molecular mechanical (MM) energy minimization
For the calculation of the molecular mechanical (MM) energies (E MM ) corresponding to the 72 quantum mechanically (QM) optimized geometries, we have used the AMBER16 software package [43] (Fig. 2). During the MM energy minimizations, the dihedral angles (as mentioned in Table S1) were restrained to the values corresponding to the QM optimized geometries by applying a force constant of 1500 kcal/ mol Å 2 . The starting structures for the MM energy minimization step were the structures equivalent to the QM optimized geometries obtained from the PES scan. The 5′-phosphate group was replaced with a hydrogen (5′-OH) and a hydrogen atom (3′-OH) was added to the 3′ end of the original topology provided by Aduri et al. [25] to create the topologies for all the modified nucleosides used in this study with the parameters corresponding to the 5′-OH and 3′-OH groups taken from the FF99 force field parameter set [44]. During the MM energy minimization, all the glycosidic torsion parameters corresponding to the Aduri et al. [25] parameter set were set to zero for all the modified nucleosides. Minimizations were carried out using the steepest descent method followed by the conjugate gradient method in order to obtain a smooth glycosidic torsional energy profile for each residue. To incorporate the non-bonded interactions during the energy minimization in vacuum, a long range cut-off of 12 Å was used.

Fitting χ torsion potentials
The potential energy due to the glycosidic torsion angle is represented by the difference (E CHI ) between the QM energy (E QM ) and MM energy (E MM ) and is given by the following equation: The 72 values for E CHI obtained from Eq. (1) were fitted to the Fourier series as shown in Eq. (2): Vn {1 + cos(n − n)} corresponding to QM calculations (black), MM calculations with the FF99 parameter sets keeping the glycosidic torsion parameters zero (red) and MM calculations with the FF99 parameter sets combined with the newly derived χ torsional parameters and the newly devel-oped partial atomic charges (FF99_χ ND ) (green) by fitting the difference between the QM and MM energies. The minimum energies were set to zero for convenience. The ranges 30°-90° and 170°-300° for the χ torsional angles along the X-axis, correspond to the syn and anti base orientations respectively where χ represents the glycosidic torsion angle, i.e. the dihedral around (O4′-C1′-C5-C6) and V n represents the potential energy barrier around the glycosidic torsion angles (χ) and ϕ n is the phase angle.

System preparation
The starting structures in this study were taken from the original PDB format files for each of the four modified ribonucleoside residues corresponding to their quantum mechanically optimized geometries provided by Aduri et al. [25], and available in the AMBER 2018 package. These initial structures were in a NORTH/anti/g + conformation. The FF99_χ IDRP _bsc0 [24] parameter set for Ψ was obtained from Deb et al. [24], and FF99_χ IDRP _bsc0 [24] parameter sets for m 1 Ψ, m 3 Ψ, and Ψm residues were obtained from Dutta et al. [26]. The FF99_χ ND _bsc0 parameter sets for Ψ, m 1 Ψ, m 3 Ψ, and Ψm residues were prepared by combining our newly derived χ torsional parameters (χ ND ) and the revised γ parameters developed by Pérez et al. [45] (par-mbsc0) with the required bond, angle and torsional parameters for each modification from the AMBER provided parameters derived from Aduri et al. parameters [25]. The revised γ torsional parameters were incorporated by replacing the atom type that described the terms corresponding to the γ torsion in the default topology files with the torsional terms provided in the revised parmbsc0 force field. The newly developed partial atomic charges for the atoms (as mentioned in the supporting information) of each of the four modified ribonucleosides were introduced replacing the partial atomic charges of these atoms in the preparatory file (prepin) provided by Aduri et al. [25]. We used these revised parameter sets for energy minimization and MD simulation steps. The revised force field parameter sets for Ψ, m 1 Ψ, m 3 Ψ, Ψm (FF99_χ ND _bsc0) are given in the supporting information. The modified ribonucleosides Ψ, m 1 Ψ, m 3 Ψ, and Ψm were separately simulated using the FF99_χ IDRP _ bsc0 and FF99_χ ND _bsc0 parameters respectively. Detailed description of the force field parameters used in this study are provided in Table 1. The newly derived glycosidic (χ) torsion parameters are listed in Table 2.

REMD simulations
All replica exchange molecular dynamics (REMD) simulations [46] were performed using the multi-sander approach in AMBER 16 [43] in explicit water. To study the effect of the water model on the conformations of these nucleosides,  [24] and for its three derivatives (m 1 Ψ, m 3 Ψ, and Ψm), FF99_χ IDRP _bsc0 parameters [24,25,45] modified by the introduction of required bond, angle and torsional parameters for each modification from the AMBER provided parameters derived from Aduri et al. parameters [25] (obtained from Dutta et al. [26]) FF99_χ ND _bsc0 χ and γ Revised glycosidic torsion parameters (χ ND ) for Ψ, m 1 Ψ, m 3 Ψ, and Ψm nucleosides and revised γ torsion parameters developed by Pérez et al. [45] (parmbsc0) in combination with the required bond, angle and torsional parameters for each modification from the AMBER provided parameters derived from Aduri et al. parameters [25] along with the newly developed set of partial atomic charges for each of these modified nucleosides REMD simulations were carried out using the combination of the FF99_χ IDRP _bsc0 and FF99_χ ND _bsc0 force fields with each of the TIP3P [31], TIP4P-Ew [47] and SPC/E [34] water models and the hydration patterns for pseudouridine and its three derivatives corresponding to the different force field-water model combinations were analyzed. The modified nucleoside residues Ψ, m 1 Ψ, m 3 Ψ, Ψm were solvated with TIP3P or TIP4P-Ew or SPC/E water molecules in truncated octahedral boxes with a closest distance of 9 Å between any solute atom and the edge of the box. The computational details of the energy minimization, equilibration and REMD production runs are provided in the supporting information ('METHODS' section).

System preparation
The initial model structures of the single stranded RNA trinucleotides AUA and AΨA and tetra nucleotides AAUA and AAΨA were prepared in the canonical A-RNA form using AMBERTools18. Topology generation, addition of hydrogens, neutralization and solvation of each system with TIP3P [31] water molecules in a cubic solvent box, were carried out using AmberTools18. The closest distance between any solute atom and the edge of the periodic box was set to 10 Å. The systems were neutralized using Na + ions.

MD simulations
All molecular dynamics (MD) simulations were performed using AMBER16 software suite [43]. MD simulations were performed using the FF99_χ OL3 _bsc0 [25,28,45] force field parameter combinations for the canonical nucleosides (adenosine (A) and uridine (U)) and the FF99_χ IDRP _bsc0 or FF99_χ ND _bsc0 parameters for pseudouridine (Ψ). The computational details of the molecular dynamic simulations of the single stranded RNA oligomers are provided in the supporting information ('METHODS' section).

Analysis of the conformational ensembles of the modified nucleosides
For the analysis of the simulated ensembles we calculated the distribution of sugar pucker conformations, distribution of the syn or anti conformations of the glycosidic torsion angle (χ) and the distribution of the γ torsional angle over different conformational states. The convention followed for the atom names and the dihedral angle nomenclatures was as given in Saenger [38]. The magnitude of the pseudorotation angle was calculated following Altona and Sundaralingam [48].
The pseudorotation angular space was divided into C3′endo/NORTH (270° ≤ P < 90°) and C2′-endo/SOUTH (90° ≤ P < 270°) regions of sugar puckering [49], which allowed us to directly compare simulated conformational distributions and the equilibrium distributions of the pseudorotation angle (P) as reported in the NMR data.
In our analysis, the χ torsional angle is defined by the atoms O4′-C1′-C5-C4 (for all the modified nucleosides) and was considered to be in the anti conformation if its magnitude was within the angular range of 170°-300° and in the syn conformation if it was within the angular range of 30°-90° [35,50,51]. The values that were beyond these ranges were referred to as others [35,50,51].
We analysed the hydrogen bonding characteristics and radial distribution function (RDF) for each of the four modified residues and the distribution of the θ torsion angle (H2′-C2′-O2′-HO2′) for the Ψ, m 1 Ψ, m 3 Ψ residues. For the calculation of the pseudorotation angle P, the χ, γ, and θ torsion angles, hydrogen bonds and RDFs, cpptraj tool from AmberTools18 [52] was used. RDFs of water oxygen atoms around the HN1 atom was calculated for each of the Ψ, m 3 Ψ and Ψm residues and RDFs of water oxygen atoms around the HN3 atom was calculated for each of the Ψ, m 1 Ψ and Ψm residues. Hydrogen bond formations were taken into account if the distance between the donor and the acceptor atoms was ≤ 3 Å and the donor-hydrogen-acceptor angle was ≥ 135°. The water occupancy maps around the average MD structure of Ψ corresponding to the FF99_χ ND _bsc0 and TIP3P force field and water model combination were calculated using the grid routine in cpptraj tool and visualization was done using UCSF-Chimera [53]. The average MD structures were obtained from 600 frames corresponding to each of the four conformations, i.e. NORTH/syn, SOUTH/syn, NORTH/anti and SOUTH/anti conformations from a set of 16 ns REMD simulations.

Analysis of the simulated trajectories of the ssRNA oligomers
The cpptraj module of AmberTools18 [52] was used to analyze the MD trajectories of the ssRNA trimers and tetramers. The distributions of the pseudorotation angle P, the χ and γ torsion angles, hydrogen bonds, waterbridges, RDFs were calculated from the 3 µs concatenated trajectory while conformational entropy (based on the quasi-harmonic approach) of each of the oligomers was calculated using individual trajectories for each of the ssRNA oligomers using suitable utilities available with the cpptraj module.
The glycosidic (χ) torsion angle defined by the atoms O4′-C1′-C5-C4 for pseudouridine and the χ torsional angle defined by the atoms O4′-C1′-N9-C4 and O4′-C1′-N1-C2 for the canonical nucleosides adenosine (A) and uridine (U), respectively, were considered for the calculation of the anti and syn conformations. The ranges considered for the definition of the different conformations of the pseudorotation angle P, the χ and γ torsion angles were same as mentioned earlier for the single modified nucleosides. Formation of hydrogen bonds was considered if the donor-acceptor distance was ≤ 3 Å and the donor-hydrogen-acceptor angle was ≥ 135°.

Conformational and hydration characteristics of modified nucleosides
In an earlier study [26] we validated the revised parameter sets for pseudouridine (Ψ) (FF99_χ IDRP _bsc0) [24] and checked the transferability of these parameters to the four pseudouridine derivatives, i.e. m 1 Ψ, m 3 Ψ, Ψm and m 1 acp 3 Ψ and our observations indicated that the revised parameters for Ψ were transferable to the Ψ derivatives. In the present study we developed new sets of partial atomic charges individually for Ψ and its three derivatives m 1 Ψ, m 3 Ψ and Ψm and reoptimized the parameters for the glycosidic torsion angle for each of these residues and compared the conformational ensembles. The REMD simulations were carried out using the combination of the force fields, i.e. FF99_χ IDRP _ bsc0 and FF99_χ ND _bsc0 with the TIP3P, TIP4P-Ew and SPC/E water models.

Pseudorotation angle (P)
With the AMBER FF99 parameter sets, the distribution of the pseudorotation angle was observed to have a smaller population of the NORTH sugar pucker conformation compared to the experimentally observed population for each of the modified residues except for Ψ [26] (Table S3, Fig. 3). Inclusion of the revised γ torsion parameters (par-mbsc0) with the AMBER FF99 parameter sets resulted in an improvement in the propensity of the NORTH sugar pucker conformation for all the Ψ-derivatives. But with the FF99_bsc0 parameters, the propensity of the NORTH sugar pucker conformation for Ψ was significantly lower than the experimentally observed value [26].
For Ψ, the FF99_χ ND _bsc0 force field in combination with the TIP3P and the SPC/E models generated a population of the NORTH sugar pucker conformation which were in general much closer to the experimentally observed population than those generated by the FF99_χ IDRP _bsc0 force field in combination with each of the water models in this study. But FF99_χ ND _bsc0 in combination with the TIP4P-Ew water model generated a much greater population of the NORTH conformers of Ψ than the other force field and water model combinations and also the experimentally observed population. However, FF99_χ IDRP _bsc0 + TIP4P-Ew reproduced the experimental value of the NORTH population for m 1 Ψ better than all the other force field-water model combinations. In the case of m 3 Ψ, it was observed that, the FF99_ χ ND _bsc0 force field in combination with each of the three water models generated a population of the NORTH sugar pucker conformation which agreed better with the NMR results than what was observed with the FF99_χ IDRP _bsc0 force field in combination with each of the water models in this study. For Ψm, the FF99_χ ND _bsc0 + TIP3P and FF99_ χ ND _bsc0 + SPC/E combinations generated population of the NORTH conformers in better agreement with the NMR results than those generated by the other force field-water model combinations.

Glycosidic torsion angle (χ)
For each of the modified nucleosides under this study, experimental (NMR) studies reported a preference for the syn conformation [54][55][56]. The FF99 and FF99_bsc0 parameters, for each of the modified residues, predicted an excess population of anti conformers (> 90%) [26,57]. Earlier, we reported that FF99_χ IDRP _bsc0 + TIP3P shifted the equilibrium towards the syn conformation. The FF99_χ IDRP _bsc0 parameter sets in combination with each of the TIP4P-Ew and SPC/E water models also generated a much greater population of syn conformation in good agreement with the NMR data than that obtained with the FF99 parameter sets (Table S4, Fig. 4). With the revised parameter sets FF99_χ ND _bsc0 in combination with each of the three water models, the modified residues adopted a much greater population of the syn conformation than what was predicted by the default AMBER parameters. But for each modified nucleoside, the population of syn conformers predicted by the FF99_χ ND _bsc0 parameters were lower than what was predicted by the FF99_χ IDRP _ bsc0 parameters for each of the water models under this study.

Gamma torsion angle (γ)
In our earlier studies, we reported that, with the FF99 parameter sets, the g + population was much lower than the experimentally observed population for pseudouridine and its derivatives [26,57]. In the present study, it was observed that all the force field and water model combinations predicted the g + population greater than what was predicted with the FF99 parameter sets, but also than the experimentally observed population (Table S5, Fig. 5). As was reported earlier [26], in the present study also, we observed that the inclusion of the revised γ torsion parameters developed by Pérez et al. [45] (parmbsc0) shifted the equilibrium almost exclusively towards the g + conformation (∼ 90%).

Correlation of the pseudorotation equilibrium with the glycosidic torsion angle (χ)
The two-dimensional scatter correlation plots of pseudorotation angle (P) vs glycosidic torsion angle (χ) revealed that for all the ribonucleosides in this study, with FF99_ χ IDRP _bsc0 + TIP3P there was a significantly large population of the SOUTH/syn conformations (Figs. S4-S6). With FF99_χ IDRP _bsc0 + TIP4P-Ew,, there were almost equal populations of SOUTH/syn and NORTH/syn conformations for all the four modified nucleosides, but the population of the SOUTH/syn conformers was a little higher in each case. The FF99_χ IDRP _bsc0 + SPC/E force field-water model combination also predicted a higher population of SOUTH/syn conformers than the others. In general, with the FF99_χ ND _bsc0 force field in combination with the TIP3P and the SPC/E water models, almost equal populations of the SOUTH/syn and NORTH/anti conformers were observed for each of the modified residues. The combination FF99_χ ND _bsc0 + TIP4P-Ew predicted a large population of NORTH/anti conformers for Ψ and m 1 Ψ nucleosides. But for m 3 Ψ, this force field-water model combination predicted almost equal populations of the SOUTH/syn and NORTH/anti conformers. With FF99_χ ND _bsc0 + TIP4P-Ew, Ψm preferentially adopted the SOUTH/syn conformation.

Correlation of the pseudorotation equilibrium with the gamma torsion angle (γ)
From the two-dimensional correlation maps (two-dimensional scatter plots), it was observed that the FF99_χ IDRP _ bsc0 force field in combination with each of the three water models in the present study, predicted a greater population of the SOUTH/g + conformers followed by that of the NORTH/ g + conformers for each of the modified nucleosides (Figs. S7-S9). In general, with the FF99_χ ND _bsc0 parameter sets in combination with each of the three water models, we observed that there were almost equal populations of the NORTH/g + and SOUTH/g + conformers for all the residues. With FF99_χ ND _bsc0 + TIP4P-Ew, Ψ preferentially adopted the NORTH/g + conformation while Ψm preferentially adopted the SOUTH/g + conformation. The populations of the gand trans conformers were extremely low due to the inclusion of the γ torsion parameters developed by Pérez et al. [45] (parmbsc0) as was observed in our earlier study [26].

Hydrogen bonding
The hydrogen bonds except O5′-H5T⋯O4 (Fig. 6) and O2′-HO2′⋯O4 hydrogen bonds were observed to be negligible (Tables 3 and 4). With each of the force field-water model combinations, for all the modified residues (not applicable to Ψm), it was observed that the number of conformers with O2′-HO2′⋯O4 hydrogen bonding interaction were very small and much lesser than that of the O5′-H5T⋯O4 hydrogen bonding interaction.
For Ψ, FF99_χ IDRP _bsc0 + TIP3P, FF99_χ ND _ bsc0 + TIP3P and FF99_χ ND _bsc0 + SPC/E force fieldwater model combinations predicted greater populations of conformers with O5′-H5T⋯O4 hydrogen bonding interaction than what were predicted by the other force field-water  All the force field-water model combinations generated almost equal populations of conformers with O5′-H5T⋯O4 hydrogen bonding interaction for the m 3 Ψ residue. For Ψm, FF99_χ ND _bsc0 force field parameters predicted greater number of O5′-H5T⋯O4 hydrogen bonding interactions than what was predicted by FF99_χ IDRP _bsc0 in combination with each of the water models in this study. For Ψ and m 1 Ψ, the FF99_χ ND _bsc0 force field predicted slightly greater population of conformers with O2′-HO2′⋯O4 hydrogen bonding interaction than the FF99_χ IDRP _bsc0 parameter sets with each of the water models. But for m 3 Ψ, all the force field-water model combinations generated similar populations of conformers with O2′-HO2′⋯O4 hydrogen bonding interaction.

Radial distribution function
From the RDF plot of water oxygen atoms with respect to the HN1 atom of Ψ, it was observed that the FF99_χ IDRP _ bsc0 force field in combination with each of the water models predicted the formation of a well-defined first hydration shell between 1.5 and 2.5 Å having a maximum at ~ 2 Å (Figs. S10-S12). This observation was consistent with that of the recent report by Deb et al. [21]. The FF99_χ ND _bsc0 force field in combination with each of the water models also predicted the formation of a well-defined first hydration shell between 1.5 and 2.5 Å having a maximum at ~ 2 Å around the Ψ-HN1 atom. For the HN1 atoms of m 3 Ψ and Ψm also, all the force field and water model combinations predicted the formation of a well-defined first hydration shell between 1.5 and 2.5 Å having a maximum at ~ 2 Å. For the Ψ and m 3 Ψ residues, the concentration of the water molecules around the HN1 atom was observed to be slightly higher with the FF99_χ ND _bsc0 force field than what was observed with the FF99_χ IDRP _bsc0 force field for each of the water models while for Ψm the concentration was observed to be slightly lower with the FF99_χ ND _bsc0 force field than what was observed with the FF99_χ IDRP _bsc0 force field for each of the water models. From the RDF plots of water oxygen atoms with respect to the HN3 atoms of Ψ, m 1 Ψ and Ψm nucleosides, with each of the force field and water model combinations, the formation of a well-defined first hydration shell was observed between 1.5 Å to 2.5 Å having a maximum at ~ 2 Å. For Ψ and m 3 Ψ, the concentration of the water molecules around the HN3 atom was observed to be similar with each of the force field and water model combinations. Interestingly, for Ψm, the FF99_χ ND _bsc0 force field parameters predicted a higher concentration of water molecules around the HN3 atom than what was predicted by FF99_χ IDRP _bsc0 in combination with each of the water models. The hydration pattern around pseudouridine (Ψ) corresponding to the FF99_χ ND _bsc0 and TIP3P force field and water model combination is shown in Fig. 7.

Orientation of the 2′-hydroxyl group of the Ψ, m 1 Ψ and m 3 Ψ nucleosides
The orientation of the 2′-hydroxyl groups of RNA has been reported to have a significant contribution to the stability of the A-form RNA helices [58] and also in RNA-protein interactions [59]. The A-RNA duplex has been suggested to be stabilized by a network consisting of water-mediated hydrogen bonds mediated by the 2′ hydroxyl groups and also the extensive individual hydration of the 2′ hydroxyl groups [60,61]. Kührova et al. (2014) reported that the choice of water model has a significant effect on the orientation of the 2′-OH atoms of nucleotides and hence also on the entire RNA structure [29]. The θ torsion angle (H2′-C2′-O2′-HO2′) populates three regions, the O3′ domain (value of θ between 50° and 140°), the O4′ domain (value of θ between 175° and 230°) and the base domain (value of θ between 270° and 345°) for the C3′-endo sugar pucker conformation [29,62]. It has been reported that the 2′-OH group when oriented towards the base domain can act as a hydrogen bond donor to a water molecule and when it is oriented towards the O3′ domain it can accept a hydrogen bond from the same water molecule  [58,60]. NMR studies at low temperatures suggested that the 2′-OH group can be oriented either towards the O3′ domain or towards the base domain and the predominant orientation of the 2′-OH group is reported to be towards the O3′ domain [63]. In the present study, we checked the effect of the combinations of the FF99_χ IDRP _bsc0 and FF99_χ ND _bsc0 force fields with the three different water models TIP3P, TIP4P-Ew and SPC/E, on the orientation of the 2′-OH atom corresponding to the Ψ, m 1 Ψ, and m 3 Ψ residues (Fig. 8). The distribution of the θ torsion angle (H2′-C2′-O2′-HO2′) angle was similar for each of the three water models for each modified residue. But the distribution differed between the two force fields. The O3′-domain was predominantly sampled (followed by the base-domain) by all the force field-water model combinations in agreement with the experimental and theoretical studies [29,63]. The population of the conformers with the 2′-OH atom oriented towards the O4′-domain were significantly lower than the population of the conformers with the 2′-OH atom oriented towards the other two domains. While a prominent peak was observed at the O4′-domain with the FF99_χ IDRP _bsc0 force field in combination with each of the three water models, the FF99_χ ND _bsc0 force field did not predict the same.

Effect of the substitution of U with Ψ in ssRNA oligomers
For further validation of the force field parameters, we have carried out molecular dynamics simulation of ssRNA trinucleotides AUA and AΨA and tetranucleotides AAUA and AAΨA and analyzed the effect of substitution of U with Ψ in ssRNA. The initial structures of the ssRNA trimers and tetramers in this study are shown in Fig. S16.

Conformational characteristics of ssRNA oligomers
Pseudouridine (Ψ) has been reported to preferentially adopt the anti base orientation within a polynucleotide chain context [16,17]. Although this modification has the same basic topology as uridine in RNA, it has been observed to confer rigidity upon both dsRNA and ssRNA regions [4,16,17,23,64,65]. It has been established that, generally, the population (in %) of the 3′-endo/NORTH conformers of an individual nucleotide, indicates the extent of base stacking corresponding to that nucleotide position within RNA oligonucleotides [66,67]. NMR study by Davis (1995) revealed that the substitution of U with Ψ promoted the C3′-endo/ NORTH sugar pucker conformation for Ψ and also for the nucleotides preceding the modified residue in the ssRNA oligoribonucleotides and hence results in enhanced base stacking and stabilization throughout the ssRNA molecule [22]. Ψ adopts a low anti conformation, constrains the base to an anti and axial conformation and hence facilitates the C3′-endo/NORTH and axial conformation of the nucleotide corresponding to the A-form RNA helix and rotation about the glycosidic bond from this C3′-endo/NORTH and anti conformation has been suggested to be highly disfavored [16,22,38,66,67].
In the present study we have theoretically investigated the effect of substituting U with Ψ in the AUA and AAUA oligomers and compared the results with the experimental observation [22,68]. It was observed that, in general, both the revised parameter sets FF99_χ IDRP _bsc0 and FF99_χ ND _bsc0 for Ψ in combination with the FF99_ χ OL3 _bsc0 for A/U reproduced the experimentally observed  [29,62] conformational properties of the ssRNA oligomers. In general, the FF99_χ OL3 _bsc0 parameter sets predicted somewhat greater population of the the NORTH conformers of the canonical nucleotides in the AUA and AAUA oligomers particularly in the 5′ direction than that observed in the experiment [22,68]. But, with each of the revised parameter sets, the AΨA and the AAΨA oligomers, adopted more stabilized A-form RNA structures compared to the canonical AUA and AAUA oligomers. For the oligomers under this study, we observed that the stabilization of the sugar pucker conformation was more prominent towards the 5′ direction than the 3′ direction which is consistent with the experimental data [22]. For the AΨA trimer, the FF99_χ ND _bsc0 parameters predicted a greater population of the NORTH conformers as well as that of the anti conformers for the 5′A and the Ψ nucleotides than what were predicted by the FF99_χ IDRP _bsc0 parameter sets (Tables S6-S7, Fig. 9). For the AAΨA tetramer, the sugar pucker conformations predicted by each of the revised parameter sets, were similar and of the parameter sets predicted a greater population of the NORTH conformers for Ψ and the preceding A nucleotide than the populations of the NORTH conformers of U and the preceding A nucleotide in the AAUA tetramer (Table S6, Fig. 10). But with the FF99_χ ND _bsc0 parameter sets, the population of the syn conformers corresponding to the 5′A nucleotide in the AAΨA tetramer was greater than what was observed with the FF99_χ IDRP _bsc0 parameter sets (Table S7, Fig. 10). The deviation of the terminal A residues (especially A(4)) from the A-RNA conformation is expected since the terminal residues in the AAΨA tetramer showed a tendency to deviate from the ideal A-form RNA helical conformation at 298 K in the NMR experiment reported by Davis (1995) [22]. In general, with each of the revised parameter sets, Ψ in AΨA trimer and AAΨA tetramer was observed to preferentially adopt a low anti conformation in agreement with the experimental data. For all the oligomers under this study, each of the constituent nucleotides preferentially adopted a g + conformation of the gamma torsion (Table S8). From the quasi-harmonic (QH) conformational entropy calculations we observed that the conformational entropies (S) of the AΨA and the AAΨA oligomers were slightly lower than those of the AUA and the AAUA oligomers suggesting the stabilizing effect of Ψ over U (Table S9).

Fig. 9
Population distributions of (1) pseudorotation angle (density vs pseudorotation angle) and (2) glycosidic torsion angle (density vs glycosidic torsion angle (χ)) of the individual nucleotides in AUA corresponding to the simulation with the FF99_χ OL3 _bsc0 force field parameters (black) and those in AΨA trimers corresponding to the simulations with the FF99_χ OL3 _bsc0 force field parameters for A and FF99_χ IDRP _bsc0 force field parameters for Ψ (green) and with the FF99_χ OL3 _bsc0 force field parameters for A and FF99_ χ ND _bsc0 force field parameters for Ψ (blue). The numbers given within braces beside the residue names indicate the residue numbers from the 5′ end to the 3′ end of the ssRNA trimers. The scale for pseudorotation angle (P) along the X-axis was converted to -90° to 270° to better delineate the NORTH (270° ≤ P < 90°) and SOUTH (90° ≤ P < 270°) regions

Fig. 10
Population distributions of (1) pseudorotation angle (density vs pseudorotation angle) and (2) glycosidic torsion angle (density vs glycosidic torsion angle (χ)) of the individual nucleotides in AAUA tetramer corresponding to the simulation with the FF99_χ OL3 _bsc0 force field parameters (black) and those in AAΨA tetramer corresponding to the simulations with the FF99_ χ OL3 _bsc0 force field parameters for A and FF99_χ IDRP _bsc0 force field parameters for Ψ (green) and with the FF99_χ OL3 _bsc0 force field parameters for A and FF99_χ ND _bsc0 force field parameters for Ψ (blue).The numbers given within braces beside the residue names indicate the residue numbers from the 5′ end to the 3′ end of the ssRNA tetramers. The scale for pseudorotation angle (P) along the X-axis was converted to − 90° to 270° to better delineate the NORTH (270° ≤ P < 90°) and SOUTH (90° ≤ P < 270°) regions The analysis of the intramolecular hydrogen bonding interaction revealed that in general, the propensity of the formation of intramolecular hydrogen bonds was greater in the oligomers containing the Ψ modification than their canonical counterparts (Tables S10-S11).

Hydration characteristics of ssRNA oligomers
The presence of an additional (N1H imino proton) hydrogen bond donor coordinating structural water molecules, has been reported to contribute to the structural and thermodynamic stabilization observed upon substitution of U with Ψ in RNA [9,15,16,64,69,70]. Auffinger and Westhof [30], reported the presence of long-lived water bridges between the OP2 atoms of Ψ32 and its preceding residue (C31) and the HN1 atom of Ψ32, from the results of MD simulations of the tRNA Asp anticodon hairpin performed using the AMBER FF94 force field in combination with SPC/E water and NH4 + ions. Interestingly, a string of two water molecules was observed to be involved in the waterbridging interaction between the N1H imino proton and the backbone phosphates of Ψ and the preceding residue within the context of a A-form RNA duplex from MD simulations using the FF99_χ IDRP _bsc0 parameter sets for Ψ and the TIP3P water model [21]. In the present study we observed certain changes in the hydration pattern of the oligomers upon replacement of U with Ψ.
From the analysis of the hydrogen bonding interactions of the N3H imino group of uridine (U) and that of the N1H and N3H imino groups of pseudouridine (Ψ) with the solvent molecules it was observed that, the number of occurrences of the N3-HN3⋯O hydrogen bonds for U were similar in the AUA and AAUA oligomers (Table S12). For the AΨA trimer, with each of the revised parameter sets, the number of occurrences of the ΨN3-ΨHN3⋯O(water) hydrogen bonds were observed to be close to that of the UN3-UHN3⋯O(water) hydrogen bonds observed in AUA. The FF99_χ ND _bsc0 parameters predicted somewhat greater number of occurrences of ΨN1-ΨHN1⋯O(water) hydrogen bonds than that predicted by the FF99_χ IDRP _bsc0 parameters. For the AAΨA tetramer, the number of occurrences of the ΨN3-ΨHN3⋯O(water) hydrogen bonds were lesser than that of the UN3-UHN3⋯O(water) hydrogen bonds observed in AAUA. With the FF99_χ ND _bsc0 parameters, the number of occurrences of the ΨN1-ΨHN1⋯O(water) hydrogen bonds was observed to be much greater than that predicted by FF99_χ IDRP _bsc0 for the AAΨA tetramer.
In general, the number of occurrences of water bridges involving the backbone atoms were low in all the oligomers under this study. The propensities of water bridge formation between the backbone atoms of Ψ with the backbone atoms of the neighbouring adenosine residues in the AΨA trimer were not much different than what was observed for U in the AUA trimer (Table S13). But with the FF99_ χ ND _bsc0 parameters, the number of occurrences of water bridge interactions between the backbone atoms of Ψ(2) and A(3) were slightly higher than what was predicted by the FF99_χ IDRP _bsc0 parameters. The presence of additional water bridging interactions involving the N1H imino group and the backbone atoms of Ψ were observed in the AΨA trimer, which are not possible for the AUA trimer due to the absence of the N1H imino group in U. The propensities of water bridge formation between the backbone atoms of Ψ with the backbone atoms of the immediate neighbour adenosine residues in the AAΨA tetramer were a little greater with the FF99_χ IDRP _bsc0 parameters than those predicted by the FF99_χ ND _bsc0 parameters (Table S14). The presence of additional water bridging interactions involving the N1H imino group Ψ(3) and the backbone atoms of Ψ(3) and its preceding adenosine (A(2)) residue were observed in the AAΨA tetramer and such interactions are not possible for the canonical AAUA tetramer. With each of the revised parameter sets, it was observed that the Ψ(3)OP2-W-Ψ(3)HN1 water bridges were more frequent than the Ψ(3) OP1-W-Ψ(3)HN1 water bridges and the A(2)OP2-W-Ψ(3) HN1 water bridges were more frequent than the A(2)OP1-W-Ψ(3)HN1 water bridges. Each of the revised parameter sets predicted the formation of the water bridge between the HN1 atom of Ψ and the OP2 (phosphate oxygen) atoms of Ψ and its preceding A nucleotide (i.e. the A(2)-OP2-W-Ψ(3)-OP2 & Ψ(3)-HN1 water bridge interaction mentioned in Table S14) within the AAΨA tetramer. The snapshots of a coordinating water molecule hydrogen-bonded to the OP2 atom of A(2) and the OP2 and HN1 atoms of Ψ(3) in the AAΨA tetramer corresponding to the simulations with the revised parameter sets FF99_χ IDRP _bsc0 and FF99_χ ND _ bsc0 for Ψ are given in Fig. S17.
The plots (Fig. S18) of the radial distribution function (RDF) of the water oxygen atoms with respect to the HN1 atom of Ψ in both the AΨA and AAΨA oligomers, indicated the formation of a well-defined first hydration shell between 1.5 and 2.5 Å having a maximum at ~ 2 Å and this observation was similar to what was observed for the Ψ nucleoside as well as for Ψ within duplex RNA [21]. The first hydration peak corresponding to the H5 atom of U was observed to be located at a further distance and with a lower concentration of water molecules. The RDF plots of water oxygen atoms about the geometric center of the OP2 and H5 atoms of U and that about the geometric center of the OP2 and HN1 atoms of Ψ indicated the presence of water molecules at a shorter distance between the base and the backbone of Ψ compared to that observed between the base and the backbone of U and the concentration of water molecules predicted by the FF99_χ IDRP _bsc0 parameters were greater than that predicted by the FF99_χ ND _bsc0 parameters (Fig.  S19). The formation of a well-defined first hydration shell with a peak at 0.55 Å, from the RDF plot of water oxygen atoms about the geometric center of the OP2 atom of A (2) and HN1 atom of Ψ(3) in the AAΨA tetramer was observed for each of the revised sets of parameters (Fig. S20a). But with FF99_χ IDRP _bsc0, the first hydration shell was located between 0 and 1.75 Å and had a much greater number of water molecules than that with FF99_χ ND _bsc0, located between 0.25 and 1.45 Å. The RDF plot of water oxygen atoms about the geometric center of the OP2 atom of A (2) and and the OP2 and HN1 atoms of Ψ(3) in the AAΨA tetramer showed formation of a well-defined first hydration shell between 0 and 1.05 Å with a peak at 0.45 Å, with the FF99_χ IDRP _bsc0 parameters (Fig. S20b). But with the FF99_χ ND _bsc0 parameters, the first hydration shell was observed between 0.15 and 1.15 Å with a peak at 0.55 Å, having a lower number of water molecules than what was observed with the FF99_χ IDRP _bsc0 parameters. In general, this observation also suggested the presence of the coordinating structural water between the HN1 and OP2 atoms of Ψ(3) and the OP2 atom of its preceding adenosine (A(2)) residue.

Conclusions
In the present study we derived a revised set of of partial atomic charges and glycosidic torsional parameters (χ ND ) for the nucleosides Ψ, m 1 Ψ, m 3 Ψ, and Ψm following a datainformed approach. At the individual nucleoside level, the partial atomic charges and glycosidic torsional parameters (χ ND ) were calculated by applying RESP fitting method to the lowest energy conformation of the quantum mechanical energy profile of a chosen conformational scheme and fitting the molecular mechanics energy profile to that scheme-specific quantum mechanical energy profile, respectively. The choice of a particular conformational scheme was dictated by the NMR results that reported a preference for the syn conformation for pseudouridine and its derivatives under study [54][55][56] and thereafter looking for the scheme that had the lowest energy value for the syn conformation.
The consequences of the application of the revised set of glycosidic torsional parameters (χ ND ) in combination with the revised γ torsion parameters (parmbsc0) developed by Pérez et al. [45] and the AMBER FF99-derived parameters [25] for these modified nucleosides were analysed using replica exchange molecular dynamics simulations. The newly derived parameters were validated by comparing the simulated conformational preferences with the available experimental (NMR) data as well as with the observations in Dutta et al. [26]. REMD simulations were carried out using the FF99_χ IDRP _bsc0 [24] and FF99_χ ND _bsc0 force fields in combination with each of the TIP3P, TIP4P-Ew and SPC/E water models. Three independent REMD simulations (each of 16 ns) were carried out in 16 temperature windows ranging from 300 to 400 K, resulting in 768 ns of simulation time in total for each system.
It was observed that there were significant differences in the description of the conformational properties of each of the modified nucleosides by different combinations of force fields and water models. The revised force field parameter sets (FF99_χ ND _bsc0) with the TIP3P water model was able to closely reproduce the experimentally observed sugar pucker preferences for each of the modified nucleosides in this study. The accuracy of the prediction of the population of the C3′-endo/NORTH conformers might be important for accurate reproduction of the C3′-endo/NORTH pucker conformation associated with the A-form RNA structures.
In general, the newly developed force field parameters (FF99_χ ND _bsc0) in combination with each of the water models under this study shifted the distribution of the base orientation for each of the modified nucleosides towards the syn conformation in contrast to the excess of anti conformations predicted by the AMBER FF99 and AMBER FF99_ bsc0 parameters [25,45]. But the population of the syn conformers predicted by the FF99_χ ND _bsc0 force field was observed to be less than that predicted by the FF99_χ IDRP _ bsc0 force field parameters. The choice of water model was not found to influence the description of the base orientation to a significant extent for the FF99_χ IDRP _bsc0 force field parameters. However, the FF99_χ ND _bsc0 force field in combination with the TIP4P-Ew water model resulted in a somewhat smaller population of the syn conformers in the case of Ψ and m 1 Ψ nucleosides and a significantly greater population of the syn conformers for Ψm than what were observed with the other two water models.
In earlier studies from our group [24,26], we reported that, at the single nucleoside level, the inclusion of the revised γ torsion parameters (parmbsc0) developed by Pérez et al. [45] along with the FF99_χ IDRP parameter sets did not reproduce the experimentally observed population of the g + conformers, but predicted a much larger g + population for pseudouridine and its derivatives. We also noted that the large population of g + conformers observed with the FF99_χ IDRP _bsc0 parameters might be necessary to maintain the g + conformation of a nucleotide as is observed in the standard A-form of RNA [37]. In the present study, we observed that the newly derived FF99_χ ND _bsc0 parameter sets also predicted a large population of the g + conformation for each of the modified residues. The populations of g + conformers for all the nucleosides under this study, predicted by each of the force field and water model combinations were similar and were much larger than that predicted with the FF99 parameters.
The observations from the calculations of the number of O5′-H5T⋯O4 and O2′-HO2′⋯O4 hydrogen bonding interactions for each of the modified nucleosides in this study, suggested that O5′-H5T⋯O4 hydrogen bonding interaction contributes to the stabilization of the syn base orientation [38] while the O2′-HO2′⋯O4 hydrogen bonding interaction may facilitate the anti base orientation.The orientation of the 2′-OH atom was observed to be similar for each of the modified residues under this study. All the force field water model combinations predicted the predominant orientation of the 2′-OH atom towards O3′ which was consistent with previous NMR results [63]. Interestingly, with the FF99_χ IDRP _bsc0 force field, a prominent peak in the O4′-domain was observed in the distribution of the θ torsion angle (H2′-C2′-O2′-HO2′).
Overall, the results from the simulations of the ssRNA oligomers in this study suggest that both the revised sets of parameters (FF99_χ IDRP _bsc0 and FF99_χ ND _bsc0) for Ψ in combination with the FF99_χ OL3 _bsc0 parameters were able to reproduce the conformational and hydration properties of the oligomers. We observed that the substitution of uridine with pseudouridine in the ssRNA oligomers resulted in the formation of a more stable A-form RNA helix conformation. With the application of the reoptimized partial atomic charges and the revised glycosidic torsion parameters (χ ND ) developed in this study, Ψ, within each of the AΨA and AAΨA oligomers, was observed to predominantly adopt the experimentally observed anti/NORTH conformation and the preferences were stronger than what was observed with the χ IDRP parameters. In the present study we also highlighted the effect of the presence of the pseudouridine modification in the hydration characteristics of the AΨA and AAΨA oligomers compared to their canonical counterparts. From our simulations, we observed and the occurrence of the water bridging interactions between the N1H imino proton and the phosphate oxygen atoms of Ψ and the preceding A residue in the AAΨA tetramer. The presence of a structural water molecule hydrogen bonded to the HN1 atom of Ψ(n) coordinating the phosphate oxygen atoms of Ψ(n) and A(n−1), is consistent with the experimental (crystallographic) evidence [70] and the model proposed in NMR studies [22,64,65,69] and might play a significant role in the stabilization of the A-form RNA structure.
Several studies have suggested the importance of the 1-methyl derivative of Ψ (m 1 Ψ) in mRNA therapeutics and this modification has a crucial contribution to the efficiency of the COVID-19 mRNA vaccines [71][72][73][74][75]. In our ongoing study, we are further validating our revised sets of parameters for the methyl derivatives of pseudouridine (i.e. m 1 Ψ, m 3 Ψ and Ψm) based on simulations of the ssRNA oligomers containing these derivatives. It would be interesting to investigate the effect of the presence of the methyl derivatives of pseudouridine within single stranded as well as double stranded RNA context on the conformational and hydration characteristics of such RNA structures, both experimentally and theoretically. The revised sets of parameters might be useful in the theoretical studies involving RNA structures containing such modifications and also in designing therapeutic antisense oligonucleotides.  Table S1. Frozen and restrained dihedrals during QM optimization in PES scan and MM energy minimizations. Table S2. Partial atomic charges for Ψ, m 1 Ψ, m 3 Ψ, and Ψm ribonucleosides. Table S3. Propensity (in %) for NORTH sugar puckering of Ψ, m 1 Ψ, m 3 Ψ, and Ψm ribonucleosides. Table S4. Fraction (in %) of base orientation states for Ψ, m 1 Ψ, m 3 Ψ, and Ψm ribonucleosides. Table S5. Fraction (in %) of γ conformational states for Ψ, m 1 Ψ, m 3 Ψ, and Ψm ribonucleosides. Table S6. Propensity (in %) for NORTH (C3′endo) sugar pucker conformation of the individual nucleotides in the ssRNA oligomers Table S7. Fraction (in %) of the anti and syn base orientation states of the individual nucleotides in the ssRNA oligomers Table S8. Fraction (in %) of g + conformation of the γ torsion angle of the individual nucleotides in the ssRNA oligomers Table S9. Conformational (quasi-harmonic entropy) entropy of the ssRNA oligomers Table S10-S11. Percent (%) of occurrence of intramolecular hydrogen bonding interaction of the ssRNA oligomers Table S12. Percent (%) of occurrence of hydrogen bonding interaction of the N3H imino group of uridine (U) and that of the N1H and N3H imino groups of pseudouridine (Ψ) with the solvent molecules for the ssRNA oligomers Tables S13-S14. Percent (%) of occurrence of water bridges formed by the backbone atoms in the ssRNA oligomers Fig. S1. Structures of Ψ, m 1 Ψ, m 3 Ψ, and Ψm ribonucleosides corresponding to the five conformational schemes. Fig. S2. Conformational scheme (SC5) used in this work for the Ψ, m 1 Ψ, m 3 Ψ, and Ψm ribonucleoside residues (along with the atom names). Figure S3. Energy profiles around χ torsional angles from QM calculations corresponding to the five schemes for the Ψ, m 1 Ψ, m 3 Ψ, and Ψm ribonucleoside residues. Figs. S4-S6. Population distribution of the Ψ, m 1 Ψ, m 3 Ψ, and Ψm residues corresponding to the different force field and water model combinations with the pseudorotation angle (P) along the x-axis and the glycosidic torsion angle (χ) along the y-axis for the three independent sets of 16 ns REMD simulations respectively. Figs. S7-S9. Population distribution of the Ψ, m 1 Ψ, m 3 Ψ, and Ψm residues corresponding to the different force field and water model combinations with the pseudorotation angle (P) along the x-axis and the gamma torsion angle (γ) along the y-axis for the three independent sets of 16 ns REMD simulations respectively. Figs. S10-S12. RDFs of water oxygen atoms around the HN1 atom of the Ψ, m 3 Ψ, and Ψm residues corresponding to the different force field and water model combinations for the three independent sets of 16 ns REMD simulations respectively. Figs. S13-S15. RDFs of water oxygen atoms around the HN3 atom of the Ψ, m 1 Ψ, and Ψm residues corresponding to the different force field and water model combinations for the three independent sets of 16 ns REMD simulations respectively. Fig. S16. Initial structures of the ssRNA trimers and tetramers in this study Fig. S17. Snapshots of a coordinating water molecule hydrogen-bonded to the OP2 atom of A(2) and the OP2 and HN1 atoms of Ψ(3) in the AAΨA tetramer Fig. S18. RDF of water oxygen atoms about H5 atom of U (for AUA and AAUA) and about HN1 atom of Ψ (for AΨA and AAΨA). Fig. S19. RDF of water oxygen atoms about the geometric center of the OP2 and H5 atoms of U (for AUA and AAUA) and about the geometric center of the OP2 and HN1 atoms of Ψ (for AΨA and AAΨA) Fig. S20. RDF of water oxygen atoms about the geometric center of the OP2 atom of A(2) and H5 atom of U(3) (for AAUA) and the geometric center of the OP2 atom of A(2) and HN1 atom of Ψ(3) (for AAΨA) and RDF of water oxygen atoms about the geometric center of the OP2 atom of A(2) and OP2 and H5 atoms of U(3) (for AAUA) and the geometric center of the he OP2 atom of A(2) and OP2 and HN1 atoms of Ψ(3) (for AAΨA).