van der Waals Parameter Scanning with Amber Nucleic Acid Force Fields: Revisiting Means to Better Capture the RNA/DNA Structure through MD

Abstract

Molecular dynamics simulations can be used in combination with experimental techniques to uncover the intricacies of biomolecular structure, dynamics, and the resulting interactions. However, many noncanonical nucleic acid structures have proven to be challenging to replicate in accurate agreement with experimental data, often attributed to known force field deficiencies. A common force field criticism is the handling of van der Waals (vdW) parameters, which have not been updated since the regular use of Ewald’s methods became routine. This work dives into the effects of minute vdW radii shifts on RNA tetranucleotide, B-DNA, and Z-DNA model systems described by commonly used Amber force fields. Using multidimensional replica exchange molecular dynamics (M-REMD), the GACC RNA tetranucleotide demonstrated changes in the structural distribution between the NMR minor and anomalous structure populations based on the O2′ vdW radii scanning. However, no significant change in the NMR Major conformation population was observed. There were minimal changes in the B-DNA structure but there were more substantial improvements in Z-DNA structural descriptions, specifically with the Tumuc1 force field. This occurred with both LJbb vdW radii adjustments and incorporation of the CUFIX nonbonded parameter modifications. Though the limited vdW modifications tested did not provide a universal fix to the challenge of simulating the various known nucleic acid structures, they do provide direction and a greater understanding for future force field development efforts.

Introduction

With the constantly expanding capabilities and applications of computer power, there is an ever-present motive to develop increasingly accurate methods to study biomolecular systems. Modeling of biomolecules using molecular dynamics (MD) simulations has been shown to be a valuable computational tool for understanding structure and subsequent dynamics.¹ This is especially the case when uncovering time-dependent motions that can be challenging to capture accurately through currently available experimental techniques.^2,3 In particular, MD simulations have been highly successful in modeling duplex DNA and well-ordered protein structures.⁴⁻⁷ These successes can be attributed to two key advances: developments in computer technology, such as adapted MD codes for accelerated GPU use,⁸ and major improvements to the available MD force fields.^3,5,9,10 Despite these advances, some challenges persist with modeling nucleic acid structures, such as the overpopulation of nonexperimental structures when simulating RNA¹¹⁻¹⁴ and the unraveling of common duplex structures.⁵

Decades of benchmarking and evaluations have provided a thorough record of the current limitations of the available Amber nucleic acid force fields.^5,15−17 These works have uncovered a hyper-tendency for hydrogen bonding, overstacking, and the overstabilization of infinite helices, to name a few.^3,18,19 Many of these issues have been attributed to a misbalance in the van der Waals (vdW) parameters, which have not been improved since their development in tandem with the original parm94 force field.²⁰ At their conception, Amber vdW parameters were defined by atom type—for example, all sp3-hybridized carbon atoms share the same vdW parameters, as do all sp2-hybridized carbon atoms.^20,21 These initial carbon and hydrogen atom type vdW parameters were originally fit to reproduce the densities and enthalpies of vaporization for alkanes and benzenes.^20,22 Concurrently, oxygen, nitrogen, and phosphorus atom vdW parameters were developed to reproduce neat liquid properties, as well as to fit lattice energies and crystal structures.²⁰ These parameters were incorporated into the parm94 force field via the Lennard-Jones (LJ) 6–12 potential—also called the LJ 12–6 potential (eq 1)—and setup so that the interactions are only calculated between two atoms in different molecules or two atoms at least three bonds apart in the same molecule (denoted “1–4 interactions”).²⁰⁻²²

1

R_ij is defined as the distance between atom i and atom j. The LJ repulsion and attraction parameters (A_ij and B_ij,, respectively) can be further defined in regards to the potential well depths of the atoms i and j interacting (ε_ij), which are specific to respective atom types—these terms are outlined in eq 2.²²

2a

2b

2c

2d

Though these parameters were considered cutting-edge, the field-wide shift to the use of Ewald’s methods as a standard practice in MD simulations disrupted the carefully calculated balance of forces within the force fields. Ewald’s methods, such as the commonly used Particle Mesh Ewald’s (PME), are a way of treating electrostatic interactions.^23,24 In these methods, rather than cutting off the electrostatic interactions at a particular radius, the potential is split into a direct space (cutoff) and a reciprocal part that together accurately represent the long-range electrostatics with the reciprocal part handled by an efficient FFT that considerably reduces the computational demand for MD simulations compared to standard Ewald methods.²⁵ Suddenly, including the long-range electrostatics that were previously omitted creates an imbalance in the force field, as the vdWs were initially fit to recreate neat liquid densities. Hence, the vdW forces became too attractive or too “sticky”. While this is a known phenomenon, this misbalance can be buried in the stability of canonical duplex nucleic acid structures. The symmetry and stability associated with base pairing and base stacking of a duplex structure can generally “hide” the issue at hand since slight over or under stabilization of base pairing or stacking does not affect the structure, only the thermal stability. Often, this force field discrepancy is prominent in single-stranded or nontypical structural simulations, such as is common in RNA structures and noncanonical DNA conformations.

While some may argue an entire reparameterization of Amber vdW parameters is required, previous works have shown that manipulation of the vdW parameters can greatly impact the resulting structural distributions.^11,26−28 Alteration of the backbone oxygen vdW radii allowed for MD simulation of the GACC RNA tetranucleotide in which the structural distribution more correctly matched experimental distributions, with lower populations of potentially anomalous structures that are inconsistent with the NMR data.¹¹ Furthermore, modifying vdW forces involved in intranucleotide base–phosphate interactions has been shown to moderately improve simulations involving RNA.²⁷ The reworking of vdW parameters has also been employed in efforts to correct the overestimation of stacking in nucleic acid systems.²⁸ Providing the knowledge that adjusting vdW parameters has had a positive impact on Amber MD with nucleic acids, this project explores the effect of vdW radii modification on both the structural distribution of this RNA tetranucleotide and B- and Z-DNA.

Methods

Multidimensional Replica Exchange Molecular Dynamics (M-REMD) Simulations

M-REMD utilizes replica exchanges across two dimensions to enhance sampling and reach convergence with less sampling time.²⁹ In this case, the two dimensions sampled were: (1) Hamiltonian: 8 topologies with modified O2′ vdW radii and (2) temperature: 24 temperatures ranging from 270 to 360 K. This created a total of 192 replicas. The model system chosen was the r(GACC) tetranucleotide. The r(GACC) tetranucleotide has been interpreted to have two NMR-observable structures: the A-Form Major and A-Form Minor, which are seen in a 3:1 Major/Minor ratio.¹² For this study, all simulations were initialized from the NMR-observable A-Form Major conformation.¹² The GACC RNA tetranucleotide was described with the Amber OL3 RNA force field parameters.³⁰ This force field includes the base AMBER ff99 force field,³¹ parmbsc0 corrections for α/γ nucleic acid backbone torsion,³² and χ OL3 torsion corrections for RNA.³⁰ Tetranucleotides were solvated in a truncated octahedral box using the OPC water model.³³ Sodium ions were added to neutralize the charge and an excess of NaCl ions was added to reach ∼200 mM concentration (estimated based on the initial volume) using the Joung–Cheatham ion model.^34,35 Modifications to the O2′ oxygen atoms were performed using parmed.py (v.3.4.0), producing a new topology file for each Hamiltonian.³⁶ In each topology, the vdW radii of the O2′ atom were increased by 10% and decreased by 7.5% in 2.5% increments. Exact radii values are provided in the Supporting Information (Table S1). A similar procedure was used for the runs with the applied vdW backbone force field modifications. Systems were built using the OL3 force field and the applied Lennard-Jones backbone (LJbb) parameters.²⁶ Then, the O4′ oxygens were modified back to the original vdW radii so that the Lennard-Jones modifications were only applicable to the OP1, OP2, O5′, and O3′ oxygen atoms.¹¹ These modifications are termed OL3 + LJbb for the remainder of the manuscript. The creation of each modified topology followed the method used for the OL3 topologies.

The 24 temperatures selected for M-REMD were calculated using a temperature predictor for REMD simulations.³⁷ Temperatures were calculated to target an ∼30% acceptance rate. Minimization and equilibration were achieved for all 192 individual replicas, following the protocols chronicled in our previous work.³⁸ Replicas for each of the independent M-REMD runs were minimized and equilibrated separately. Production dynamics for each of the 192 replicas were carried out in the NVT ensemble. Temperature was regulated using the Langevin thermostat with a collision frequency of 2 ps^–1 using the “ig = −1” option to randomly set the random number seeds at each restart.^39,40 An integration time step of 2 fs was used, and an exchange attempt time interval was set to 1 ps.⁴¹ The nonbonded direct space cutoff was set to 8.0 Å, and default AMBER particle mesh Ewald settings were used.²⁵ SHAKE was used to constrain the hydrogen bonds.⁴² Each replica was run for 450 ns for a combined total of 86 μs per independent run. All M-REMD simulations were performed with parallelized GPU pmemd (pmemd.CUDA.MPI) of the Amber22 modeling package⁴³ at the Texas Advanced Computing Center. Trajectory analysis was performed using CPPTRAJ v.6.1.0.^44,45 Conformational clustering was performed using the DBSCAN clustering algorithm.⁴⁶ Representative cluster structures were identified and named by comparing these structures to anomalous structures previously discovered by Bergonozo et al.²⁹ All representative structures varied by less than 1 Å (via RMSD) from previously determined structures and were confirmed to match through visual inspection. Example analysis scripts can be found in the Supporting Information.

DNA + LJbb Modification Simulations

The effect of increased van der Waals (vdW) radii was also investigated on the benchmark Drew–Dickerson Dodecamer (DDD) B-DNA system, as well as a Z-DNA hexamer. A clean starting structure was generated by removing any excess water molecules and counterions in the experimental structures (PDB 1NAJ(47) and PDB 1ICK(48) for B-DNA and Z-DNA, respectively). To investigate the role these alterations have in multiple settings, three of Amber’s most recent DNA force fields were used to parametrize the nucleic acids (bsc1,⁴⁹ OL21,⁵⁰ or Tumuc1⁵¹). The structures were then explicitly solvated with one of two popular water models, TIP3P⁵² or OPC,³³ in a truncated octahedron having a 10 Å buffer distance between the solute and the edges of the box. Using the Joung and Cheatham ion models,^34,53 net neutralizing NaCl was incorporated into the systems, followed by excess NaCl to create a biologically representative salt concentration of ∼200 mM.³⁵ This method follows the protocol described in our previous work evaluating Amber DNA force fields.⁵

Three sets of topology files were generated using parmed.py (v.3.4.0): one in which the vdW radii of the backbone oxygen atoms of just the terminal base pairs were increased, one in which the vdW radii of the backbone oxygen atoms were increased throughout the entirety of the DNA duplex, and one control system in which no edits were made to the atoms. Edits to the vdW radii follow the Lennard-Jones backbone (LJbb) parameters,^11,26 which increase the vdW radii (R_ieq 2c) of the phosphate oxygens by 0.0884 Å. Explicit R values for each force field and the modifications, as well as an infographic breaking down system set up, can be found in Supporting Information Table S2 and Figure S1, respectively.

For each parametrization method and vdW radii edited system, five independent replicas were created with randomized ions generated using CPPTRAJ.^44,45 Minimization and equilibration methods aligned with those from our previously published work.^5,15,54 Hydrogen mass repartitioning was used to double the time step from 2 to 4 fs in all DNA simulations.⁵⁵ Periodic boundary conditions alongside the particle mesh Ewald method were utilized to treat long-range electrostatics with a cutoff of 10 Å.^23,56,57 For DNA duplex systems of this size, a sampling time of no less than ∼3–5 μs is necessary to potentially reach convergence for the internal base pair structure and dynamics, excluding Hoogsteen base pair formation which occurs on a longer time scale.^2,58,59 Noting that, MD productions were run until each replica achieved at least 5 μs of simulation time, totaling 25+ μs for each force field parametrization setup. All DNA simulations were performed with parallelized GPU (pmemd.CUDA) of the Amber20 modeling package⁴³ at the Center for High Performance Computing at the University of Utah as well as at the Texas Advanced Computing Center. Analyses utilized the AmberTools20 CPPTRAJ package,^44,45 highlighting structural alignment between simulation and experiment.

Simulations Implementing CUFIX with DNA

CUFIX refers to the employment of the nonbonded fix (NBFIX) parameters in conjunction with Amber force fields. These corrections calibrate intermolecular forces with respect to experimentally measured values focusing on osmotic pressure through altering pair-specific atoms to the nonbonded interactions.^60,61 In nucleic acid systems, CUFIX introduces an additional atom type, ON2, for the phosphate oxygen atoms in order to differentiate them from the traditional Amber carboxylate atom type O2. The system set up for using CUFIX adjustments paralleled that of the LJbb modifications: the DDD and Z-DNA duplexes were separately parametrized by an Amber DNA force field (bsc1,⁴⁹ OL21,⁵⁰ or Tumuc1⁵¹), and CUFIX modifications were loaded into LEaP. More about conjoining CUFIX parameters with Amber force fields can be found on the Aksimentiev group’s webpage (https://bionano.physics.illinois.edu/CUFIX). The CUFIX parameters are essentially a systematic refinement of Lennard-Jones parameters and are brought in here to ensure a thorough survey of multiple popular methods for vdW modifications, alongside observing their influence on multiple Amber DNA force fields.

The solvation, minimization, and production followed that of the LJbb-modified systems. Production simulations were executed on parallelized GPU (pmemd.CUDA) of the Amber20 modeling package⁴³ at the Center for High Performance Computing at the University of Utah as well as at the Texas Advanced Computing Center. The AmberTools20 CPPTRAJ package^44,45 was utilized in analyses focusing on comparing structural aspects from simulation to experiment.

Results and Discussion

vdW Scanning in RNA

M-REMD Allows for an Apparent Convergence of the Complete Structural Distribution

Achieving convergence in simulation is critical in force field development, validation, and comprehensively understanding biomolecular dynamics.^29,62 However, conventional MD simulations struggle to achieve convergence of flexible RNA structures, even in simulations of lengthy timescales.⁶³ Enhanced sampling methods, such as replica exchange molecular dynamics, help biomolecules overcome high energy barriers more easily and achieve convergence in less sampling time.^29,62−65 In this project, the combination of Hamiltonian and temperature changes allowed for the simulations to achieve convergence in 86 μs per conformational ensemble. The overlapping histograms of the root-mean-square deviation (RMSD) histogram analysis in Figure 1 confirm that independent runs, in both sets of simulation parameters, sampled the same structures with the same frequency and are an indicator of convergence. To further evaluate convergence, we used the Kullback–Leibler divergence analysis of RMSD⁶⁶ and observed agreement between runs (Supporting Information, Figure S2) as well as similar exchange acceptance rates and round trip times between the runs (Supporting Information, Tables S3 and S4). With apparent structural distribution convergence achieved, we feel confident moving forward in analyzing the specific effects of modified vdW radii on the ensemble.

Figure 1.

RMSD histogram plots showcasing the frequency (population) of structures at a specific RMSD value from the A-Form Major reference structure. RMSDs were calculated every ten frames and included all replicas (every Hamiltonian and temperature combination) from each independent run. Calculations included all non-hydrogen atoms, mass-weighted, and referenced to the A-Form Major structure of r(GACC). Histograms of the independent runs are shown in red and blue, while the average between the two runs is shown in black. Error bars represent the standard deviation between the two runs.

Modified Oxygen vdW Radii Affect Structural Distribution

Previous studies have shown the large effects of small vdW radii modifications on the resulting structures and dynamics of RNA in simulations.^11,12,26,67 Our results follow these same observations. First, we observed a difference in the frequency in which each RMSD space is sampled with the inclusion of the LJbb force field modifications (Figure 1). Looking at the total aggregated ensembles of the two runs, there are prominent differences in the structural distributions; for example, the ensemble with the LJbb modifications produces a larger population peak at 0–2 Å and smaller population peaks for the remaining space sampled (Supporting Information, Figure S3). This is not a new finding; rather, it validates previous work performed on improving structural distributions of this same RNA tetranucleotide.¹¹

Sorting the ensemble by Hamiltonian, we can see that the modifications of the vdW radii of the O2′ have a compounding effect on many of the resulting structural populations (Figure 2). Here, results are focused on the 277K trajectories based on previous work done with the RNA tetranucleotide, though these trends are consistent across all temperatures sampled (Supporting Information, Figure S4).^11,29 Interestingly, the modifications do not vastly change the resulting A-Form Major populations. Most of the population peaks around ∼0.75 Å overlap, except for Hamiltonians that decrease the O2′ vdW radii of the OL3 simulations. This is confirmed by the clustering analysis, which revealed similar A-Form Major populations across the Hamiltonians between 30 and 36% of all frames with OL3 and between 48 and 53% of all frames with OL3 + LJbb modifications at 277K (Table 1). Thus, it can be concluded that increasing just the O2′ vdW radii is not enough to increase the percentage of frames spent in the A-Form Major structure. Rather, the addition of the LJbb modifications has the largest effect on the resulting A-Form Major population, which increases the percentage of frames from 33.6 to 52.5% with the “no change” populations. With the resulting A-form Minor populations, a combination of the LJbb modifications and O2′ vdW radii manipulations impact the frequency at which this structure is sampled. The OL3 + LJbb modifications generally decrease the time spent in the A-Form Minor structures compared to simulations without the LJbb modifications. However, in both simulation protocols, as the O2′ vdW radii decreases, the A-Form Minor population increases. This can be seen with the OL3 A-Form Minor populations (ranging 4.8–20.2%) and to a lesser extent with the OL3 + LJbb A-Form Minor populations (ranging from 5.2–9.7%). While the population changes within the NMR-observable structures are informative, a large portion of the simulation still samples nonexperimental structures regardless of which modifications are included.

Figure 2.

RMSD histogram plots depicting the populations of structures sorted by Hamiltonian at 277 K. RMSDs were calculated to include all non-hydrogen atoms, mass-weighted, and referenced to the A-Form Major structure of r(GACC). RMSDs included sorted trajectories from both independent runs, calculated using every ten frames. Trajectories with the O2′ vdW radii increased 10, 7.5, 5, and 2.5% are shown in red, orange, yellow, and gray, respectively. The trajectory with no vdW change is shown as a dashed black line. Trajectories with the O2′ vdW radii decreased by 2.5, 5, and 7.5% are shown in green, teal, and blue, respectively.

Table 1. Table Describing the Populations of A-Form Major, A-Form Minor, all Nonexperimental Structures, and the Largest Nonexperimental Structure Populations as Determined from DBSCAN Clustering of Trajectories at 277K^a.

Hamiltonian	% NMR Maj	% NMR Min	All non-NMR	largest non-NMR
OL3
10% increase	34.4	4.8	60.8	10.3% 3-extruded
7.5% increase	34.9	6.2	58.9	8% 3-extruded
5% increase	35.1	8.1	56.8	6.1% AformMin.1syn-dangle
2.5% increase	36.3	10.5	53.2	4.8% AformMin.1syn-dangle
no change	33.6	12.4	54.0	3.8% AformMin.1syn-dangle
2.5% decrease	32.1	14.8	53.1	2.9% intercalated Anti
5% decrease	30.9	17.5	51.6	3.5% intercalated Anti
7.5% decrease	29.2	20.2	50.6	4.4% intercalated Anti
OL3 + LJbb
10% increase	48.7	5.2	46.1	7.9% AformMin.1syn-dangle
7.5% increase	50.7	6.1	43.2	6.6% AformMin.1syn-dangle
5% increase	52.4	6.7	40.9	5.6% AformMin.1syn-dangle
2.5% increase	51.1	7.1	41.8	4.3% AformMin.1syn-dangle
no change	52.4	7.7	39.9	3.5% AformMin.1syn-dangle
2.5% decrease	53.1	8.3	38.6	3.2% AformMin.1syn-dangle
5% decrease	52.5	8.6	38.9	2.5% intercalated Anti
7.5% decrease	51.8	9.7	38.5	3.3% intercalated Anti

^aMore details on the cluster analysis, including all determined clusters, molecular graphics depicting cluster average structures, and a sample script of the cluster analysis used, can be found in the Supporting Information.

The resulting nonexperimental (anomalous) structures provide insight into the impact of manipulating the O2′ vdW radii. These anomalous structures lie in the RMSD space from ∼2.2 to 6 Å (Figure 2), and their trends are consistent across the simulation protocol. Populations between ∼2.2 and 3.5 Å from the reference structure increase with an increasing O2′ vdW radii. In particular, a shoulder at 3 Å begins to emerge with the OL3 simulations. This is characterized as the “3-extruded” structure, as revealed by clustering analysis (Supporting Information, Tables S5 and S6). As is seen with all of the characterized anomalous structures, the “3-extruded” structure has been previously reported on using a related simulation protocol.¹¹ This structure is similar to the A-Form Major structure, except the third base rotates 180° to remove itself from the base stack and interact with the solvent environment (Supporting Information, Figure S5). In addition, a population emerges at 4 Å as O2′ vdW radii decreases in both sets of simulation protocols. This structure is characterized as the “Intercalated Anti” structure in which the backbone curves into a loop and the bases stack in the newly created core. From the clustering analysis, a variation on the A-Form Minor, the AformMin.1syn-dangle structure appears. Though this structure is visually similar to the A-Form Minor, C4 is angled away from the other bases, violating the NMR restraints. Specifically, the C3 H2′ to C4 H6 and C3 H3′ to C4 H6 distance restraints are violated.¹² Various other anomalous structures, including but not limited to the “1–4 stack”, “2-extruded”, and “Inverted Syn” are revealed by cluster analysis. Molecular graphics depicting the A-Form Major, A-Form Minor, and resulting anomalous structures from each cluster can be found in the Supporting Information.

The rise in specific anomalous structures provides a window into the various inter- and intramolecular interactions that are influenced by changing the vdW radii. As the vdW radii of the O2′ atoms increase, structures stabilized by stacking and backbone–backbone interactions are the most populous clusters. These include the A-Form Major, A-Form Minor, A-Form Minor-1syn.Dangle, and the 3-Extruded. In all of the structures, the O2′ atom of each sugar faces the solvent environment, allowing for unobstructed Lennard-Jones interactions with the surrounding water. The stabilization of these structures may also be attributed to the water model choice. The selected OPC water model has an increased Lennard-Jones parameter compared to the widely used TIP3P water model.³³ This may contribute to the perceived favorable solvation of the O2′ atoms. On the other hand, as the vdW radii decrease, structures in which the O2′ atoms interact with the nucleobases increase in frequency. Particularly, interactions between the O2′ atoms and nitrogen atoms of the nucleobases are observed. Examples of this can be seen in the 1–4 base stack and Intercalated Anti anomalous structures that show an interaction between the backbone and nucleobase of the G1 nucleotide (Supporting, Figure S5). This can also be seen across bases with the G1 and C4 of the Inverted Anti (conformation 2) structure and Intercalated Anti-3-extruded structures. The increasing populations of these structures suggest that the electrostatic interactions between the partially positive N–H groups of the bases and the partially negative O2′ atom are overpowering the Lennard-Jones forces, among others. Supporting this theory, the average distance of the Na+ ions in solution decreases with decreasing O2′ vdW radii, suggesting increasing electrostatic interactions (Figure 3). Thus, we can conclude that these small vdW radii changes have a large impact on the balance between Lennard-Jones and electrostatic interactions. This leads to changes in environments that the O2′ atoms find favorable and therefore changes in the resulting stabilized structures.

Figure 3.

Histogram plots showcasing the frequency (population) of Na+ ions at each distance from the O2′ atoms of the RNA tetranucleotide. Trajectories with the O2′ vdW radii increased 10, 7.5, 5, and 2.5% are shown in red, orange, yellow, and gray, respectively. The trajectory with no vdW change is shown as a dashed black line. Trajectories with the O2′ vdW radii decreased 2.5, 5, and 7.5% are shown in green, teal, and blue, respectively. Only trajectories run at 277 K are shown here.

LJbb vdW Radii in DNA

Structural Agreement between Simulation and Experiment is Mildly Affected by Increased vdW Radii

Generally speaking, the available Amber DNA force fields model B-DNA rather well. The DDD sequence, d(CGCGAATTCGCG), is routinely used in benchmarking and evaluating parameters in DNA force fields^{5,32,49,68−72} due to its high-resolution NMR data in the solution phase (PDB 1NAJ(47)). For that reason, the dsDNA DDD sequence was employed to model the B-DNA structure and dynamics when vdW radii are adjusted. However, not all nucleic acid helices embody B-DNA characteristics and recent efforts in force field development have made strides in modeling noncanonical DNA structures (e.g., quadruplexes, Z-DNA).^15,50,54,73 In the continuing interest of progressing MD modeling of noncanonical nucleic acid structures, the LJbb modifications were incorporated into a Z-DNA hexamer, d(CGCGCG) (PDB 1ICK(48)), to observe the effect of helical stability when the vdW radii are altered. It is worth noting that DDD is an NMR structure while the Z-DNA structure is from X-ray diffraction (0.95 Å). Solution-phase MD does not inherently mimic crystal structures due to the absence of crystallization conditions (e.g., crystal packing) and other materials that may be present during the refinement process^5,74,75—though the structural deviations are markedly small.

Oftentimes, data describing structural alignment is shown in analyses excluding the terminal base pairs of a DNA sequence due to the known and expected presence of terminal base pair fraying^{5,16,59,76,77} (more on this later). With the addition of the LJbb modifications, we wanted to investigate the impact that the alternate vdW radii had on structural agreement when the terminal base pairs are included. To clarify terminology, the “CONTROL” systems have no modifications and strictly use the default vdW of the respective force field, “TERMINAL” systems have LJbb modifications made to the terminal two base pairs, and last, the “WHOLE” systems incorporate LJbb modifications throughout the DNA duplex.

When comparing the average DDD structure from the modified simulations to those of the default force field parameters, the adjustments made to the backbone oxygen atoms moderately improve structural agreement with the average NMR structure (Table 2). The OL21 force field sees the greatest impact in root-mean-square deviation (RMSD) value with an average decrease of ∼0.2 Å with the vdW modifications compared to the control. This is followed by bsc1 with an average decrease of ∼0.1 Å and Tumuc1 with ∼0.05 Å. Additionally, when parametrized with the TIP3P water model, OL21 and Tumuc1 saw a greater decrease when the vdW radii were modified only at the termini versus the whole backbone. These details aside, the overall improvement observed in the average RMSDs with the LJbb modifications on DDD is mild. Looking at the Z-DNA simulations, the bsc1 and Tumuc1 force fields see some improvement with the LJbb modifications (average change in RMSD value ∼0.3 Å and ∼0.2 Å, respectively), more so when paired with OPC water compared to TIP3P. When OL21 is used to parametrize the Z-DNA hexamer, the variations in vdW radii seem to have a negative effect by increasing the RMSD values—with the effect being amplified in the TIP3P systems—indicating that the structure is less consistent with the experimental.

Table 2. RMSD Values for the Average DNA Duplex Structures from Simulation Relative to the Respective Experimental Structure (DDD/B-DNA: PDB 1NAJ,⁴⁷ Z-DNA: PDB 1ICK(48)), Values Reported in Angstroms (Å)^a.

		DDD		Z-DNA
		TIP3P (Å)	OPC (Å)	TIP3P (Å)	OPC (Å)
bsc1	CONTROL	1.12	1.01	3.57	3.38
	TERMINAL	1.06	0.98	3.50	2.70
	WHOLE	1.05	0.93	3.33	3.06
OL21	CONTROL	1.31	1.36	0.72	0.68
	TERMINAL	1.09	1.18	1.13	0.73
	WHOLE	1.28	1.13	1.26	0.73
Tumuc1	CONTROL	0.81	0.85	3.51	4.01
	TERMINAL	0.72	0.88	3.49	3.71
	WHOLE	0.78	0.83	3.68	3.72

^aThe analysis excluded hydrogen atoms but included terminal base pairs in order to grasp the effect of the varying modification scenarios on the system dynamics.

Altering vdW Radii of Backbone Oxygen Atoms has a Minimal Impact on the DDD Structure

Honing in on the DDD dsDNA structure, the RMSD versus time analyses do not show a significant impact beyond there being a broader range of RMSD values when the modified vdW radii are present. The root-mean-square fluctuation (RMSF) of the atoms in the DDD duplex is not heavily influenced by the alternate radii apart from potentially increased fluctuations at the termini of the OL21 parametrized systems; this data can be found in Supporting Information, Figure S6. However, looking at the RMSD throughout the various simulations, we observe changes in the populations of various anomalous structures, largely in the TIP3P paired systems (Figure 4).

Figure 4.

RMSD histograms for the analysis of the DDD + LJbb systems, with the reference structure being the average NMR structure (PDB 1NAJ(47)). The top row shows systems modeled with TIP3P water, and the bottom shows systems modeled with OPC water. The analysis included all base pairs in the DDD duplex, highlighting the heavy atoms (excluding hydrogen atoms).

Focusing on the RMSD in Figure 4 from the TIP3P, the bsc1 parametrized systems appear to be the ones most largely affected by the vdW-modified radii. Modifications to the terminal (TERMINAL), as well as all (WHOLE) of the backbone oxygens atoms, reduce the population present between 2 and 3 Å. Furthermore, these alternate vdW radii increase the population existing less than 2 Å from the average NMR. The modifications made to the terminal oxygen vdW radii seem to have the greatest impact in this regard; however, there is an emergence of a noncanonical structure between 3 and 4 Å that is not present in the WHOLE or CONTROL systems. A similar scenario is observed in systems parametrized by OL21—the WHOLE systems have a rise in a structure between 3 and 4 Å that is not seen in the TERMINAL or CONTROL systems. When these modifications are added to the Tumuc1 parametrized B-DNA, there does not appear to be a significant change in structural population. This observation continues with the systems modeled with OPC water—there is minimal effect on RMSD values with the inclusion of the LJbb modifications.

If we look at the structures from the populations present in the TIP3P systems, the deviations from the NMR structure seem to lie largely in the terminal bases, this can be seen in Figure 5. The primary structures populated in all force field simulations lie ≤2 Å in RMSD value in reference to the average NMR structure, with the noticeable variation being a narrowing in the distance between the terminal base pairs, though this is rather minute. The straying of the terminal base pairs becomes more extreme in other lesser populated structures when DDD is modeled with bsc1 and OL21, where there are likely events of fraying opening the termini to alternate base-pairing interactions.

Figure 5.

(I) Reprint of the DDD + LJbb RMSD with TIP3P from Figure 4 with the addition of letters denoting populations of interest. (II) Average structures from the populations of interest in the DDD + LJbb RMSD analysis. Notable anomalies are highlighted in ROYGBIV colors, this includes bases noticeably closer in proximity and alternate base interactions.

Modified vdW Backbone Oxygen Radii Reduce Anomalous Populations at DDD Termini

With the continuous improvement of Amber nucleic acid force fields, fraying events are a common topic of discussion when modeling double-stranded nucleic acid systems, particularly dsDNA.^2,77,78 Characterization of fraying events has provided clarity in systems that have undergone extensive MD yet shown to be too dynamic to produce a single conformation.⁷⁶ Furthermore, simulations with Amber force fields have observed fraying events up to the sixth base pair in an 18-mer system, noting that there was eventual repairing and reformation of the duplex.⁵⁹ With that in mind, the DDD system is used here to probe the impact of these small vdW radii changes on various Amber DNA force fields and whether they lead to a change in fraying tendencies.

While modifying the vdW radii of the backbone oxygen atoms did not seem to have a dramatic impact on the overall structural agreement of DDD to experiment, it did reduce the population of an anomalous structure at the terminal base pairs (Figure 6). This impact can be best observed in the OL21 parametrized systems, namely OL21 + TIP3P. The OL21 terminal base pairs populate a distance closer than what is observed in the NMR (∼8.5 Å compared to ∼10.3 Å, respectively). The OL21 force field, in conjunction with the LJbb modifications, seems to reduce this anomalous conformation while increasing the population in greater alignment with the NMR distance. Similar behavior is observed in the bsc1 and Tumuc1 systems, although the change is arguably less notable. Tumuc1 had previously shown reduced fraying in modeling B-DNA,⁵ and the LJbb changes did not appear to have a negative effect on this and mildly improved the population distribution to be in greater agreement with the experiment. Overall, the improvement observed could be considered rather minor; however, the increase of vdW radii was small and modified only one aspect of the nonbonded force (eq 1). The positive influence is intriguing and could reveal a potential path of focus in improving the parametrization of terminal backbone atoms.

Figure 6.

Distance analysis of the terminal base pairs in the DDD + LJbb systems, the top half being systems modeled with the TIP3P and the bottom with the OPC water model. The distance was measured with respect to the center of mass (COM) of the terminal residues, ignoring hydrogen atoms. The orange dashed line denotes the measurement taken from the average NMR.

Modified vdW Radii Improve Z-DNA Structural Sampling with Tumuc1

The initial observations made with the average structure RMSD values from Table 2 did not lead to much optimism in terms of force field improvement in the presence of increased vdW backbone oxygen radii. As we looked at the B-DNA/DDD system, there was some minor decrease in RMSD values; however, as noncanonical structures become more common in MD research, it is important to evaluate the force field performance on a variety of structures. Here, we evaluated the same conditions imposed on the DDD structure with a Z-DNA hexamer (PDB 1ICK(48)), as Z-DNA possesses a left-handed helix in opposition to its right-handed B-DNA counterpart. We made a similar observation from Table 2 as those seen in the DDD system: though there is some improvement when the backbone oxygen vdW radii are increased, there is no drastic reduction in the average RMSD value to indicate a massive improvement in structural sampling. That is until we looked at the population distribution in Figure 7.

Figure 7.

RMSD histograms for the analysis of the Z-DNA + LJbb systems, with the reference structure being the X-ray structure (PDB 1ICK(48)). The top row shows systems modeled with TIP3P water and the bottom row shows systems modeled with the OPC water model. The analysis included all base pairs, highlighting the heavy atoms (omitting hydrogen atoms).

Looking at the Z-DNA RMSD histograms (Figure 7), bsc1+TIP3P and OL21+OPC parametrized systems did not see notable changes with the LJbb modifications. The OL21 + TIP3P experienced some adverse effects when the modifications were applied to the entire backbone—an increase in a population with RMSD ∼2.5 Å—but otherwise, no prominent impact. Similarly, bsc1 + OPC showed minimal changes beyond an uptick in population with RMSD ∼ 4.1 Å when the vdW radii are adjusted only at the duplex termini. The main point of interest for us was the change in distribution when the Z-DNA hexamer is parametrized by Tumuc1. Previous studies have shown an inability of Tumuc1 to model noncanonical DNA structures—specifically, DNA mini-dumbbells¹⁵ and Z-DNA.⁵ In the work modeling Z-DNA, Tumuc1 lacked the ability to establish and maintain key characteristics of the duplex—most notably the left-handed helicity.⁵ With the addition of the vdW radii modifications, there is a substantial increase in populations of structures with lower RMSD values and this is seen when the modifications are incorporated at just the termini as well as throughout the entire duplex backbone. Moreover, the RMSF analysis of the Tumuc1 + OPC parametrized Z-DNA shows a substantial reduction in atomic fluctuations when the LJbb modifications are employed—the RMSF alongside RMSD plotted against time analyses can be found in Supporting Information, Figure S7.

Separating the systems by the water model, we can get a better look at the structures being populated in the RMSD analysis (Figures 8 and 9). The bsc1 + TIP3P systems minorly populate a structure ∼1.3 Å from the experimental (A, Figure 8) and another at ∼2.6 Å (B, Figure 8) that strays from the X-ray structure at terminal nucleotides (residues 6 and 12). The straying intensifies in the dominant structure of this parametrization scenario (C, Figure 8) with the terminal nucleotides migrating toward the major groove. The variation in the presence of the LJbb modifications is that the A and B populations only exist when the vdW radii are increased and are entirely absent in the control systems. This suggests that the alteration in vdW radii of the Z-DNA backbone oxygen atoms may help populate structures closer to the experiment when parametrized by bsc1 + TIP3P. The primary structure (D, Figure 8) adopted by the OL21 + TIP3P parameters lies ∼1 Å from the experimental X-ray structure. The second populated structure (E, Figure 8) deviates at a terminal nucleotide (residue 12) and largely exists when the LJbb modifications are employed throughout the backbone oxygen atoms. This could mean that an increase of the vdW radii alone may not be necessary in the OL21 + TIP3P parametrization of Z-DNA to improve the experimental agreement. The addition of the LJbb modifications had the greatest positive impact on the Tumuc1 parametrization of the Z-DNA hexamer. Tumuc1 alone struggles to replicate Z-DNA, specifically the left-handedness that is essential to the structure. However, when the backbone oxygen vdW radii are increased, conformations populated lie ≤5 Å compared to spanning up to 10 Å without modifications. Before inciting too much excitement, the structures populated are still not perfect but they are an improvement. When the LJbb modifications are present at just the termini, there is a rise in a population ∼3.5 Å (F, Figure 8) similar to that of the primary conformation populated by bsc1 + TIP3P where the terminal nucleotides drift toward the major groove. Both modification scenarios grow the population at ∼4.5 Å (G, Figure 8), where the terminal nucleotides continue to move away from their intended positions, specifically residues 6 and 12. When only the default Tumuc1 parameters are in play, there is a complete loss of structural integrity (H, Figure 8). This indicates that a comprehensive re-evaluation of vdW radii could be imperative in enhancing the modeling of Z-DNA with Tumuc1.

Figure 8.

(I) Reprint of the Z-DNA + LJbb RMSD with TIP3P from Figure 7 with the addition of letters denoting populations of interest. (II) Average structures from the populations of interest in the Z-DNA + TIP3P RMSD analysis. Notable abnormalities are highlighted in the ROYGBIV colors.

Figure 9.

(I) Reprint of the Z-DNA + LJbb RMSD with OPC water from Figure 7 with the addition of letters denoting populations of interest. (II). Average structures from the populations of interest in the Z-DNA + OPC RMSD analysis. Notable structural aversions are highlighted in the ROYGBIV colors.

Moving to the OPC systems, the bsc1 parametrized system closest in RMSD value to experiment lies at ∼2.5 Å (A, Figure 9)—this population is absent in the control systems—but there are discrepancies at the termini similar to its TIP3P counterpart (B, Figure 8). The termini continue to divert toward the major groove in the highest populated structure (B, Figure 9), following suit with the TIP3P system. Adding the LJbb modifications at the terminal nucleotides does reduce this population; however, it establishes a third conformational population ∼4.2 Å (C, Figure 9) in which the terminal nucleotides do not appear to be as prominently in the major groove as other populations but there is alternate backbone orientation and base pair distances. The OL21 + OPC systems populate almost exclusively a single conformation ∼1 Å from the X-ray experimental structure. Moreover, the increase in vdW radii did not appear to have an impact on force field performance with this Z-DNA model. Again, where we see the most promising impact of the LJbb modifications is in the Tumuc1 parametrized systems. Without the vdW alterations, the structural populations exist to upward of 10 Å in the RMSD value. The three most prominent populations in the Tumuc1+OPC control systems (I, J, K in Figure 9) are all severely unrecognizable as Z-DNA duplexes; J and K arguably resemble B-DNA. The Z-DNA characteristics first start to be lost ∼5.5 Å (H, Figure 9), where nucleotides up to three bases can be seen straying dramatically from the midline. Fortunately, when the vdW radii of the backbone oxygen atoms are increased, the aforementioned populations decrease, if not become completely absent. The primary structures that are populated (E, F, G in Figure 9) are still, undesirably, 3–5 Å from the experimental but demonstrate alternate vdW radii being a promising route to pursue in terms of improving Tumuc1’s ability to model Z-DNA.

Increased vdW Radii did not Substantially Impact Terminal Base Pair Distances in Z-DNA

The distance between terminal base pairs was measured in relation to the COM of the nucleotides in order to observe the effect of alternated vdW radii on base pair fraying (Figure 10). In the bsc1 systems, there is minimal improvement when the LJbb modifications are present compared with when they are not. The increased vdW radii had no distinguishable effect on the OL21 parametrized systems, regardless of the water model. There is moderate improvement in the Tumuc1 + LJbb systems at the penultimate base pair, where the population nearing the experimental distance increased. Beyond that, the increased vdW radii do not appear to have an effect on terminal base pair fraying in these systems.

Figure 10.

Distance analysis of the terminal base pairs of the Z-DNA+LJbb systems: the top half shows systems modeled with TIP3P and the bottom with OPC water models. The distance was measured with respect to the COM of the terminal nucleotides, disregarding hydrogen atoms. The orange dashed line references the distance from the average X-ray structure.

CUFIX vdW Adjustments with DNA

Effect of CUFIX is Structure and Force Field Dependent

CUFIX references the NBFIX corrections in conjunction with Amber force fields. The expected effect of the modifications is a significant enhancement of the realism of MD simulations of supramolecular nucleic acid systems, for example, multilevel nucleic acid systems in which the nucleic acids interact with each other and with surrounding ions, nucleic acid–protein systems, and nucleic acid–lipid bilayer systems. Functionally, the parameters distinguish between phosphate oxygen atoms and carboxylate oxygen atoms, something not differentiated in bsc1 or OL21. CUFIX refines vdW parameters by redescribing amine–carboxylate, amine–phosphate, and aliphatic carbon–carbon interactions by fitting the osmotic pressure of simulated systems to experiential data. In theory, the refinement does not influence the existing parameters of bonded interactions and maintains solvation-free energies due to it only affecting the behavior of the water molecules in proximity to the solute and not explicitly altering solute-water interactions.^60,61 They are brought in here to benchmark with the DDD duplex and to ensure a thorough assessment of popular modified vdW parameters.

As with the LJbb modifications, the terminal nucleotides were included in all analyses in order to evaluate how the CUFIX modifications affected the modeling of the DNA duplexes in their entirety. Table 3 shows the RMSD values of the average structures from each parametrization setup of the DDD and Z-DNA simulations with CUFIX. In regards to the DDD systems, the CUFIX corrections bring the RMSD values subangstrom in reference to the experimental NMR structure in all bsc1 and OL21 simulations. The low values are notable as base pair fraying at the termini of nucleic acid duplexes typically affects the overall structural alignment with simulation and experiment, causing the RMSD value to be higher when the terminal base pairs are included (as they are here) in the analysis. This effect is not observed in the Tumuc1+CUFIX parametrization of DDD—rather, the RMSD values increase. When CUFIX is applied to the Z-DNA systems, there is a varying reduction in RMSD values of the bsc1 and Tumuc1 systems, but the OL21 + CUFIX systems have significantly higher RMSD values compared to the default parameters.

Table 3. RMSD Values of the Average Structures of the CUFIX DDD and Z-DNA Simulations in Reference to Their Corresponding Experimental Structures—1NAJ⁴⁷ and 1ICK,⁴⁸ Respectively^a.

		DDD		Z-DNA
		TIP3P (Å)	OPC (Å)	TIP3P (Å)	OPC (Å)
bsc1	CONTROL	1.12	1.01	3.57	3.38
	CUFIX	0.77	0.84	3.09	2.97
OL21	CONTROL	1.31	1.36	0.72	0.68
	CUFIX	0.75	0.82	3.32	2.83
Tumuc1	CONTROL	0.81	0.85	3.51	4.01
	CUFIX	1.00	0.89	3.07	3.00

^aAnalysis focused on heavy atoms, including terminal residues, and omitted hydrogen atoms.

Looking at histograms from the RMSD analysis (Figure 11), we can see that the CUFIX corrections have varying effects on the Amber DNA force fields. The bsc1 + CUFIX with the DDD system does make subtle improvements compared to the control parameters, especially when comparing the force field in conjunction with TIP3P water. When DDD is parametrized by OL21 + CUFIX, there is a noticeable shift in the RMSD histogram, indicating increased agreement with the experimental NMR structure. With Tumuc1 + CUFIX, the DDD structures appear to populate near identical space as the default parameters. Shifting to the Z-DNA portion of RMSD histograms (Figure 11, bottom row), the CUFIX modifications do not have a positive impact when used alongside bsc1 and OL21. There is quite a negative effect in the OL21 + CUFIX systems as RMSD values more than double. Lastly, consistent with the Tumuc1 + LJbb observations, there is a large improvement in distribution when the Z-DNA systems are parametrized by Tumuc1 + CUFIX. The structures sampled remain far from the experimental X-ray structure, especially when compared to the OL21 modeling of the structure, but this suggests that improvement in the vdW parameters is needed in the Tumuc1 force field to better model noncanonical DNA structures. Additional RMSD/RMSF analyses of the DDD and Z-DNA structures can be found in Supporting Information, Figures S10 and S11.

Figure 11.

RMSD histograms for the analysis of the CUFIX DDD (top) and Z-DNA (bottom) systems. Reference structures were the system’s relevant experimental structure (1NAJ⁴⁷ and 1ICK,⁴⁸ respectively). The analysis included all residues, omitting hydrogen atoms. The “CONT” label indicates the control parameters without any external modifications.

The results from the RMSD analysis of the Z-DNA + CUFIX simulations were somewhat surprising in that the addition of the CUFIX corrections worsened the performance of OL21 in modeling Z-DNA. Provided the results from the simulations with LJbb modifications, we hypothesized that the CUFIX corrections would have minimal, if any, impact on the parametrization of the DNA systems with the OL21 force field. However, there is an RMSD value increase from ∼1 Å in the default OL21 parameters to ∼3.5–4.5 Å when CUFIX is included (Figure 11, bottom row). The conformations at significant RMSD populations were extracted to gain a better picture of what structures were sampled throughout the simulations of Z-DNA + CUFIX (Figure 12). The results from the bsc1 + CUFIX parametrization of the Z-DNA structure almost mirrored the results of the bsc1 + LJbb Z-DNA simulations (Figure 9), with the most notable difference being in the conformation sampled by the third populations (denoted with the letter “C” in both Figures 9 and 12). The CUFIX corrections appear to maintain the backbone conformation, whereas the terminal residues collapse toward the major groove with the LJbb modifications. In the OL21 + LJbb simulations, the addition of the vdW modifications had no apparent impact on the modeling of the Z-DNA. When those modifications are exchanged for the CUFIX corrections, the force field accuracy in Z-DNA modeling is significantly reduced and produces major populations 3–5 Å away from the experimental structure (E, F, G in Figure 12), which is a dramatic contrast to the ∼1 Å RMSD value produced by default OL21 parameters. Looking at the structures sampled, the deviations arise in the modeling of the terminal residues where we observe the migration of those nucleotides toward the major groove when the CUFIX modifications are present. A prominent variation the CUFIX corrections impose on nucleic acid parametrization is the differentiation of the phosphate oxygen atoms from other carboxylate oxygens in the system, which are not separate atom types in the bsc1 and OL21 force fields. A misbalance here may contribute to insufficient backbone modeling of noncanonical DNA helices, such as the left-handed Z-DNA, allowing for increased dynamics in those terminal residues and movement toward the major groove. Similar to the LJbb modifications, the CUFIX corrections improved modeling of the Z-DNA structure when used in conjunction with the Tumuc1 force field. The population with the lowest RMSD value (H, Figure 12) is the closest to the experimental one (∼2.5 Å) we observe when the Z-DNA system is parametrized by a variation of Tumuc1 and the notable deviations lie in terminal residues 6 and 7. Apart from that, we continue to observe the degradation of Z-DNA structural maintenance, beginning with dramatic drifting of terminal residues toward the major groove (I, J in Figure 12) and culminating in complete loss of structural integrity in the absence of any force field modification (K, L, M in Figure 12). To reiterate previous observations, the addition of the CUFIX corrections does greatly improve the modeling of the noncanonical Z-DNA structure when parametrized by Tumuc1, but the structures sampled in these improved simulations remain to be an overall poor representation of the left-handed Z-DNA helix.

Figure 12.

(I) Reprint of the Z-DNA + CUFIX RMSD from Figure 11 with the addition of letters denoting populations of interest. (II) Average structures from the populations of interest in the RMSD analysis. Notable structural aversions are highlighted in ROYGBIV colors.

CUFIX has a Larger Impact on the Terminal Base Pair Distances than the LJbb Modifications

To observe the influence on terminal base pair fraying, the same distance analysis performed with the LJbb modifications was performed on the simulations with the CUFIX corrections (Figures 13 and 14). Observations made here in the DDD systems reflect those of the LJbb modifications, with CUFIX making an arguably greater impact than prior vdW alterations (Figure 13). The OL21 parametrized systems have the same increase in population in greater alignment with the experiment as observed with the LJbb modifications (Figure 6); however, the decrease in anomalous and increase in experimental populations is greater with the CUFIX corrections regardless of the water model. The bsc1 and Tumuc1 force fields do not show significant changes in terms of the populations of terminal base pair distances when the modifications are present compared to when they are absent.

Figure 13.

Distance analysis of the terminal base pairs of the DDD + CUFIX systems. The distance was measured with respect to the COM of the terminal residues, disregarding hydrogen atoms. The orange dashed line references the distance from the average NMR structure. The “CONT” label indicates the control parameters without any modifications.

Figure 14.

Distance analysis of the terminal base pairs of the Z-DNA + CUFIX systems. The distance was measured with respect to the COM of the terminal nucleotides, ignoring hydrogen atoms. The orange dashed line references the distance from the average X-ray structure. The “CONT” label indicates control parameters without any external modifications.

The behavior of the Z-DNA systems’ terminal base pair analysis follows suit of its RMSD analysis. That is, the CUFIX somewhat negatively affects the bsc1 and OL21 parametrization of the noncanonical structure, but Tumuc1 benefits from the addition of the corrections (Figure 14). The bsc1 + CUFIX and OL21 + CUFIX have decreased populations of structures closer in alignment with the experiment and this is amplified when they are conjoined with TIP3P water. In contrast, the structural distribution is more solidified in the Tumuc1 + CUFIX systems, with the termini establishing relational distances closer to the X-ray value compared to the control. These observations, alongside those regarding the LJbb modifications, jointly indicate that refinement of the vdW parameters is necessary to advance Tumuc1 as a reliable force field to model Z-DNA.

With terminal base pair fraying being a common occurrence in simulations of double-stranded nucleic acid systems, it is important to know what to expect from a force field. As stated previously, we are both aware of and anticipate base pair fraying at the termini of nucleic acid duplexes in MD. Furthermore, we have observed fraying up to six residues into an 18-mer duplex.⁵⁹ Due to its flexibility, there is no concrete way of experimentally benchmarking terminal base pair fraying, at least not yet. What needs to be taken into consideration is that these opening events are transient and reversible. In other words, it is critical that while terminal fraying is expected and will happen in MD, the bases return to a conformation that coincides with its relevant experimental structure. With that in mind, the terminal base pair distance analysis as a function of time for all DNA systems—both LJbb and CUFIX modifications—can be found in the Supporting Information (Figures S8, S9, S12 and S13). The figures illustrate the transient and dynamic nature of the terminal base pairs under the provided force field parameters. The glycosidic torsion angle χ has shown to be integral in base pair opening of nucleic acids,⁷⁶ and perhaps we have shown another variable—vdW parameters—that impacts this modeling of terminal base pairs. Biologically, fraying maintains important roles in the enzymatic processing of nucleic acids and a deeper understanding of the process may elicit more information to improve computational description of the phenomena.

Conclusions

Utilizing a variety of nucleic acid structures, we observed notable changes in the structure and dynamics of MD simulations as a result of the alteration of the vdW representations. With the RNA tetranucleotide, the M-REMD method was used to achieve apparent convergence and elucidate the effects of incorporating the LJbb parameters while scanning across various O2′ vdW radii. The largest change in the populations of the NMR-observable structures can be attributed to the addition of the LJbb force field modifications compared to solely using the OL3 force field. However, scanning across the vdW radii of the O2′ played a role in the distribution of structures between the NMR minor (A-Form Minor) and nonexperimentally observed structures. The resulting anomalous structures provided key insights into the specific interactions favored with changing O2′ vdW radii. For instance, with increasing O2′ vdW radii, structures for which the solvation of the O2′ atom was favored were more populous. With decreasing radii, structures with electrostatic interactions between the bases and ions in solution were more prominent. Further, O2′ vdW radii scanning did not produce new anomalous structures. All structures observed in this work have been previously reported in simulations using the r(GACC) tetranucleotide and the Amber OL3 force field.¹¹ Though these results did not improve the NMR Major to NMR Minor ratio to better match the experimentally determined 3:1, they do provide a better understanding of the influence that singular atomic vdW radii can have on the resulting MD simulation.

In regard to the DDD B-DNA structure evaluated, we did not observe a meaningful improvement in terms of simulation structural alignment with the experiment with the single increase of vdW radii of the backbone oxygen atoms (LJbb modifications). There was minorly improved occupancy of base pair distance values of the terminal nucleotides in the OL21 parametrized systems with the modified vdW radii. Though the LJbb modifications had minimal effect on the DDD simulations, the increase in the vdW radii was rather small, and given more comprehensive scanning, alternate vdW radii could be a promising route for the enhancement of terminal base pair modeling without impacting the overall force field performance, at least in the case of OL21. We saw more dramatic results of modified vdW radii in the Z-DNA simulations, specifically when the Z-DNA hexamer was parametrized by Tumuc1. We knew from previous work that, regardless of the water model, OL21 models Z-DNA significantly better than bsc1 and Tumuc1. The increased vdW radii did not necessarily have a positive impact when joined with the OL21 force field, suggesting that the OL21 parameters alone perform best in modeling the Z-DNA hexamer. There was a slight improvement in the bsc1 systems, but more substantial vdW radii changes may be necessary to make a definitive conclusion on the potential benefit of alternate vdW to the force field. The Tumuc1 simulations without the alternate vdW radii showcase a lack of ability to maintain the structural integrity of a Z-DNA structure, explicitly in the insufficient presence of left-handed helicity. However, when the backbone oxygen vdW radii are increased, there is a significant improvement in sampling conformations that somewhat preserve Z-DNA structural characteristics. These structures still fall short of the OL21 modeling of Z-DNA, so we continue to recommend the OL21 force field in conjunction with the OPC water model for the modeling of noncanonical DNA structures. Nonetheless, this could point to a deficiency in the Tumuc1 force field in regard to modeling Z-DNA and vdW radii may be an optimal direction to pursue in terms of force field development.

To evaluate multiple widely used vdW modifications, we employed the CUFIX corrections on the various Amber DNA force fields tested. Though the parameters were incorporated into all force field-water model combinations, it is important to note that the CUFIX has yet to be thoroughly validated for use with the OPC water model. That being said, in the systems shown here, we are not inclined to conclude that the alternate water model impacted the performance of the CUFIX parameters. The bsc1 showed subtle improvement in modeling DDD; however, there was generally no substantial impact of the CUFIX modifications on the force field. This, coinciding with the LJbb observations, suggests that vdW adjustments may not be an impactful route for bsc1 force field development. With OL21, we noted the positive impact CUFIX had in terms of simulating the B-DNA DDD structure and also the subsequent adverse impact when modeling Z-DNA. These OL21 observations, alongside those from the LJbb modification simulations, hint at vdWs playing a critical role in accurate force field function but that there is a harmony to uphold in order to successfully model both B- and Z-DNA well. Though there was minimal impact when modeling DDD, we did observe serious improvement when the CUFIX corrections were coupled with Tumuc1 to model Z-DNA. As with the LJbb modifications, the conformations sampled were undoubtedly more aligned with the experiment with the addition of CUFIX but still paled in comparison to the OL21 modeling of Z-DNA. All observations made with regard to Tumuc1 strongly indicate that the vdW parameters need to be re-evaluated before the force field can be aptly used to model noncanonical DNA helices.

The scope of vdW changes implemented here was relatively narrow and our intent was to investigate the influence this parameter had on the performance of various Amber nucleic acid force fields. We illustrated both the subtle and rather substantial impacts that alternate vdWs can have on simulating RNA, B-DNA, and Z-DNA helices. In their current state, we would continue to suggest MD simulations of nucleic acids, canonical and noncanonical, be parametrized with OL21 for DNA and OL3 with LJbb modifications for RNA, both accompanied by the OPC water model. It is clear that refinement of vdW parameters is a relevant track for force field advancement and more detailed testing, alongside scanning of other nonbonded parameters, will elucidate force-field-specific deficiencies and facilitate further force field development.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jctc.3c01164.

• Specific simulation details; modified vdW radii values for M-REMD; flowchart of system setup; RMSD versus Time, RMSF of DDD + LJbb; terminal base pair distances versus Time of DDD + CUFIX representative structures; and example CPPTRAJ analysis scripts (PDF)

Author Contributions

^† O.L. and L.W. contributed equally to this work.

The authors declare no competing financial interest.

Notes

Software Accessibility Free software used in this work can be accessed at the following links: AmberTools (https://ambermd.org/AmberTools.php), Grace (https://plasma-gate.weizmann.ac.il/Grace/), and VMD (https://www.ks.uiuc.edu/Development/Download/download.cgi?PackageName=VMD).