Simulations of RNA base pairs in a nanodroplet reveal solvation-dependent stability

Abstract

We show that RNA base pairs have variable stability depending on their degree of solvation. This finding has far-reaching biological implications for nucleic acid structure in a partially solvated cellular environment such as inside RNA–protein complexes. Molecular dynamics simulations of partially solvated Watson–Crick RNA base pairs show that whereas water serves to destabilize a base pair by competing for and disrupting base–base hydrogen bonds, when sufficient water molecules are present, fewer hydrogen bonds are available to disrupt the base pairs and the destabilization effect is reduced. The result is that base pairs exist at a stability minimum when solvated in between 20 and 100 water molecules, the upper limit of which corresponds to the approximate number of water molecules contained in the first hydration shell.

At the local level, the 3D structure of RNA is dominated by base-pairing and base-stacking interactions(1). Together base-pair and base-stacking interactions combine to form the ubiquitous double helix, which comprises a significant fraction of RNA structure.

Many different types of base pairs have been identified in RNA (2–4). A sheared base pair between adenine and guanine (throughout the text we refer to the nucleotides or nucleosides by the identity of their nitrogenous base) often terminates a tetraloop (5), whereas a reverse Hoogsteen base pair is often observed as part of a loop E or sarcin/ricin loop motif (6, 7). The most common and most recognizable are the Watson–Crick base pairs, with 60% of nucleotides in the ribosome being involved in these canonical interactions (8). Adenine and uracil form two hydrogen bonds and the AU base pair, and guanine and cytosine form three hydrogen bonds and the GC base pair, with the latter being more stable (9).

Hydrogen bond strengths have been shown to depend on their environment. In particular, it was shown that hydrogen bonds can strengthen in nonaqueous solutions because, in part, of increased charge density on the atoms involved (10). It follows that base pairs can also vary in stability depending on their surroundings, and isolated base pairs have been shown to be significantly more stable in vacuum than in solution (11). The supposition is that water alters the balance between the various factors stabilizing a base pair, including hydrogen bonding, the hydrophobic effect, and charge–charge interactions. For instance, water might act to destabilize the base–base hydrogen bonds, which in turn destabilizes the base pair. Furthermore, the interaction of RNA with the surrounding water has been shown to heavily influence the stability of duplexes (12). RNA is not alone in this as the interaction of proteins with water also plays a significant role in their stability (13, 14).

In biology molecules typically do not exist in a vacuum or fully solvated in water, instead finding themselves partially solvated in a cellular matrix. At one extreme lies viral genomes, which are compressed up to 800-fold compared with their solution structures when packaged inside viral capsids (15). A more moderate example is RNA polymerase II where the DNA–RNA hybrid duplex is largely surrounded by protein rather than fully exposed to the solvent (16).

In this work, we simulate AU and GC base pairs under a variety of solvation conditions, including in a vacuum, fully solvated in bulk water, and contained in different sizes of water nanodroplets (17). Nanodroplets are small systems where we solvate base pairs in an arbitrary number of water molecules to obtain partially hydrated structures. We show that, as expected, the GC base pair is more stable than AU, but that rather than being the least stable in bulk water, base pairs exist at a stability minimum between ≈20 and 100 water molecules. The net stability is the result of the hydrogen bonding potential of the surrounding water and not the number of water molecules itself. This finding may have implications for cellular environments where molecules are not completely solvated in water.

Results and Discussion

A Stability Minimum for Base Pairs.

We use the term nanodroplet to refer to a droplet of water on the order of size of a single macromolecule. For our RNA base pairs this means nanodroplets containing between 1 and 250 water molecules. Typical nanodroplets are illustrated in Fig. 1. We use 100 different starting configurations of each hydration condition and also perform simulations of base pairs in a vacuum and fully solvated in bulk water.

Fig. 1.

Two different nanodroplets are shown: one with 10 water molecules (Upper) and the other with 100 water molecules (Lower). The base pair is shown in green, and the water is in blue. With only 10 water molecules, the surface coverage of the base pair is sparse; with 100 water molecules, it is completely covered.

Rmsd is not a good metric to monitor base-pair stability as different nonpaired conformations give vastly different rmsd values. Instead we analyze 100 frames from each simulation (1 frame every 2 ps) and determine whether or not the two nucleosides are in a base-paired conformation by their hydrogen-bonding patterns. Rather than a continuous function like rmsd, we now have only two values: paired or unpaired. From this we calculate the time of first breakage, which is the amount of time it takes for the base pair to break for the first time in the simulation, and the total amount of time the two nucleosides are base-paired during the simulation. Both quantities are informative because the base pair is capable of breaking and reforming several times over the course of a simulation. We can also subtract the time to first breakage from the total amount of time paired to give us a more specific measure of how often the base pair reforms during the simulation.

Fig. 2 shows each of these three values for both AU and GC over the complete range of nanodroplet sizes, and a similar trend is observed in each case. As expected, GC is more stable than AU for every simulation condition. The base-pair stability is initially high, but decreases sharply as water molecules are added to the system, until a stability minimum is obtained between ≈20 and 100 water molecules. Then, as the number of water molecules increases above 100, both AU and GC are slightly stabilized, approaching the stability observed in bulk water as determined by simulations using periodic boundary conditions.

Fig. 2.

Calculated values for different size of nanodroplets. (A) The time (percentage of the 200-ps simulation) at which the base pair breaks for the first time in the simulation, with each data point showing an average over 100 simulations. (B) The total amount of time (percentage) spent base-paired over the course of the simulation. (C) The time (percentage of remaining time) that the system is base-paired after the initial breakage. In all three cases, values for AU are indicated by blue circles, and GC values are indicated by red squares. Solid horizontal lines indicate the values obtained from corresponding simulations in bulk water. Error bars indicate the standard deviation of averages between 10 random subsets of 10 simulations each. The trend for all three plots is similar with a sharp initial drop in stability, a minimum between ≈20 and 100 water molecules, and then a small rise in stability to approach the value observed in bulk water.

In bulk water hydrogen bonds are constantly breaking and forming, but the overall network of water–water hydrogen bonds remains similar over time. As we change the nanodroplet sizes, however, this is not the case. With only a few water molecules in a nanodroplet there are few water–water hydrogen bonds, and water molecules are most likely to form hydrogen bonds with the base pair. When additional water molecules are added, the network of water–water hydrogen bonds slowly builds up as water molecules more readily find other water molecules to hydrogen-bond with. As this network grows, it affects the way in which water molecules are able to interact with the base pair in the system. We propose that as water molecules are added beyond the first 100, they serve to distract other water molecules from the base pair, yet contribute no added potential for disrupting the base pair. It simply becomes easier for a water molecule to hydrogen-bond with another water molecule, rather than disrupt the base pair.

To test this theory we calculated how many potential hydrogen bonds were “available” to disrupt the base-pair hydrogen bonds in each size of nanodroplet. The number of available hydrogen bonds is the sum of all possible hydrogen bonds from all water molecules at the surface of the base pair minus all water–water hydrogen bonds that are already formed by those surface water molecules. In essence, the higher the number of available hydrogen bonds, the greater the potential for the water molecules to hydrogen-bond with the base pair.

Each water molecule can contribute up to four available hydrogen bonds. For example, in the nanodroplet with only one water molecule, there will be four available hydrogen bonds because there are no other water molecules with which to interact. In a nanodroplet with two water molecules there would be eight available hydrogen bonds if the water molecules are not interacting, or only six if the two water molecules form a hydrogen bond (each water molecule has formed one hydrogen bond and has three potential hydrogen bonds remaining). We include only potential hydrogen bonds from surface water molecules, which are defined as water molecules whose oxygen atoms are within 5.4 Å of any base-pair heavy atom. This classification corresponds to the definition of a Shell 1 water from Raschke and Levitt (18). We calculate the number of available hydrogen bonds for the first 10 ps of all 100 simulations, a period during which the water molecules have had time to equilibrate but the base pair is still intact.

Fig. 3 shows the total number of available hydrogen bonds for every nanodroplet size. The number of available hydrogen bonds increases quite sharply initially, reaching a maximum between ≈70 and 100 total water molecules before dropping off again. As the number of available hydrogen bonds drops, it approaches the number seen in bulk water. This trend correlates with the observed base-pair stability, where base-pair stability is at a minimum when hydrogen-bond availability is at a maximum. This observation suggests that the stability or rather the instability of base pairs is a direct result of hydrogen-bond interactions with water.

Fig. 3.

The average number of available hydrogen bonds for different sizes of nanodroplets and the AU base pair (blue circles). Available hydrogen bonds are the total number of potential hydrogen bonds from water molecules on the surface of the base pair that are not involved in water–water hydrogen bonds. Error bars indicate the standard deviation of averages between 10 random subsets of 10 simulations each. The average number of available hydrogen bonds in bulk water is indicated by the dashed line. The number of available hydrogen bonds correlates well with the stability of the base pairs; base pairs become less stable as the number of available hydrogen bonds increases.

Water Is a Hydrogen-Bond Disrupter.

Visualizing our simulations reveals the role of water as a hydrogen-bond disrupter. In the very small nanodroplets a water molecule is free to roll across the surface of the base pair until it comes into contact with a base–base hydrogen bond, which it often then breaks. The water molecule mediates the base–base hydrogen bond breakage by forming a hydrogen bond with one of the bases itself. In the larger nanodroplets the water molecules have less freedom to migrate over the base-pair surface, but still seek out and disrupt base–base hydrogen bonds.

In addition to our simulations where we randomly vary both starting water configuration and random number seed for the simulation, we performed simulations where we varied only the random number seed, but kept the same starting nanodroplet configuration for 100 simulations. In these simulations there was very little variability in the time to first breakage (data not shown), especially as compared with the simulations with 100 different water configurations. We noticed that the fortuitous placement of a water molecule immediately beside one of the base-pair hydrogen bonds would routinely cause rapid breakage of the base pair. This observation highlights the role of water as a hydrogen-bond disrupter that breaks base–base hydrogen bonds by directly interacting with them.

The Relative Contributions of Hydrogen Bonds to Stability.

Given that the GC base pair has three hydrogen bonds, whereas the AU base pair has only two, it seems almost a given that the GC base pair is more stable. Indeed, our own results confirm this fundamental observation, but it is interesting to note that the stability difference is not consistent across the entire range of nanodroplet sizes.

In Fig. 4 we plot the total amount of time spent in the base-paired conformation (Fig. 2B), normalized by the number of hydrogen bonds in each base pair. We then subtract the AU value from the GC value, giving us the difference in stability on a per-hydrogen-bond level. In systems with more than ≈15 water molecules, every hydrogen bond contributes equally toward stability, and the AU and GC base pairs have essentially the same normalized stability. However, with <15 water molecules, each GC hydrogen bond has a greater contribution to stability, and the difference between the AU and GC base pairs is magnified.

Fig. 4.

The total amount of time spent in the base-paired conformation over the entire simulation, normalized by the number of hydrogen bonds (two for AU and three for GC). The original values are seen in Fig. 2B. AU (blue circles) and GC (red squares) have approximately the same per-hydrogen-bond stability in systems with more than ≈15 water molecules, but at smaller sizes each hydrogen bond in the GC base pair has a higher relative contribution to stability compared with the hydrogen bonds in AU (orange diamonds). In each case, the bulk water values are indicated by a dashed line, and error bars represent the standard deviation between averages of 10 random subsets of 10 simulations each.

When the pool of available water molecules is limited, the additional hydrogen bond is significantly more stabilizing. Two water molecules might be sufficient to completely disrupt an AU base pair, whereas a GC base pair would remain paired, albeit probably briefly, by a single hydrogen bond. However, as the number of water molecules increases, they are present in sufficient number to interact with all base-pair hydrogen bonds, and the additional GC hydrogen bond is relatively less important.

Relevance to Molecular Dynamics.

The observation that a base pair inside a large nanodroplet mimics the behavior of a base pair in bulk water provides one possible method by which molecular dynamics simulations might be accelerated. A typical simulation spends a large portion of its computational time dealing with the numerous water molecules. By removing a large fraction of the water molecules, one could reduce the computational burden and thus accelerate the simulation while still obtaining the same results. Indeed, recent simulations of hen lysozyme solvated in a layer of water only two or three molecules thick shows similar results to bulk water simulations (19). Further simulations under a wide variety of conditions, especially including positively charged ions that are crucial to the tertiary structure of RNA, are required to confirm that the observation bears out in more complex systems.

Relevance to DNA and Proteins.

Although we include only RNA nucleosides in our simulations, their structure is similar enough to the DNA nucleosides that we do not anticipate any major differences between the two nucleic acids in terms of the stability effects observed. A recent study (20) compared the effect of mild dehydration on hydrogen-bond lengths in both DNA and RNA using NMR spectroscopy. Manalo et al. (20) demonstrated that the addition of 8 mol% ethanol to an aqueous solution caused a slight hydrogen-bond length shortening in both nucleic acids, suggesting that DNA base pairs should respond similarly to RNA in our own simulations.

Furthermore, although we do not present any data on proteins or amino acids, it is reasonable to assume that similar stability effects could be demonstrated in these systems as well. Both protein and RNA molecules contain networks of hydrogen bonds, and although there is no direct counterpart to the base pair in a protein, both α-helices and β-sheets are stabilized by hydrogen bonding.

Relevance to Structured RNAs.

Although our simulations deal entirely with single base pairs, it is important to consider the potential impact of the observed effects on structured RNAs. To do this we collected the positions of all of the water molecules responsible for attacking and hydrogen bonding with the base pairs in all of our simulations. To eliminate redundancy, we considered only the frames from our molecular dynamics simulations before the time of first breakage and only the first attack on each base pair hydrogen bond. We oriented the water molecules around a reference base pair, and then superimposed these positions onto an RNA double helix. We then eliminated all water molecules that overlapped with the double helix, based on overlapping van der Waals radii of any atoms.

For the AU base pair, only 33% of water molecules attack from a position that is not completely blocked by the double helix, and for the GC base pair the figure rises to 44%. This increase is caused by the third hydrogen bond in GC, which enables water access from the minor groove of the double helix. These results suggest that the solvation-dependent effects we observe will be reduced, but not eliminated in base pairs that are part of a double helix or other tertiary structure elements. Fig. 5 illustrates the positions of attacking water molecules for the GC base pair.

Fig. 5.

GC water attack positions of a single base pair superimposed on a double helix. The double helix is shown in green with a surface representation, and the blue sticks indicate water molecules in position to attack a base-pair hydrogen bond. (Left) The major-groove view. (Right) The major-groove view rotated 180° to show the minor groove. These are the water molecules that attack the base-pair hydrogen bonds, which remain after filtering for overlap with the double helix.

It is also worth noting that for both AU and GC the major-groove hydrogen bond is attacked first in the majority of cases. In the AU base pair there is a 5-fold enrichment compared with initial attacks on the second hydrogen bond, whereas in GC the major-groove hydrogen bond is attacked first almost twice as often as the minor-groove hydrogen bond. We do notice cases of simultaneous attack on multiple hydrogen bonds, but it is impossible to say whether or not there exists any cooperativity strictly from our simulations.

Relevance to Biology.

By changing the number of surface water molecules, we are able to alter the stability of a base pair. This suggests a possible mechanism by which molecular stability might be modified in a cell where a vast range of environmental conditions is possible. An enzyme or organelle might change the number of water molecules at the surface of an RNA, thereby changing the number of potential hydrogen bonds presented to the RNA and increasing or decreasing its stability. Although we do not suggest that our nanodroplets are an effective mimic of the cellular matrix, it is plausible that any condition we are able to generate could be easily duplicated inside a cell. Incorporating the full complement of cellular components could only have the potential for a more dramatic effect in vivo.

Consider, for example, viral capsids, which are densely packed with a nucleic acid genome. When a dsDNA genome is packaged into a bacteriophage, it undergoes an 800-fold compression in terms of its volume compared with the free DNA in solution (15). Bhella et al. (21) estimated the genomic radius of human cytomegalovirus and herpes simplex virus type 1 based on the method of Earnshaw and Harrison (22). Their figures of 497 and 472 Å for the genomic radii matched very closely the internal capsid radii of 500 and 475 Å of the two virions, respectively. The result of such dense packaging is that there is little room for water inside the viral capsid, and the internal conditions are more similar to our small nanodroplets. One possibility is that the increased stability of the base pairs at low water conditions contributes to the stability of the viral genomes, which are under both increased mechanical stress and increased electrostatic stress from the compaction of the nucleic acid backbone's positive charge.

Another situation where semiaqueous conditions occur is in large supramolecular complexes. The structure of the RNA polymerase II elongation complex revealed a DNA–RNA hybrid duplex surrounded by a large protein complex (16). Using the x-ray structure (Protein Data Bank entry 1I6H), we solvated both the entire protein–nucleic acid complex and the isolated nucleic acid component in a box of water. Without performing any simulations, we simply counted the number of water molecules surrounding the nucleic acid's surface in the shell 1 region. The nucleic acid component in the context of the protein complex is surrounded by only 70% of the shell 1 water molecules that surround the isolated nucleic acid in bulk water, because space is being occupied by the protein. This represents a significant reduction in the solvation of the hybrid duplex, with the potential for affecting its stability.

Admittedly, it is difficult to precisely predict the effect that the reduction in solvation will have on any of these biological systems based on our simple base-pair simulations. In addition to fewer water molecules, there is the introduction of other external factors, such as RNA polymerase itself in our second example. The protein introduces hydrophobic moeities and additional hydrogen-bonding possibilities with its many amino acid side chains.

Conclusion

We have confirmed that the GC base pair is more stable than the AU base pair under a complete range of solvation conditions with the Encad force field. With >15 water molecules in the system, each hydrogen bond contributes equally, but below this number the GC hydrogen bonds have a higher relative contribution to stability than the AU hydrogen bonds. Unexpectedly, base pairs are not least stable in bulk water, but exist at a stability minimum in nanodroplets containing between ≈20 and 100 water molecules. This is a function of the number of water hydrogen bonds that are available to compete with base-pair hydrogen bonds. This number tends to increase until nonsurface water molecules start to accumulate in the system, at which point the base pair stability increases to reach the level seen in bulk water. These nanodroplet simulations support the biological relevance of molecular dynamics simulations in bulk water and give a glimpse into how the cell might affect stability by altering the surrounding environment of a molecule.

Methods

Simulation Conditions.

We started by generating standard Watson–Crick geometry AU and GC base pairs using the Encad package (23). We include the nucleoside, meaning the nitrogenous base and sugar moeities but not the phosphate group, resulting in a system with neutral charge. From 1 to 250 water molecules were then placed randomly around the base pair within a specified radius. The water positions were selected from those of a hypothetical standard water box surrounding the base pair. For each size of nanodroplet, 100 different configurations were generated representing 100 different initial arrangements of water molecules around the base pair. The radius around the base pair was selected such that the total number of possible water molecules within that radius always exceeded the actual number of water molecules, while still being small enough to ensure all waters were contiguous. This radius ranged from 4.0 Å for nanodroplets with up to 20 water molecules to 8.5 Å for nanodroplets with 225 or more water molecules. In addition to the nanodroplets, we solvated each base pair in a complete box of water. To sample the starting configurations of the base pair inside the periodic box, we oriented the base pair in 100 different random ways. Our experiences indicated that using significantly <100 simulations introduced a nontrivial level of variability between different sets of simulations. This is reflected in the error bars in Figs. 2–4, which represent standard deviations in the averages of 10 sets of 10 simulations at each data point.

We then ran a 200-ps molecular dynamics simulation of each starting configuration by using the Encad force field under conditions of constant particle number and energy (also constant volume in the periodic box simulations) with a 2-fs time step and the Encad F3C flexible three-point water model (23). The base pairs solvated in complete water boxes used periodic boundary conditions, whereas the systems with nanodroplets did not. The nanodroplets were not constrained in any way apart from their initial configurations. In addition to the 100 simulations of each size of nanodroplet and the 100 periodic box simulations, we ran 100 simulations of the completely unsolvated base pair in a vacuum. Because there was no water in the unsolvated base pair, the starting configuration was identical for all 100 cases. Different random number seeds were used to start the simulations in all cases. In each run, the temperature was slowly increased, reaching room temperature (300 K) after ≈100 ps. Although this represents a significant portion of the total simulation time, we preferred a gradual heating over swifter heating, which might have introduced artifacts into the simulation and masked subtle differences between the nanodroplet sizes.

For the periodic box simulations, the box volumes were 17.6 ± 0.3 nm³ for AU and 17.7 ± 0.3 nm³ for GC. The equivalent base-pair concentration is 29 M, although this number is not very meaningful. Unlike real solutions, no aggregation of base pairs can occur at high concentrations because only one copy of each base is present in the periodic box. A given base can, however, leave the box, reentering on the opposite side to potentially reform a base pair with the second base. This is not the case for the nanodroplets as periodic boundary conditions are not used, and once sufficiently separated the bases can actually leave the nanodroplet and will never reform a base pair. As a result, comparisons between the periodic box and nanodroplets are not relevant at long time scales beyond those used in our simulations. At infinite time the nanodroplets would approach the limit of zero stability with the base pairs having left the nanodroplet, which itself has completely dispersed.

Apart from placing the water molecules close to the base pair in the starting configurations, we did not place any constraints on the nanodroplets during the course of our simulations. It is possible that one or more water molecules can become disconnected from the nanodroplet during the course of the simulation. This occurs in a small fraction of the simulations, and we did not compensate for it other than running the 100 duplicate simulations for each nanodroplet size to avoid biasing the data based on a single simulation.

Definition of a Base Pair.

For the purposes of our work, we define the AU and GC base pairs as being intact when any one of the characteristic hydrogen bonds is intact. The base pair is broken only when all of the hydrogen bonds are broken. Hydrogen bonds are defined geometrically (18) and are considered to be intact when the distance between the hydrogen atom and acceptor is ≤2.2 Å, and the angle between hydrogen atom, donor, and acceptor is ≤25°.