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BIOLOGICAL SCIENCES / BIOPHYSICS
Simulations of RNA base pairs in a nanodroplet reveal solvation-dependent stability
Department of Structural Biology, Stanford University School of Medicine, D100 Fairchild Building, Stanford, CA 94305
Contributed by Michael Levitt, June 13, 2007 (received for review May 25, 2007)
| Abstract |
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hydrogen bond | limited hydration
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 |
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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.
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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.
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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.
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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
-helices and
-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.
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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 |
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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 |
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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°.
| Acknowledgements |
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| Footnotes |
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Freely available online through the PNAS open access option.
Author contributions: M.T.S. and M.L. designed research; M.T.S. performed research; M.T.S. and M.L. analyzed data; and M.T.S. and M.L. wrote the paper.
The authors declare no conflict of interest.
© 2007 by The National Academy of Sciences of the USA
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