Computational tests of a thermal cycling strategy to isolate more complex functional nucleic acid motifs from random sequence pools by in vitro selection

Abstract

The dual information-function nature of nucleic acids has been exploited in the laboratory to isolate novel receptors and catalysts from random DNA and RNA sequences by cycles of in vitro selection and amplification. This strategy is particularly effective because, unlike polypeptides with random amino acid sequences, nucleic acids with random base sequences are often capable of stably folding into defined three-dimensional structures. However, the pervasive base-pairing potential of nucleic acids is also known to lead to kinetic traps in their folding landscapes. That is, the same DNA or RNA sequence can often adopt alternative base-paired structures that are local energy minima, and these folds may interconvert very slowly. We have used simulations with nucleic acid folding algorithms to evaluate the effect of misfolding on in vitro selection experiments. We demonstrate that kinetic traps can prevent the recovery of novel families of complex functional motifs by two mechanisms. First, misfolding can lead to the stochastic loss of unique sequences in the first round of selection. Second, frequent misfolding can reduce the average activity of multiple copies of a sequence to such an extent that it will be outcompeted after multiple rounds of selection. In these simulations, adding thermal cycling to sample multiple folds of one sequence during a selection for a self-modifying catalytic activity can improve the recovery of rare examples of more complex structures. Although newly isolated sequences may fold poorly, they can represent footholds in sequence space that can be improved to reliably fold after a few mutations. Thus, it is plausible that thermal cycling by day-night cycles or other mechanisms on the primordial earth may have been important for the evolution of the first RNA catalysts, and a fold sampling strategy might be used to search for more effective nucleic acid catalysts in the laboratory today.

Introduction

Catalytic and ligand-binding nucleic acids have diverse applications in gene therapy, synthetic biology, and biotechnology (Breaker, 2004). However, most functional nucleic acids that have been designed or isolated in the laboratory by in vitro selection or directed evolution do not perform adequately for advanced gene control and biosensor applications, especially under in vivo conditions. In some cases, it is clear that there are no inherent chemical limitations that preclude identifying better nucleic acid catalysts and receptors: biological nucleic acid families exist that perform identical functions more effectively. For example, natural metabolite-binding RNA aptamers from riboswitches (Barrick and Breaker, 2007) far outclass their laboratory counterparts that bind the same molecules (Burgstaller and Famulok, 1994; Kiga, et al. 1998). Riboswitches have larger and more complex structures that achieve greater binding affinities and discriminate better against closely related compounds.

Enriching new functional nucleic acid molecules from random sequence pools by rounds of in vitro selection and enzymatic amplification tends to recover the shortest motifs with the required activity. Thus, the simple consensus motif of the 8–17 deoxyribozyme family usually dominates DNA pools selected for RNA-cleavage activity (Santoro and Joyce, 1997; Cruz, et al. 2004), and RNA pools selected for self-cleavage teem with small hammerhead ribozymes (Salehi-Ashtiani and Szostak, 2001). These simple motifs may obscure more complex families of structures that exist in the same random sequence pool simply because they are numerically so much more likely to be specified by arbitrary nucleotide sequences. In fact, additional families of deoxyribozymes and ribozymes have been found in these two cases by efforts to detect rare variants (Tang and Breaker, 2000; Lam, et al. 2011).

An increase in complexity of five additional base pairs or five new invariant base constraints in the consensus structure of an RNA family has the potential to increase the optimal binding affinity or catalytic rate of a functional RNA family by an order of magnitude (Carothers, et al., 2004). When only a few “winning” sequences are sampled at the end of an in vitro selection experiment, rare sequences—potentially representing more complex structural motifs—may not be recovered solely due to this “tragedy of the commons” (Wilson and Szostak, 1999). However, it is possible that other factors also limit the recovery of more sophisticated functional nucleic acid from random sequence pools.

Many natural RNA molecules from biology are known to adopt multiple, stable base-paired structures. Sometimes this structural degeneracy is necessary for function, as in the case of riboswitches, where different conformations in an “expression platform” sequence are triggered by ligand binding to an “aptamer” domain (Barrick and Breaker, 2007). Alternative conformations have also been harnessed to engineer allosteric ribozymes in the laboratory that use ligand binding to restructure and thereby modulate the activity of the catalytic domain so that they can act as gene control elements or biosensors (Breaker, 2002; Win and Smolke, 2007).

More often structural degeneracy is an undesirable trait, and molecules that misfold into off-pathway conformations are functionally “dead”. RNAs from biological systems that form complex structures often require protein chaperones to overcome these kinetic traps and reliably achieve their functional folds (Herschlag, 1995). For example, the group I self-splicing intron misfolds in vitro into a long-lived intermediate that can only refold to reach the native state on timescales of many minutes (Russell, et al. 2006). Even “winning” nucleic acid sequences from laboratory selection experiments often have problems folding reliably. For example, a sizeable subpopulation of misfolded molecules was found to contribute to incomplete self-cleavage of RNA-cleaving deoxyribozymes (Carrigan, et al. 2004). Misfolding is more likely to be a problem for large structures, thus it may prevent the recovery of the most interesting sequences present in random nucleic acid pools.

The nucleotide sequences flanking a functional RNA can profoundly affect its activity, presumably because certain sequence contexts can promote or inhibit correct folding of the functional motif. In one case, the apparent in vitro binding affinity of the same riboswitch aptamer changed by 20-fold depending on the surrounding sequence context (Winkler, et al. 2002). In another, addition of random flanking sequences to a family of laboratory evolved RNA ligases caused their apparent rate constants to vary over more than two orders of magnitude (Sabeti, et al. 1997). It is possible that many functional motifs in random sequence libraries are present in unfavorable contexts that cause them to misfold. Perhaps for this reason, isoleucine aptamers were actually more abundant in 50- and 70-base random regions than in a longer library with 90 random bases, which is a counterintuitive result from a pure probability standpoint (Legiewicz, et al, 2005).

Secondary structure prediction programs have been used as model systems for examining evolutionary trajectories and the overall distribution of function in nucleic acid sequence space (Ancel and Fontana, 2000; Stadler, et al. 2001; Cowperthwaite, 2006). These studies typically use the predicted minimum free energy structures of RNA sequences to construct genotype-to-phenotype maps and an associated fitness landscape. Other studies have calculated the theoretical representation of motifs in random sequence pools (Sabeti, et al. 1997) and used secondary structure prediction algorithms to estimate how often a motif will be correctly folded in the context of flanking sequences (Knight, et al. 2005). These approaches consider the effects of sequence probability and thermodynamic stability on in vitro selection, but they do not take into account what folds are actually accessible and likely to be sampled by each sequence when misfolding into kinetic traps is possible.

Knowledge of protein folding principles has been used to engineer improved strategies for the directed evolution of proteins (Voigt, et al. 2000; Bloom, et al. 2006). Here, we computationally evaluate a potential strategy for recovering more complex nucleic acid structures from in vitro selection experiments based on properties of their folding landscapes. First, we examine how misfolding can impact the recovery of rare motifs from in vitro selection experiments using kinetic simulations of RNA folding. Then, we show that fold sampling by thermal cycling during selection can theoretically enable the recovery of new classes of rare self-modifying ribozymes with more sophisticated structures.

Results

Kinetic folding model of functional nucleic acids

To model how nucleic acid misfolding impacts in vitro selection, we require (1) a method for scoring the functional capacity of a particular nucleic acid structure and (2) an algorithm for simulating the kinetics of the folding process. In general, larger and more complex RNA structures are necessary (but not sufficient) to achieve better functional characteristics. On the basis of aptamer and ribozyme families that have been optimized by re-selection, an empirical rule has been proposed that requiring 10 additional bits of information to be specified (equivalent to 5 new invariant bases or base pairs) in the consensus structure for a functional RNA family has the potential to improve reaction rate (k_cat) or binding affinity (K_d) 10-fold (Carothers, et al., 2004). It is reasonable to assume that additional functional information in a structural motif could instead improve specificity against noncognate ligands or reduce requirements for high-concentration divalent metal ion cofactors, two other desirable traits for nucleic acids used to make advanced biosensors or deployed in vivo.

To score functional capacity, we test RNA folds against an arbitrary set of target structures consisting of different arrangements of helical elements with three to seven base pairs (Fig. 1). These structures range from very simple (a hairpin with one helical element) to more complex (a four-way junction of helical elements). Folded sequences receive a score equal to how many base pairs they match in a target structure. For simplicity, we constrain the linker and loop regions between helical elements to fixed lengths. Additional pairs formed by bases in these connectors count neither for nor against the score. Folded sequences are considered functional members of a target family if they match a certain number of the possible base pairs in the consensus pattern.

Figure 1. Nucleic acid structure targets.

Secondary structure models representing functional RNA families. Circles designate where nucleotides must be present. Each target structure specifies an arrangement of one to four helices, each with three to seven base pairs (colored), and bases with no pairing constraints (black). The functional score of a folded sequence for a particular target is the number of consensus base pairs matched in the structure.

In consensus secondary structure models of real functional DNAs and RNAs, the identities of bases at certain positions are invariant (e.g., always an adenine) or are limited to a subset of the four nucleobases (e.g., always a purine). Requirements for specific bases may exist at motif positions that contribute to non-canonical base interactions, tertiary structure contacts, ligand binding, or catalysis (Barrick and Breaker, 2007). These bases are often key determinants of function in an RNA family. However, we do not consider invariant base requirements in our target RNA structures for two reasons. First, secondary structure prediction algorithms used to model folding only calculate the energies of structures with canonical Watson-Crick and G-U base pairs. Second, we are testing hypotheses about misfolding in our model, rather than attempting to calculate the abundance of known functional RNA structures in sequence space, as has been the aim of other studies (Knight, et al. 2005). Adding additional constraints on the identities of bases in our target structures would reduce the chances of sampling “functional” sequences, but because these constraints would be arbitrary, it would probably not enhance the realism of the model.

To simulate RNA folding trajectories, we used version 1.3 of the software program Kinfold (Flamm, et al. 2000), distributed with version 2.02 of the Vienna RNA Secondary Structure Package (Hofacker, et al. 1994). Given an input sequence, Kinfold traverses the energy landscape of possible secondary structures by the stepwise formation or dissociation of base pairs. We overrode the default behavior which stopped a folding trajectory when the global minimum energy structure was reached. This choice allowed thermal fluctuations to continue for the entirety of the specified folding period. To reduce the number of structures that had to be scored for function, we also used the option to only output states encountered during folding trajectories that were local energy minima. As these structures are typically maximally base paired, this set should generally contain the best possible matches to the target structures of all folds traversed. All simulations used the default folding temperature of 37°C.

We further assumed that a fold with a functional score in our model system possesses an efficient catalytic activity (such as self-cleavage or self-ligation) that needs to be triggered only once to allow it to “pass” an in vitro selection step. Therefore, as a first approximation, we assigned a sequence the maximum score achieved by any base-paired conformation that it adopted during a folding run, without taking into account the overall residence time in different structures. Nucleic acid folding in selection experiments is typically initiated by adding divalent cations (such as Mg²⁺) to a sample. These positively charged metal ions coordinate the negatively charged phosphate backbone and enable collapse to a compact tertiary structure. We simulated this experimental treatment by beginning each computational folding trajectory with a fully extended strand containing no base pairs.

As an example, we show the results of the entire folding and scoring procedure applied to one sequence (Fig. 2). This sequence achieved a perfect match to the bulged-stem loop structure in 183 of 1000 folding trials (18.3%) lasting 100 seconds. In the other trials, it collapsed into alternative secondary structures that were unable to rearrange into the functional target structure during the remainder of the folding trajectory, even though it is thermodynamically far more stable. Thus, this poorly folding sequence demonstrates that our computational model recapitulates the key features of real RNA folding landscapes where kinetic traps can prevent many individual molecules of a potentially functional sequence from reaching an active conformation.

Figure 2. Example of a poorly folding RNA sequence.

(A) Ten folding trajectories initiated from an extended strand for the same example sequence. The maximum functional score for the bulged stem-loop target structure encountered up to the given time is shown. Two trials reached the maximum score of 10 within 100 seconds and were judged functional. Only integer scores are possible, so some lines have been offset slightly to avoid overlap. (B, C) Two example folding trajectories. Structures encountered during the initial and final portions of the kinetic simulations are shown. Dots represent unpaired bases and nested sets of parentheses indicate that two bases are paired. The final folded structures are drawn in each case with base pairs that contribute to the score highlighted in red. The first trajectory in (B) achieves a perfect match. The second trajectory in (C) becomes kinetically trapped in an alternative, misfolded structure that is not functional. Only structures that are local energy minima encountered during the simulation of the folding trajectory are shown and scored.

Misfolding reduces the effective library size

A typical experimental design when trying to isolate new functional RNA families is to begin in vitro selection with a collection of as many random sequences as possible. Each sequence in this “pool” or “library” is often represented just once. Therefore, if a molecule fails to reach the active conformation during the first round of selection, due to becoming energetically trapped in an alternative base-paired structure, that unique sequence will be forever lost from the experimental population. Molecules that do make it through this initial selection step are amplified into hundreds to thousands of copies each before the next selection cycle. Thus, they are generally not expected to be subject to the same dangers of stochastic loss in later rounds. Given the importance of the first round in determining how many unique sequences are interrogated for function, we first investigated the impact of misfolding on this step of in vitro selection.

To what degree does misfolding prevent RNA sequences that are theoretically capable of adopting a functional fold, with all the required base pairs, from achieving this structure? We can calculate p, the probability that a random sequence is capable of perfectly matching one of our target structures, as

$$p=\left(L-l+1\right)b^n$$

where L is the total length of each random sequence, l is the length of the functional target motif, n is the number of base pairs in the target structure, and b is the chance of a randomly selected base being able to pair with an existing base at a specific position elsewhere in the target structure. For random sequences with equal probabilities of each nucleotide, the parameter b is 0.375 when allowing Watson-Crick or G-U base pairs. Note that this calculation does not guarantee that this structure is the most thermodynamically favorable conformation for a sequence, only that it could adopt this fold. Thus, these calculations yield a theoretical upper limit on the frequency of functional sequences matching a target in a random pool.

To evaluate the effects of misfolding, we simulated a single 10-second folding trajectory for each of 1,000,000 random sequences of length 100. Under the assumption that we are selecting for self-modifying ribozymes, as explained above, we assigned each sequence the best score achieved by any structure encountered in its folding trajectory. We classified the folding trial as resulting in catalytic activity, which would enable that sequence to survive the first round of in vitro selection, if it had a perfect score that matched all base pairs. This procedure enabled us to compare the actual frequency of sequences that were able to kinetically fold to match each target structure to the theoretical calculations (Fig. 3).

Figure 3. Simulated and theoretical maximum frequencies of random sequences folding to match target structures.

Chances that a random sequence could possibly fold to perfectly match each target family were calculated according to the formula in the text (open squares). Sequences actually folded to perfectly match the target structures during kinetic folding simulations at much lower frequencies (filled circles). Error bars are Clopper-Pearson (exact) binomial 95% confidence intervals. Structure abbreviations are given in the Fig. 1 legend. No perfect matches were observed for the 3J or 4J families in the 1,000,000 total sequences that were tested.

The theoretical probability of finding each target structure in a random sequence library decreases nearly uniformly as additional base pairs are added. The chance of finding a random sequence that adopts each target structure in a simulated folding trajectory declines more rapidly as the structures become more complex. The ratio of the two frequencies represents the effective reduction in library size for that structure, i.e., how many times as many sequences as expected would have to be interrogated by in vitro selection to recover a properly folded example of that motif.

The effective library size reduction due to misfolding is 13, 200, 9400, and 430 for the four motifs where perfect matches were found, ordered by the number of base pairs in each target structure. These reductions demonstrate that misfolding disproportionately decreases the likelihood of more complex structures surviving the first round of selection. Thus, not only are more complex RNA structures less likely to be specified by random sequences in the first place, but their inability to reliably fold into the active conformation may compound the combinatorial difficulty of recovering them from a selection.

There is also substantial family-to-family variation in these results. While the effective library size reduction is roughly the same for the double hairpin (DH) and bulged stem-loop (BSL) structures, the effect of misfolding is more than 20-fold greater for the intermediate hairpin & bulged stem-loop (HBSL) structure. This result suggests that the requirement for three helical elements in this motif, compared to two in the others, may have a bigger influence on complexity and misfolding than the relative number of base pairs.

Misfolding reduces the average activity of sequences

In later rounds of in vitro selection, each surviving nucleic acid sequence has been amplified so that it is present many times in the pool. At this stage, the hazard of stochastic loss due to sampling is not as great, as it was in the first round of selection. However, misfolding may still decrease the apparent activity of a sequence if some fraction of a set of identical molecules becomes kinetically trapped in a “dead” structure upon folding and do not react. If misfolding is prevalent, it can potentially disfavor certain sequences to such an extent that they will not be recovered by in vitro selection. If a structural family is so rare that it is only represented by a few sequences in the entire random pool, all of these may be so poorly folding that they are outcompeted by well-folding examples of more common families at each round of selection. Depending on the extent of misfolding and selection conditions, this can be true even if the rare structure has better performance characteristics when it is correctly folded.

In our simulations, the average activity of many copies of one RNA sequence is equal to the fraction of folding trajectories that sample a conformation with a functional score above some threshold. To more closely examine how kinetic traps can affect average activity and winners over multiple rounds of selection, we simulated 10,000 folding trajectories lasting 10 seconds for each of 10,000 random sequences of length 100. Since we were limited to fewer total sequences, we scored as functional not only perfectly scoring matches, but also structures with as many as two missing base pairs. To summarize the results we plotted the folding characteristics of the ensembles of structures achieved by each sequence in separate folding trials as the cumulative distribution of the number of different sequences that achieved a functional score in some fraction of their folding trajectories (Fig. 4).

Figure 4. Reduction in average activity due to misfolding.

The cumulative numbers of sequences that folded to achieve a functional conformation in a given fraction of simulated secondary structure folding trajectories are shown. For these simulations the score judged to be “functional” for each family was the maximum possible score minus two. Structure abbreviations are given in the Fig. 1 legend.

We found that even the best-folded examples of each family in this limited sample of sequences encountered kinetic traps such that they were not able to reach the functional structure a large fraction of the time. To get an idea of the impact this might have on an experiment, assume that selection takes place under permissive conditions where all correctly folded sequences react to completion. Then, the relative enrichment of the best examples of each family (y-intercepts in Fig. 4) as they replace fully nonfunctional sequences would be equal to their relative chances of folding into an active structure. Under these conditions, the three most complex structures (HBSL, 3J, and 4J) would be outpaced by the simpler structures by at least 10-fold in every round of selection.

It is possible that more complex structures might have improved performance characteristics, such as tighter binding or a higher catalytic rate. To some extent, this might mitigate the advantage of the smaller structures. With suitably stringent selection conditions, which capture ligand binding with very low off rates for a receptor or very rapid initial kinetics for a catalyst, increased function can almost directly translate into better recovery of a sequence. Under these conditions, a representative of the 3-way junction (3J) motif family would still need almost 100-times the activity of a representative of the double hairpin (DH) structure to compete on equal footing for enrichment and recovery, for example. However, this high stringency could also put each structure at risk for stochastic loss again, as in the first round of selection. In the example, only one in 10³ molecules with an active sequence would be recovered after a selection step that was stringent enough to yield equal enrichment of the two motifs.

The advantages of smaller structures in the average effective activity they realize compared to larger structures will occur in each of the 8 to 15 total rounds of in vitro selection and amplification in a typical experiment. Thus, the large reduction in the effective activity of the more complex structures due to misfolding would be a substantial obstacle to recovering a rich collection of functional RNA families.

Thermal cycling relaxes selection against misfolding

Because we are simulating selection for a self-modifying catalytic function, a molecule only needs to reach the active state once to pass selection. We reasoned that giving each RNA molecule multiple opportunities to refold within a single round of selection would relax selection against poorly folding sequences. This effect could improve the recovery of complex nucleic acid families, which will be rarer in a random pool, and therefore more likely to be lost due to misfolding during the first round of selection or to be disfavored relative to simpler structures by reduced activity in later rounds.

Thermal cycling would be a simple way to implement fold sampling. We simulated thermal cycling by splitting up a folding interval of constant total length (1,000 sec) into one, ten, or one hundred separate folding cycles and examining the maximum activity achieved by 100,000 sequences of length 100 during this time (Fig. 5A). We simulated each thermal cycling step by restarting a new folding trajectory from an extended conformation with no secondary structure. This procedure is equivalent to heating achieving perfect unfolding followed by an instantaneous return to normal temperature.

Figure 5. Fold sampling by thermal cycling increases the chances that random sequences achieve active structures.

(A) 10,000 sequences were folded for a total of 1,000 seconds each, divided into 1, 10, or 100 folding cycles as illustrated. (B) The cumulative distributions of the maximum scores achieved by each of these sequences for the bulged stem-loop target structure in each folding treatment. (C) The average score achieved for each structure in each folding treatment. Black bars are the maximum possible scores. (D) The frequency of sequences scoring above the given high score cutoffs for each target structure. Error bars are exact binomial (Clopper-Pearson) 95% confidence intervals to show the error due to sparsely sampling low numbers of active structures. They are hidden behind symbols in many cases. Structure abbreviations are given in the Fig. 1 legend.

Overall, thermal cycling treatments increased the functional scores achieved by the random sequences that were tested, as expected (Fig. 5B). We quantified this improvement in two ways. First, we asked how the average score that sequences achieved for each target family changed (Fig. 5C). We found that the ten folding cycle treatment improved the average score for each family by 0.61 to 0.82 points (mean: 0.72). The one-hundred folding cycle treatment improved the average score by 1.06 to 1.17 points (mean: 1.12). This result roughly translates into the 100-fold treatment matching one additional base pair in the target compared to the 1-fold treatment.

Since truly functional sequences are better represented by the high-scoring tail of this distribution than by its average, we also asked how often sequences scoring above a threshold value were found in the multiple folding treatments (Fig. 5D). For the more complex sequence families the average increase in the frequency of sequences that achieved a high score (defined as within three of the maximum where activity was observed, for example 8, 9, or 10 for the three-way junction) was roughly constant across all structures. We found that, on average, the effective library size for those structures after cycling would be increased approximately 2.4-fold for 10 cycles and 3.4-fold for 100 cycles, excluding the hairpin structure. Again, this is roughly equal to increasing the effective library size for finding complex structures by one consensus base pair. Despite the larger apparent hazards of complex structures misfolding in the first round of selection described above, there was no apparent effect of the structural complexity of the target motif on the improvement in effective library size from thermal cycling.

Multiple folding by thermal cycling could also mitigate the reduction in average activity due to misfolding at each round of selection. Due to computational costs, we were unable to repeat the longer 100-second and 1,000-second folding trials multiple times for each sequence to fairly judge the relative success of sequences under these conditions. To estimate the possible magnitude of this effect, we again consider just the best-folding examples from the experiment where each sequence was folded 10,000 different times for 10 seconds. Here every ten cycles of re-folding theoretically increases the fraction of molecules that achieve the active structure by about 10-fold, until it becomes close to one. Therefore, the 100-cycle folding treatment should bring the three smallest structures up to parity in terms of effective activity per round of selection. Therefore, this consequence of thermal cycling might have an even more substantial impact on the eventual recovery of complex structural motifs.

Poorly folding sequences may be evolutionary footholds

Thus far we have provided evidence that thermal cycling can theoretically increase the number of functional structures recovered by in vitro selection by relaxing selection against misfolding. However, a majority of the new sequences recovered by this procedure would be poorly folding: by definition their “function” is conditional on being thermally cycled many times. Our primary interest is to recover rare examples of larger, more complex structures that would not be found otherwise. Due to sparse sampling of sequence space, recovering even a handful of poorly folding examples of new structural motifs might establish evolutionary “footholds” in the sequence-structure landscape. It is possible that some of these beachhead sequences could be readily optimized to well-folded examples of a structural family in only a few additional mutational steps. Alternatively, most sequences newly recovered by the thermal cycling strategy might be pathologically poor folders that are not near any well-folding examples in sequence space, causing them to remain trapped in a poorly functioning limbo that cannot be improved.

To determine whether it was plausible that this procedure would find useful evolutionary footholds, we surveyed the local mutational landscape of two random poorly folding examples of structural classes found in the thermal cycling simulations. We measured the fraction of the time that the original sequence, and all of its one-mutation neighbors, reached functional folds in 10-second trajectories. Then, we took the best one-mutant neighbor and looked at its one-mutant neighborhood. This procedure is roughly analogous to a re-selection experiment from a doped pool, where a single master sequence (that was recovered by the original selection) is resynthesized with a probability of error at each position, and selection is used to find variants with optimized function.

We found that the original example of the three-way junction (3J) class folded to within one base pair of a perfect score in 10/10000 trials. Its best single-mutant neighbor folded to this level of function in 6/1000 trials after a change in the flanking sequences. However, there are 300 possible single-step mutations for this sequence of length 100, and the observed increase is not statistically significant when corrected for multiple testing (Bonferroni corrected Fisher’s exact test, p = 0.60). A second single mutant of this sequence improved to be capable of a perfect score by changing a base in the outermost pair of the target, but it only reached this structure in 1/1000 trials.

An example of the bulged stem-loop (BSL) structure initially folded to a perfect match in 137/10000 folding trajectories. The best single mutant reached this score in 35/1000 trials and the best further single mutant of this sequence was active in 46/1000 trials. The first of these increases is highly significant (Bonferroni corrected Fisher’s exact test, p = 0.0016) and resulted from changing a G-U base pair to a more thermodynamically stable G-C base pair. In this second case, we see evidence that some of the poorly folded structures isolated by the thermal cycling procedure can be improved with very few mutations. Since changes to more realistic RNA structures often require simultaneous changes to covarying base pairs, it may be that our step-wise procedure is not as effective as a real re-selection experiment where substantially more variation can be introduced and filtered.

Discussion

We have used kinetic secondary structure folding simulations to examine how misfolding into kinetic traps can hamper the recovery of novel families of functional nucleic acids by in vitro selection. We showed that misfolding could reduce both the effective library size, by preventing sequences from surviving the first round of selection, and lower the effective activity of sequences in later rounds of selection such that they are outcompeted. Both of these processes bias selection against the recovery of larger motifs, which have the most potential for achieving the greatest function. We found these disadvantages could be mitigated somewhat by using thermal cycling to re-fold molecules multiple times during a selection step, allowing more complex structures to be recovered from experiments. It is our hope that this work serves as a proof-of-principle and prelude for experimentally investigating fold sampling procedures.

Many question remain about how adjusting the critical parameters in this model will affect the utility of thermal cycling. In particular, we did not systematically examine how the effectiveness of this strategy depended on the duration of each folding step. We also used rather small target structures, as only 10⁵ sequences could be simulated. Much larger functional motifs are usually isolated from real random nucleic acid libraries that contain upwards of 10¹⁵ sequences. While we expect the general properties of the folding landscape to remain the same for larger structures, the magnitude of many effects could be quite different. Future studies might examine larger structures by using inverse folding algorithms (Hofacker, et al. 1994) to design sequences with minimum free energy structures that are functional, and examining how misfolding affects their recovery.

A number of other folding strategies could also be investigated with this kinetic folding model. First, adding chaperones (Herschlag, 1995) during the selection step could enable sequences to more reliably reach their global energy minimum rather than being stuck in more shallow local minima. This treatment might be implemented by simply assigning sequences to their minimum free energy structure. Second, it is possible that certain types of less extreme temperature fluctuations would allow useful exploration of multiple, folded conformations to achieve function. Third, performing selection at elevated temperatures could disfavor poorly folded sequences and give rise to active pools of molecules where only highly structured, and perhaps more complex, sequences that do not melt remain functional.

Temperature cycling has been previously used in limited contexts in nucleic acid selection experiments. In a notable selection with a very large random region consisting of 220 nucleotides, “the temperature was cycled between 25°C and 37°C to encourage individual RNA molecules to explore alternative conformations” (Bartel and Szostak, 1993). Perhaps not coincidentally, a class of ligase ribozymes from this selection formed the basis for the eventual creation of the exceptionally complex RNA-dependent RNA polymerase ribozyme (Johnston, et al. 2001). Temperature cycling has also been used to fold allosteric ribozymes multiple times in the absence of ligand to prevent selecting ribozymes that probabilistically fold some fraction of the time into a conformation capable of self-cleavage. This bet-hedging behavior allows these “cheaters” to be triggered some fraction of the time that they fold and pass selection despite not recognizing the desired ligand (Soukup, et al. 2000).

We have neglected discussing experimental procedures that introduce new mutations, i.e. “evolution” rather than pure “selection”. RNA’s penchant for adopting alternative structures is a type of phenotypic noise or plasticity (Ancel and Fontana, 2000). A “lookahead effect” has been modeled where phenotypic misexpression of a genotype can enable evolution to more quickly cross fitness valleys to complex traits under certain circumstances (Whitehead, et al. 2008). RNA folding may have more relevant rates of “phenotypic misexpression” for this effect than transcription or translation errors. It has already been shown experimentally that the ability of one RNA sequence to adopt multiple folds can create nearly neutral single-mutation walks between functional structures (Schultes and Bartel, 2000). Thermal cycling during one of these experiments could bring such valley-crossing events even closer to full neutrality.

Early chemical evolution might have relied on fold cycling to give poorly folded, compositionally mixed, or chemically heterogeneous sequences extra chances to function. One can imagine the early earth as a very large and slow thermal cycler, with day-night cycles re-folding primordial heteropolymers in the soup repeatedly until the “spark” of hitting an active conformation. Fluctuating or interfacial microenvironments, such as thermal vents or hypersaline pools, might cause fold sampling on more rapid timescales.

Not captured by the current kinetic folding model, but also possibly very important in an early RNA World, is the capacity for interstrand base pairing. At each refolding cycle, molecules have multiple opportunities to interact, not only with themselves to form new structures, but also with different partners in a mixture to form functional conglomerates. Thermal cycling could also drive systems that rely on interstrand base pairing for polymerization or ligation (Johnston, 2001; Lincoln and Joyce, 2009). While in many cases these interactions may lead to inhibition or even the evolution of parasites (Hanczyc and Dorit, 1998), they represent another potential type of phenotypic plasticity that can multiply the functional possibilities of nucleic acids.