# Prebiotically plausible mechanisms increase compositional diversity of nucleic acid sequences

J. Derr, Michael Manapat, Sudha Rajamani, Kevin Leu, Ramon

Xulvi-Brunet, Isaac Joseph, Martin Nowak, Irene Chen

► To cite this version:

J. Derr, Michael Manapat, Sudha Rajamani, Kevin Leu, Ramon Xulvi-Brunet, et al. Prebiotically plausible mechanisms increase compositional diversity of nucleic acid sequences. Nucleic Acids Research, 2012, 40 (10), pp.4711-4722. 10.1093/nar/gks065. hal-03679092

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# Prebiotically plausible mechanisms increase compositional diversity of nucleic acid sequences

Julien Derr¹, Michael L. Manapat²,³, Sudha Rajamani¹, Kevin Leu¹, Ramon Xulvi-Brunet¹, Isaac Joseph¹, Martin A. Nowak³ and Irene A. Chen¹,*

¹FAS Center for Systems Biology, ²School of Engineering and Applied Sciences and ³Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA

Received October 14, 2011; Revised December 24, 2011; Accepted January 18, 2012

## ABSTRACT

During the origin of life, the biological information of nucleic acid polymers must have increased to encode functional molecules (the RNA world). Ribozymes tend to be compositionally unbiased, as is the vast majority of possible sequence space. However, ribonucleotides vary greatly in synthetic yield, reactivity and degradation rate, and their non-enzymatic polymerization results in compositionally biased sequences. While natural selection could lead to complex sequences, molecules with some activity are required to begin this process. Was the emergence of compositionally diverse sequences a matter of chance, or could prebiotically plausible reactions counter chemical biases to increase the probability of finding a ribozyme? Our *in silico* simulations using a two-letter alphabet show that template-directed ligation and high concatenation rates counter compositional bias and shift the pool toward longer sequences, permitting greater exploration of sequence space and stable folding. We verified experimentally that unbiased DNA sequences are more efficient templates for ligation, thus increasing the compositional diversity of the pool. Our work suggests that prebiotically plausible chemical mechanisms of nucleic acid polymerization and ligation could predispose toward a diverse pool of longer, potentially structured molecules. Such mechanisms could have set the stage for the appearance of functional activity very early in the emergence of life.

## INTRODUCTION

The biology of modern organisms is based on RNA, DNA and proteins, but this biochemistry was probably preceded by a stage in which RNA molecules acted both as chemical

catalysts and carriers of genetic information. Evidence for this early stage of life (the 'RNA world') includes the similarity of ancient chemical cofactors to certain ribonucleotides and the discovery that the catalytic core of the ribosome is composed of RNA (1–5). Possible pathways for the prebiotically plausible synthesis of the components of RNA and the polymerization of ribonucleotides have been reported by several groups (3,6–8). While natural selection could enhance low catalytic activity, the very earliest ribozymes must have arisen through chemical processes (3). Understanding the details of this initial emergence is a deep conceptual puzzle (9).

The first ribozymes must have emerged from pools of short sequences that were low in diversity and information content, but it is unclear how the complexity of these pools could be increased (10,11). These sequence pools would have been limited for at least two reasons. First, monomers would have different abundances because they are synthesized and degraded by different pathways. For example, a concentrated eutectic phase solution of ammonium cyanide yields significantly more adenine than guanine, uracil and cytosine (roughly 10× or more) (6). Degradation affects the nucleobases differently, with cytosine being particularly susceptible to spontaneous deamination (12). Indeed, the abundances of nucleobases detected in meteorites also vary by one or more orders of magnitude (13–16). Second, the rate at which different monomers are polymerized can vary by an order of magnitude (6,17–20). In one study of montmorillonite-catalyzed RNA synthesis, this bias led to a large reduction in diversity, as only 3 out of 32 possible pentamer sequences were formed in detectable amounts from a mixture of activated A and C monomers (21). These biases reduce the diversity of the sequences generated, restricting exploration of sequence space and thus reducing the probability of generating a sequence with biological function. While compositional biases might increase the probability of generating functional RNA (22–24), the magnitude of the biases associated with prebiotically plausible polymerization is still substantially larger than potentially favorable biases. Interestingly, ribozymes with

<footnote>*To whom correspondence should be addressed. Tel: +1 617 384 9647; Fax: +1 617 496 5425; Email: ichen@lsdiv.harvard.edu</footnote>
limited compositional diversity have been made by a com-
bination of rational design and *in vitro* evolution on re-
stricted alphabets, but the resulting ribozymes exhibited
decreased catalytic efficiency (the three-letter alphabet
gave a 2500-fold decrease in *k*<sub>cat</sub> relative to the four-letter
alphabet; the two-letter alphabet gave a further 10-fold
decrease in *k*<sub>cat</sub> as well as a large decrease in total
product conversion due to ribozyme misfolding) (25,26).
While fine-tuning the conditions—e.g. by adjusting
monomer ratios to counteract reduced reactivity or
limiting UV irradiation to attain an appropriate
monomer ratio (7,27,28)—could potentially overcome
these biases, such conditions would be unlikely early on.
Therefore, we sought more general mechanisms to counter
compositional bias in nucleic acid pools undergoing
prebiotically plausible reactions. Our experiments using
DNA and simulations of binary sequences demonstrate
that template-directed ligation is one such mechanism.
Our RNA folding simulations suggest that composition-
ally diverse sequences are more likely to fold into stable
structures compared with the substantially biased se-
quences that would be derived from template-independent
processes. Greater stability is one of the factors promoting
greater functional activity in RNA aptamers (29,30). In
addition, our simulations indicate that template-directed
ligation would shift the pool toward longer sequences,
another important factor for activity (31,32). Our results
suggest that a broad exploration of interesting sequence
space was possible in prebiotic sequence pools despite
initial chemical biases.

MATERIALS AND METHODS

Simulations

Two types of simulation were performed (stochastic and deterministic). Both simulations are limited for computational reasons. The stochastic simulation keeps track of each monomer or oligomer and implements a specific reaction at each time step. In practice, the simulation cannot keep track of an infinite number of reactants and possible reactions, so the system is limited by the total number of monomers considered. This mimics a protocell containing a relatively small number of monomers (e.g. 400, in which case the longest possible sequence would be 400 monomers). The stochastic simulation can generate sequences of ribozyme length. In contrast, the deterministic simulation keeps track of all possible species and reactions among them simultaneously, mimicking a very large, well-mixed system. In practice, the deterministic simulation cannot keep track of an infinite number of species, so the system must be truncated at a certain maximum length (e.g. 12).

The stochastic simulation was based on the Gillespie
algorithm (33). Each simulation began with a pool of
monomers. The total number of monomers in the
system was typically limited to 400. During each iteration,
an exponential waiting time was generated before a single
reaction (concatenation, template-directed ligation or hy-
drolysis) occurred according to the relative rates of all
possible reactions. Concatenation could occur between

any two monomers or polymers. Realistic bias was
introduced in the simulation as either a concatenation
rate that depended on the identity of the 5' monomer
(e.g. reactivity ratio of 19:1), or as a difference in the
initial number of monomers of each type (e.g. abundance
ratio of 9:1). Template-directed ligation was possible if a
6-mer segment of one sequence (the template) was com-
plementary to the trimer at the 3'-end of one substrate and
the trimer at the 5'-end of the second substrate. Any
sequence of length 6 or greater was a potential template;
any sequence of length 3 or greater was a potential sub-
strate. Circularization reactions were not considered.
Hydrolysis of phosphodiester bonds occurred at a
constant rate per bond. Characteristics of the system
(average length and C<sub>k</sub>) were measured at exponentially
increasing time steps (i.e. 0, 1, 2, 4, 8, etc), and steady state
was considered to be achieved when the characteristics at
consecutive time steps deviated by <0.1%. SEs for these
measurements were calculated from multiple simulation
runs. The deterministic simulation used the same reactions
as the stochastic simulation and kept track of the abun-
dances of all possible sequences as the system evolved. The
system was truncated at a maximum polymer length (typ-
ically 12) for computational tractability (i.e. polymers of
the maximum length could not undergo further concaten-
ation or ligation). Average C<sub>k</sub>, average length and diver-
sity were computed using steady-state abundances. The
simulations were performed on the Odyssey Cluster of
the FAS Research Computing Group at Harvard
University. See Supplementary Data for simulation
details.

Experiment: degenerate oligonucleotides for template-directed ligation of a heterogeneous sequence pool of DNA (four bases)

In heterogeneous pool reactions, all oligonucleotides were composed of A,C,G,T. Degenerate DNA oligonucleotides were obtained from Keck Oligo Synthesis Resource (Yale University, New Haven, CT, USA). Octamers and templates (40-mer) were synthesized as 5'-NNNN... using the facility's standard procedure for equimolar, degenerate oligonucleotides. Oligos were purified by reverse-phase cartridge. Octamers were phosphorylated as noted below, using non-radiolabeled ATP.

Experiment: template-directed chemical ligation reactions
(four bases)

Reagents were purchased from Sigma-Aldrich (St Louis, MO, USA) unless otherwise specified. Synthetic degenerate oligonucleotides (templates of length 40; 5'-phosphorylated substrates of length 8) were mixed and ligated using cyanogen bromide following a previously published procedure (34). Reactions contained 1-2 µM DNA template and 16 µM DNA octamers. DNA sequences were mixed with buffer [0.23 M 2-(*N*-morpholino)ethanesulfonic acid, pH 7.4] and 19 mM MgCl₂, in 4.5 µl of aqueous solution, heated to 95° for 3 min and annealed by cooling on the benchtop for 15 min. The solution was placed on ice for 5 min and 0.5 µl CNBr (5 M in acetonitrile) was added (final
<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /><figcaption>**Figure 1.** Compositional diversity, sequence space and predicted RNA folding energy. (a) Most of sequence space is of high compositional diversity. Histogram of C₄ for RNA sequences, computed from random sampling of 10⁹ sequences of length 50 (black dots) in silico. The complete histogram for all possible sequences of shorter length is computable and is similar to that of the random sample of 50-mers (length 10 = blue, 12 = pink, 14 = green, 17 = orange). (b) Compositional diversity (C₄) and predicted minimum folding energy (Eₘ) for known ribozymes (length 40–60; see Supplementary Data) (45) are shown as blue dots with mean and SD (blue lines). (c) C₄ versus Eₘ (black dots) predicted by Viennafold (41) for 2.5 × 10⁶ RNA sequences of length 50. To minimize effects from GC-content, we restricted the in silico sampling to sequences whose GC content is 40–60%. To avoid sampling artifacts, sequences were assigned to five bins according to C₄, and an equal number of unique sequences were analyzed in each bin. The bin averages are shown as the red line (see Supplementary Data for values and SDs).</figcaption></figure>

correlated with C₄, and collectively the Cₖ explain 61% of the variance in Eₘ according to principal components regression analysis (Supplementary Data). There is a notable paucity of energetically stable, low C₄ sequences.

While stable folding is believed to be a prerequisite for function (46), Cₖ is not a perfect predictor of function. For example, sequence libraries containing deliberate repetitive patterns (alternating purine/pyrimidine) would have lower Cₖ on an average, but they perform at least as well as random libraries during SELEX because the design favors hairpin formation (46). Also, some rare structures might only be formed if the composition is biased. For example, sequences depleted in U and enriched in G are more likely to form stable structures, presumably because small regions of base-pairing are stabilized by this composition (22). Computational studies suggest that structures with long loop regions are favored by enrichment for A and C, and the optimal composition depends on the desired motif and structure (24). Loop regions in ribosomal RNAs tend to be A-rich, while G, C and U tend to comprise the stems (47). RNA folding simulations suggest that folding could be improved by a small compositional bias (nucleotide frequencies within 2-fold of each other) (23). It should be noted that the relationship of sequence, structure and function is complex and not yet fully understood, and well-folded structures are not always functional; mutations that preserve ribozyme fold might still destroy activity. Nevertheless, to the extent that structure may be important for function, in general Cₖ is a measure of compositional diversity and structural potential for a given sequence.

## Measuring diversity of a pool

To quantify the diversity among different sequences in a pool, we also measure the population-level entropy D of a pool of molecules:

$$D = - \sum_{i=1}^{N} n_i \log_2(n_i),$$

where i is an index for unique sequences, N is the total number of unique sequences in the pool and nᵢ is the fraction of sequences in the pool that consist of copies of the ith sequence. D is zero if all molecules are identical and D is maximal when molecules are distributed uniformly through sequence space. In contrast to Cₖ (a property of each sequence), D is a property of the entire pool.

## Simulations of prebiotically plausible reactions

To understand the effect of prebiotically plausible chemical reactions on compositional diversity, we first simulated a population of binary sequences undergoing three reactions: concatenation, template-directed ligation and hydrolysis. During concatenation, the 5'-end of one monomer (or polymer) reacts with the 3'-end of another monomer (or polymer) with rate constant kcon. This process first polymerizes monomers into oligomers, and later joins monomers and oligomers in
template-independent reactions. Template-directed ligation can occur when two oligomers anneal adjacent to one another on a template sequence, leading to the ligation of the two oligomers with rate constant $k_{\text{lig}}$ (48). Template-directed ligation appears to be a general phenomenon, occurring with peptides, small molecules and nucleic acids (49–51), and it can greatly accelerate bond formation (52–54). Interestingly, template-directed ligation of oligonucleotides appears to be relatively unbiased compared to monomer polymerization, permitting the incorporation of nucleotides that are effectively unreactive as monomers (55). For the purpose of modeling, we assume that three or more adjacent ‘Watson–Crick base-pairs’ (i.e. 0’s pairing with 1’s in our two-letter model) are required for annealing (34,54,56,57). Finally, hydrolysis of phosphodiester bonds, an important process for RNA molecules, occurs in our model at a constant rate per bond ($k_h$).

## Model parameters

The parameters of our simulations are the two dimensionless ratios: $r_{\text{con}} = k_{\text{con}}c_0/k_h$, where $c_0$ is the concentration of monomers, which gives the relative strength of concatenation and hydrolysis; and $r_{\text{lig}} = k_{\text{lig}}c_0/k_{\text{con}}$, which gives the relative strength of template-directed ligation and concatenation. In experiments, $c_0$ is usually in the millimolar range, $r_{\text{con}}$ is roughly 1–100, and $r_{\text{lig}}$ is between $10^3$ and $10^7$ (see Supplementary Data), so we use these parameters in our simulations. For computational tractability, we use a two-base system in the modeling for the purpose of building intuition. A two-base system has been proposed as a progenitor of the four-base system (12,58), and a ribozyme can be composed of only two bases (25). However, because a four-base system would be more realistic and it has been argued that this alphabet size is optimal (59), we also investigated the four-base system to the extent that it was computationally tractable. Regardless, a four-base system is used in our DNA-based experiments testing the predictions of the simulations.

Based on these chemical reactions, we implemented a stochastic simulation of a small reactor (e.g. a protocell) and a deterministic simulation mimicking a very large reactor. The stochastic simulations were initiated with ~400 monomers (corresponding to a concentration of ~10 mM in a protocell ~50–100 nm in diameter). We recorded the average $C_k$, $D$ and the length distribution after the reactors reached steady state (Supplementary Data). While the stochastic results are most relevant to prebiotic protocells, we used the deterministic results to understand diversity for computational reasons. The deterministic simulations are generalizations of a previously described ‘prelife’ framework (Supplementary Data) (60–62). We examined both possible sources of bias: (i) biased reactivity and (ii) biased initial monomer abundance. Based on the reactivity and abundance differences of the literature cited earlier, the bias examined in each case was roughly one order of magnitude.

## RESULTS

### Simulation: template-directed ligation causes a shift toward longer sequences

In the absence of template-directed ligation, both sources of bias resulted in an exponential relationship between length and abundance at steady state, with the scaling determined by the ratio $r_{\text{con}}$. We give an analytical proof of this relationship, which has been seen in other models of polymerization (63), in Supplementary Data. While increasing concatenation would also create longer products due to greater bond formation, even high concatenation rates would still give an exponentially decreasing distribution of lengths. In contrast, template-directed ligation skewed the distribution qualitatively toward longer lengths (Figure 2a and Supplementary Data), resulting in a substantial excess of long sequences compared to an exponential distribution. The skew may occur because this process uses somewhat long substrates (greater than or equal to three bases) to make longer products in relatively few steps. Since ribozymes and

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /><figcaption>**Figure 2.** Template-directed ligation increases average length and compositional diversity in silico. (a) Length distribution of binary sequences with or without template-directed ligation [$r_{\text{lig}}$ = 0 (red) or $10^6$ (blue); $r_{\text{con}}$ = 10 in both cases]. Length is the number of bases per molecule. (b) Compositional diversity $C_3$ at several $r_{\text{con}}$ values, with or without template-directed ligation, when monomer reactivity is biased [19-fold difference between $k_{\text{con}}$; $r_{\text{lig}}$ = 0 (red) or $10^6$ (blue); length = 15].</figcaption></figure>
aptamers typically have a length of 30 bases or greater (45), template-directed ligation could improve the chance of obtaining functional molecules simply by increasing the number of long polymers. For example, as $r_{\text{lig}}$ increased from 0 to $10^6$ ($r_{\text{con}} = 10$), the mass fraction of ribozyme-length sequences (>30 bases) increased from 0% (numerically undetectable) to >5%. A similar trend is seen using a four-base simulation (Supplementary Data).

## Simulation: template-directed ligation increases compositional diversity

Template-directed ligation increased the average compositional diversity $C_3$ beyond that achieved by concatenation alone when analyzing product sequences of the same length. When reactivities were biased, $C_3$ depended on the rates of both concatenation and template-directed ligation. Without template-directed ligation, a system with higher $r_{\text{con}}$ had higher average $C_3$ (Figure 2b). This effect appears to be a consequence of mass action, as the less reactive monomer is increasingly incorporated into polymers when concatenation is fast relative to hydrolysis. A simplified analytical model demonstrates this effect (Supplementary Data). However, at a given $r_{\text{con}}$, template-directed ligation further increased average $C_3$ (Figure 2b), particularly at low concatenation rates. A four-base system appears to give similar results, with the caveat that our analysis was limited by computational tractability (Supplementary Data). Since template-directed ligation, like concatenation, increased the amount of bond formation relative to hydrolysis, one possible explanation might again be mass action. Therefore, we also measured $C_3$ as a function of the total rate of bond-forming events (concatenation and template-directed ligation). At the same rate of bond formation, template-directed ligation still increased the $C_3$ of the sequences, such that the majority of the increase of $C_3$ with $r_{\text{lig}}$ was not simply the result of increased bond formation (Supplementary Data). Another possible mechanism for this increase is that template-directed ligation is a relatively unbiased mode of ligation compared to concatenation. To illustrate this point, we performed simulations in which we artificially relaxed the requirement for complementary base-pairing in template-directed ligation, which we call 'relaxed-ligation'. Relaxed-ligation retains the effect of introducing unbiased reactions while eliminating the more subtle effects stemming from the information content of the reacting sequences. Relaxed-ligation produces average $C_3$ that are similar to comparable template-directed ligation simulations (Supplementary Data). This result suggests that the unbiased nature of template-directed ligation is an important explanation for the increase of $C_3$ with template-directed ligation.

In simulations where monomer abundance was biased, concatenation alone resulted in relatively low average $C_3$ (~0.4), independent of $r_{\text{con}}$. The effect of template-directed ligation was complicated but it tended to increase compositional diversity (Supplementary Data). This may be due to increased incorporation of the less

abundant monomer through complementary base pairing in addition to the effects detailed below. Overall, both sets of simulations suggested that template-directed ligation caused a relative increase of compositionally diverse sequences.

## Simulation: diversity of the pool

While $C_k$ measures internal heterogeneity in a sequence and D measures population-wide diversity, we found that these measures were highly correlated in our simulations across a range of parameters (Supplementary Data). Therefore, increased average compositional diversity within a sequence implied increased diversity among molecules in the pool.

## Experimental: compositional diversity in template-directed ligation of DNA

To experimentally test our main prediction that template-directed ligation increases the average compositional diversity of a heterogeneous pool of sequences containing all 4 nt, we performed template-directed ligation in a pool of sequences made by degenerate DNA oligonucleotide synthesis with all four bases (A, C, G, T). The experiments described here were performed with DNA (not RNA). We chose to use DNA because reactivity differences during synthesis are well known (64). Slight differences in phosphoramidite reactivity result in small biases in the composition of a degenerate pool, analogous to the larger biases resulting from reactivity differences in prebiotic syntheses. Since the reactivity biases in phosphoramidite synthesis are relatively small, this experiment is a stringent test of whether template-directed ligation can increase average $C_k$. We studied whether the bias would be countered by template-directed ligation. Degenerate templates (length 40; four bases) and octamer substrates (four bases) were used to perform ligation. The size difference between the templates, substrates and expected ligation products permitted later gel purification of the products. Bond formation was catalyzed by cyanogen bromide after an annealing step (34) and the products of ligation were isolated by gel purification. Templates, octamers and products were sequenced using the Illumina platform (Supplementary Data). We measured the proportion of sequences that had $C_3$ close to that of ribozymes ($C_3$ of 0.95 or greater) and found that the ligation products were significantly shifted toward higher $C_3$ compared to the templates (Figure 3a and Supplementary Data). Ligation products also had higher $C_3$ than sequences predicted from random concatenation of the sequenced octamers, indicating that template-directed ligation could increase average $C_3$ beyond unbiased concatenation by favoring compositionally diverse templates. The proportion of ligation products of high $C_3$ was similar to that of a uniform random pool, indicating that template-directed ligation quantitatively countered the initial bias of synthesis (Figure 3a). The shift was not due to artifacts from comparing samples of different length, experimental bias during sequencing or a shift in GC content (Supplementary Data). We attempted to ascertain whether sequence elements from a recently
<figure><img src="image_7.png" /><figcaption>**Figure 3.** Experimental relationship between compositional diversity and template-directed ligation. (a) Fraction of DNA sequences having high compositional diversity ($C_3 > 0.95$; analysis length = 16) after template-directed ligation in a heterogeneous pool of degenerate oligonucleotides including four bases. A greater fraction of reaction products (yellow) have high $C_3$ relative to the templates (red = average $C_3$ of 16-mers contained in sequenced 40-mer templates) and substrates (orange = $C_3$ of 16-mers from *in silico* non-templated, random concatenation of experimentally sequenced octamers). The fraction of high $C_3$ sequences in a uniform random pool is shown in green. Error bars are SDs from replicate sequencing experiments. (b) Polyacrylamide gel showing higher molecular weight products of template-directed ligation for different single templates from a binary alphabet. Molecular weight markers are given in the left lane. ‘O’ indicates a reaction without template added. Template $C_3$ increases from left ($C_3 = 0$) to right ($C_3 = 0.97$; see ‘Materials and Methods’ section for list of sequences).</figcaption></figure>

described RNA replicase (65) could be found at greater frequency in the pool of template-directed ligation products compared with random concatenation of the octamers; no difference was apparent by this test (Supplementary Data), but the importance of this finding is tempered by our incomplete understanding of the sequence elements supporting ribozyme function.

The error of our measurements of compositional diversity in ligation reactants and products could be calculated in two ways: (i) SD among experiments, as shown in Figure 3a or (ii) SD from bootstrapping subsamples. The error (i) reflects the deviation between experiments. The error (ii) reflects the sampling error of sequencing. The sampling error is similar in magnitude to the error between experiments (Supplementary Data). Also, a possible source of differences between templates, octamers and ligation products is bias introduced by RNA ligase during preparation for deep sequencing. This bias is most pronounced at the 5'- and 3'-ends of the sequence reads (66). To confirm that the differences in measured $C_k$ among these samples were not due to artifacts from bias at the ends of the sequences, we randomized the first and last base of each sequence read (i.e. replaced the 3' and 5' bases with a randomly chosen base: A,C,G,T). The $C_k$ of this end-randomized set of sequences were calculated. We found that end-randomization did not affect the conclusion that ligation products had significantly higher $C_k$ than the templates and octamers (Supplementary Data).

These results confirmed the prediction that template-directed ligation increases the compositional diversity of a heterogeneous pool of DNA sequences comprising four bases. One possible mechanism for this increase could be that internally diverse sequences were better templates. We can calculate the ratio $R$ of the

probabilities of template-directed ligation occurring on a high $C_k$ ($p_{high}$) versus low $C_k$ ($p_{low}$) template:

$$R = \frac{p_{high}}{p_{low}} = \frac{1 - (1 - p_1 p_2)^N}{p_1 \times (1 - (1 - p_2)^N)}$$

where $p_1$ is the probability of the template annealing to two adjacent fragments and $p_2$ is the probability of bond formation. Both $p_1$ and $p_2$ are <1 in practical situations. The ratio $R$ is therefore always >1 (Supplementary Data), meaning that high $C_k$ sequences are more likely to be templates. Therefore, templates with high $C_k$ should be more likely to propagate their sequence information.

To test this experimentally, we studied the dependence of ligation efficiency on $C_3$ for different templates. A set of binary DNA templates (two bases: C,T; 32-mer) of varying $C_3$ was designed such that any 8-mer subsequence within the templates was 1 of 25 known octamer sequences (two bases: A,G), allowing the use of a defined set of substrates. Although this base composition is not a good mimic of a prebiotic reaction, it was chosen to minimize intramolecular secondary structure in order to focus on the effect of sequence heterogeneity. The templates were mixed with an excess of radiolabeled 5'-phosphorylated binary DNA octamers (A,G; Supplementary Data). All sequences had a GC content of 47-50% except for the template with $C_3 = 0$. Ligation reactions were analyzed by polyacrylamide gel electrophoresis to visualize higher molecular weight products. We found a positive relationship between $C_3$ and amount of products formed (Figure 3b). A similar trend was observed using random degenerate octamers and longer templates (Supplementary Data). This suggests that ligation efficiency on heterogeneous templates is one mechanism by which $C_k$ increases in the products of template-directed ligation.
<figure><img src="image_8.png" /><figcaption>**Figure 4.** Proposed prebiotic scenario. Monomers first concatenate into compositionally biased short oligomers. When the oligomers are long enough to act as templates, template-directed ligation produces relatively long, compositionally diverse sequences. These sequences can fold into stable structures, some of which may be catalytically active, leading to the RNA world.</figcaption></figure>

DISCUSSION

Our simulations and experiments suggest that compos-
itional diversity in a pool of nucleic acids could have
emerged early on, despite biases in monomer abundance
and reactivity. The increase due to template-directed
ligation may have at least two causes. First,
template-directed ligation is relatively unbiased
compared to concatenation, so it would counter the intrin-
sic bias of the system. Second, ligation may happen more
efficiently on a compositionally diverse template, because
internal sequence correlations in a low C<sub>k</sub> template reduce
the number of independent possibilities for ligation.
Essentially, a compositionally diverse template could
utilize a greater fraction of the substrate pool while the
subsequences within a repetitive template would compete
with each other for substrates.

While it may be possible to imagine scenarios where
different biases cancel one another to produce complex
pools, such finely tuned rates are unlikely in real
systems. Based on our results using two-letter simulations
and template-dependent DNA ligation, we can suggest the
following prebiotic scenario (Figure 4). Initially the
sequence pool would consist of short, highly composition-
ally biased sequences resulting from differences in reactiv-
ity among the nucleotides. However, once these sequences
become long enough to serve as templates (length ≥ 6), the
general mechanism of template-directed ligation would
favor propagation of internally diverse sequences. A
small increase in diversity would correspond to an expo-
nentially large increase in the fraction of sequence space
that would be explored. One should note that the optimal
compositional diversity for forming secondary structures
may be less than the maximum possible. For example,
compositional bias toward GC-rich sequences may be a
reasonable criterion for identifying non-coding RNAs in
the genome due to the effect on folding stability (67),
although formal structure itself does not appear to be a
good criterion (perhaps because the compositional diver-
sity of a genome tends to be fairly high, giving a relatively
large probability of forming structures). Nevertheless, it is
unclear whether the bias from prebiotic processes would
be in the correct direction to favor structures, and it would
still be desirable to increase diversity over the substantial
~10-fold initial compositional bias estimated for prebiotic
reactions. As the compositional bias disappeared,
well-folded sequences could emerge. In addition,
template-directed ligation would rapidly stitch together
short sequences to produce a qualitative shift toward

long sequences. The combined effects on diversity and
length would enable the generation of ribozymes. These
first inefficient ribozymes could then ‘jump-start’ the evo-
lution of sequences with greater function and complexity
through natural selection, especially within a spatially
restricted context (44,63,68).

Although it has been previously hypothesized that
abstract measures of primary sequence information are
unrelated to RNA function (11,69), we found a correl-
ation between folding energy and C<sub>k</sub> *in silico*. This
suggests that internal heterogeneity, which is calculable
from primary sequence alone, is an interesting measure-
ment in addition to functional information or genomic
complexity (which require knowledge of functional
activity or fitness, respectively) (36,69). An important
caveat regarding this relationship is that the minimum
free energy of a sequence is only one of several features
that would be important for functional activity. Other
features would also be desirable [e.g. a large energy gap
between the most stable fold and misfolded structures, or
low structural ‘plasticity’ (70)]. Many desirable features
are poorly understood. Interestingly, our simulations
results suggest that, although template-independent
processes result in exponential length distributions,
template-directed ligation would skew the distribution
qualitatively toward long sequences. A minimum length
appears to be required to find certain activities. This was
demonstrated by a series of selections for isoleucine
aptamers that differed only by the length of the random
region; no aptamers were isolated at the shortest length
(16 bases) (32). Therefore, template-directed ligation may
increase the probability of finding functional molecules by
increasing the frequency of long sequences. Our results
also highlight the importance of templating as a special
property of nucleic acids during the origin of life: in
addition to enabling the faithful replication of informa-
tion, the ability to template could have promoted a search
of functionally rich regions of sequence space.

Our modeling, while adequate for generating a hypoth-
esis that could be experimentally tested, could be made
more realistic in several ways. The alphabet size could
be increased to include four bases, although this modifi-
cation is computationally expensive because longer se-
quences would be needed to differentiate among the
more varied compositions. Secondary structure could be
included, which might interfere with templating and
protect against degradation (71). The fact that our DNA
experiments (including a four-letter alphabet and the
possibility of secondary structure) show that template-
directed ligation increases compositional diversity
suggests that the overall result is not greatly influenced
by the simplifications in the modeling. The rate of
non-templated concatenation might depend on the
length of the reactants, and circularization reactions
might select against certain lengths. Interestingly, models
of prebiotic polymerization of monomers that neglect the
concatenation of oligomers (i.e. strong dependence of rate
on substrate length) also yield exponential length distribu-
tions at equilibrium (61–63,72), suggesting that the quali-
tative distribution is not changed by the inclusion of
oligomer concatenation. More experimental investiga-
tion would be required to understand the possible
dependencies. Advances in the modeling based on such
realistic features would be worthwhile for a more
detailed prediction of the outcome of prebiotically plaus-
ible reactions. Our experiments used DNA because biases
during synthesis are well known and we expect DNA to
resemble RNA with respect to annealing of oligonucleo-
tides. While the details of formation of secondary struc-
ture differ for DNA and RNA, both types of molecule can
fold into catalytically active structures (73). Nevertheless,
an investigation of compositional diversity using RNA
would be more realistic as a model of the RNA world.

It is generally assumed that the emergence of ribozymes
was the result of natural selection for replication in a pool
of RNA sequences (3,44), but the pathway for generating
the very first ribozymes is unknown. The probability of
finding functional sequences also depends on the desired
activity. Functions that can be performed by short motifs,
such as aminoacylation or self-cleavage (24,31,74), could
potentially be found even in highly biased sequence pools
since the probability of finding the motif is relatively large.
However, more sophisticated functions that appear to
require longer motifs, such as an RNA polymerase
(27,65), would be more likely to arise in a sequence pool
if the prebiotic compositional bias were at least somewhat
mitigated. It has been suggested that physical ordering
effects alone could not produce functional molecules
(11). Here, we have shown how long, compositionally
diverse and well-folded sequences might be produced as
a consequence of prebiotically plausible chemical
mechanisms.

SUPPLEMENTARY DATA

Supplementary Data are available at NAR Online:
Supplementary Figures 1–24 and Supplementary
References [75–86].

ACKNOWLEDGEMENTS

We thank Niles Lehman, Jeffrey Bada, Jim Collins, Allan
Drummond, Suckjoon Jun, Arthur Lander, David Liu,
Andrew Murray, Eugene Shakhnovich and Jack Szostak
for comments.

FUNDING

Human Frontiers Science Program (postdoctoral fellow-
ships to J.D. and R.X.); Harvard University (I.A.C.,
Bauer Fellow); NIH grant GM068763 to the Center for
Modular Biology at Harvard; NSF/NIH Joint Program in
Mathematical Biology (NIH grant R01GM078986 to
M.A.N.); John Templeton Foundation (M.A.N.); Bill
and Melinda Gates Foundation (Grand Challenges grant
37874 to M.A.N.) and J. Epstein (M.A.N.). Funding for
open access charge: NIH (grant GM068763).

*Conflict of interest statement.* None declared.

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