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# Origin of the RNA world: The fate of nucleobases in warm little ponds

Edited by Donald E. Canfield, Institute of Biology and Nordic Center for Earth Evolution, University of Southern Denmark, Odense M., Denmark, and approved August 28, 2017 (received for review June 7, 2017)

## Significance

There are currently two competing hypotheses for the site at which an RNA world emerged: hydrothermal vents in the deep ocean and warm little ponds. Because the former lacks wet and dry cycles, which are well known to promote polymerization (in this case, of nucleotides into RNA), we construct a comprehensive model for the origin of RNA in the latter sites. Our model advances the story and timeline of the RNA world by constraining the source of biomolecules, the environmental conditions, the timescales of reaction, and the emergence of first RNA polymers.

## Abstract

Before the origin of simple cellular life, the building blocks of RNA (nucleotides) had to form and polymerize in favorable environments on early Earth. At this time, meteorites and interplanetary dust particles delivered organics such as nucleobases (the characteristic molecules of nucleotides) to warm little ponds whose wet–dry cycles promoted rapid polymerization. We build a comprehensive numerical model for the evolution of nucleobases in warm little ponds leading to the emergence of the first nucleotides and RNA. We couple Earth’s early evolution with complex prebiotic chemistry in these environments. We find that RNA polymers must have emerged very quickly after the deposition of meteorites (less than a few years). Their constituent nucleobases were primarily meteoritic in origin and not from interplanetary dust particles. Ponds appeared as continents rose out of the early global ocean, but this increasing availability of “targets” for meteorites was offset by declining meteorite bombardment rates. Moreover, the rapid losses of nucleobases to pond seepage during wet periods, and to UV photodissociation during dry periods, mean that the synthesis of nucleotides and their polymerization into RNA occurred in just one to a few wet–dry cycles. Under these conditions, RNA polymers likely appeared before 4.17 billion years ago.

One of the most fundamental questions in science is how life first emerged on Earth. Given its ubiquity in living cells and its ability to both store genetic information and catalyze its own replication, RNA probably formed the basis of first life (1). RNA molecules are made up of sequences of four different nucleotides, the latter of which can be formed through reaction of a nucleobase with a ribose and a reduced phosphorous (P) source (2, 3). The evidence suggests that first life appeared earlier than 3.7 Gy ago (Ga) (4, 5), and thus the RNA world would have developed on a violent early Earth undergoing meteoritic bombardment at a rate of ^{12} kg/y (6), which is ∼8 to 11 orders of magnitude greater than today (7). At that time, the atmosphere was dominated by volcanic gases, and dry land was scarce as continents were rising out of the global ocean. What was the source of the building blocks of RNA? What environments enabled nucleotides to polymerize and form the first functioning RNA molecules under such conditions? Although experiments have produced simple RNA strands in highly idealized laboratory conditions (8, 9), the answers to these questions are largely unknown.

As to the sources of nucleobases, early Earth’s atmosphere was likely dominated by CO_{2}, N_{2}, SO_{2}, and H_{2}O (10). In such a weakly reducing atmosphere, Miller–Urey-type reactions are not very efficient at producing organics (11). One solution is that the nucleobases were delivered by interplanetary dust particles (IDPs) and meteorites. During these early times, these bodies delivered

A central question concerning the emergence of the RNA world is how the polymerization of nucleotides occurred. Warm little ponds (WLPs) are excellent candidate environments for this process because their wet and dry cycles have been shown to promote the polymerization of nucleotides into chains possibly greater than 300 links (8). Furthermore, clay minerals in the walls and bases of WLPs promote the linking of chains up to 55 nucleotides long (19). Conversely, experiments simulating the conditions of hydrothermal vents have only succeeded in producing RNA chains a few monomers long (20). A critical problem for polymerizing long RNA chains near hydrothermal vents is the absence of wet–dry cycles.

## Model: Fates of Nucleobases in Evolving WLPs

We compute a well-posed model for the evolution of WLPs, the fates of nucleobases delivered to them, and the emergence of RNA polymers under early Earth conditions. The sources of nucleobases in our model are carbonaceous meteorites and IDPs whose delivery rates are estimated using the lunar cratering record (6, 11, 21), the distribution of asteroid masses (21), and the fraction of meteorites reaching terminal velocity that are known to be nucleobase carriers (13, 22). The WLPs are “targets” in which molecular evolution of nucleobases into nucleotides and subsequent polymerization into RNA occur. The evolution of ponds due to precipitation, evaporation, and seepage constitutes the immediate environments in which the delivered nucleobases must survive and polymerize. [We don’t emphasize groundwater-fed ponds (hot springs) because their small number on Earth today—approximately thousands—compared with regular lakes/ponds—

To calculate the number of carbonaceous meteorite source depositions in target WLPs on early Earth, we combine a continental crustal growth model (29), the lake and pond size distribution and ponds per unit crustal area estimated for ponds on Earth today (23), the asteroid belt mass distribution (21), and three possible mass delivery models based on the lunar cratering record (6, 21). This results in a first-order linear differential equation (Eq. **S18**), which we solve analytically. The details are in *SI Text*, and the main results are discussed in *Meteorite Sources and Targets*.

Nucleobase abundances in WLPs from IDPs and meteorites are described in our model by first-order linear differential equations (Eqs. **S34** and **S38**, respectively). The equations are solved numerically (see *SI Text* for details).

Our fiducial model WLPs are cylindrical (because sedimentation flattens their initial bases) and have a 1-m radius and depth. We find these ponds to be optimal because they are large enough to not dry up too quickly but small enough that high nucleobase concentrations can be achieved (see *SI Text*).

## SI Text

## Calculating WLP Surface Area on Early Earth

The earliest fairly conclusive evidences of life are in the form of light carbon signatures in graphite globules formed from marine sediments, and stromatolite fossils, both which are dated to be 3.7 Gy old (4, 5). Therefore, nucleobase deposition in WLPs and subsequent reactions to form nucleotides and RNA would have occurred sometime between

Once Theia impacted the proto-Earth

An estimate of the surface area of WLPs on early Earth has not been previously attempted; however, it is often suggested that they were typical on early Earth continents (33, 44, 48). Water-deposited sediments dated at 3.8 Ga indicate early erosion and transport of sediment; therefore, at that time, at least some continental mass must have been exposed above sea level, on which WLPs could have formed (33).

### Continental Crust Growth Model.

The number of WLPs present at any given time depends on the fraction of continental crust above sea level. Calculations from a continental crust growth model show a linear formation of early crust, increasing from 0 to 12.8*t* is the time in gigayears (

We assume the number of bodies of water per unit area of continental crust is constant over time; thus, by multiplying Eq. **S1** by the number of lakes and ponds on Earth today, we get the number of bodies of water on Earth at any date from 4.5 Ga to 3.7 Ga. The number of lakes and ponds on Earth today (down to 0.001 km^{2}) is estimated to be 304 million (23); therefore, the equation becomes

### Lake and Pond Size Distribution.

The size distribution of lakes and ponds on Earth today follows a Pareto distribution function (23).*k* is the smallest lake/pond area in the distribution. The shape parameter was calculated for lakes and ponds down to 0.001 km^{2} to be

The total area of ponds on Earth in a given size range can then be calculated by multiplying Eq. **S3** by ^{2}).

There is also a lower size limit, as ponds that evaporate too quickly spend the majority of their time in the dry state. This would prevent nucleobase outflow from the pores of meteorites. Moreover, the probability of meteorite deposition in WLPs decreases for decreasing pond radii. A cylindrical WLP at 65 °C with a radius and depth of

## Calculating Carbonaceous Meteorite Depositions in WLPs

Aerodynamic forces fragment meteoroids that enter the atmosphere, which increases their total meteoroid cross-section, and thus their aerodynamic braking (32). Numerical simulations show that the fragments of carbonaceous meteoroids with initial diameters up to 80 m and atmospheric entry velocities near the median value [15 km/s (31)] reach terminal velocity (32). These fragments do not produce craters upon impact (49) and can be intactly deposited into WLPs. Larger meteoroids produce fragments with impact speeds too fast to avoid cratering and partial or complete melting or vaporization of the impactor. The same numerical simulations calculate the largest fragments from an 80-m-diameter carbonaceous meteoroid of initial velocity 15 km/s to be

The optimal diameter range for carbonaceous meteoroids to deposit a substantial fraction of mass into WLPs at terminal velocity is therefore 40 m to 80 m. We base our calculation of carbonaceous meteoroid fragment depositions on this range.

### Mass Delivery Models.

The lunar cratering record analyzed by the Apollo program has revealed a period of intense lunar bombardment from

Analyses from both dynamic modeling and the lunar cratering record estimate the total mass delivered to early Earth during the LHB to be

Equations for the minimum and maximum mass delivered to early Earth, given that a sustained declining bombardment preceded 3.9 Ga, are (6)^{18} kg), *b* = 0.47, *R*_{moon} = 1737.1 km), and

Taking the derivatives of Eqs. **S7** and **S8** gives us the corresponding rates of mass delivered to early Earth.

### Impactor Mass Distribution.

Chemical analyses of lunar impact samples, and crater size distributions, suggest that the impactors of Earth and the moon before

The early Earth impactor mass distribution for impactors with radii 20 m to 40 m, adjusted for the total mass delivered during the LHB, follows the linear relation

To get the impactor mass distributions for the mass delivered between **S11** by Eq. **S6**, **S9**, or **S10**, and divide by

### Impactor Number Distribution.

Eq. **S12** can be turned into a number distribution (from

### Total Number of Carbonaceous Impactors.

Although some carbonaceous chondrites may have originated from comets (53), for this calculation, we conservatively assume that all carbonaceous meteorites originated from asteroids.

Integrating Eq. **S13** from

### Probability of WLP Deposition.

The probability of an infinitesimally small object hitting within a target area, given that the probability of hitting anywhere within the total area is equal, is the geometric probability

To use Eq. **S15** to calculate the probability for the fragments of a single meteoroid landing in a primordial WLP,

The area of the asymmetric “lens” in which any two circles intersect is

In Fig. S6, the asymmetric lens created by the intersection of the combined WLP surface area at a given time and the meteoroid fragment debris area corresponds to the area of the largest individual WLP in our distribution. Because the effective target area radius, **S16** at ^{−4} km^{2},

Finally, the probability of the fragments from all CM-, CI-, or CR-type meteoroids (Mighei type, Ivuna type, and Renazzo type, respectively) with radii **S14** and **S15**.

In Fig. S7, we plot the normalized probability distributions (

One assumption is made in our deposition probability calculation, which is, given that the largest WLP considered is completely within the carbonaceous meteoroid’s strewnfield, at least one fragment will land in the WLP. (An equivalent assumption would be, given that 100 of the smallest WLPs considered are completely within the meteoroid’s strewnfield, at least one fragment will deposit into one of the ponds.) To determine whether this is the case, we need a good estimate for the number of fragments that spread over a debris field from a single carbonaceous meteoroid. For the Pułtusk stony meteoroid, which entered Earth’s atmosphere above Poland in 1868 (55), the number of fragments is estimated to be 180,000 (55). Although the Pułtusk meteorites may not represent the typical fragmentation of stony meteoroids, since this meteoroid is about 1.6 times denser than the average carbonaceous meteoroids in our study (56), we would expect a carbonaceous meteoroid to fragment more than the typical stony meteorite. If meteoroid fragments are randomly spaced within a strewnfield, then Eq. **S15** multiplied by the number of meteoroid fragments will give us roughly the number of fragments that will enter a WLP. (In this case,

### Sensitivity Analysis.

In our estimate of the number of carbonaceous meteoroids that led to WLP depositions on early Earth, we assume that, from 4.5 Ga to 3.7 Ga, the continental crust grows at 16**S18**) is directly proportional to the number of WLPs on early Earth, varying the growth rate of WLPs by plus or minus one order of magnitude equates to a plus or minus one order of magnitude uncertainty in the WLP deposition expectation values (Fig. 1).

## Sources and Sinks Model Overview

Calculating the water and nucleobase content in WLPs over time is a problem of sources and sinks. These sources and sinks are illustrated in Fig. 2 and displayed in Table S1.

Because nucleobase diffusion from carbonaceous meteorite fragments is slow (*Nucleobase Outflow and Mixing*), this source is only turned on in the wet phase. Although it may be possible for nucleobases to occasionally enter WLPs from runoff, we do not consider this as a source. IDPs that fall on dry land are the most likely nucleobase source to be carried by runoff into WLPs (because of their low mass). However, these IDPs are exposed to photodissociating UV light until they are picked up by a runoff stream, by which time few if any enclosed nucleobases likely remain. Hydrolysis of nucleobases only occurs in the presence of liquid water; therefore, we only turn on this sink when our ponds are wet. Similarly, seepage of nucleobases through the pores in the bases of WLPs only occurs during the wet phase. A 1-m column of pond water can absorb UV radiation up to

## Pond Water Sources and Sinks

### Evaporation.

There are many variables that could go into a pond evaporation calculation. However, a simple relation was obtained by measuring the depth and temperature of a

This relation is converted to meters per year,

### Seepage.

Unless the material (e.g., basalt, soil, clay) at the base of a WLP is saturated in water, gravity will cause pond solution to seep through the pores in this material. The average seepage rate of 55 small ponds in Auburn, Ala., was measured to be 5.1 mm^{−1} (26). This value is high compared with the average seepage rates from small ponds in North Dakota and Minnesota (1.0 mm^{−1}) and the Black Prairie region of Alabama (1.6 mm^{−1}) (26). These seepage rates are comparable in magnitude to the pond evaporation rates in *Evaporation*, and therefore must be considered as a sink for water and nucleobases in our WLP model. We take an average of the above three values and apply a constant seepage rate of 2.6 mm^{−1} to our WLP water evolution calculations.*Nucleobase Sinks*.

### Precipitation.

If we ignore the possibility of local water geysers, the main source of pond water is likely to be precipitation. It has been shown that the vast majority of monthly precipitation climates around the world can be adequately described by a sinusoidal function with a 1-y period (24). That is,

From 1980 to 2009, the mean precipitation on Earth ranged from ^{−1} to 10 m^{−1} (with a global mean of ^{−1}), the seasonal precipitation amplitudes ranged from

### Summary.

The evaporation and seepage rates minus the rate of water rise due to precipitation gives us the overall rate of water decrease in a WLP.**S23** is too complex to be solved by standard analytical techniques or mathematical software; therefore, we solve it numerically using a forward time finite difference approximation with the boundary conditions 0 ^{−3}.

## Nucleobase Sinks

### Hydrolysis.

The first-order hydrolysis rate constants for adenine (A), guanine (G), uracil (U), and cytosine (C) have been measured from decomposition experiments at pH 7 (28). These rate constants are expressed in the Arrhenius equations,**S25**–**S28** into the first-order reaction rate law,^{−1}.

The hydrolysis rates of adenine, guanine, and cytosine remain relatively stable in solutions with pH values from 4.5 to 9 (28, 59). WLPs may have been slightly acidic (from pH 4.8 to 6.5) due to the higher partial pressure of CO_{2} in early Earth atmosphere (34).

### UV Photodissociation.

The photodestruction of adenine has been studied by irradiating dried samples under Martian surface UV conditions (27). This quantum efficiency of photodecomposition (from 200 nm to 250 nm)—which is independent of the thickness of the sample—was measured to be

For the calculation of the quantum efficiency of adenine, a beam of UV radiation was focused on a thin compact adenine sample formed through sublimation and recondensation (27). In this case, all of the photons in the beam of UV radiation were incident on the nucleobases. In the WLP scenario, not all of the incoming UV photons will be incident on nucleobases. Instead, large gaps can exist between nucleobases that collect at the base of the pond. Therefore, the number of photons incident on the pond area is not the same as those incident on the scattered nucleobases unless there are at least enough nucleobases present to cover the entire pond area. Since the nucleobases are mixed well into the pond water before complete evaporation, we assume nucleobases will spread out evenly as they collect on the base of the pond. This means we assume that all locations on the base of the pond are covered in nucleobases before nucleobases stack on top of one another. For low abundances of total nucleobases in a WLP, this approach will lead to a slightly higher estimate for the rate of photodissociation than expected. We deem this acceptable for a first-order estimate of nucleobase photodissociation.

The mass of nucleobases photodestroyed per year, per area covered by nucleobases (i.e., the photodestruction flux), is constant over time and is dependent on the experimentally measured quantum efficiency of photodecomposition.^{−1},

Our estimation of the photodestruction rate of a nucleobase depends on the total mass of the nucleobase within the WLP. If there is enough of the nucleobase present for the entire base of the pond to be covered, we can multiply the photodestruction flux by the entire pond area. Otherwise, we must multiply the photodestruction flux by the combined cross-sectional area of the nucleobase present in the WLP to get the photodestruction rate.

Assuming cloudless skies, an upper limit on early Earth integrated UV flux from 200 nm to 250 nm is ^{−2} (36, 60). UV wavelengths of _{2} and H_{2}O in the early atmosphere (36). The mass density of solid adenine is 1,470 kg^{−3}, making the distance between two stacked adenine molecules in the solid phase ^{−3}, respectively.

### Seepage.

The constant pond water seepage ^{−1} was determined in *Pond Water Sources and Sinks*. This can be used to calculate the nucleobase seepage rate via the equation

## Nucleobase Outflow and Mixing

Chondritic IDPs and meteorites are porous (61⇓–63). With the exception of the nucleobases potentially formed due to surface photochemistry (12), any soluble nucleobases delivered to prebiotic Earth by carbonaceous IDPs and meteorites would have lain frozen in the pores of these sources upon their entering the atmosphere. Pulse heating experiments show that approximately

We model the outflow of nucleobases from carbonaceous IDPs and meteorites and the mixing of a local concentration of nucleobases into a WLP using finite difference approximations of the one-dimensional advection–diffusion equation (see *Advection and Diffusion Model* for complete details).

Our model of nucleobase outflow is run for average-sized IDPs (*r* = 100 *r* = 1 cm), medium (*r* = 5 cm), and large (*r* = 10 cm) carbonaceous meteorites. The fraction of nucleobases remaining in each of these sources as a function of time is plotted in Fig. S4.

Our models show that the duration of nucleobase diffusion from carbonaceous IDPs and meteorites into WLPs is mostly determined by the radius of the source. For typical, 100-

For nucleobase mixing, we model a base-to-surface convection cell within cylindrical ponds with equal radii and depths of 1 m, 5 m, and 10 m. This model gives us the timescale of mixing a local concentration of nucleobases within WLPs. The maximum percent local nucleobase concentration difference from the average is plotted as a function of time in Fig. S8. This metric allows us to characterize the nucleobase homogeneity in a convection cell of the WLP.

Our simulations suggest that the mixing of local deposits of nucleobases in WLPs, resulting from their diffusion out of carbonaceous IDPs and meteorites, is a very efficient process. For a cylindrical WLP 1 m in depth, it will take about 35 min for a local deposition to homogenize in a convection cell within the pond. For larger WLPs, with 5- and 10-m depths, the nucleobase mixing time increases to 104 and 150 min, respectively. These short mixing times make it clear that, for carbonaceous meteorites

## Nucleobase Evolution Equation from IDPs

It is estimated that, at 4 Ga, approximately ^{−1} of carbonaceous IDPs were being accreted onto Earth (11). Since IDPs are tiny (typically

IDPs are thought to correspond to origins of asteroids or comets (11); therefore, at best, the average nucleobase abundances in IDPs could match the average nucleobase content within the nucleobase-rich CM, CR, and CI meteorites. The average abundances of adenine, guanine, and uracil in CM, CR, and CI meteorites are listed in Table S2, along with the weighted averages based on relative fall frequencies. These abundances might be an upper limit for the guanine, adenine, and uracil content of IDPs, because, unlike the interior of large meteorites, molecule-dissociating UV radiation can penetrate everywhere within micrometer-to-millimeter-sized pieces of dust.

The amount of cytosine that could have formed on the surfaces of primordial IDPs is not well constrained. Cytosine has been detected in experiments exposing IDP analogs to UV radiation, but hasn’t been quantified (12). Furthermore, these analog experiments formed cytosine via photoreactions involving pyrimidine: a molecule that has no measured abundance in IDPs or meteorites. For this analysis, we explore a best-case scenario, and set the maximum cytosine IDP abundance to 141.3 ppb (the possible upper limit of guanine in carbonaceous IDPs).

In *Nucleobase Outflow and Mixing*, we learned that nucleobase diffusion from IDPs is quick (lasting ^{−1} accretion rate of IDPs uniformly across the surface of Earth—assuming IDPs are all 100-^{−3})—then IDPs would drop into 1- to 10-m-radius primordial WLPs at approximately 0.05 h^{−1} to 5 h^{−1}. Since each carbonaceous IDP can only carry a tiny mass in nucleobases (

Thus, the differential equation for the mass of nucleobase

Using Eq. **S34**, we compute the nucleobase mass as a function of time numerically using a forward time finite difference approximation. We then divide the nucleobase mass by the water mass at each time step to obtain the nucleobase mass concentration over time. Because some ponds are seasonally dry, we freeze the water level at 1 mm during the dry phase to calculate a nucleobase concentration during this phase.

## Nucleobase Evolution Equation from Meteorites

Simulations show that the fragments from carbonaceous meteoroids with diameters from 40 m to 80 m and initial velocities of 15 km/s will expand over a radius of

After the deposition of meteoroid fragments into a WLP, the frozen meteorite interiors will thaw to pond temperature, allowing hydrolysis to begin inside the fragments’ pores. This means the total mass of nucleobases that diffuse from the fragments’ pores into the pond will be less than the total initial nucleobase mass within the deposited fragments. By integrating the nucleobase hydrolysis rate (Eq. **S29**), we obtain the mass of nucleobase

Unlike carbonaceous IDPs, which unload their nucleobases into a WLP in seconds, nucleobases may not completely outflow from all deposited carbonaceous meteoroid fragments before the WLP evaporates. (However, the nucleobases that do outflow from the meteorites will mix homogeneously into the WLP within a single day–night cycle.) Thus, we calculate the nucleobase outflow time constants for 1-, 5-, and 10-cm-radius carbonaceous meteorites by performing least-squares regressions of our nucleobase diffusion simulation results to the function

The results of the fits give diffusion time constants for 1-, 5-, and 10-cm-radius fragments of ^{−3} y, 0.12 y, and 0.48 y, respectively.

Adding up the sources and sinks gives us the nucleobase mass within the WLP from meteorite sources as a function of time and hydration time.

Since there are many possibilities for the sizes of meteoroid fragments that will enter a WLP, we consider three simplified models: All fragments that enter a WLP from a meteoroid of radius 20 m to 40 m are either 1 cm in radius, 5 cm in radius, or 10 cm in radius. These three models represent a local part of the strewnfield that deposited either many small fragments, mostly medium-sized fragments, or just a couple to a few large fragments.

Cytosine is unlikely to have sustained within meteorite parent bodies long enough to be delivered to early Earth by meteorites (15); therefore, we only model the accumulation of adenine, guanine, and uracil in WLPs from meteorite sources.

We solve Eq. **S38** numerically using a forward time finite difference approximation. Nucleobase concentration is then obtained by dividing the nucleobase mass by the water mass in the WLP at each time step.

## Additional Results

### Pond Water.

In Fig. S9, we explore the effects of changing temperature on wet environment WLPs of 1-m radius and depth (see Table 1 for wet environment model details). To do this, we vary our fiducial model temperatures (65 °C for a hot early Earth and 20 °C for a warm early Earth) by

### Nucleobase Accumulation from IDPs.

In Fig. S1, we explore the evolution of adenine concentration from only IDP sources in WLPs of 1-m radius and depth. We model the adenine accumulation in three environments (dry, intermediate, and wet) on a hot and warm early Earth (see Table 1 for precipitation model details). Fig. S1*A* is for 65 °C on a hot early Earth and 20 °C on a warm early Earth, and Fig. S1*B* is for 50 °C on a hot early Earth and 5 °C on a warm early Earth.

All adenine concentration curves reach a stable seasonal pattern within

In Fig. S2, we explore guanine, uracil, and cytosine accumulation in degenerate dry environment WLPs for a hot early Earth at 65 °C and a warm early Earth at 20 °C (see Table 1 for details). The differences in each nucleobase mass fraction over time are caused by the different initial abundances of each nucleobase in IDPs (Table S2). Although hydrolysis rates differ between nucleobases, decay due to hydrolysis is negligible over

In Fig. S5, we turn off seepage, e.g., resembling a scenario where a lipid biofilm has covered the WLP base, and explore the evolution of adenine concentrations from IDP sources. This model is displayed for a hot early Earth at 65 °C and a warm early Earth at 20 °C (see Table 1 for details). UV photodissociation is always the dominant nucleobase sink for the dry and intermediate environments; therefore, for this model, we only display the evolution of adenine in the wet environment, where hydrolysis takes over as the dominant nucleobase sink.

In the absence of seepage, adenine concentrations can build up in wet environment WLPs until the rate of incoming adenine from IDPs matches the decay rate due to hydrolysis. Hydrolysis rates are faster at hotter temperatures; therefore, maximum adenine concentrations are higher and take longer to converge in the 20 °C pond compared with the 65 °C pond. However, these maximum adenine concentrations are 145 and 0.3 ppq, respectively, which are negligible in comparison with the parts per billion–parts per million-level adenine concentrations reached in WLPs from carbonaceous meteorite sources.

### Nucleobase Accumulation from Meteorites.

In Fig. S10, we explore the evolution of adenine concentrationin WLPs with radii and depths of 1 m, from 1-cm fragments of an initially 40-m-radius carbonaceous meteoroid. The models correspond to degenerate environments on a hot (65 °C) and warm (20 °C) early Earth. The maximum adenine concentration in the intermediate environment is

The adenine mass fraction curves in Fig. S10, over a 2-y period, do not change, as pond radii and depths increase equally. This is because, although the mass of water in a WLP increases for larger collecting areas, larger pond areas also collect more meteorite fragments, which counterbalances the water mass and keeps the nucleobase concentration the same.

In Fig. S11, we explore how initial meteoroid radius affects the maximum concentration of adenine accumulated (from its fragments) in WLPs with radii and depths of 1 m. The maximum adenine concentration only differs by at most a factor of 8 when varying the initial meteoroid radius from 20 m to 40 m. This is because the nucleobase mass to enter a WLP scales with the meteoroid mass, i.e., ^{3}.

Finally, in Fig. S3, we explore guanine and uracil accumulation in intermediate and wet environment WLPs with radii and depths of 1 m. These models correspond to a hot early Earth at 65 °C and a warm early Earth at 20 °C. The small differences between each nucleobase mass fraction over time are due to the different initial nucleobase abundances in the deposited meteorite fragments (Table S2). Although each nucleobase has a different hydrolysis rate (Eq. **S25**), the decay of guanine, adenine, and uracil due to hydrolysis is negligible in

## Advection and Diffusion Model

Advection and diffusion are the two main considerations of solute transport in water. Because nucleobases will diffuse out of the pores of carbonaceous IDPs and meteorites at a different rate than they will mix homogeneously in the WLP, we separate our nucleobase transport model into two distinct parts. In part one, we model the outflow of nucleobases from carbonaceous IDPs and meteorites. In part two, we model the mixing of a local concentration of nucleobases into a WLP.

Both parts of our simulation can be modeled with the advection–diffusion equation below, with either one or both right-hand side terms “turned on.”

For a 1D case, where the diffusion coefficient and fluid velocity are constant along the simulated path, the advection–diffusion equation can be written as

We do not consider hydrolysis in our nucleobase transport model, as we only intend on estimating nucleobase outflow and mixing timescales from these models (rather than the nucleobases remaining after these processes). Since nucleobase decay is uniform within the carbonaceous sources and WLPs, and is also very slow at WLP temperatures [*Nucleobase Evolution Equation from IDPs* and *Nucleobase Evolution Equation from Meteorites*).

The advection–diffusion equation also does not include adsorption or formation reactions. However, for the diffusion of soluble nucleobases from small porous environments which previously reached chemical equilibrium, the effects of these extra sources and sinks will probably be minimal. Also, to adjust the diffusion equation for a free water medium, one simply needs to set

The effective diffusion coefficient of a species is proportional to, but smaller than, its free water diffusion coefficient. Many equations exist for modeling the effective diffusion coefficient in porous media (65⇓⇓–68). These equations depend on variables such as the porosity, tortuosity, and constrictivity of the medium, which represent the void space fraction, the curves in the pores, and the bottleneck effect, respectively. These equations are listed in Table S3.

Carbonaceous meteorites of type CM, CR, and CI have average porosities of 24.7

The constrictivity of a porous medium is only important when the size of the species is comparable to the diameter of the pores (68). Therefore, given that nucleobases are

Tortuosities of chondritic meteorites have an average value of 1.45 (70), and the empirical exponent

Finally, the free water diffusion coefficient of a single nucleobase has not been measured, however the free water diffusion coefficient of a single nucleotide is 400 ^{−1} (71). Since nucleotides are heavier than nucleobases by a ribose and phosphate molecule, they will likely diffuse slower than nucleobases. Therefore, 400 ^{−1} is a good estimate of the lower limit of the free water diffusion coefficient of a single nucleobase.

Using the above estimates, we calculate the effective diffusion coefficients for nucleobases in carbonaceous meteorites and IDPs using each of the four models and display them in their respective columns in Table S3. The average value of the effective diffusion coefficient across all four models is 5.36 ^{−11} m^{−1}.

As previously stated, convective velocity within the pores of carbonaceous IDPs and meteorites is considered negligible. However, this is not the case within 1- to 10-m-radius WLPs. Due to the day–night cycles of Earth, WLPs likely experienced a temperature gradient from the atmospherically exposed top of the pond to the constant geothermally heated base. Since convection is likely the dominant form of heat transport within hydrothermal ponds (72), convection cells would have formed, with warm (higher pressure) parcels of water flowing upward and recently cooled (lower pressure) parcels flowing downward.

The convective fluid velocity can be estimated with the equation^{−4} K^{−1}, respectively (74).

Small ponds and even lakes can experience a temperature difference of 1 °C to 5 °C over the course of a day–night cycle (75). However, convection begins cycling water well before temperature differences of this magnitude are reached. To estimate the lower bound of a constant temperature difference between the surface and the base of a WLP during a day-to-night period, we assume that each convection cycle cools a surface parcel of water by

Using Eq. **S42**, the minimum constant temperature difference between the surface and the base of a cylindrical WLP with a radius and depth of 1 m, at 65 °C, is

Given a constant temperature difference of 0.01 K between the base and surface of 1-, 5-, and 10-m-deep WLPs at around 65 °C, the convective flow velocities would be ∼0.7, 1.7, and 2.4 cm^{−1}, respectively.

Due to the 1D nature of our simulations, we are assuming a radially symmetric outflow of nucleobases from spherical carbonaceous IDPs and meteorites. We also assume that local concentrations of nucleobases that recently flowed out of these sources will remain within a single convection cell. Lastly, we assume that the nucleobase homogenization timescale within a 1D convection cell of a WLP is mostly representative of the nucleobase homogenization timescale within the entire WLP. Although the 1D handling of this part of our model is a simplification of advection and diffusion within WLPs, since we are only attempting to estimate nucleobase homogenization timescales to within a few factors, a 1D model is probably sufficient.

For both model parts, we use a backward time, centered space (BTCS) finite difference method for the diffusion term in the advection–diffusion equation. For part two of the model, we use the upwind method to approximate the additional advection term. The BTCS method was selected over the more accurate Crank–Nicolson method based on the former’s stability for sharply edged initial conditions and convergence for increasing levels of refinement. However, differences in diffusion timescales are found to be within rounding error upon comparison of these methods for a 100-

For part one of our nucleobase transport model, the simulation frame starts at the center of the IDP or meteorite, and ends at the rock–pond interface. The left (

For part two, the simulation frame is an eccentric 1D convection cell, which loops between the bottom and the top of the WLP (length = 2

Example simulations, including initial conditions, for parts one and two of our nucleobase transport model are plotted in Fig. S12. Because the time it takes for complete nucleobase outflow from a source, or complete nucleobase homogenization in a WLP, is independent of initial nucleobase abundance, the solution to the diffusion equation at each grid point is displayed as a fraction of the total initial nucleobase concentration. For ease of viewing, part two of the model is displayed in the convection cell’s moving frame, with coordinate

## Meteorite Sources and Targets

In Fig. 1*A*, we show the history of meteoritic mass delivery rates on early Earth, and of WLP targets. From total meteoritic mass, we extract just the nucleobase sources, i.e., only carbonaceous meteoroids whose fragments slow to terminal velocity in the early atmosphere. In Fig. 1*B*, we show the history of depositions of such nucleobase sources into 1- to 10-m-radius WLP targets from 4.5 Ga to 3.7 Ga.

The lunar cratering record either shows a continuously decreasing rate of impacts from 4.5 Ga forward or shows a brief outburst beginning at

Our calculations show that 10 to 3,840 terminal velocity carbon-rich meteoroids would have deposited their fragments into WLPs on Earth during the Hadean Eon. Given the large uncertainty of the ponds per unit area and the growth rate of continental crust, we vary the WLP growth function by

## Life Cycles of WLPs

Fig. 2 illustrates the variation of physical conditions for WLPs during the Hadean Eon, ∼4.5 Ga to 3.7 Ga. Annual rainfall varies sinusoidally (24), creating seasonal wet and dry environments. The increased heat flow from greater abundances of radiogenic sources at this time (33) causes temperatures of around 50 °C to 80 °C (34). The various factors that control the water level and thus the wet–dry cycles of WLPs are precipitation, evaporation, and seepage (through pores in the ground).

In Fig. 3*A*, we present the results of these calculations. We select two different temperatures (65 °C and 20 °C) as analogues for hot and warm early Earths. For each of these, we examine three different environments: dry, intermediate, and wet (see Table 1 for details). The water levels in the wet environment WLPs range from ∼60 to 100

## Nucleobase Evolution in WLPs

As shown in Fig. 2, the buildup of nucleobases in WLPs is offset by losses due to hydrolysis (28), seepage (26), and dissociation by UV radiation that was incident on early Earth in the absence of ozone (27, 36). Some protection would be afforded during WLP wet phases, as a 1-m column of pond water can absorb UV radiation up to

Nucleotide formation and stability are sensitive to temperature. Phosphorylation of nucleosides in the laboratory is slower at low temperatures, taking a few weeks at 65 °C compared with a couple of hours at 100 °C (39). The stability of nucleotides on the other hand, is favored in warm conditions over high temperatures (40). If a WLP is too hot (

In Fig. 3*B*, we focus on the adenine concentrations in WLPs from only IDP sources. The combination of spikes, flat tops, and troughs in Fig. 3*B* reflects the variations of adenine concentration in response to drying, balance of input and destruction rates, and precipitation during wet periods. In any environment and at any modeled temperature, the maximum adenine concentration from only IDP sources remains below 2^{−7} ppb (Fig. S1). This is two orders of magnitude below current detection limits (14), making subsequent reactions negligible. The nucleobase mass fraction curves are practically independent of pond size (1 m _{p}

## Dominant Source of Surviving Nucleobases

In Fig. 4, we assemble all of these results and compare carbonaceous IDPs to meteorites as sources of adenine to our fiducial WLPs. Small meteorite fragments (1 cm in radius) are compared with IDPs in Fig. 4*A*. The effects of larger meteorite fragments (5 cm and 10 cm) on adenine concentration are displayed in Fig. 4*B*.

The maximum adenine concentration in our model WLPs from carbonaceous meteorites is 10 orders of magnitude higher than the maximum adenine concentration from carbonaceous IDPs. The reason for this huge disparity is simply that carbonaceous meteoroid fragments—each carrying up to a few milligrams of adenine—are deposited into a WLP in a single event. This allows adenine to reach parts per billion–parts per million-level concentrations before seepage and UV photodissociation efficiently remove it from the WLP in one to a few wet–dry cycles. The maximum guanine and uracil accumulated in our model WLPs from meteorites are also more than 10 orders of magnitude higher than those accumulated from IDPs (Figs. S2 and S3). A maximum adenine concentration of 2 ppm is still approximately one to two orders of magnitude lower than the initial adenine concentrations in aqueous experiments forming adenosine and AMP (2); however, these experiments only ran for an hour.

Adenine within larger fragments diffuses over several wet–dry cycles, and, during the dry phase, no outflow occurs. For fragments 1, 5, and 10 cm in radius, 99

Thus, even though the carbon delivery rates from IDPs to early Earth vastly exceed those from meteorites, it is the meteoritic material that is the dominant source of nucleobases for RNA synthesis.

## Nucleotide and RNA Synthesis

To form nucleotides in WLPs, ribose and a reduced P source must be available. Ribose may have formed and stabilized in borate-rich WLPs via the formose reaction (polymerization of H_{2}CO) (41). Additionally, phosphite has been detected in a pristine geothermal pool representative of early Earth, suggesting the potential availability of reduced P to WLP environments (42). Only the AMP nucleotide has been experimentally synthesized in a single step involving ribose, reduced P, and UV radiation (2).

Because of the rapid rate of seepage [^{−1} to 5.1 mm^{−1} (26)], nucleotide synthesis would need to be fast, occurring within a half-year to a few years after nucleobase deposition, depending on meteoroid fragment sizes. This is ample time given that laboratory experiments show that hour-to-week-long timescales are sufficient to form adenosine and AMP (2, 3).

Nucleotides, once synthesized using meteorite-delivered nucleobases, are still subject to seepage, regardless of the temperature. Therefore, nucleotide polymerization into RNA would also need to be fast, occurring within one to a few wet–dry cycles, to reduce their likelihood of seeping through the estimated 0.001- to 400-

## Discussion and Conclusions

Seepage is one of the dominant nucleobase sinks in WLPs. It will be drastically reduced if nucleobases are encapsulated by vesicles (spheres of size 0.5

Also, we note that a cold early Earth [if it occurred (30)] with seasonal or impact-induced freeze–thaw cycles could also be suitable for RNA polymerization and evolution for reasons similar to those we have analyzed for WLPs. The cyclic thawing and freezing resembles wet–dry cycles (8).

We conclude that the physical and chemical conditions of WLPs place strong constraints on the emergence of an RNA world. A hot early Earth (50 °C to 80 °C) favors rapid nucleotide synthesis in WLPs (39). Meteorite-delivered nucleobases could react with ribose and a reduced P source to quickly (less than a few years) create nucleotides for polymerization. Polymerization then occurs in one to a few wet–dry cycles to reduce the likelihood that these molecules are lost to seepage. This rapid process also reduces the likelihood of setbacks for the emergence of the RNA world due to frequent large impacts, also known as impact frustration (45). Sedimentation would be of critical importance as UV protection for nucleobases, nucleotides, and RNA (27, 46, 47).

The mass delivery model providing the most WLP depositions indicates that the majority of meteorite depositions occurred before 4.17 Ga. The first RNA polymers would have formed in WLPs around that time, prefiguring the emergence of the RNA world. This implies that the RNA world could have appeared within

## Acknowledgments

We thank the referees for their thoughtful insights. We thank M. Rheinstädter for providing valuable comments on the manuscript. B.K.D.P. thanks the Max Planck Institute for Astronomy for their hospitality during his summer abroad, supported by a Natural Sciences and Engineering Research Council of Canada (NSERC) Michael Smith Foreign Study Supplement. R.E.P. thanks the Max Planck Institute for Astronomy and the Institute of Theoretical Astrophysics for their support during his sabbatical leave. The research of B.K.D.P. was supported by an NSERC Canada Graduate Scholarship and Ontario Graduate Scholarship. R.E.P. is supported by an NSERC Discovery Grant. This research is part of a collaboration between the Origins Institute and the Heidelberg Initiative for the Origins of Life.

## Footnotes

- ↵
^{1}To whom correspondence should be addressed. Email: pearcbe{at}mcmaster.ca.

Author contributions: B.K.D.P., R.E.P., D.A.S., and T.K.H. designed research; B.K.D.P. performed research; B.K.D.P. and R.E.P. analyzed data; and B.K.D.P., R.E.P., D.A.S., and T.K.H. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

See Commentary on page 11264.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1710339114/-/DCSupplemental.

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- Model: Fates of Nucleobases in Evolving WLPs
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- Calculating WLP Surface Area on Early Earth
- Calculating Carbonaceous Meteorite Depositions in WLPs
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- Nucleobase Evolution Equation from IDPs
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