Emergence of Information Transmission in a Prebiotic RNA Reactor

A poorly understood step in the transition from a chemical to a biological world is the emergence of self-replicating molecular systems. We study how a precursor for such a replicator might arise in a hydrothermal RNA reactor, which accumulates longer sequences from unbiased monomer influx and random ligation. In the reactor, intra- and intermolecular base pairing locally protects from random cleavage. By analyzing stochastic simulations, we find temporal sequence correlations that constitute a signature of information transmission, weaker but of the same form as in a true replicator.

Figure 1

Illustration of the RNA reactor. Left: Combined action of convection and thermophoresis in narrow pores subject to a temperature gradient results in strong accumulation of nucleotides, as indicated by the darker shading. Right: The region of high concentration defines an open reaction volume where nucleotides enter and bonds are formed through ligation reactions. Equilibrium base-pair formation protects bonds next to paired nucleotides (dark) from cleavage. Length-dependent outflux accounts for the preferential accumulation of long molecules.

Figure 2

Steady-state properties of the sequence pool: (a) length distribution $⟨N_L⟩$, (b) total number $⟨N_{\mathrm{tot}}⟩$ of molecules, and (c) their mean length $⟨L⟩$. (d) Base-pairing probability $⟨{\overline{p}}_L⟩$ averaged over sequences of length $L$, with mean $⟨\overline{p}⟩$ shown in (e). (f) Structural repertoire of long sequences: steady-state probabilities for sequences longer than $L^{*}=35$ (shaded parts: $L^{*}=50$), which fold into a structure of similar shape as the indicated schematic drawings. Selection strength increases from light to dark color as indicated in the legend. All observables are averaged over time and 10 independent replicas. Remaining parameter values were $J=1$, $\alpha =0.001$, ${\beta }_0=0.01$, $d_0=0.005$, $L_c=10$.

Figure 3

Information transmission among sequence motifs. (a) and (b) Auto- and cross-correlation functions $C_{a,c}(t)$ from simulation data for $\ell =6$ (dots) together with analytical expressions from Eq. (6) (solid lines). The rates $k_{-}$ and $k_{+}$ have been computed from Eqs. (3, 4), with $r$ as the only fit parameter. (c) Schemata for different birth-death processes: (i) motifs are created with constant rate $k_{+}$ and destroyed with linear rate $k_{-}h(n^{*}/n)$, which is reduced by hybridization to their complements; (ii) motifs are destroyed with fixed rate $k_{-}$, but are copied from their complements with rate $r$. To leading order in $r/k_{-}$, both processes give rise to identical correlation functions $C_{a,c}(t)$, where a nonconstant $C_c(t)$ signifies information transmission between a motif and its complement. (d) Dependence of the replication efficiency $r/k_{-}$ on the cleavage rate ${\beta }_0$ (error bars indicate 95% confidence intervals). Color code as in Fig. 2.