Computer simulations of Template-Directed RNA Synthesis driven by temperature cycling in diverse sequence mixtures

Abstract

We present simulations of non-enzymatic template-directed RNA synthesis that incorporate primer extension, ligation, melting, and reannealing. Strand growth occurs over multiple heating/cooling cycles, producing strands of several hundred nucleotides in length, starting with random oligomers of 4 to 10 nucleotides. A strand typically grows by only 1 or 2 nucleotides in each cycle. Therefore, a strand is copied from many different templates, not from one specific complementary strand. A diverse sequence mixture is produced, and there is no exact copying of sequences, even if single base additions are fully accurate (no mutational errors). It has been proposed that RNA systems may contain a virtual circular genome, in which sequences partially overlap in a way that is mutually catalytic. We show that virtual circles do not emerge naturally in our simulations, and that a system initiated with a virtual circle can only maintain itself if there are no mutational errors and there is no input of new sequences formed by random polymerization. Furthermore, if a virtual sequence and its complement contain repeated short words, new sequences can be produced that were not on the original virtual circle. Therefore the virtual circle sequence cannot maintain itself. Functional sequences with secondary structures contain complementary words on opposite sides of stem regions. Both these words are repeated in the complementary sequence; hence, functional sequences cannot be encoded on a virtual circle. Additionally, we consider sequence replication in populations of protocells. We suppose that functional ribozymes benefit the cell which contains them. Nevertheless, scrambling of sequences occurs, and the functional sequence is not maintained, even when under positive selection.

Fig 1. Examples of structures that form via annealing of strands.

(a) If a helix forms in the middle of the strands, so that the ends of the strands are in single-stranded tails, then no growth is possible at these ends. (b) If the 3’ end of a strand is the last base in a helix (orange squares), this is a site for monomer addition. If the 5’ end of a strand is the last base in a helix (green squares), we assume that monomer addition cannot occur, but this is a potential site for ligation, if the 3’ end of another strand grows to be adjacent to this site. (c) Connection of multiple strands forms branching clusters with many tails and many potential points of sequence growth. We assume that formation of an additional helix is not possible between strands that are already in the same cluster. This prevents unrealistic loops and knots forming within a cluster.

Fig 2. Mean length and Maximum length as a function of time in cycles for four simulations with varying values of the monomer addition rate k_add.

Fig 3. Number of sequences, N_seq, and number of free A nucleotides, NA, as a function of time in cycles for four simulations with varying values of the monomer addition rate k_add.

Fig 4. Distibution of sequence lengths, N(n), and mean increase in length, Δn, for four simulations with varying values of the monomer addition rate k_add.

Fig 5. Mean number of helices, h(n), and mean number of paired bases, m(n), as a function of total sequence length n for four simulations with varying values of the monomer addition rate k_add.

Fig 6

(i) A circular path of 10 steps formed from words taken from a virtual circular genome of length 10. (ii) A circular path of length 5 existing in a mixture in which all 5-mers are present. (iii) and (iv) Short circular paths arising when there is a repeating structure in the 5-mer sequence.

Fig 7

Connectivity X, Specificiy S, and Circularity C functions for (a) perfect virtual circle mixture, (b) complete random mixture with all words present, (c) simulation run 500Y1.

Fig 8

(a) Word graph from the perfect virtual circle of length 10. (b) Word graph of the diverse mixture arising in simulation 500Y1.

Fig 9. The graph functions and word graph for run 40N2 shows disconnected elements with no cycles.

Fig 10. The graph functions and word graph for run 100N2 show the presence of cycles of period 1, 2 and 4.

Fig 11. The graph functions and word graph for run 100N6 show the presence of cycles of period 14,18 and 22.

Fig 12. Number of complete ribozymes as a function of time for simulations beginning with the fragments and splits of the F ribozyme catalytic core.

The simulation with ligation only shows that multiple copies of the complete ribozyme are assembled from fragments. The simulation with standard parameters allows monomer addition and nucleation, inflow/outflow of monomers and outflow of oligomers, as well as ligation. The full ribozyme is synthesized from the original fragments but disappears after some time because the correct fragments are not resynthesized.

Fig 13. Simulation beginning with the fragments of the F ribozyme (as in Fig 12) using standard parameters. g(n) is the fraction of sequences of length n in the mixture that are still part of the ribozyme sequence or its complement after 1000 temperature cycles.

Fig 14. Simulations of a population of 50 cells beginning with 5 copies of the F ribozyme per cell plus fragments and splints.

The ribozyme either has no function, or has a beneficial function as a ligase or a polymerase. In all cases the ribozyme is lost due to sequence scrambling.