Sequence patterns in RNA replication via the virtual circular genome mechanism

We ask whether functional RNA sequences could be stably copied nonenzymatically at the time of the origin of life. We show that random sequence mixtures spontaneously reduce to short overlapping sequence sets that have been called virtual circular genomes (VCGs). VCG patterns can be classified as irreducible sets of words. Short VCG sequences replicate stably if they cannot reduce to shorter cycles, but longer VCG sequences tend to collapse to shorter sequence patterns, a problem we call scrambling. The VCG mechanism works for relatively short sequences when the error rate is small. Using stochastic computer simulations, we demonstrate successful replication of sequences with a potentially useful function, including a hairpin capable of loop-closing ligation, and an autocatalytic ligase of length 20. However, a hammerhead ribozyme sequence of length 44 is found to be barely stable even for optimistic parameter choices, suggesting that this is an upper limit to the length that could be encoded on a VCG. The recent discovery of short polymerase ribozymes of only length 45 gives hope that nonenzymatic replication might begin to approach what is required for origin of a polymerase.