Escalation of error catastrophe for enzymatic self-replicators

Abstract

Abstract. -It is a long-standing question in origin-of-life research whether the information content of replicating molecules can be maintained in the presence of replication errors. Extending standard quasispecies models of non-enzymatic replication, we analyze highly specific enzymatic self-replication mediated through an otherwise neutral recognition region, which leads to frequency-dependent replication rates. We find a significant reduction of the maximally tolerable error rate, because the replication rate of the fittest molecules decreases with the fraction of functional enzymes. Our analysis is extended to hypercyclic couplings as an example for catalytic networks.Introduction. -According to the RNA world hypothesis [1], prebiotic biochemical life is thought to have emerged through four steps: starting from the primordial non-enzymatic synthesis of nucleotides and their subsequent non-enzymatic polymerization into random RNA, which in a third step would non-enzymatically replicate, natural selection would finally produce a set of functional RNA enzymes (ribozymes), establishing exponential growth and initiating RNA evolution. Despite considerable experimental progress [2,3], as of today no truely self-replicating system has been evolved according to this hypothetic schedule. To assess its intrinsic plausibility, theory has mainly focused on the third step, usually based on the Eigen model [4] for prebiotic evolution: here, autocatalytic self-replication of L-nucleotide sequences proceeds non-enzymatically via stepwise template-directed polymerization, with a non-negligible error probability µ per single nucleotide. Assuming that one specific "master" template replicates with the highest rate α > 1, while all other sequences have unit replication rate, it is found that faithful replication of the master is possible only for error probabilities smaller than a critical value µ c ≈ ln α/L. In this regime, the population in sequence space is concentrated about the master in a rather broad distribution, giving rise to the notion of a "quasispecies". Larger values µ > µ c lead to a delocalized state with completely random sequences in the population. Many aspects of the

Periodic versus Intermittent Adaptive Cycles in Quasispecies Coevolution

“…Finally, in a somewhat model-specific "degenerate" regime bounded by . Interestingly, for α = γ and symmetric mutation rates µ x,y ≡ µ, the critical condition of coexistence can be approximated by µ ≈ (1/2L) ln (α/2) for large α and L, which generalizes a comparable result for mutualistic frequency-dependent fitness [32] to the case of antagonistic interactions. This correspondence also suggests that the error thresholds derived here should be largely unchanged if recognition between the two population tolerates some mismatches [33].…”

Error thresholds for self- and cross-specific enzymatic replication

“…In the stationary state, we easily find that the delocalized state x 0 = 0 is stable for all µ, while a branch of solutions with nonzero x 0 emerges for (1 − µ) L > 2( α(α + β) − α)/β through a discontinuous transition (see also Campos et al (2000); Obermayer and Frey (2009);Wagner et al (2010) for similar results in related models). Whereas for the somewhat related sharply-peaked fitness landscape, where only the master sequence has a higher replication rate, the error threshold arises through a continuous bifurcation (Baake and Wiehe, 1997), the discontinuity observed here expresses the qualitatively different behavior we previously termed "escalation of error catastrophe" (Obermayer and Frey, 2009): as the mutation rate grows, the proportion of fittest sequences, i.e., of the necessary replicase enzymes, is diminished and therefore their replication rate. This in turn reduces their concentration, until at the error threshold the concentration of enzymes x 0 is not large enough to have them replicate with an efficiency sufficient for localization.…”

“…Hence, we effectively only model the recognition regions of ribozymes, which are often clearly separated from the catalytic domains (Lilley, 2005). Of course, the proper function of the latter region is indispensable, but in our idealized model we neglect the influence of mutations: as we have shown previously in a simple model, their effect on the error threshold is largely independent from the more interesting consequences of mutations in the recognition region (Obermayer and Frey, 2009). The sequence length L is thus restricted to the number of nucleotides that take part in recognition.…”

“…The "coupling constant" is only half as large because only one half of the population is available as enzymes for the other. In particular, the negligible interaction between the respective mutant clouds allows one to employ the error-tail approximation assuming independent species and error tails as in (Campos et al, 2000;Obermayer and Frey, 2009). Further, we find that the pitchfork bifurcation is always subcritical, i.e., that µ c >μ c .…”

How Catalytic Order Drives the Complexification of Molecular Replication Networks

“…Recently, Obermayer et al. 85,86 and our own group87 have independently formulated catalytic quasispecies models, applicable to the replication of biopolymer genome sequences. In the generalized two‐stage formulation proposed: …”