Error thresholds for self- and cross-specific enzymatic replication

Abstract

The information content of a non-enzymatic self-replicator is limited by Eigen's error threshold. Presumably, enzymatic replication can maintain higher complexity, but in a competitive environment such a replicator is faced with two problems related to its twofold role as enzyme and substrate: as enzyme, it should replicate itself rather than wastefully copy non-functional substrates, and as substrate it should preferably be replicated by superior enzymes instead of less-efficient mutants. Because specific recognition can enforce these propensities, we thoroughly analyze an idealized quasispecies model for enzymatic replication, with replication rates that are either a decreasing (self-specific) or increasing (cross-specific) function of the Hamming distance between the recognition or "tag" sequences of enzyme and substrate. We find that very weak self-specificity suffices to localize a population about a master sequence and thus to preserve its information, while simultaneous localization about complementary sequences in the cross-specific case is more challenging. A surprising result is that stronger specificity constraints allow longer recognition sequences, because the populations are better localized. Extrapolating from experimental data, we obtain rough quantitative estimates for the maximal length of the recognition or tag sequence that can be used to reliably discriminate appropriate and infeasible enzymes and substrates, respectively.

Periodic versus Intermittent Adaptive Cycles in Quasispecies Coevolution

“…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].…”

“…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].Noise-driven oscillations in the coexistence regime. Performing a linear stability analysis in the coexistence regime reveals that the oscillations seen in the simulations are caused by n − 1 pairs of purely imaginary eigenvalues.…”

Theories of Lethal Mutagenesis: From Error Catastrophe to Lethal Defection

“…Since the mutation rate from the master to the mutant phenotype is determined by the size of the sequences that compose them, the entry into error catastrophe establishes a maximum limit to the amount of information that a self-replicative system can maintain at a given mutation rate (Wilke 2005;Takeuchi et al 2005;Obermayer and Frey 2010). After the RNA viruses have been conceptualised as quasispecies (Domingo et al 1978), the possibility of pushing RNA viruses into error catastrophe by means of mutagenic drugs (Eigen 1993(Eigen , 2002 was the origin of the first lethal mutagenesis experiments, as well as the first explanation for the extinction of the virus in these conditions (Cameron and Castro 2001;Holland et al 1990;Loeb et al 1999).…”

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: …”