Host-parasite coevolution and optimal mutation rates for semiconservative quasispecies

In this paper, we extend a model of host-parasite coevolution to incorporate the semiconservative nature of DNA replication for both the host and the parasite. We find that the optimal mutation rate for the semiconservative and conservative hosts converge for realistic genome lengths, thus maintaining the admirable agreement between theory and experiment found previously for the conservative model and justifying the conservative approximation in some cases. We demonstrate that, while the optimal mutation rate for a conservative and semiconservative parasite interacting with a given immune system is similar to that of a conservative parasite, the properties away from this optimum differ significantly. We suspect that this difference, coupled with the requirement that a parasite optimize survival in a range of viable hosts, may help explain why semiconservative viruses are known to have significantly lower mutation rates than their conservative counterparts.

Figure 1

A schematic model of DNA replication. The original, double stranded genome unzips to create two single stranded genomes. Each of these is copied to produce two new complementary strands. Methyl-directed and post-methylation DNA repair keep the effective error rate low. Adapted from Tannenbaum et al. [11].

Figure 2

Optimal immune system mutation rate vs $n_{is}$. The dashed lines represent experimental values for somatic hypermutation of B-cell complementary determining regions, adapted from Ref. 9.

Figure 3

Optimal viral mutation rate vs $n_v$ for a conservative and semiconservative virus interacting with a semiconservative immune system; $n_{is}=100,{\sigma }_{is}={\sigma }_v=100,{\eta }_{is}={\eta }_v=1,\delta =200,{ϵ}_{is}=\mathrm{0.001.}$

Figure 4

${\left(1-ϵ∕2\right)}^n$ for the optimal mutation rate of a semiconservative immune system and virus. This parameter can be used as a measure of the “conservativeness” of a semiconservative system; ${\sigma }_{is}={\sigma }_v=100,{\eta }_{is}={\eta }_v=1,\delta =200,{ϵ}_{is}=0.001$.

Figure 5

${\kappa }_v$ vs ${ϵ}_v$ for a conservative and semiconservative virus interacting with a semiconservative immune system; $n_{is}=n_v=100,{\sigma }_{is}={\sigma }_v=100,{\eta }_{is}={\eta }_v=1,\delta =200,{ϵ}_{is}=0.001$.