Comments on “growth of a hypercycle” by king (1981)

Abstract

The notion of hypercycles has been introduced (Eigen, 1971) in order to characterize a functional entity which integrates information stored in individual self-replicating elements. Commonly, these self-replicating elements compete, like polynucleotides do in test tube experiments (Spiegelman, 1971; Biebricher et al., 1981) or, like species do in nature. A single species is selected eventually together with its most frequent mutants and the less efficient competitors disappear. In order to suppress competition, specific coupling terms of second order - these are coupling terms which are proportional to the product of two population numbers or concentration - have to be introduced into the kinetic equations such a link has to extend to all members, requiring the formation of a closed catalytic cycle (Eigen and Schuster, 1979). The copying of polynucleotide sequences, like every transfer of information, can only occur with finite accuracy (Eigen et al., 1981). This physical restriction imposes a limit upon the content of information that can be transmitted. A higher content of information requires more precise replication. A more involved replication machinery, however, presupposes more information to build it. Thus, a single autocatalyst will not be able to increase its content of information over the given threshold. How does one escape from this vicious circle? Hypercycles present a solution to the problem: many information carriers coexist and may cooperate to build a more sophisticated and more precisely copying replication machinery. Optimization of growth rates has never been the goal for which hypercycles were conceived. Any first order process can proceed at a higher rate than a second order process if low enough concentrations are chosen. On the other hand, any realistic hypercycle involves both first and second order terms. At low concentrations first order terms provide for accumulation of material while at higher concentration second order terms stabilize cooperation. At which concentration level such a prevalence changes is a matter of quantitative values of rate parameters rather than of basic principle. An autocatalyst may outgrow a hypercycle under certain conditions but it can never solve the problem of integrating information.