Inheriting biological information : transmission limits

The second unit of the lecture focused on the evolutionary propagation of information, as seen through the classical model of Manfred Eigen, in which sequences reproduce with errors in a flow reactor. The model gives rise to a system of differential equations describing sequence abundance as a function of time, fitness and error rate. The mild non-linearity can be transformed and the system solved using standard linear algebra. The stationary solution describes a distribution of sequences, called " quasi-species ". For some adaptive-value landscapes and error models, we find that accurate reproduction determines a maximum sequence length beyond which the information represented by the best-adapted sequence can no longer be preserved. The sharpness of this error threshold depends on the roughness of the adaptive value landscape, and for some smooth landscapes there is no clear threshold. The model also shows that the quasispecies, as a whole and not a particular sequence, is the unit of selection. What counts is the structure of the fitness landscape that is populated by the mutant cloud surrounding the fittest sequence ; a better environment can lead a less adapted sequence to dominate a more adapted one. The inclusion of neutral networks (lecture 1) in the model gives a phenotypic error threshold that occurs at a higher error rate than the genotypic threshold : genotype transmission can be lost without this implying a loss of phenotype transmission. Mathematically, the quasispecies model is a molecular version of the Crow-Kimura model of mutational selection in population genetics. The difference is that, in the molecular version, replication and mutation are jointly occurring processes, whereas, in the population genetics version, they occur independently.