A model of error propagation in the presence of an error-enhancing drug

A mathematical model is considered that describes error propagation in protein synthesis, with emphasis on the role of an error-enhancing drug such as streptomycin. The subject of error propagation has been investigated in a number of works since an original proposal by Orgel in 1963. From experiments, it is known that streptomycin given to a bacterium culture in small concentration increases the error level, but at a certain concentration threshold the bacteria die. This two-fold behavior has, in some papers, lead to the proposal that another effect of the drugs besides that of error propagation leads to the death of the bacteria. In the present work, we use a model related to kinetic models of selection in protein synthesis which include the combined effect of ribosome and synthetase action. The model shows very clear threshold effects: for small values of the parameter that represents the drug action, a stable situation is found that has an increased error level but still attains a rather high accuracy. At a certain threshold, this is no longer maintained. The main emphasis here is on the time evolution of relevant parameters, and it is also shown how this can be quite drastic: the accuracy may decrease rather smoothly to a critical point, where it is drastically lost and where the bacteria may die out very suddenly.