UAH > Math > Colloquia > 10/13/2006
Prokaryotic Toxin-Antitoxin systems are self-selecting or addictive genetic elements that are easily acquired but difficult to lose. They encode a protein toxin and a cognate protein antitoxin that binds and neutralizes the toxin. The antitoxin is generally both synthesized and degraded at a greater rate that the toxin. In the steady state, there is sufficient antitoxin to neutralize the toxin. However if expression of the system ceases (due to loss of the genes, addition of antibiotics, or other such circumstances) the continuing degradation of the antitoxin will produce a transient pulse of free toxin that then arrests or kills the cell. Transcription of the system is generally negatively autoregulated by the protein products. We are developing a general mathematical model for the acquisition and loss of toxin-antitoxin systems in a prokaryotic population. The general model presumes that individuals in the population either possess A, an addictive element or B, a defective element that encodes the antitoxin but lacks full toxin activity or C, no element at all. We can then determine the equilibrium proportions of these three types of individuals, as a function of the growth and survival rates that characterize the three states and the mutation and horizontal gene transfer rates that characterize the various transitions between states. Preliminary results, given an asymmetry in horizontal gene rates (due to addiction) and no difference in growth or survival rates (a simplifying neutral assumption), indicate that addictive and defective elements should be found, at equilibrium, in approximately equal frequencies. There is some controversy about whether Toxin-Antitoxin systems are beneficial regulators of cell growth or genetic parasites. The first hypothesis predicts that they should be well conserved and fully functional, the second, according to our models, predicts that they should be polymorphic and frequently defective. Thus, the controversy may be susceptible resolution by bioinformatics and/or physiological analyses.