Information dynamics of in vitro selection-amplification systems

Selection-amplifications systems provide a means of engineering biomacromolecules with new properties. The combination of stringent functional selection with the ability to amplify single molecules confers great specificity on the evolving population. Yet such systems like many complicated chemical kinetic mechanisms can show a range of unstable and metastable behavior. These instabilities can be investigated using the Shannon entropy of the evolving population. It is shown that the Shannon entropy provides a Lyapounov function for exploring dynamic stability. A simple model of in vitro evolution is presented and stability conditions are established. It is seen that fairly simple directed evolution models can exhibit a range of dynamical behavior.