Navigating exponentially large spaces in biology

The recent explosion of high throughput technologies in many fields of biology has necessitated the use of sophisticated algorithms to guide experimental design and analyze results. This thesis explores two such fields: directed protein evolution and single molecule fluorescence resonance energy transfer analysis. Although the methodologies and applications of the fields differ greatly, they are both limited by a process which scales exponentially with problem size. In the former case, the problem is determining which combination of amino acids should be mutated to enhance or create protein function. In the latter case, the problem is inferring the number of conformations a molecule explores during an experiment and the probability of being in each state at each time point in the experiment. Methods to address both problems will be presented in this thesis.