Metropolis-Hastings Algorithm and Continuous Regression for finding Next-State Models of Protein Modification using Information Scores

The reverse engineering of protein modification networks from protein modification time sequence data is an important and challenging problem. We utilize continuous regression-based techniques to generate next-state models. Three statistical diagnostics are applied to test the stationary Markov, the equal time interval influence, and the continuous regression assumptions. The standard Metropolis-Hastings algorithm is modified to use a focused model initialization based on Pearson correlations. Additionally, an infrequent step forcing multiple changes, as opposed to the predominate single change, is incorporated into the standard Metropolis-Hastings algorithm which improves the opportunity to escape local minima of information criterion scores. Both Bayesian and corrected Akaike information criteria are used in conjunction with the Metropolis-Hastings algorithm. Real protein modification data often involves only a small number of proteins which allows a direct computation of some models. Our techniques and diagnostics are applied to two sets of time course protein modification data to produce models which score optimally with respect to information criteria. These techniques and diagnostics lend themselves to applications with similar data sets.