Maximum Likelihood Superposition of Protein Structures
Superposition of protein structures has been a central issue in computational biology, and many methods have been proposed. However, most works employ ad hoc or physically-motivated approaches, and probabilistic models (e.g. HMMs) are rather out of focus. One of the reasons would be that the probabilistic models for estimating 3-dimensional rigid-body transformation get so complicated that direct maximization of likelihood e.g. by gradient descent is almost hopeless. However, there are crucial advantages of employing probabilistic models. For example, one can attach confidence levels on the estimated rotation and translation. Also one can embed the probabilistic model as one node of a Bayesian network for higher-level inference. In this paper, we model protein structures by an HMM where each state outputs a 3-dimensional vector according to an ellipsoidal Gaussian. 1 Each of the 3-dimensional vectors indicates the coordinate of Cα atom of an amino acid. We then present a variational EM algorithm for estimating the rigid-body transformation as well as HMM parameters.