Hidden Markov Models With Applications in Cell Adhesion Experiments

Abstract

Estimation of the number of hidden states is challenging in hidden Markov models. Motivated by the analysis of a specific type of cell adhesion experiments, a new framework based on a hidden Markov model and double penalized order selection is proposed. The order selection procedure is shown to be consistent in estimating the number of states. A modified expectation–maximization algorithm is introduced to efficiently estimate parameters in the model. Simulations show that the proposed framework outperforms existing methods. Applications of the proposed methodology to real data demonstrate the accuracy of estimating receptor–ligand bond lifetimes and waiting times which are essential in kinetic parameter estimation. Supplementary materials for this article are available online.

KEY WORDS:

• Consistency
• Expectation conditional maximization
• Order selection
• Single molecule

Acknowledgments

This research is supported by NIH GM096187 grants. The authors thank Wei Chen for sharing his data and Jiahua Chen for helpful discussions. We are grateful to the Editor, an AE, and a referee for their helpful comments and suggestions.