The Mixture of Autoregressive Hidden Markov Models of Morphology for Dentritic Spines During Activation Process

The dendritic spines play a crucial role in learning and memory processes, epileptogenesis, drug addiction, and postinjury recovery. The shape of the dendritic spine is a morphological key to understand learning and memory process. The classification of the dendritic spines is based on their shapes but the major questions are how the shapes changes in time, how the synaptic strength changes, and is there a correlation between shapes and synaptic strength? Because the changes of the classes by dendritic spines during activation are time dependent, the forward-directed autoregressive hidden Markov model (ARHMM) can be used to model these changes. It is also more appropriate to use an ARHMM directed backward in time. Thus, the mixture of forward-directed ARHMM and backward-directed ARHMM (MARHMM) is used to model time-dependent data related to the dendritic spines. In this article, we discuss (1) how to choose the initial probability vector and transition and dependence matrices in ARHMM and MARHMM for modeling the dendritic spines changes and (2) how to estimate these matrices. Many descriptors to classify dendritic spines in two-dimensional or/and three-dimensional (3D) are available. Our results from sensitivity analysis show that the classification that comes from 3D descriptors is closer to the truth, and estimated transition and dependence probability matrices are connected with the molecular mechanism of the dendritic spines activation.