Estimation of Intracellular Calcium Ion Concentration by Nonlinear State Space Modeling and Expectation-Maximization Algorithm for Parameter Estimation

Abstract

A calcium imaging method has superior ability in recording of spatial–temporal variations in ion concentration. However, it has two major problems. First, the imaging signals are very noisy. Second, the observation data are only the fluorescence intensities of Ca 2+ indicator dyes that provide indirect information about the Ca 2+ concentration. We develop a nonlinear state-space model for Ca imaging series involving Ca 2+ kinetics and a noisy fluorescence intensity pickup process. We devise recursive update algorithms for estimating the Ca 2+ concentration and Ca 2+ flux, and give the expectation-maximization algorithm for inferring model parameters.