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Statistical inference for ratiometric imaging of excitable cells: a self‐organizing state‐space model

Concentrations of free intracellular calcium ions ([Ca2+]i) in excitable cells are often measured using indicator dyes, such as fura‐2. Of note, however, these indicator dyes are divalent metal ion chelators that affect intrinsic changes in [Ca2+]i. To examine whether indicator dyes alter calcium signaling, we estimated [Ca2+]i using a novel statistical inference method that examines fluorescence signals and the calcium current through the cell membrane. We first constructed a model of transient [Ca2+]i, which was then translated into a state‐space model with such state variables as [Ca2+]i, endogenous calcium buffer, and calcium indicators. Then, a self‐organizing state‐space model was defined by augmenting a state vector with unknown parameters from the original state‐space model. In the model, some unknown parameters were estimated with the original state vector. Next, we used a recursive Bayesian estimation to obtain a set of state vectors and the unknown parameters associated with a set of observation vectors. To calculate the recursive Bayesian estimation, we used a sequential Monte Carlo method, which is referred to as a particle filter method. To verify the effectiveness of the proposed method, we carried out experiments with a set of test data from a model with known parameters. The results show that our proposed method properly estimated the temporal profiles of [Ca2+]i, the indicator dye concentration, and certain model parameters in a noisy environment. © 2012 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.