Analysis of Circadian Cellular Bioluminescence Recordings using a Kalman Smoother

Circadian clocks permit mammals to adapt to their periodic natural environment. These clocks generate rhythms in the expression of genes and proteins in most tissues within the organism. Real-time bioluminescence recordings of gene or protein expression in an important tool to study the clock under different manipulations and conditions. Here, we present a tool to extract useful characteristics of the cellular rhythms, such as period and damping rate, using maximum-likelihood estimation in a stochastic damped oscillator model. The tool uses the expectation-maximization algorithm in combination with a Kalman Smoother to perform the joint state and parameter estimation. We apply this tool to quantify the differences between rhythms in the master circadian clock in the brains of two different knockout mice and compare the results to a standard autocovariance fitting-based approach for parameter estimation.