A simple method for getting standard error on the ratiometric calcium estimator

The ratiometric fluorescent calcium indicator Fura-2 plays a fundamental role in the investigation of cellular calcium dynamics. Despite of its widespread use in the last 30 years, only one publication (Joucla et al., 2010)) proposed a way of obtaining confidence intervals on fitted calcium dynamic model parameters from single ‘calcium transients’. Shortcomings of this approach are its requirement for a ‘3 wavelengths’ protocol (excitation at 340 and 380 nm as usual plus at 360 nm, the isosbestic point) as well as the need for an autofluorence / background fluorescence model at each wavelength. Here, we propose a simpler method that eliminates both shortcommings: 1. a precise estimation of the standard errors of the raw data is obtained first, 2. the standard error of the ratiometric calcium estimator (a function of the raw data values) is derived using both the propagation of uncertainty and a Monte-Carlo method. Once meaningful standard errors for calcium estimates are available, standard errors on fitted model parameters follow directly from the use of nonlinear least-squares optimization algorithms.