Measuring [Ca2+] with fluorescent indicators: theoretical approach to the ratio method

In this work we present a theoretical analysis of the ratio method, a widely used technique for measuring intracellular calcium concentration, [Ca2+]i, in isolated cells. From the ratio of fluorescence measured at two different excitation or emission wavelengths, [Ca2+]i may be estimated from the equation: [Ca2+]i = Kd.beta.(R-Rmin)/(Rmax-R). From this equation we determined the method sensitivity showing that its maximum is located at [Ca2+] = Kd.beta.(Rmin/Rmax)1/2, i.e. for [Ca2+] < Kd.beta. We also analyzed the error propagation due to inaccuracies in the calibration parameters. The fluorescence phenomenon was described, aiming at providing a basis for the microscopic interpretation of the method and giving physical meaning to the calibration parameters. In this sense beta, is shown to depend not only on the set-up, but also on the spectrum of the indicator for the particular sample studied. A new approach to estimate beta with higher accuracy is also proposed. Experimentally obtained beta values using this approach were not statistically different from those determined as Fmin2/Fmax2. A graphical interpretation of the method is presented to provide users of fluorescence systems with a simple technique to help understand equipment performance and design.