Bounds on the estimation of calcium by aequorin luminescence in the presence of inhomogeneity

The photoprotein aequorin, which emits light as a nonlinear function of calcium concentration, is often used to measure intracellular calcium. In the presence of inhomogeneities or fluctuations of calcium concentration, the nonlinearity results in discrepancies between mean calcium concentration estimated from average aequorin light and the true mean. It is usually assumed that the error is an overestimation, but in the presence of large calcium fluctuations, errors of either direction are possible. Here we show that for aequorin to overestimate the mean calcium, the point in the calcium-light plane representing the true mean calcium and measured mean aequorin light must lie in the convex envelope of that segment of the aequorin response curve that lies between the minimum and maximum values of fluctuating calcium, and must lie above the curve. By explicitly constructing this region, we derive a quartic equation that gives the largest measured calcium for which aequorin can be assumed to give an overestimate, as a function of the maximum calcium fluctuation. In particular, if calcium fluctuations do not exceed 1 mM, aequorin measurements below 7.25 microM may be assumed to overestimate the true mean calcium