Numerical construction of estimators for single-molecule fluorescence measurements.

A novel scheme to estimate the values of the underlying physical quantity and those of any functions of the quantity from measured observable(s) contaminated with stochastic noise is presented for any arbitrary probability distribution. The constructed estimators can either maximize the unbiasedness (i.e., minimize the amount of the deviation of the expectation value from the true value buried in the measurement) or minimize the risk (the average deviation from the true value) depending on the relative priority of unbiasedness and risk in the data analysis. The performance of the constructed estimators is demonstrated with computer simulations of Förster-type resonance energy transfer (FRET) measurements and also with FRET experimental data of the agonist-binding domain of the GluA2 subunit of AMPA receptors with agonists chloro- and iodo-willardiines and with adenylate kinase both in the apo form and with substrates AMP-PNP and AMP. It is shown that the estimators constructed by the present method can quantify faithfully not only the physical quantity to be monitored but also the functions of that quantity for a wide range of values.