Fundamental Limits of Measuring Single-Molecule Rotational Mobility

Various methods exist for measuring molecular orientation, thereby providing insight into biochemical activities at nanoscale. Since fluorescence intensity and not electric field is detected, these methods are limited to measuring even-order moments of molecular orientation. However, any measurement noise, for example photon shot noise, will result in nonzero measurements of any of these even-order moments, thereby causing rotationally-free molecules to appear to be partially constrained. Here, we build a model to quantify measurement errors in rotational mobility. Our theoretical framework enables scientists to choose the optimal single-molecule orientation measurement technique for any desired measurement accuracy and photon budget.