Photon Shot Noise Limits on Optical Detection of Neuronal Spikes and Estimation of Spike Timing

Optical approaches for tracking neural dynamics are of widespread interest, but a theoretical framework quantifying the physical limits of these techniques has been lacking. We formulate such a framework by using signal detection and estimation theory to obtain physical bounds on the detection of neural spikes and the estimation of their occurrence times as set by photon counting statistics (shot noise). These bounds are succinctly expressed via a discriminability index that depends on the kinetics of the optical indicator and the relative fluxes of signal and background photons. This approach facilitates quantitative evaluations of different indicators, detector technologies, and data analyses. Our treatment also provides optimal filtering techniques for optical detection of spikes. We compare various types of Ca(2+) indicators and show that background photons are a chief impediment to voltage sensing. Thus, voltage indicators that change color in response to membrane depolarization may offer a key advantage over those that change intensity. We also examine fluorescence resonance energy transfer indicators and identify the regimes in which the widely used ratiometric analysis of signals is substantially suboptimal. Overall, by showing how different optical factors interact to affect signal quality, our treatment offers a valuable guide to experimental design and provides measures of confidence to assess optically extracted traces of neural activity.