Kinetic Requirements for Spatiotemporal Chemical Imaging with Fluorescent Nanosensors

Fluorescent nanosensors are powerful tools for basic research and bioanalytical applications. Individual nanosensors are able to detect single molecules, while ensembles of nanosensors can be used to measure the bulk concentration of an analyte. Collective imaging of multiple nanosensors could provide both spatial and temporal chemical information from the nano- to the microscale. This type of chemical imaging with nanosensors would be very attractive to study processes such as chemical signaling between cells (e.g., neurons). So far, it is not understood what processes are resolvable (concentration, time, space) and how optimal sensors should be designed. Here, we develop a theoretical framework to simulate the fluorescence image of arrays of nanosensors in response to a concentration gradient. For that purpose, binding and unbinding of the analyte is simulated for each single nanosensor by using a Monte Carlo simulation and varying rate constants (k_on, k_off). Multiple nanosensors are arranged on a surface and exposed to a concentration pattern c_A(x,y,t) of an analyte. We account for the resolution limit of light microscopy (Abbe limit) and the acquisition speed and resolution of optical setups and determine the resulting response images ΔI(x,y,t). Consequently, we introduce terms for the spatial and temporal resolution and simulate phase diagrams for different rate constants that allow us to predict how a sensor should be designed to provide a desired spatial and temporal resolution. Our results show, for example, that imaging of neurotransmitter release requires rate constants of k_on = 10⁶ M^-1 s^-1and k_off = 10² s^-1 in many scenarios, which corresponds to high dissociation constants of K_d > 100 μM. This work predicts if a given fluorescent nanosensor array (rate constants, size, shape, geometry, density) is able to resolve fast concentration changes such as neurotransmitter release from cells. Additionally, we provide rational design principles to engineer nanosensors for chemical imaging.