## Differential Equations Seminar: Mingkai Yu

#### UMBC

Monday, November 11, 2019 · 11 AM - Noon

**Title:**Analysis and Simulation of Fluorescence Correlation Spectroscopy

**Abstract:**Fluorescence Correlation Spectroscopy (FCS) is a tool to determine the diffusivity of fluorescently labeled molecules in the solution by measuring the fluctuation of fluorescence intensity. We provide a mathematical derivation to illustrate how the correlation of the intensity signal reveals the diffusivity. In FCS experiment, particles are doing reflected Brownian motion in a container and as they diffuse into and out of the very small confocal volume illuminated by a laser beam, the fluorescence intensity fluctuates. The fluorescence intensity could be modeled as a stochastic process governed by the motion of particles. The autocorrelation of the intensity has an analytical form as a function of time lag and diffusion coefficient, so the diffusion coefficient could be fitted from the experimentally measured autocorrelation function. To quantify the uncertainty, we derive a formula for the variance of the autocorrelation function in integral form and we find a closed-form upper bound. Monte Carlo simulations will be presented to compare with the theory.