Simulation and analysis of diffusion of cell membrane proteins in different confinement models.

The manuscript can be viewed here

Note

This is my undergraduate research project that was done for PHYS 449 at McGill. It was in supervision of Dr. Paul Wiseman.

The simulations

The confinement models simulated are

1. No confinement (free diffusion)
2. Lattice of variable size (from underlying cytoskeleton of cell membrane)
3. Transient diffusion in nanoscale circular domains

The goal and short theoretical description

The goal was to compare STICS and iMSD image fluctuation anaylses in extracting diffusion coefficients of a simulated environment. STICS method relies on fluctuation of fluorescence intensity in pixels of an image that models microscopy where

$$ G(\zeta, \eta, \tau) = \frac{\langle i(x,y,t) \cdot i(x + \zeta, y + \eta, t + \tau) \rangle}{\langle i(x,y,t) \rangle^2} - 1 = \frac{\mathcal{F}^{-1} { \mathcal{F}(i_{2D}) \cdot \mathcal{F}^{\ast} (i_{2D})}}{\langle i(x,y,t) \rangle^2}-1, $$

for which $G(\zeta, \eta, \tau)$ is a approximated by a Gaussian surface. By fitting this Gaussian surface there exists a relationship between the diffusion coeffient of the system and the amplitude decay of the correlation function.

In the iMSD method, the growth of the radius of $G(\zeta, \eta, \tau)$ as a function of time lag $\tau$ can be found through

$$ (\zeta_e, \eta_e) = \left(\sqrt{-2 \ln\left(\frac{1}{e} - \frac{g_0}{g}\right)\sigma_\zeta^2} + \zeta_0 , \eta_0\right), $$

with $\sigma_r(\tau_i) = |\zeta_e - \zeta_0|$ as the radius at time $\tau_i$. $\zeta_r(\tau)$ is related to the diffusion coefficient of the system through

$$ \sigma_r^2(\tau) \approxeq \frac{L^2}{3} \left( 1 - \exp{-\frac{\tau}{\tau_c}}\right) +4D\tau+ \sigma_0^2. $$