Rotational Correlation Functions of Single Molecules

Single molecule rotational correlation functions are analyzed for several reorientation geometries. Even for the simplest model of isotropic rotational diffusion our findings predict nonexponential correlation functions to be observed by polarization sensitive single molecule fluorescence microscopy. This may have a deep impact on interpreting the results of molecular reorientation measurements in heterogeneous environments.

Figure 1

Schematic experimental setup: the polarization of light emitted by a single fluorophore depends on the orientation of the transition dipoles with respect to the detection system. The two orthogonally polarized components of the signal are separated by a polarizing cube beam splitter.

Figure 2

Rotational correlation function $C_d(t)$ for isotropic diffusion (solid line). For comparison the exponential correlation function $l=2$ [Eq. (10): $A_2=1,A_{l\ne 2}=0$] is plotted as a dotted line.

Figure 3

(a) Stretching exponent $\beta$ depending on the anisotropy $\delta =D_z/D_x$ ($D_x=D_y$). ${\theta }_{PD}$ denotes the angle between the $z$ axis of the diffusion tensor and the transition dipole $\overrightarrow{\mu }$. (b) Correlation times normalized by ${\tau }_0=\tau (D_z\parallel \overrightarrow{\mu })$. $\tau$ and $\beta$ were obtained by fitting $C(t)$ with $\exp [-(t/\tau {)}^{\beta }]$.

Figure 4

Influence of the reorientation mechanism on the stretching (○) and the time scale (●) of the correlation function, calculated for rotational jump processes with varying jump angles $\gamma$. For comparison the correlation times were normalized by the pure $l=2$ correlation time ${\tau }_2$.