Polymer Dynamics, Fluorescence Correlation Spectroscopy, and the Limits of Optical Resolution

In recent years, fluorescence correlation spectroscopy has been increasingly applied for the study of polymer dynamics on the nanometer scale. The core idea is to extract, from a measured autocorrelation curve, an effective mean-square displacement function that contains information about the underlying conformational dynamics. This Letter presents a fundamental study of the applicability of fluorescence correlation spectroscopy for the investigation of nanoscale conformational and diffusional dynamics. We find that fluorescence correlation spectroscopy cannot reliably elucidate processes on length scales much smaller than the resolution limit of the optics used and that its improper use can yield spurious results for the observed dynamics.

Figure 1

Fourier power spectra of the MDF and the eigenfunctions ${\varphi }_j$ entering the Green’s function for confined diffusion. The curves $j=0,1,\dots$ represent the power spectra $|{\tilde{\varphi }}_j(k){|}^2$ for $a=50\mathrm{nm}$. The triangular shaded region is the power spectrum $|\tilde{U}(k){|}^2$, and the shaded (yellow) region outside the triangular region is that of the Gaussian approximation of $U(x)$. Vertical lines delimit the finite support of the optical transfer function. The positions of the maxima of the functions $|{\tilde{\varphi }}_j(k){|}^2$ scale with the inverse value of $a$. Thus, the smaller the confinement region, the more the maxima will be shifted away from the Fourier modes that can be probed by the MDF.

Figure 2

Behavior of the function $\alpha (t)$ for different values of the confinement parameter $a$ and for $D_0=1\mu {\mathrm{m}}^2/\mathrm{time}\mathrm{unit}$. The inset shows the different ACFs for the selected values of $a$.

Figure 3

Mean-square displacement $⟨x^2⟩$ as a function of time determined by inverting Eq. (14) for the parameter values given in the text. The inset shows the corresponding ACF as calculated from Eqs. (12, 13). The dashed line is a linear fit of $\ln t$ to $\ln ⟨x^2⟩$ at the point of minimum slope.

Figure 4

Minimum value of $\alpha (t)$ as a function of the ratio $D/D_0$. Also shown are the expected values of $\alpha$ for Zimm and Rouse dynamics.