lambda-Repressor oligomerization kinetics at high concentrations using fluorescence correlation spectroscopy in zero-mode waveguides

Abstract

Fluorescence correlation spectroscopy (FCS) has demonstrated its utility for measuring transport properties and kinetics at low fluorophore concentrations. In this article, we demonstrate that simple optical nanostructures, known as zero-mode waveguides, can be used to significantly reduce the FCS observation volume. This, in turn, allows FCS to be applied to solutions with significantly higher fluorophore concentrations. We derive an empirical FCS model accounting for one-dimensional diffusion in a finite tube with a simple exponential observation profile. This technique is used to measure the oligomerization of the bacteriophage lambda repressor protein at micromolar concentrations. The results agree with previous studies utilizing conventional techniques. Additionally, we demonstrate that the zero-mode waveguides can be used to assay biological activity by measuring changes in diffusion constant as a result of ligand binding.

FIGURE 1

Zero-mode waveguides are 50 nm in diameter by 100 nm deep holes in an aluminum film deposited on a fused silica substrate. They are excited by confocal epi-illumination which produces an atto- to zeptoliter illumination volume at the excited end. Fluorescence generated by the molecules in the observation volume is collected back through the end of the waveguide by a microscope objective. The incident, circularly polarized light, propagates in the z direction.

FIGURE 2

Histogram of K_M values for 30,000 enzymes taken from the Brenda Database (www.brenda.uni-koeln.de). The effective concentration ranges for diffraction limited and zero-mode waveguide FCS are shown in blue and red, respectively. Kinetics for the vast majority of enzymes are out of reach for diffraction limited FCS. FCS is not yet a viable tool above the 100 μM regime.

FIGURE 3

(A) Two CI dimers cooperatively bound to the O_R1 and O_R2 operator sites. When bound, they prevent the transcription of genes responsible for the bacteriophage's lytic path and enhance the transcription of CI. (B) When the concentration of CI is high enough, the proteins bound to the right operator (O_R) octamerize with CI bound to the left operator (O_L). This induces a loop structure in the DNA that leaves P_RM active (top). The loop structure enables binding of a third CI tetramer to the O_R3 and O_L3 binding site (bottom). This prevents RNA polymerase from binding to P_RM and terminates CI production. (C) Oligomerization kinetics established by convention biochemical techniques.

FIGURE 4

(A) Plot of the exact (solid line) and approximate (dashed line) autocorrelation curves for a single diffusing species in a zero-mode waveguide for R = 0.15 (red) and R = 0.25 (blue). (B) The difference between the approximate and exact autocorrelation curves for R = 0.10, 0.15, 0.20, and 0.25. The approximation is quite good for small holes but less reliable for larger ones. The parameters N and τ_d were both set to 1 for these curves.

FIGURE 5

Representative autocorrelation curve and fit from the kinetics measurements. Two distinct time constants are visible in the autocorrelation curve. Fit is in black.

FIGURE 6

A molecule's diffusion time is expected to vary with the size of the zero-mode waveguide being used for the observation. Plotted here are the diffusion time and R parameters for FCS curves taken in several different waveguides. The solid line is a plot of τ_d(R) = AR². With A = 7.6 × 10⁻⁴ ± 2 × 10⁻⁵ s established by fitting the data. Equation 7 suggests that A = H²/D, implying that D = 1.3 × 10⁻⁷ cm²/s.

FIGURE 7

Results from background correction. (A) Number of dimers and tetramers in the observation volume plotted as a function of the observation volume. Linear fits reveal the concentrations of the two species. [N_dim] = 0.4 μM. [N_tet] = 0.03 μM. (B) The background, B, is seen here to have a dependence on the parameter R and, hence, on the size of the waveguide.

FIGURE 8

Representative autocorrelation curves from (A) the mRFP-CI sample and (B) the O_R1 with mRFP-CI sample. The full width at half-maximum provides a good estimate of the diffusion time. Because the curves were acquired in two waveguides of differing size and observation volume, the diffusion times cannot simply be compared. Instead, the diffusion constants must be calculated. Both curves have G₀ normalized to 1. Fits are in black.