Spatial mapping of single QDs. (a) Representative plot of the fitted spatial centroids (± asymptotic standard error) of a single QD for all image frames (394 out of 600) that had integrated peak intensities within J₁ ± 1.64σ₁, indicative of a single QD, and the mean fitted position (white) of the single QD superimposed on the approximate pixel array of our optical system (pixel size, 108 nm). (b) Mean spatial centroids of 14 single QDs identified in Fig. 1 a superimposed on the approximate pixel array of our imaging system (pixel size, 108 nm) were randomly distributed. (c) Separation distances between all 91 possible pairs of QD ranged from 13 to 121 nm. (d) Mean precisions (± SE) (, ) for mapping a single QD along the x (triangles) and y (squares) axes increased as a function of the number (N_k) of sequential frames that were averaged.

Accuracy of spatial mapping of QD pairs. (a) The fitted distance of separation plotted versus the actual calculated distance of separation was well fit to a line with a slope of 0.91 ± 0.02 (R² = 0.94). (b and c) Mean accuracy of the fitted distances (91 points) and positions (182 points), respectively, as a function of the actual distance of separation with 10 nm bins (91 points). The number of data points for each distance is shown in Fig. 2 c.

Identification of single QDs. (a) A single image from a 600-frame sequence acquired at 30 Hz of QDs immobilized on a glass coverslip (scale bar, 4 μm). The full time sequence, which illustrates the observed QD blinking, is shown as a movie in Supplementary Material. (b) The integrated peak intensities, J (Eq. 1), of single blinking QDs typically showed distinct fluctuations as a function of time. (c) Histograms constructed from the 600 integrated peak intensities, J, for single QDs also typically showed distinct “on” and “off” states. (d) Cumulative histogram of the integrated intensities derived from data for the 14 out of 26 diffraction-limited peaks in an image sequence (of which one frame is shown in a) that were firmly identified as single QDs (8400 points) and the best fit to the sum of two 1D Gaussians (Eq. 2 with q = 1). In b–d, the dashed line corresponds to the integrated peak intensities, J = J₁ ± 1.64σ₁, indicative of a single QD being in the “on” state, and the dotted line corresponds to the integrated peak intensity, J = J₁ ± 3.89σ₁, indicative of more than one QD being in the “on” state. In c and d, the leftmost peak arises from background (J₀).

Spatial mapping of QD pairs. (a) A histogram of the integrated intensities per frame, J, of all 91 pairs of QDs shows three distinct intensity states. The number of points used to generate the plot was 91 × 600 = 54,600. The solid line shows the best fit to the sum of three 1D Gaussians (Eq. 2 with q = 2). (b–d) Representative example of a QD pair with a separation distance of 39 ± 18 nm. (b) The integrated peak intensities, J, of the QD pair as a function of time show intensity levels corresponding to all three states. (c) Fitted spatial centroids (± asymptotic standard error) of the QD pair when both QDs are simultaneously “on” give a single mean fitted position (white). (d) Fitted spatial centroids (± asymptotic standard error) of the QD pair when the QDs are separately “on” give two separate fitted mean QD positions (white). In a and b, the dashed line corresponds to the integrated peak intensities, J = J₁ ± 1.64σ₁, indicative of a single QD being in the “on” state, and the dotted line corresponds to the integrated peak intensity, J = J₁ + 3.89σ₁, indicating that more than a single QD is in the “on” state. The fitted distance of separation in this case was found to be 34 ± 14 nm, whereas the errors in the fitted positions of the two QDs were found to be 9 ± 17 nm and 4 ± 16 nm.

End-to-end distance of 122-bp dsDNA. (a) A histogram of the frequency of events of the distance of separation between two nearby QDs with 10-nm bins. The observed distances of separation in the absence of DNA (open bars; N = 12) are <30 nm, whereas several of the observed distances of separation in the presence of DNA (solid bars; N = 24) are >30 nm. We determined the mean and standard deviation of the distance of separation in the absence of DNA to be 19 ± 13 nm (R² = 0.97) by curve-fitting the observed distance distribution to a single 1D spatial Gaussian (dashed lines). We determined the means and standard deviations of the aggregates in the presence of DNA to be 27 ± 19 nm and 48 ± 9 nm (R² = 0.96) by curve-fitting the observed distance distribution to the sum of two 1D spatial Gaussians (dot-dashed line). (b) A typical example of a QD aggregate in the presence of 122-bp dsDNA. These two nearby QDs were found to be separated by 47 ± 16 nm.