Nanometer-scale mapping and single-molecule detection with color-coded nanoparticle probes

Agrawal et al. 10.1073/pnas.0712351105.

Supporting Information

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SI Text
SI Figure 6
SI Table 1




SI Figure 6

Fig. 6. Histogram plots showing colocalization events as a function of distance for rigid DNA molecular structures. (a) Statistical data from a noncomplementary control sample showing colocalization events (background) caused by random particle distribution and nonspecific binding or aggregation. (b) Statistical data from a rigid 24-bp DNA construct showing a peak at 54 nm, which is remarkably close to the expected contour length (55 nm) for this structure. (c) Statistical data from a rigid 40-bp DNA construct showing a peak at 61 nm, which differs from the expected length (60.5 nm) by only 0.5 nm.

Table 1. Image processing and colocalization algorithms Using the IDL Astronomy User's Library

PSF, point-spread function.

SI Text

Image Processing and Colocalization Analysis

The DAOPHOT astrophysical method was used for image processing and colocalization analysis in three steps: (i) finding the centers of the nanoparticles by convoluting the input image with a two-dimensional Gaussian intensity distribution; (ii) selecting a library of input point spread functions (PSFs) to calculate intensity deviations between the nanoparticles and their Gaussian model; and (iii) using the PSF deviations to adjust the Gaussian model for a better estimate of the nanoparticle's intensities and photometric centers. The first step exploits several pieces of information that are readily available: (i) the readout noise of the CCD detector; (ii) the number of photoelectrons corresponding to one analog-to-digital converter unit (ADU); (iii) the saturation limit of the CCD in ADUs; (iv) the approximate size [full width at half maximum (FWHM)] of a nanoparticle's fluorescence image; and (v) the smallest brightness value that would be expected from random noise in the CCD image. The first three parameters were obtained from the technical specifications of the CCD camera, and the image size (FWHM = 10 pixels) was computed from the input image frame by measuring several intensity profiles from selected nanoparticles. The algorithm then computed a two-dimensional, unit-height, circular Gaussian kernel (24 ´ 24 pixels) by using the measured FWHM value as the input parameter. This kernel is convolved with the input image. The operation of convolution takes the input kernel and multiplies it with each pixel in the image being convolved. Through this operation, the image areas with strong positive intensity deviations from the background are smoothed, and the image regions are selected preferentially if their input FWHM value matches that of the PSF. Thus, the peak heights in the convolved image are proportional to the brightness of the original particle image, and one only needs to locate the pixels with the most positive brightness deviation within an image area that is roughly the size of the Gaussian kernel. By working in Fourier domain, this convolution operation can be performed rapidly even on a desktop computer. We note that this procedure works well in the center of the image, where the focus is nearly perfect. Toward the outermost periphery of the image, the Gaussian fitting procedure works less well, because some of the particles are out of focus. To address this problem, we do not convolve the kernel in the outer boundary of the image and leave a margin half the size of the convolution kernel, which does not affect our conclusions because the total number of particles in the image is significantly large relative to the ones that are lost in the margin.

After image convolution, the next step is to locate all of the nanoparticles. The DAOPHOT method was developed for crowded-field stellar photometry. It uses two input parameters to verify whether two adjacent but resolved signals are from two stars that are very near to each other in projection or a combination of a star and a distant galaxy. Another complication for the astronomical images is the presence of cosmic-ray hits on the CCD, which gives rise to false star-like images. For nanoparticle image analysis, we do not need to contend with such extremes, but there are false particle signals caused by bleed-through in the optical filters. These false signals are often not completely circular in size and have a fuzzy appearance. The two parameters in locating such false particles are called the sharpness and roundness criteria. Just like stars, the particles in our images are expected to be round instead of being elongated in either the x or y dimension. The sharpness criterion helps to filter out fuzzy and faint bleed-through effects. If one sets these two parameters at the start of an image-processing run, the output list of candidate particles can be filtered automatically to remove such defects. The sharpness criterion compares the data value at the central pixel of the convolution box with that of the height of the convolution peak in a convolved image area. For fuzzy-appearing particles (caused by the bleed-through), the sharpness parameter is close to zero. If the image has a single, isolated hot pixel, the sharpness will be close to 1. Thus, the roundness criterion can be used to remove elliptically distorted signals in the image. The limits for sharpness and roundness for stars are commonly set as 0.2 < sharpness <1.0 and -1.0 < roundness < 1.0, respectively, but we have used more stringent limits for particle detection.

The initial candidate list of nanoparticle positions is fed to a group-generating routine, which locates particles that are nearby on the basis of a given minimum distance and then assigns all of these particles to a group ID. This group listing along with the original coordinate list is fed to a routine that performs PSF fitting for individual particles. This PSF fitting is performed by using a library of input PSFs generated from the original image. The final routine generates better estimates of both the coordinate positions and particle intensities on the basis of the PSF fitting. Using this final list of coordinates for the red and green channels, we calculate the distances between the particles to find the colocalization peak.

The algorithms for DAOPHOT are implemented in Interactive Data Language (Visual Information Solutions) by various contributors in the Interactive Data Language astronomy user's library. We used the programs listed in SI Table 1 for stepping through the DAOPHOT procedure. The input parameters were adopted for the nanoparticle images. Using these procedures, we obtained the lists of x and y coordinates along with error estimates at each position, which then were used to find distances between the red and green particles. This final list of particle distances is filtered to remove the most common separation between any given red/green particles (which occurs because of the finite image size). The remaining peak in the histogram plots corresponds to the actual distance between particles.

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