Molecular Density in Super-Resolution Microscopy

Among the critical aspects that must be considered in single-molecule super-resolution imaging are the accuracy of each individual localization measurement, the density of probes that have been localized in the final image (commonly termed molecular density), and the physical size of the labels themselves. The relationship between resolution and the localization precision of a single molecule is readily determined. The ability to resolve two fluorescent molecules as separate entities is limited by the localization precision, which determines the position (and uncertainty) of each molecule and thus the distance between the pair. The localization precision, in turn, is primarily dependent upon the number of photons collected from the fluorescent molecules during a single activation-deactivation cycle, provided the background noise is negligible. This interactive tutorial explores the concept of molecular density and image resolution.

The tutorial initializes with a sparse set of localization points in the window, representing a low degree of molecular density in a virtual specimen. In order to operate the tutorial, use the Localized Molecule Density slider to increase the number of localized molecules, and thus the resolution of the image appearing in the window. At the highest molecular density, fine specimen details become apparent. A new specimen can be selected using the pull-down menu.

The relationship between molecular density and final image resolution is best described in terms of the Nyquist sampling theory, which requires approximately two data points per resolution unit. In cases where the labeling efficiency (in effect, the fraction of targets that are labeled) of a specimen is insufficient, artifacts such as discontinuity in fine structural details can appear in super-resolution images. Thus, for a two-dimensional image having spatial features of size α, the minimum required molecular density of localized fluorescent probes necessary to meet the Nyquist criterion is:

Formula 1 - Nyquist Molecular Density

Nyquist Molecular Density ≈ (2/α)2

Therefore, for example, in order to achieve 20-nanometer resolution in two dimensions, one fluorophore has to be positioned at least every 10 nanometers and an extremely high molecular density of around 10,000 molecules per square micrometer is required. For super-resolution in three dimensions, 20-nanometer resolution requires about a million fluorophores per cubic micrometer. In practice, a much lower molecular density is often sufficient when the geometry of the specimen is taken into consideration. Biological structures are often heterogeneous so that even saturation labeling with a relatively high abundance of target sites can result in a relatively low overall density. In general, a sufficient density of fluorescent probes must be present in order to fully map the fine details of a labeled structure. By the same criterion, a sufficient number of these fluorescent probes must be successfully localized during the imaging process

Figure 1 - Molecular Density in Single-Molecule Super-Resolution Imaging

In single-molecule super-resolution techniques that temporally separate the fluorescence emission by employing photoswitchable fluorophores (such as PALM and STORM), the ratio of the on and off switching kinetics is a critical experimental parameter that should be fine-tuned to the molecular density. In the case described above for a molecular density of 10,000 fluorophores per square micrometer, in order to achieve a final resolution of 20 nanometers in the lateral plane, approximately 600 fluorophores must reside in the lateral projection of the point-spread function. Such high molecular densities can be complicated by the fact that the majority of photoswitchable fluorophore are not in their dark state, leading to high background noise. These fluorophores either emit weak fluorescence or they can spontaneously switch to the fluorescent state in the total absence of activation illumination. Nonspecific activation can be either spontaneous or the artifact can be induced by the imaging laser. In situations where the molecular density is very high, a large number of nonspecifically activated fluorophores can generate overlap of single-molecule images, thus compromising the ability to achieve high-precision localization. It is therefore advisable to employ photoswitchable fluorophores that exhibit low dark-state emissions and low nonspecific activation rates.

Presented in Figure 1 is an important concept involving one of the most critical factors influencing spatial resolution in single-molecule super-resolution imaging. The resolution versus molecular density is represented in Figure 1 as a series of yellow pixels in a test pattern. Features that might be present in a specimen are imaged at a progressively lower signal-to-noise ratio (fraction of pixels measured) as the molecular density decreases (from the bottom to the top of Figure 1) and these features become unresolvable when the mean molecular separation approaches feature size (the top row in Figure 1). Thus, as described in Equation (1), in order to achieve N-fold higher resolution in dimensions DND-fold more pixels must be acquired. In order to realize such a resolution gain without compromising either the imaging speed or the signal-to-noise ratio, the signal collection rate (photons detected per second) must increase by a factor of at least ND, which requires an ND-fold higher exposure to the excitation laser for each image required.

In terms of temporal resolution, single-molecule based super-resolution approaches do not directly generate an image, but rather are used to map specific molecular localizations that are determined from thousands of individual imaging frames. In this case, temporal resolution is determined by the number of imaging frames that are required to obtain a suitable image. Additionally, the nature of the photoswitchable fluorophores used in PALM and STORM imaging, as performed using Nikon's N-STORM system, can produce constraints on temporal imaging speed. Fluorescent proteins are excellent for use as genetically-encoded probes in cases where localization to a specific subcellular compartment or biomolecular assembly is required. Unfortunately however, fluorescent proteins exhibit relatively slow photoswitching kinetics compared to many of the synthetic probes, such as Cy5 and Alexa Fluor 647. The latter can exhibit high switching speeds that enable 1-millisecond imaging cycles at a resolution of approximately 30 nanometers, which are several orders of magnitude greater than those obtainable with fluorescent proteins. Switching cycle speeds that help determine the temporal resolution in single-molecule super-resolution microscopy will be the ultimate limitation in adapting this methodology to live-cell imaging.

Contributing Authors

Joel S. Silfies and Stanley A. Schwartz - Nikon Instruments, Inc., 1300 Walt Whitman Road, Melville, New York, 11747.

Stephen P. Price and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.

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Molecular Density in Super-Resolution Microscopy