On characterizing protein spatial clusters with correlation approaches.

Spatial aggregation of proteins might have functional importance, e.g., in signaling, and nano-imaging can be used to study them. Such studies require accurate characterization of clusters based on noisy data. A set of spatial correlation approaches free of underlying cluster processes and input parameters have been widely used for this purpose. They include the radius of maximal aggregation ra obtained from Ripley's L(r) - r function as an estimator of cluster size, and the estimation of various cluster parameters based on an exponential model of the Pair Correlation Function(PCF). While convenient, the accuracy of these methods is not clear: e.g., does it depend on how the molecules are distributed within the clusters, or on cluster parameters? We analyze these methods for a variety of cluster models. We find that ra relates to true cluster size by a factor that is nonlinearly dependent on parameters and that can be arbitrarily large. For the PCF method, for the models analyzed, we obtain linear relationships between the estimators and true parameters, and the estimators were found to be within ±100% of true parameters, depending on the model. Our results, based on an extendable general framework, point to the need for caution in applying these methods.

High-Resolution Correlative Microscopy: Bridging the Gap between Single Molecule Localization Microscopy and Atomic Force Microscopy.

Nanoscale characterization of living samples has become essential for modern biology. Atomic force microscopy (AFM) creates topological images of fragile biological structures from biomolecules to living cells in aqueous environments. However, correlating nanoscale structure to biological function of specific proteins can be challenging. To this end we have built and characterized a correlated single molecule localization microscope (SMLM)/AFM that allows localizing specific, labeled proteins within high-resolution AFM images in a biologically relevant context. Using direct stochastic optical reconstruction microscopy (dSTORM)/AFM, we directly correlate and quantify the density of localizations with the 3D topography using both imaging modalities along (F-)actin cytoskeletal filaments. In addition, using photo activated light microscopy (PALM)/AFM, we provide correlative images of bacterial cells in aqueous conditions. Moreover, we report the first correlated AFM/PALM imaging of live mammalian cells. The complementary information provided by the two techniques opens a new dimension for structural and functional nanoscale biology.

Accounting for limited detection efficiency and localization precision in cluster analysis in single molecule localization microscopy.

Single Molecule Localization Microscopy techniques like PhotoActivated Localization Microscopy, with their sub-diffraction limit spatial resolution, have been popularly used to characterize the spatial organization of membrane proteins, by means of quantitative cluster analysis. However, such quantitative studies remain challenged by the techniques' inherent sources of errors such as a limited detection efficiency of less than 60%, due to incomplete photo-conversion, and a limited localization precision in the range of 10-30 nm, varying across the detected molecules, mainly depending on the number of photons collected from each. We provide analytical methods to estimate the effect of these errors in cluster analysis and to correct for them. These methods, based on the Ripley's L(r) - r or Pair Correlation Function popularly used by the community, can facilitate potentially breakthrough results in quantitative biology by providing a more accurate and precise quantification of protein spatial organization.

MosaicIA: an ImageJ/Fiji plugin for spatial pattern and interaction analysis.

BACKGROUND: Analyzing spatial distributions of objects in images is a fundamental task in many biological studies. The relative arrangement of a set of objects with respect to another set of objects contains information about potential interactions between the two sets of objects. If they do not "feel" each other's presence, their spatial distributions are expected to be independent of one another. Spatial correlations in their distributions are indicative of interactions and can be modeled by an effective interaction potential acting between the points of the two sets. This can be used to generalize co-localization analysis to spatial interaction analysis. However, no user-friendly software for this type of analysis was available so far. RESULTS: We present an ImageJ/Fiji plugin that implements the complete workflow of spatial pattern and interaction analysis for spot-like objects. The plugin detects objects in images, infers the interaction potential that is most likely to explain the observed pattern, and provides statistical tests for whether an inferred interaction is significant given the number of objects detected in the images and the size of the space within which they can distribute. We benchmark and demonstrate the present software using examples from confocal and PALM single-molecule microscopy. CONCLUSIONS: The present software greatly simplifies spatial interaction analysis for point patterns, and makes it available to the large user community of ImageJ and Fiji. The presented showcases illustrate the usage of the software.