Similarity Metrics for Subcellular Analysis of FRET Microscopy Videos

Abstract

Understanding the heterogeneity of molecular environments within cells is an outstanding challenge of great fundamental and technological interest. Cells are organized into specialized compartments, each with distinct functions. These compartments exhibit dynamic heterogeneity under high-resolution microscopy, which reflects fluctuations in molecular populations, concentrations, and spatial distributions. To enhance our comprehension of the spatial relationships among molecules within cells, it is crucial to analyze images of high-resolution microscopy by clustering individual pixels according to their visible spatial properties and their temporal evolution. Here, we evaluate the effectiveness of similarity metrics based on their ability to facilitate fast and accurate data analysis in time and space. We discuss the capability of these metrics to differentiate subcellular localization, kinetics, and structures of protein-RNA interactions in Forster resonance energy transfer (FRET) microscopy videos, illustrated by a practical example from recent literature. Our results suggest that using the correlation similarity metric to cluster pixels of high-resolution microscopy data should improve the analysis of high-dimensional microscopy data in a wide range of applications.

Figure 1.. Data workflow for spectral clustering of FRET microscopy videos.

Each pixel in a microscopy video is in a 3-dimensional matrix, with two positional coordinates and a time coordinate. To compare signal across time, the data is flattened into a 2-dimensional matrix where preprocessing methods such as normalization and smoothing can be applied. For spectral clustering, an adjacency matrix is generated by evaluating the similarity between each pixel or sample. This similarity metric is chosen based on the desired comparison. Since the matrix is symmetric, it can be efficiently spectrally decomposed to get the eigenvalues of the adjacency matrix. This acts as a dimensionality reduction so that clustering can be performed more efficiently in fewer dimensions.

Figure 2.. Ability of similarity metrics to distinguish function parameters.

a) A 51 x 51 pixel grid was subdivided into six regions, each simulating a specific function whose parameters are varied across groups, as detailed in Table S1. These parameter variations model changes within the function’s characteristics. b) Representative time series from each region in a are depicted, with color coding consistent with the respective group. This helps illustrate how sensitive the clustering is to the different time series. c) The clustering outcomes of each similarity metric, tested against simulated sigmoidal curves with varying midpoints. Each metric’s ability to cluster pixels according to the underlying parameter variations are displayed, highlighting the differences in performance and suitability for this analysis context. d) Quantitative evaluation of the clustering accuracy for each similarity metric, applied to two different functions, sigmoid and exponential decay, with varying parameters. The accuracy is shown across four scenarios: (i) sigmoid functions with a shifted midpoint, (ii) sigmoid functions with an altered slope, (iii) exponential decay functions with modified decay rates, and (iv) exponential decay functions with changing amplitude. These scenarios are designed to test each metric’s sensitivity to specific types of parameter alterations within the function.

Figure 3.. Comparative clustering of similarity metrics on cylinder-bell-funnel (CBF) data set

a) Example time series for the three illustrative of the three function types: cylinder (blue), funnel (orange), and bell (green). A target segmentation map delineates the ideal clustering arrangement with each function type assigned to discrete segments represented by different colors in the vertical layout: cylinder (top), funnel (middle), and bell (bottom), signifying the benchmark for subsequent clustering comparison. b) Results depicted are a typical clustering performance of each similarity metric when applied to the CBF dataset with color consistency indicating greater accuracy. The variation in patterns shows the sensitivity of each similarity metrics to the different shapes of the time-series. Accuracies are quantified in Fig. S4a.

Figure 4.. Similarity metric sensitivity to event frequencies.

a) The underlying probability distributions for spike occurrence across different regions of a video (red, blue, green, yellow, and black), consisting of overlapping Gaussian functions peaking at 20%. b) Representative time-series data of spikes for two pixels taken from each region. It is unlikely that two pixels in the same region behave identically, however, they behave similarly based on their underlying probability distribution. The probability distributions in (a) are aligned with representative time-series data of individual pixels in (b). Pixels from the same region have a high probability of spiking when the probability distribution in that region is high. These distributions are combined with a baseline spike probability set at 5% (black) to model the stochastic nature of spike generation. c) A target data segmentation map is created based on the probability parameters, displaying the idealized classification of data into four categories, each color-coded to represent a different spike probability region. This map serves as the reference standard for clustering accuracy. d) Results depicted are a typical clustering performance of each similarity metric when applied to the dataset with color consistency indicating greater accuracy. The variation in patterns visualizes the sensitivities of each similarity metric to resolving the different regions in comparison to the background. Accuracies are quantified in Fig. S4b.

Figure 5.. Analysis and Clustering of U1A-SL2 Binding Dynamics Using Spectral Clustering.

a) Schematic representation of the U1A-SL2 FRET construct showing the U1A protein (green) and SL2 RNA (red) bound together. b) Fluorescence images from the initial frame of the FReI experiment displaying the donor (U1A labeled with Alexa 488, green) and acceptor (SL2 labeled with Alexa 594, red). c) Example data of FReI experiment which gives us three outputs. (left) FRET efficiency data over time, shows the change in energy transfer efficiency as a function of the temperature jumps and changes in interactions. (middle) Thermodynamic profile of the binding interaction, with FRET efficiency plotted against temperature to assess the stability and binding changes under varying thermal conditions. (right) Kinetic analysis data, depicting normalized FRET efficiency decay over time, indicative of the rates of binding and unbinding. d) Clustering results from spectral clustering using correlational self-similarity. e-g) The calculated K_d k_on, k_off values based on the average signal for each cluster. Results show that the changes in the K_D (e) are from changes in the dissociation rates (g) and not the association rates (f).