QUANTIFICATION OF MITOCHONDRIAL MEMBRANE CURVATURE BY THREE-DIMENSIONAL LOCALIZATION MICROSCOPY

Abstract

Mitochondrial membrane organization is important for many biological functions, and is implicated in a number of diseases, but conventional microscopy has insufficient resolution to image biologically relevant structures. We present methods to quantify nanoscale membrane curvature using three-dimensional localization-based super-resolution microscopy. Localizations are analyzed using a cluster algorithm followed by principal component analysis to determine local membrane curvature. Results are shown for mitochondria in C2C12 mouse myotubes labeled with Tom20-Dendra2

Mitochondrial morphologies are essential to their function, and significant changes to mitochondrial membrane curvature have been implicated in a number of neurodegenerative diseases ^[1]. Mitochondria are often too small to properly resolve with conventional fluorescence microscopy techniques. However, the advent of super-resolution methods, such as FPALM ^[2], PALM ^[3], and STORM ^[4], have opened new opportunities for noninvasive observation at the nanoscale. Here we present a method for estimating the curvature of super-resolved mitochondrial membranes in three dimensions. In addition to its specific application to mitochondria presented here, this method can be useful for quantification of membrane curvature in a variety of cellular contexts, such as other intracellular organelles, viral protein clustering and budding in the plasma membrane, and modulation of membrane curvature by cytoskeletal elements.

In this case, we used astigmatic FPALM ^{[5, 6]} to image mitochondria in C2C12 mouse myotubes expressing pTOM20-Dendra2, a marker for the outer mitochondrial membrane fused with a photoswitchable fluorescent protein. Individual molecules were localized by fitting point spread functions to a 2D Gaussian, whose x and y radii vary according the molecules z position. Then, from coordinates of localized molecules, the local membrane curvature could be determined through a 3-step process: mitochondrial identification, edge detection, and curve fitting.

To identify mitochondria (i.e. clusters of localized points), the data is passed through single linkage cluster analysis (SLCA) which iteratively links points within Rmax of each other (here R_max=75nm) and is based on a previously published algorithm ^[7]. Any clusters reaching a minimum of 150 points were considered individual mitochondria and saved for further analysis.

Once each mitochondrion has been identified, the cluster edges need to be determined prior to fitting. To do this, we find an appropriate alpha shape which describes the set of points that lie along the boundary of each cluster. Alpha shapes are a generalization of the convex hull that contain a tunable parameter, the alpha radius, which describes how closely boundary points are followed ^[8]. To best describe the details of the surface, the alpha radius should be chosen such that it is as small as possible while still producing contiguous shapes. If an alpha shape is found with multiple regions, only the region with the largest volume should be used, as this represents the outermost boundary of the shape. Since the ideal alpha radius depends, in part, on the sampling density and localization precision, it should be chosen empirically.

Within each alpha shape, we further select a subset of points within a sampling radius, Rs=200nm, of each point which are used for curve fitting. To reduce errors from fitting, Rs is chosen so that it is smaller than the size of any individual mitochondrion but larger than the localization precision of the individual molecules. Principle component analysis (PCA)^[9] is then used to rotate this subset of points and the Z-axis is set as the principal component with the least variance. Rotated sections are fitted by least squares to a paraboloid of the form:

$$z=z_0+C_x{\left(x-x_0\right)}^2+C_y{\left(y-y_0\right)}^2$$

where the sum of the absolute values of C_x and C_y represent the commonly reported mean curvature ^[10,11] (μm⁻¹), C_mean = C_x + C_y, and where x₀ and y₀, and z₀ are position offsets. This process is repeated for each point in each alpha shape and a colormap is applied to visually represent various degrees of curvature along the mitochondrial membrane.

Figure 1A shows an example of local membrane curvature fitting from pTOM20-Dendra2 labeled mitochondria in fixed C2C12 cells. From the local curvature obtained at each location, a map of the magnitude of local curvature can be made throughout the sample (Figure 1B). Note the variation in curvature over the surface of the mitochondria, as reflected in the changes in color within the image. Based on fitting to simulated data with known curvature and simulated localization precision, we estimate the error in the mean curvature, C_mean, to be σ_c ~ ±0.25 μm⁻¹ (see supplement for further details) which will in general depend on the localization uncertainties for molecular coordinates in x, y, and z, as well as on the localization sampling density ^[12].

Figure 1 |.

(A) A sampled region of localized points on the surface of a mitochondrion with the best fit paraboloid surface overlaid. (B) Plotted points from the alpha shapes of super-resolved mitochondria, where each point is mapped to a different color according to the local curvature identified through curve fitting.

https://www.youtube.com/watch?v=0r8UpmhY4zA&feature=youtu.be

While other work has established methods for measurement of membrane curvature using diffraction-limited microscopy ^[13,14] this methodology can employ super-resolution localization microscopy to determine membrane curvature at far smaller length scales than are accessible by conventional fluorescence imaging. Because of the pervasiveness and importance of lipid bilayers in cellular organization, we expect this capability to be useful for a variety of biological applications.