Five significant shape modes explain 86% of the variance in growth cone shape.
(a) Typical sequence of frames (here 2 min apart) from a time-lapse movie of an SCG growth cone in vitro. Scale bar: 10 µm. (b) Schematic of the steps involved in the eigenshape analysis to extract the shape dimensions that capture the most variance: outline capture, parameterisation of outline by 250 evenly spaced points, principal component analysis of the resulting 500-dimensional space. Scale bar: 10 µm. (c) Variance explained as a function of number of mode shapes for the in vitro (no gradient) dataset (see Table 1). (d) The significant modes and their variance explained, shown as the mean shape plus the shape one standard deviation in each direction along the shape axis. Our naming convention for each mode is that the letter represents the type of symmetry, while the number is used to distinguish between different R/S/M modes. M1 and M2 approximately represent linear combinations of shapes R2 and S2 (see later). Note that all fine details (for instance, relating to filopodia) occur with a fairly random distribution around the growth cone, and are thus smoothed out once the dataset of images is appropriately large. (e) Higher-order shape modes and their variance explained. It is remarkable that the split between R and S symmetry persists across many higher-order modes. M3 could be arising here as an attempt to explain slight asymmetries in the underlying data. M modes in pairs, such as M1 and M2 in (c), can sometimes be understood as a linear combination of an R mode and an S mode. This occurs because when two modes have similar eigenvalues, any two orthogonal directions in that two-dimensional subspace can appear in the principal component decomposition. (f) Illustration of shape reconstruction using different numbers of modes. The red curve is the traced outline of a growth cone at one instant, and the blue curve is the best reconstruction of this shape given the specified number of eigenshape modes. Higher modes provide additional levels of detail for reproducing the true shape, but each individually only reproduces a tiny proportion of the variance across the full dataset. M, mixed; R, reflective; S, symmetric; SCG, superior cervical ganglion; SD, standard deviation; var, variance.