The Kohonen self-organizing map: a tool for the clustering and alignment of single particles imaged using random conical tilt

An important step in determining the three-dimensional structure of single macromolecules is to bring common features in the images into register through alignment and classification. Here, we took advantage of the striking computational properties of the Kohonen self-organizing map (SOM) to align and classify images of channels obtained by random conical geometry into more homogeneous subsets. First, we used simulations with artificially created images to deduce simple geometrical rules governing the mapping of bounded (differing in size and shape) and unbounded (differing in in-plane orientation) variations in the output plane. Second, we measured the effect of noise on the accuracy of the algorithm to separate homogeneous subsets. Finally, we applied the rules ascertained in the previous steps to separate freeze-fracture images of the cytoplasmic and external domains of the small (approximately 118 kDa) aquaporin-0 water channel. Comparison with the results obtained from a similar input set using alignment-through-classification showed that both methods converged to stable classes exhibiting the same overall shapes (tetragonal and octagonal) for the cytoplasmic and external views of the channel. Processing with the SOM, however, was simplified by the utilization of the geometric rules governing the mapping of bounded and unbounded variations as well as the lack of subjectivity in selecting the reference images during alignment.