Mitochondria are cellular structures involved in metabolism that take the form of a network of membrane-based tubes that undergo continuous re-arrangement by a set of morphological processes, including fission and fusion, carried out by protein-based machinery. Because of their network structure, mitochondria can be represented as graphs, and the morphological operations that take place in the cell, referred to as mitochondrial dynamics, can be represented by changes to the graphs. Prior studies have classified mitochondrial graphs based on graph-theoretic features, but an alternative approach is to focus not on the graphs themselves but on the set of morphological operations inducing mitochondrial dynamics, since this may provide a simpler representation. We derive a mathematical representation of mitochondrial network dynamics as a discrete vector space with an asymmetric distance metric. We then use this distance metric to develop a measure of similarity between mitochondria networks that is used to cluster pre-existing data sets and to compare mitochondria networks generated in silico by random walks to those observed in vivo. Through this analysis, we find that some dynamical processes cannot be modeled stochastically, suggesting the potential existence of certain regulatory mechanisms. Beyond the potential immediate insights into the dynamics of mitochondrial networks, this work points to a general strategy for formulating a comprehensive mathematical representation of a cell structure state-space, based not on the shapes of cellular structures, but on relations between the dynamic operations that produce them.
Mostov et al. (Sun,) studied this question.
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