Joint Data and Computational Science Seminar Series: Graph-theoretic properties of mitochondrial tubular networks
Mitochondria of eukaryotic cells contain tubular networks that are critical to a cell’s energy production. Mitochondrial tubular networks overwhelmingly have nodes of only degree 1 or 3, with degree 3 predominating (approx. 80%). An abstract mitochondrial graph is a graph with vertices of only degree 1 or 3. We describe recent work of Mostov, Lewis and Marshall showing via random graphs that combinatorial constraints alone, without additional biological considerations, predict that mitochondrial networks contain a large, connected component. We detail joint work with Elisha Rogatch, in progress, on assessing synchronizability of connected abstract mitochondrial graphs via the ratio R of the maximum eigenvalue of the unnormalized Laplacian matrix of the graph (diagonal degree matrix – adjacency matrix) to the smallest non-zero eigenvalue of the Laplacian (Fiedler eigenvalue). We describe statistics of the values for R that indicate as the fraction of degree 1 vertices increases mitochondrial tubular networks become increasingly far from synchronizable for purely graph-theoretic reasons.
Reference: Mostov, R., Lewis, G. R., Das, M. & Marshall, W. F. (2026). Combinatorial constraints predict that mitochondrial networks contain a large component. bioRxiv, 2026-03.
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