Mitochondrial networks through the lens of mathematics

Abstract

Mitochondria serve a wide range of functions within cells, most notably via their production of ATP. Although their morphology is commonly described as bean-like, mitochondria often form interconnected networks within cells that exhibit dynamic restructuring through a variety of physical changes. Further, though relationships between form and function in biology are well established, the extant toolkit for understanding mitochondrial morphology is limited. Here, we emphasize new and established methods for quantitatively describing mitochondrial networks, ranging from unweighted graph-theoretic representations to multi-scale approaches from applied topology, in particular persistent homology. We also show fundamental relationships between mitochondrial networks, mathematics, and physics, using ideas of graph planarity and statistical mechanics to better understand the full possible morphological
space of mitochondrial network structures. Lastly, we provide suggestions for how examination of mitochondrial network form through the language of mathematics can inform biological understanding, and vice versa.

Mitochondrial network branching enables rapid protein spread with slower mitochondrial dynamics

“…An important mitochondrial network feature is their three-way junctions, formed via end-to-side fusion, as they enable branching and looping of mitochondrial networks [9][10][11]. Our model explores both branching model mitochondrial networks with three-way junction formation and non-branching networks that are not permitted to form three-way junctions.…”

“…While often depicted as bean-shaped puncta, mitochondrial fusion and fission dynamics allow formation of mitochondrial tubes of a range of sizes [8]. Tip-toside mitochondrial fusion forms three-way junctions that branch mitochondrial tubes, allowing mitochondria to form extended network structures that include loops [9][10][11]. Mitochondrial dynamics are important to mitochondrial quality control and function [12], as well as to cell metabolism [13], motion [14], and differentiation [15].…”