Representing mitochondrial dynamics with abstract algebra

Our cells get their power from mitochondria, tiny structures inside cells that produce chemical energy and control many other cellular processes like cell death. Although often depicted as bean-shaped objects, in most cell types, mitochondria form complex, branching networks.

Our cells get their power from mitochondria, tiny structures inside cells that produce chemical energy and control many other cellular processes like cell death. Although often depicted as bean-shaped objects, in most cell types, mitochondria form complex, branching networks. This network structure is thought to help to transport energy-carrying chemicals throughout the cell, and also to help ensure that the mitochondria can be transmitted to daughter cells when the cell divides. Perhaps the most exciting feature of mitochondrial networks is that they are constantly changing. Protein machines in the cell can cut branches of the mitochondria, cause existing branches to resorb, form new branches, and glue existing branches together. It is usually assumed that these processes, working together, give rise to the networks structures that are observed, but we lack a clear understanding of how this happens. For example, we would lik eto be able to predict how the network structures would change if the rate of one or more of these basic processes became faster or slower. A further question is whether the different processes occur randomly, or are they coordinated in some way. Answering this type of question falls into the domain of graph theory, the branch of math that deals with the structure of networks. Each of the processes like breakage or outgrowth of a branch can be represented as making changes to a graph. The problem is that for a complex network, there can be many different ways of applying the same process at different positions on the graph, which create different results. It becomes extremely difficult to keep track of all the possible outcomes. To get around this problem, we are developing a simpler way to represent the network structures of mitochondria, using methods of abstract algebra, a branch of math that has played an important role in theoretical physics but has seen very little application in cell biology. We expect that by developing this simplified representation, we will be able to make inroads into the question of how mitochondria networks are formed. One outcome we hope to achieve is to explain why in some cells, such as the popular model organism budding yeast, the mitochondrion tends to consist of a single large network together with a few much smaller networks. A second outcome is to develop a new way to compare how similar two mitochondrial networks are to each other, which can be the basis for a new way of classifying cells into different cell types based on their mitochondrial networks. But the biggest outcome, we hope, will be a new way to ask about the statistical distribution of networks that should exist in a cell, given the rates of the different processes that alter network structure. This work will be carried out by two professors: Wallace Marshall at the University of California San Francisco (UCSF), and Moumita Das at Rochester Institute of Technology (RIT), working together with a postdoctoral fellow Ximena Garcia Arceo at UCSF and two undergraduate students, one at UCSF and one at RIT.