Possible and impossible cells

Mukund Thattai, NCBS Bangalore

Biology is molecules plus mechanisms. Theory allows us to extrapolate mechanisms far beyond the regimes where they were originally observed, but also places bounds on the capabilities of living systems given assumptions about their molecular constituents. We study the logistics system of eukaryotic cells, whose warehouses are micron-scale "organelles" and whose trucks are 10-nanometer-scale "vesicles". Organelles form the nodes and vesicle fluxes form the edges of a transport graph. Unlike traditional logistics systems, this graph is self-organized: vesicles are regulated by the very molecular cargo they carry, and organelle chemical identities arise as a balance of molecular gain and loss. James Rothman, Randy Schekman and Thomas Sudhof shared the Nobel Prize in 2013 "for their discoveries of machinery regulating vesicle traffic." We ask: given this molecular machinery, what is the set of possible and impossible transport graphs? Surprisingly, the answer can be framed purely in terms of the graph theoretic concept of "k-edge-connectedness," where a minimum of k edges must be removed in order to disconnect a graph. Traditional logistics systems are at least 2-connected, all vesicle traffic systems are at least 3-connected, and Rothman-Schekman-Sudhof vesicle traffic systems are at least 4-connected. Our constructive proof of this result explains many puzzling properties of vesicle traffic molecules and makes testable predictions about how they must move about inside cells.