Discovering vesicle traffic network constraints by model checking

Abstract

A eukaryotic cell contains multiple membrane-bound compartments. Transport vesicles move cargo between these compartments, just as trucks move cargo between warehouses. These processes are regulated by specific molecular interactions, as summarized in the Rothman-Schekman-Sudhof model of vesicle traffic. The whole structure can be represented as a transport graph: each organelle is a node, and each vesicle route is a directed edge. What constraints must such a graph satisfy, if it is to represent a biologically realizable vesicle traffic network? Graph connectedness is an informative feature: 2-connectedness is necessary and sufficient for mass balance, but stronger conditions are required to ensure correct molecular specificity. Here we use Boolean satisfiability (SAT) and model checking as a framework to discover and verify graph constraints. The poor scalability of SAT model checkers often prevents their broad application. By exploiting the special structure of the problem, we scale our model checker to vesicle traffic systems with reasonably large numbers of molecules and compartments. This allows us to test a range of hypotheses about graph connectivity, which can later be proved in full generality by other methods.

Evolutionary origins and specialisation of membrane transport

“…One pathway became two, and by simple iteration, many. This mechanism, the `organelle paralogy hypothesis’, found experimental support and has been elaborated upon repeatedly since the original proposal [ 2 , 9 , 17 • , 18 , 19 • , 20 , 21 ].…”

Synthesis for Vesicle Traffic Systems

“…Can we find a simple test to see whether any information is missing, given the experimental data? We have shown that graph k-connectedness furnishes precisely such a test [5]. If the data provided by cell-biologists, suitably represented as a graph, does not have a certain degree of connectivity, this implies that some biological data has been missed.…”

“…Our result about k-connectedness being a useful test of missing information [5] was obtained using SAT solvers for graphs up to a certain size, and a certain number of molecules. This was due to limitations in how we encoded the problem.…”

“…Most generally, the activity state of a given SNARE can be a Boolean function of all the molecular types on a compartment or vesicle. We have also tested [5] a particularly simple regulation mechanism in which two SNAREs that can pair to drive fusion inhibit one another; this is the pairing inhibition. This is motivated by the idea that pairing must generate an inactive bi-molecular complex.…”

“…We have recently used ideas of graph theory to address this question [4]. We have shown that SNARE regulation places constraints on the structure of the traffic network [5]. One informative constraint is graph connectivity.…”