Discovering vesicle traffic network constraints by model checking

Ankit Shukla,Mandayam Srivas,Lakshmanan Kuppusamy,Mukund Thattai,Arnab Bhattacharyya,Yongtang Shi

doi:10.1371/journal.pone.0180692

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.

Highlights

Molecular interactions regulate the movement of cargo between different locations of eukaryotic cells
We study a hierarchy of regulation models of increasing complexity, and show that not all directed graphs can represent the transport graph of a physically realizable vesicle traffic network
We find that the model checker approach, with a few additional workarounds, scales reasonably well for studying the vesicle traffic network

Summary

Introduction

Molecular interactions regulate the movement of cargo between different locations of eukaryotic cells The hubs of this traffic network are large membrane-bound compartments known as organelles, between which cargo are transported within small vesicles [1,2,3]. Schekman, and Sudhof were awarded the Nobel Prize for identifying key molecules involved in this process These include Arf and Rab GTPases whose presence or absence encodes compartment identity [4, 5]; coat proteins that regulate cargo loading from source compartments onto vesicles [6, 7]; and SNARE proteins that regulate fusion of vesicles into target compartments [8, 9]. These molecules form the basis of an abstract representation of vesicle traffic [10, 11]: compartments are the nodes, and vesicles are the directed edges, of a transport graph; different molecules move in cyclical fluxes along this graph

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