A formal methods approach to predicting new features of the eukaryotic vesicle traffic system

Abstract

Vesicle traffic systems (VTSs) transport cargo among the intracellular compartments of eukaryotic cells. The compartments are viewed as nodes that are labeled by their chemical identity and the transport vesicles are similarly viewed as labeled edges between the nodes. Several interesting questions about VTSs translate to combinatorial search and synthesis problems. We present novel encodings for the problems based on Boolean satisfiability (SAT), satisfiability modulo theories and quantified Boolean formula of the properties over vesicle traffic systems. We have implemented the presented encodings in a tool that searches for the networks that satisfy properties related to transport consistency conditions using these solvers. In our numerical experiments, we show that our tool can search for networks of sizes that are relevant to real cellular systems. Our work illustrates the potential of novel biological applications of SAT solving technology.

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Notes

  1. 1.

    There are total 68,715 simple (no parallel edges) 3-connected graphs with 8 nodes.

  2. 2.

    https://github.com/arey0pushpa/pyZ3.

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Correspondence to Ankit Shukla.

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AG was partly supported in part by MPG Partner group grant. AS was partly supported by Austrian Science Fund (FWF) Project W1255-N23.

The natural VTSs

The natural VTSs

Fig. 5
figure5

A found-in-nature VTS. Nodes and edges are labelled with sets of molecules. \(\hat{}\) indicates that the molecule is active

Here we will present the two VTS collected from the literature.

Mammalian VTS

The Fig. 5 represent mammalian SNARE map created by studying the wide array of literature. To construct the map, we have assumed that vesicles only contain a single active v-SNARE, and we have attributed t-SNAREs and inactive v-SNAREs that travel between compartments to one of the known vesicles that go between the same source and target compartments. In order to identify the active SNARE complex involved in any particular vesicle fusion, we used two criteria. The SNARE complex is formed in vivo. In most papers, this is determined by immunoprecipitation of the SNARE complex from the relevant cell fraction. Blocking SNARE complex formation (for example, using antibodies against these SNAREs, or using cytosolic forms of these SNAREs) blocks the specific transport step. Note that these vesicles have been collected from multiple cell types, and any given cell type is likely to contain only a subset of the vesicles in the map.

In this figure, the rectangles represent compartments, the identities of compartments are written within ER = endoplasmic reticulum, ERGIC = ER-Golgi intermediate compartment, RE = recycling endosome, EE = early endosome, LE=late endosome, LYS = lysosome, PM = plasma membrane. The arrows represent vesicle edges.

Fig. 6
figure6

Yeast VTS

Yeast VTS

In Fig. 6, we present the yeast VTS. We have borrowed the VTS from [16]. It has been adapted from the paper by separating the v and the t SNAREs. It is clear that it is an incomplete description of the VTS. For example, the inactive molecules were not reported in the reference. We are currently searching for more literature that can help us complete all known information about the VTS.

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Bhattacharyya, A., Gupta, A., Kuppusamy, L. et al. A formal methods approach to predicting new features of the eukaryotic vesicle traffic system. Acta Informatica (2019). https://doi.org/10.1007/s00236-019-00357-3

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