## Section: New Results

### Modeling Macro-molecular Assemblies

**Keywords:** macro-molecular assembly, reconstruction by data integration,
proteomics, modeling with uncertainties, curved Voronoi diagrams,
topological persistence.

#### Unveiling Contacts within Macro-molecular assemblies by solving Minimum Weight Connectivity Inference Problems

Participants : Frédéric Cazals, Deepesh Agarwal.

In collaboration with C. Caillouet, and D. Coudert, from the COATI project-team (Inria - I3S (CNRS, University of Nice Sophia Antipolis)).

Consider a set of oligomers listing the subunits involved in
sub-complexes of a macro-molecular assembly, obtained e.g. using
native mass spectrometry or affinity purification.
Given these oligomers, connectivity inference (CI) consists of finding
the most plausible contacts between these subunits, and minimum
connectivity inference (MCI) is the variant consisting of finding a
set of contacts of smallest cardinality.
MCI problems avoid speculating on the total number of contacts, but
yield a subset of all contacts and do not allow exploiting a priori
information on the likelihood of individual contacts.
In this context, we present two novel algorithms, `MILP-W` and `MILP-W` ${}_{\text{B}}$ [14] . The former solves the *minimum weight connectivity inference*
(MWCI), an optimization problem whose criterion mixes the number of
contacts and their likelihood.
The latter uses the former in a bootstrap fashion, to improve the
sensitivity and the specificity of solution sets.

Experiments on three systems (yeast exosome, yeast proteasome lid, human eIF3), for which reference contacts are known (crystal structure, cryo electron microscopy, cross-linking), show that our algorithms predict contacts with high specificity and sensitivity, yielding a very significant improvement over previous work, typically a twofold increase in sensitivity.

The software accompanying this paper is made available in the `SBL` , and should
prove of ubiquitous interest whenever connectivity inference from
oligomers is faced.