## Section: New Results

### Modeling macro-molecular assemblies

**Keywords:** macro-molecular assembly, reconstruction by data integration,
proteomics, mass spectrometry, modeling with uncertainties, connectivity inference.

#### Complexity dichotomies for the minimum F-overlay problem

Participants : D. Mazauric, R. Watrigant.

In collaboration with N. Cohen (LRI, UMR de l'Université Paris-Sud et du CNRS), F. Havet (Université Côte d'Azur, I3S, UMR de l'Université Nice Sophia et du CNRS), I. Sau (LIRMM, UMR de l'Université Montpellier et du CNRS, and Universidade Federal do Ceará, Brazil).

The *connectivity inference* problem for native mass spectrometry aims at
finding the most plausible pairwise contacts between the individual
subunits of a macro-molecular assembly, given the composition of overlapping
oligomers.
The associated combinatorial optimization problem consists in determining a minimal-cardinality set of contact (edges) such that all the subunits of each oligomer must be “connected” (each oligomer must induce a connected graph).
We studied in [18] the general inference problem that consists of considering more general properties on oligomers.
For this new problem, we are given a list of possible topologies (graphs) for each oligomer and we aim at minimizing the total number of contacts between subunits.
In terms of graphs, we are given a family of subgraphs that can match the structure of the oligomers.
These new constraints reflect biophysical properties: a subunit has a limited number of neighbors (bounded maximum degree of the subgraphs), selected contacts are already known (a given subgraph contained in the complex), etc.
We prove that the problem is NP-complete (no polynomial time algorithm, unless P = NP) for almost all cases.