Methods and Models
for 3D Protein Retrieval

Proteins are dynamic molecular structures whose biological functions often depend on their ability to undergo conformational changes. Some proteins, such as titin, also play essential mechanical roles, stretching under tension and contributing to muscle elasticity. Understanding how protein sequences, three-dimensional architectures, and structural dynamics determine mechanical behavior remains an important challenge in structural biology.

Using representative domains from titin, cadherin-23, and cell adhesion molecules, I will illustrate how proteins respond to mechanical forces, how their unfolding pathways can be characterized, and how specific residues and structural interactions influence their mechanical resistance.

Finally, I will discuss how these findings connect to the challenges of representing, comparing, and classifying proteins as dynamic and deformable objects, highlighting how mechanical properties could complement conventional structure-based approaches to protein characterization.

The DAMM team study molecular machines and assemblies across scales (atomistic, coarse-grained, normal mode analysis and kinetic modeling) to understand and control their function in cellular and pathological contexts. Combining high-performance simulations, structural bioinformatics, computational chemistry and integrative modeling with experimental data, we aim to decipher complex molecular structures and interactions.

I will present the computational methods and services we offer to the molecular modeling community, and illustrate how a multi-scale approach sheds light on the regulation of a sophisticated biological system: the ubiquitin ligase pathway.

In this talk, I will present a unified computational framework for the estimation of distances, geodesics and barycenters of merge trees. We extend existing work on the edit distance and introduce a new metric, called the Wasserstein distance between merge trees, which is purposely designed to enable efficient computations of geodesics and barycenters. Specifically, our new distance is strictly equivalent to the L2-Wasserstein distance between extremum persistence diagrams, but it is restricted to a smaller solution space, namely, the space of rooted partial isomorphisms between branch decomposition trees. This enables a simple extension of existing optimization frameworks for geodesics and barycenters from persistence diagrams to merge trees. We introduce a task-based algorithm which can be generically applied to distance, geodesic, barycenter or cluster computation. The task-based nature of our approach enables further accelerations with shared-memory parallelism. Extensive experiments on public ensembles and SciVis contest benchmarks demonstrate the efficiency of our approach -- with barycenter computations in the orders of minutes for the largest examples -- as well as its qualitative ability to generate representative barycenter merge trees, visually summarizing the features of interest found in the ensemble. We show the utility of our contributions with dedicated visualization applications: feature tracking, temporal reduction and ensemble clustering. We also provide a lightweight C++ implementation that can be used to reproduce our results.