## Section: Research Program

### Modeling the Flexibility of Macro-molecules

**Keywords:** Folding, docking, energy landscapes, induced fit,
molecular dynamics, conformers, conformer ensembles, point clouds,
reconstruction, shape learning, Morse theory.

Proteins in vivo vibrate at various frequencies: high frequencies
correspond to small amplitude deformations of chemical bonds, while
low frequencies characterize more global deformations. This
flexibility contributes to the entropy thus the `free energy` of
the system *protein - solvent*. From the experimental standpoint,
NMR studies generate ensembles of conformations, called `conformers` , and so do molecular dynamics (MD) simulations.
Of particular interest while investigating flexibility is the notion
of correlated motion. Intuitively, when a protein is folded, all
atomic movements must be correlated, a constraint which gets
alleviated when the protein unfolds since the steric constraints get
relaxed (Assuming local forces are prominent, which in turn
subsumes electrostatic interactions are not prominent.).
Understanding correlations is of special interest to predict the
folding pathway that leads a protein towards its native state.
A similar discussion holds for the case of partners within a complex,
for example in the third step of the *diffusion - conformer
selection - induced fit* complex formation model.

Parameterizing these correlated motions, describing the corresponding energy landscapes, as well as handling collections of conformations pose challenging algorithmic problems.

At the side-chain level, the question of improving rotamer libraries is still of interest [29] . This question is essentially a clustering problem in the parameter space describing the side-chains conformations.

At the atomic level, flexibility is essentially investigated resorting to methods based on a classical potential energy (molecular dynamics), and (inverse) kinematics. A molecular dynamics simulation provides a point cloud sampling the conformational landscape of the molecular system investigated, as each step in the simulation corresponds to one point in the parameter space describing the system (the conformational space) [44] . The standard methodology to analyze such a point cloud consists of resorting to normal modes. Recently, though, more elaborate methods resorting to more local analysis [40] , to Morse theory [35] and to analysis of meta-stable states of time series [36] have been proposed.