Section: New Results

Modeling the flexibility of macro-molecules

Keywords: protein, flexibility, collective coordinate, conformational sampling dimensionality reduction.

Energy landscapes and persistent minima

Participants : Frédéric Cazals, Dorian Mazauric.

In collaboration with David Wales and Joanne Carr, from Cambridge University (UK).

In this work [15], we consider a coarse-graining of high-dimensional potential energy landscapes based upon persistences—which correspond to lowest barrier heights to lower-energy minima. Persistences can be calculated efficiently for local minima in kinetic transition networks that are based on stationary points of the prevailing energy landscape. The networks studied here represent peptides, proteins, nucleic acids, an atomic cluster, and a glassy system. Minima with high persistence values are likely to represent some form of alternative structural morphology, which, if appreciably populated at the prevailing temperature, could compete with the global minimum (defined as in- finitely persistent). Threshold values on persistences (and in some cases equilibrium occupation probabilities) have therefore been used in this work to select subsets of minima, which were then analysed to see how well they can represent features of the full network. Simplified disconnectivity graphs showing only the selected minima can convey the funnelling (including any multiple-funnel) characteristics of the corresponding full graphs. The effect of the choice of persistence threshold on the reduced disconnectivity graphs was considered for a system with a hierarchical, glassy landscape. Sets of persistent minima were also found to be useful in comparing networks for the same system sampled under different conditions, using minimum oriented spanning forests.

Hybridizing rapidly growing random trees and basin hopping yields an improved exploration of energy landscapes

Participants : Frédéric Cazals, Tom Dreyfus, Andrea Roth.

In collaboration with Charles Robert (IBPC / CNRS, Paris, France).

The number of local minima of the potential energy landscape (PEL) of molecular systems generally grows exponentially with the number of degrees of freedom, so that a crucial property of PEL exploration algorithms is their ability to identify local minima which are low lying and diverse. In this work [18], we present a new exploration algorithm, retaining the ability of basin hopping (BH) to identify local minima, and that of transition based rapidly exploring random trees (T-RRT) to foster the exploration of yet unexplored regions. This ability is obtained by interleaving calls to the extension procedures of BH and T-RRT, and we show tuning the balance between these two types of calls allows the algorithm to focus on low lying regions. Computational efficiency is obtained using state-of-the art data structures, in particular for searching approximate nearest neighbors in metric spaces. We present results for the BLN69, a protein model whose conformational space has dimension 207 and whose PEL has been studied exhaustively. On this system, we show that the propensity of our algorithm to explore low lying regions of the landscape significantly outperforms those of BH and T-RRT.