2019-01494 - PhD Position F/M [CORDIS2019-ABS] Geometric analysis of high dimensional potential energy surfaces, with applications to biomolecular simulation

Contract type : Public service fixed-term contract

Level of qualifications required : Graduate degree or equivalent

Fonction : PhD Position

About the research centre or Inria department

The Inria Sophia Antipolis - Méditerranée center counts 37 research teams and 9 support departments. The center's staff (about 600 people including 400 Inria employees) is composed of scientists of different nationalities (250 foreigners of 50 nationalities), engineers, technicians and administrators. 1/3 of the staff are civil servants, the others are contractual. The majority of the research teams at the center are located in Sophia Antipolis and Nice in the Alpes-Maritimes. Six teams are based in Montpellier and a team is hosted by the computer science department of the University of Bologna in Italy. The Center is a member of the University and Institution Community (ComUE) "Université Côte d'Azur (UCA)".

Context

The ABS project team develops novel geometric / topological / combinatorial algorithms for Computational Structural Biology. In investigating the Structure - Dynamics - Function conumdrum, three main veins of research are explored:

  • Modeling protein complexes
  • Modeling macro-molecular flexibility
  • Algorithmic foundations

Software developments will be integrated to the Structural Bioinformatics Library (http://sbl.inria.fr), a state-of-the-art environment providing both low level methods (in generic C++) and specific applications in molecular modeling.

Assignment

Keywords

high-dimensional spaces, dimensionality reduction, importance sampling, molecular simulation.

Context

All biological functions (cognition, immune response, metabolism, etc) rely on biomolecules. The functions of these biomolecules depend on their structure but also dynamics, requiring the identification of meta-stable states (i.e. states stable on long time scales) together with transitions between these. As of today, except in rare cases where massive molecular dynamics or Monte Carlo simulations are used [1], these time scales remain out of reach.

The goal of this thesis will be to develop novel methods, ideally orders of magnitude faster than current ones, delivering accurate information on complex multi-scale mechanisms.

Goals

Since each atom has three Cartesian coordinates, the conformation of a molecule with n atoms is described by 3n coordinates and d = 3n − 6 degrees of freedom or dof. (One removes the dof for 3D translations and rotations, whence 3n − 6.) All properties of the molecule are thus determined by an energy surface of dimension d, typically several thousands, called the potential energy surface (PES). Despite intensive research, the exploration and the characterization of such surfaces is currently an open problem.

From a computer science / applied mathematics standpoint, the problems faced as well posed, though.  From the structural standpoint, stable structures correspond to local minima of the PES. From the thermo- dynamic viewpoint, meta-stability is characterized by occupancy probabilities (for Boltzmann’s distribution) of selected basins of the PES. Finally, dynamics may be modeled by a Markov state model involving meta- stable states.
The derivation of such properties and models intrinsically requires a dimensionality reduction step, as average properties are best inferred using collective variables providing an abstraction of the aforementioned degrees of freedom.

 

The goal of the thesis will be to develop novel methods delivering accurate models for biomolecules, by combining dimensionality reduction via diffusion maps [2, 3, 4, 5], importance sampling [6, 7], as well as geometric/topological techniques to explore and characterize PES [8, 9, 10].

Software developments will be integrated to the Structural Bioinformatics Library (http://sbl.inria.fr), a state-of-the-art environment providing both low level methods (in generic C++) and specific applications in molecular modeling.  



References

[1] D. E. Shaw, P. Maragakis, K. Lindorff-Larsen, S. Piana, R. O. Dror, M. P. Eastwood, J. A. Bank, J. M. Jumper, J. K. Salmon,
Y. Shan, and W. Wriggers. Atomic-level characterization of the structural dynamics of proteins. Science, 330(6002):341–346,
2010.

[2] R.R. Coifman, S. Lafon, A.B. Lee, M. Maggioni, B. Nadler, F. Warner, and S.W. Zucker. Geometric diffusions as a tool for
harmonic analysis and structure definition of data: Diffusion maps. PNAS, 102(21):7426–7431, 2005.

[3] M. Rohrdanz, W. Zheng, M. Maggioni, and C. Clementi. Determination of reaction coordinates via locally scaled diffusion map.
J. of Chemical Physics, 134(12), 2011.

[4] L. Nedialkova, M. Amat, I. Kevrekidis, and G. Hummer. Diffusion maps, clustering and fuzzy markov modeling in peptide folding
transitions. The Journal of chemical physics, 141(11):09B611 1, 2014.

[5] E. Chiavazzo, R. Covino, R. Coifman, C.W. Gear, A. Georgiou, G. Hummer, and I. Kevrekidis. Intrinsic map dynamics exploration
for uncharted effective free-energy landscapes. Proceedings of the National Academy of Sciences, 114(28):E5494–E5503, 2017.

[6] T. Lelièvre, G. Stoltz, and M. Rousset. Free energy computations: A mathematical perspective. World Scientific, 2010.

[7] A. Chevallier and F. Cazals. Wang-landau algorithm: an adapted random walk to boost convergence. NA, 2018.

[8] F. Cazals, T. Dreyfus, D. Mazauric, A. Roth, and C.H. Robert. Conformational ensembles and sampled energy landscapes:
Analysis and comparison. J. Comp. Chem., 36(16):1213–1231, 2015.

[9] J. Carr, D. Mazauric, F. Cazals, and D. J. Wales. Energy landscapes and persistent minima. The Journal of Chemical Physics,
144(5):4, 2016.

[10] A. Roth, T. Dreyfus, C.H. Robert, and F. Cazals. Hybridizing
rapidly growing random trees and basin hopping yields an improved
exploration of energy landscapes. J. Comp. Chem., 37(8):739–752, 2016.

Main activities

  • Algorithms: designing,  analyzing and  implementing novel methods.
  • Validation: running molecular simulations and analyzing the output.

Benefits package

  • Subsidized meals
  • Partial reimbursement of public transport costs
  • Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
  • Possibility of teleworking (after 6 months of employment) and flexible organization of working hours
  • Professional equipment available (videoconferencing, loan of computer equipment, etc.)
  • Social, cultural and sports events and activities
  • Access to vocational training
  • Social security coverage

Remuneration

Duration: 36 months
Location: Sophia Antipolis, France
Gross Salary per month: 1982€ brut per month (year 1 & 2) and 2085€ brut/month (year 3)