Organisers

• Eric Vanden-Eijnden (Courant Institute of Mathematical Sciences)
• Christoph Dellago (University of Vienna)
• Simone Meloni (CASPUR)
• Sara Bonella (Dip. Di Fisica, Universita' di Roma )

Supports

 CECAM

 COST - MolSimu

CASPUR

Description

Activated processes are characterised by time-scales longer than the simulation times accessible at present and in the foreseeable future. In an opportune set of variables, they correspond to transitions between metastable states separated by a (free) energy barrier too high to be overcome by thermal fluctuations. Although very difficult to tackle numerically, such processes are relevant in many scientific fields: chemical reactions, phase transitions that require rearrangement of atomistic configurations, formation of nano-materials in complex matrices,biological processe, etc. Examples of activated processes in biological meterials are protein folding, ion and, in particular, proton transfer in intra-membrane channels, electron transfer, conformational changes in poly-peptides and proteins, enzyme catalysis, protein and DNA binding, etc.
Methods for studying activated processes have a long and rich history that ranges from thermodynamic integration [1, 2] to metadynamics [3]. Most of these techniques however are hindered by severe limitations when many degrees of freedom are involved in the process, or if an a priori knowledge of the reaction coordinate is impossible. Recently, two strategies have been proposed that start from different but firm theoretical ground and share similar potential to tackle condensed phase problems. The methods are Transition Path Sampling (TPS) of C. Dellago et al. [4] and the combination of the temperature accelerated sampling (TAS) and string method (SM) of E. Vanden Eijnden [5,6].

The aim of this school is to disseminate these modern techniques to the broader community of scientists interested in the simulation of processes and reactions that cannot simulated by standard molecular dynamics at the relevant temperature.

Scientific Objectives

Recently, two strategies have been proposed that start from different but firm theoretical ground to study activated processes in complex systems. The methods are Transition Path Sampling (TPS) of C. Dellago et al. [4] and the combination of the temperature accelerated sampling (TAS) and string method (SM) of E. Vanden Eijnden [5,6].

In Transition Path Sampling, the ensemble of reactive trajectories (i.e. trajectories connecting the metastable states) is defined and sampled by means of a generalized Monte Carlo procedure. The sampling is constructed in such a way as to start from a guess trajectory connecting the basins and then populate the reactive part of the phase space of the system represented in Cartesian atomistic coordinates and velocities. The ensemble thus generated can be used for calculating reaction rates or to obtain an insight of the activated process mechanism. The method requires knowledge of a good set of collective variables to identify the metastable states.
The appropriate combination of a set of methods proposed by E. Vanden-Eijnden allows both to explore the free energy profile of a high dimensional system to identify relevant metastable states given an appropriate set of collective variables, and to determine the activated process mechanism by studying the quantity that the theory univocally identifies as the reaction coordinate, the committor function. The first part of the program is carried out by an accelerated sampling scheme in which the evolution of physical variables is coupled to that of a set of fictitious degrees of freedom. The fictitious degrees of freedom are evolved at a temperature that is higher than the physical one, so allowing to overcome (free) energy barriers. However, the coupling term is such that the physical space is sampled at the physical temperature. The MFEP approach then proceeds by combining the string method with a sampling technique to determine minimum free energy paths from one metastable basin to another. Only the calculation of a mean force along a path in collective variables space is required, a task that can be accomplished by molecular dynamics (constrained or restrained). This force can then be used to iteratively minimize the reactive path.
This school will present the students with a unique opportunity to learn about them and to compare the advantages and shortcomings of the techniques in a set of coordinated lectures delivered by C. Dellago and E. Vanden-Eijnden, two of the originators of TST and TAS-SM. Students will be exposed to presentations both of the theory and of the technical aspects of the implementation and the use of the algorithms, the latter completed with numerical exercises in the afternoons. Guided discussion sessions on the material will provide an opportunity to deepen the audience’s understanding. Students will also have the chance to present short talks to illustrate problems related to their work that would benefit from knowledge and implementation of the methods explained in the course. This will promote collaborations and favour the diffusion of these advanced techniques in the community.














- disseminate modern simulation techniques for studing activated processes
- discuss the application of these techniques to a braod range of different scientific problems
- put researchers in contact with originators of these simulation techniques so that difficulties in encountered in specific applications can be discussed end (hopefully)overcame

References

[1] J. G. Kirkwood , J. Chem. Phys 3 300 (1935)

[2] T. P. Staatsma and J. A. McCammon , Ann. Rev. Phys. Chem. 43 407 (1992)

[3] A. Laio and M. Parrinello , PNAS 99 12562 (2002)

[4] C. Dellago and P. G. Bolhuis and F. S. Csajka and D. Chandler , J. Chem. Phys 108 1964 (1998)

[5] E. Weinan and W. Ren and E. Vanden Eijnden , Phys. Rev. B 66 52301 (2002)

[6] L. Maragliano and E. Vanden Eijnden , Chem. Phys. Lett. 426 168 (2006)