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Modelling the Dynamics of Complex Molecular Systems
1. Description and Aims
Mathematics and physical chemistry have a long history of collaboration and interaction, which has been of great benefit to both communities. An even more intense partnership is needed, for the development of sensible computer algorithms and theories which can be "scaled up" to address challenging problems, such as the simulation of proteins and nucleic acids, or prediction of structures in nano-engineered materials. Simply using a larger computer will not work; new principles and methodologies are needed. Crossing scale boundaries requires mathematical approaches that provide a seamless transition between formulations. This programme, consisting of a series of workshops brought together researchers interested in the design of new theories and algorithmic principles for a broad range of phenomena formulated at atomistic and coarsened scale regimes, and integrated multiscale approaches. Four threads ran through the programme:
1) Mathematics of molecular and stochastic dynamics. This includes the theory of molecular dynamics and numerics for incorporating stochastic perturbations to recover averages in various thermodynamic ensembles.
2) Accessing long time scales by rare event simulation. Here, the aim is the sampling and understanding of rare event processes in complex systems.
3) Accessing larger systems via coarse grained (mesoscale) models. Particularly important is the theory and numerics of techniques behind coarsening the description of a molecular system, while reproducing the thermodynamics as well as dynamic properties.
4) Integrating different levels in multiscale simulations. This integration is paramount in concurrent simulation methods, in which at least two levels of description have to communicate.
2. Tangible Outcomes
No papers have come out of the workshops yet but several collaborations have been started in the workshop period. In addition, an exchange of algorithms and concepts has taken place between researchers. Finally, the two communities that were working parallel to each other have been able to interact and exchange ideas, to the benefit of both.
3. Scientific Breakthroughs
During the workshops many new and exciting methodologies were discussed connected to each of the daily topics: dynamical integrators, enhanced phase space sampling, trajectories space sampling, non-equilibrium methods, analysis of trajectories. Open questions were identified, including fundamental ones such as: How to correct for sampling errors in rare event methods? How to compute rates with enhanced sampling methods without prior knowledge of a reaction coordinate.
Also more practical issues appeared. Can we develop a software package for rare event methods a la PLUMED? How do we test whether enough collective variables are incorporated in a given approach? Can we introduce benchmarks for our methodology, so that people may compare techniques? In the second workshop we discussed many new approaches and applications of multiscale modeling connected to the daily topics: Coarse graining, Dynamical coarse graining /hydrodynamics, adaptive hybrid multiscale modeling, Lifting/restriction/equation free methods, and reaction coordinates. Fundamental issues were discussed within the topic of coarse graining such as the representability issue. An important new topic is the design of the CG model: which degrees of freedom should be kept and which integrated out? Is bottom up better than top down? Do we want potentials or rather a Markov model description? If dynamics is important: how do we build it in? In the adaptive multiscale modeling session we worried about several issues: what the applications were, whether one should mix forces and potentials, how to develop an efficient yet simple scheme. The lifting and restriction schemes raised the topic of slow equilibration. On the topic of reaction coordinates the question was discussed whether it is more informative to have a universal coordinate such as a PCA or diffusion map, or a specific one pertinent only to the system at hand. How do we analyse configurations or trajectories to find good reaction coordinates without performing a full-scale committor test? Can dynamical consistency help?
All these discussions pointed to many new developments and a very active community.
4. ``Aha’’ Moments
The interaction between the mathematics and biophysical chemistry community was excellent. There was certainly overlap between the work of both communities, although of course usually from a slightly different perspective. As an example, only during the discussion on stochastic integrators during the first focus group session did many researchers realize how important the correct implementation of the Langevin algorithm was. This realization is tremendously useful.
5. Format of the Workshops
The format of this series of workshop was rather unique; instead of a single one-week workshop the program comprised 2 workshops interspersed with 2 focus weeks in which a smaller research really worked on specific topics. The workshops were different in topic and composition, and the outcome was discussed above. During the focus groups people were really working together on several subject, e.g. an adaptive multiscale modeling with conserved extended Lagrangian. We consider this setup a great success, and so did the participants with whom we spoke. It became clear that this programme was a crucial necessity to make the mathematics and physical chemistry communities better aware of each other’s work and bring the communities closer together.
The workshops had only limited slots for speakers, leaving plenty of time for discussion. The daily plenary discussion session worked very well, and was truly useful in putting developments in perspective.
6. Other Comments
Although it is not, strictly speaking, a research outcome, we mention that a grant preparation meeting was organized by several of the participants during workshop 2 building on themes related to both of the workshops (diffusion maps, reaction coordinates and molecular integrators), involving math and chemistry collaboration, and this has resulted in a successful bid for over $2M in funds from the EPSRC and the National Science Foundation. A collaborative bid for an EU project involving Wim Briels, Giovanni Samaey and Ben Leimkuhler was also an outgrowth of the second workshop and specifically addressed the theme of coarse graining for complex molecular systems.
Suggestions for Future Workshops
During the focus groups (weeks 2 and 4) the schedule was less intense, and there were only one ore two talks a day. In fact this left much time to collaboration and discussion, something that people really enjoyed and took advantage of, especially in the first focus week. The Oort facility was extremely popular with the participants as it provided a close working environment and made possible longer more in-depth discussions. A one hour talk initiated in the morning sometimes continued after a break for coffee up to and even on the other side of the lunch period as participants felt comfortable to ask very detailed questions. It should be mentioned that the facility can be somewhat noisy and it is important that some care is taken in explaining this to participants at the outset.
The decision to have the final focus group at the end of the workshops meant that this week was less popular resulting in a small group at the very end of the four weeks. Therefore it is recommended for future long-term programs to put the focus weeks in between workshops rather than at the end.
Another recommendation is that the decision to grant a four-week workshop proposal should be made at least a year in advance, rather than the regular period of 4-6 months. This is important in order to secure a long-term commitment from eminent researchers.
The LC staff was extremely helpful and reliable in all dealings with the participants and organizers. The hotel was very suitable and well run (if slightly far from the city centre).