Lorentz Center

International center for scientific workshops

International center for scientific workshops

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## Modelling the Dynamics of Complex Molecular Systems |

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.
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.
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.
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.
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.
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.
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). [Back] |