Main challenges in simulation of complex molecular processes such as protein folding or ligand-protein binding is modelling of water: behaving as a structureless continuum in the bulk it needs to be represented at the atomistic level in a relatively small ‘core’ area of the system. The simulation of atomistic (explicit) water takes up to 90% of computing resources and makes the calculation prohibitively expensive. It is intuitively clear that the atomistic details are unnecessary in the areas distant from the biomolecule. However, in the vicinity of the biomolecule some water molecules are known to contribute to the biomolecular process in a very non-trivial way and their explicit modelling is decisively important. The most natural representation of water in the bulk is provided by continuum hydrodynamics (CH). Computer modelling in both representations, MD and CH, is well developed, but separated by a gap in the time and space scales accessible to simulations. Closing this gap is only possible if two directions are developed coherently: (i) new generation hardware, currently approaching the CH scales in MD simulations and (ii) theory and software correctly joining the MD and CH representations.

This underlines the objectives of our project:

1) to develop a new efficient theoretical and computational framework for hybrid MD-CH simulation of bio-chemically important processes at realistic time and space scales;

2) to implement and test this framework in the world fastest supercomputing facility;

3) to conduct large scale simulations of trimethoprim (TMP) binding to dihydrofolate reductase (DHFR) and compare the predicted kinetic properties, the binding rate, with measured experimental values.

The kinetics of biomolecular processes define many biomedical technologies and for this reason represent the fundamental basis for a large segment of pharmaceutical industries. Because of the problem complexity, computer simulations are the only available tool that can capture the mechanisms of binding at the required resolution level. Indeed, in many cases the processes are very short lived which makes them hardly detectable by experiment. Intermediate complexes that may be rate limiting can change the rates by orders of magnitudes rendering potential drug candidates inactive (or vice versa). Currently this can be checked only by expensive and time consuming experimental tests. Thus, the possibility of calculating the rates using computer simulation can make very significant impact on drug design studies.

Attempts of incorporating a group of classical atoms into a continuum solvent (implicit solvent) are known for a long time. However, the most consistent approach describing a structured continuum, the hydrodynamics, is a direction that becomes active only very recently. Conceptually, modelling the MD particles in the ‘transfer’ region where the MD and CH domains overlap (the ‘runaway’ MD particles) remains the most pressing problem of essentially all approaches of this type.

We propose a fundamentally new hybrid model that aims at solving this problem. It is based on a generalised description of the MD and CH components within the flux coupling approach. The proposed framework will ensure that the transition between the CH and MD representations is smooth and characterised by (i) the _absence of numerical “fixes”_ such as artificial repulsive barriers between the atomistic and continuum parts or adding new particles, (ii) unified treatment of the solution parts using the same equations throughout the system’s volume, (iii) the full control by a single empirical function that can be of _arbitrary form both in space and time_. The new method will lead to a large reduction of the simulation cost due to a large truncation of the MD domain, achieved _without loosing either the detailed atomistic simulation in the MD zone or the macroscopic conservation laws for both mass and momentum_.

The project is a well balanced combination of state of the art computer hardware development, advanced numerical modelling (the triad of molecular dynamics, continuum fluid mechanics, and numerical methods) and cutting edge investigation of biomedically important molecular system (including experiment).

The Consortium consists of five teams. 1. Prof. Makoto Taiji group, Yokohama RIKEN Institute, Japan, will coordinate the project. The team is the author of MDGRAPE computer, a petascale special purpose computer for protein molecular dynamics simulations, that has been awarded three Gordon Bell prizes proving the best in the world. Many years of experience in high performance biomolecular (in particular, drug design) simulations [M Harada et al, Nature Genetics 41(3), 289 (2009)] will serve as a solid foundation for the project. 2. Dr Dmitry Nerukh group, in Aston University, UK will provide the molecular dynamics part of the theoretical framework. The group’s expertise in complex dynamics of molecular systems using modern mathematical approaches and non-trivial numerical implementations [D Nerukh, Makoto Taiji, Physica A, 388(22), 4719 (2009)] will complement the hydrodynamics part of the theoretical work. Also, the physical chemistry expertise of the team will be used to perform the simulations of the DHFR-TMP system. 3. Prof. Vasily Goloviznin group, Moscow Institute of Nuclear Safety, Russia will bring in the world leading expertise in computational mathematics that is essential for implementing high resolution numerical algorithms that remain robust for solving small scale hydrodynamics equations with coarse grids. This group has had a long term collaboration on high resolution methods for computational fluid dynamics with 4. Dr Sergey Karabasov group, Cambridge University, UK. The group will lead the continuum hydrodynamic development of the theory and its numerical framework implementation. Because of the fluctuating hydrodynamics involved, the Eulerian modelling will be based on the novel high-resolution advection method [Karabasov and Goloviznin, J. Comput. Phys., 228, 7426 (2009)]. 5. Prof. Masahiro Ueda group, Osaka University, will bring the world leading expertise in single molecular imaging experimental work that will be used to measure the kinetics of the simulated system and compare the results.

The consortium includes well experienced scientist (the Japan and Russia group leaders) with a large fraction of early career independent (the UK group leaders) and young researches (5 postdoctoral and 1 PhD student). The project will produce five highly trained early career researchers: two computer scientists/molecular dynamists (Yokohama), one molecular dynamist (Aston), two computational fluid dynamists (Cambridge and Moscow). Each of the young postdoctoral researchers will be assigned a mentor and will have benefited from regular supervision by other investigators with diverse and in depth expertise. The project will also train a PhD student supervised by the Aston team.