**Lecturer**

Mathematics Non-linearity and Complexity Research Group (NCRG) ** **

**Phone number**** **

+44 (0)121 204 3533

**Email**** **

D.Nerukh@aston.ac.uk

**Room number**

Main Building 314B

For my

**CV** and

**publications** see my

**Personal web page**

## Research areas

**Kinetics of ligand binding**. Obtaining the rates of binding of small molecules to proteins from realistic full-atom molecular dynamics simulations. Developing approaches for calculating correct bio-molecular transformation rates, taking into account non-Markvoian behaviour of states.

**Self-organising molecular systems**. Adapting and evolving chemical systems. Applications to self-organising materials.

**Hybrid hydrodynamics – molecular dynamics simulation**. Modelling bio-molecular systems where fully atomistic and purely hydrodynamic representations coexist and smoothly transform into each other at different spatial locations.

**Complexity of dynamical systems**. Quantitative approaches to computing the complexity of physical systems. Informational contents of classical dynamics of molecular systems. Molecules as non-linear dynamical systems.

**Protein folding**. Molecular Dynamics simulation of protein folding. Complexity of the dynamics of folding. “Controlled MD” – a correct methods for accelerated folding simulations.

**Bohmian quantum dynamics**. Application of Bohmian mechanics to realistic molecular systems. Developing methods for effective propagation of Bohmian quantum trajectories for multidimensional systems.

## Newly funded research project:

**Using next generation computers and algorithms for modelling the dynamics of large biomolecular systems **

### Background

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: 1) new generation hardware, currently approaching the CH scales in MD simulations and 2) 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.

### Methodology

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.

### Consortium

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, Vladimir Ryabov, and 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.