# Linear Scaling Density Functional Theory for Biochemistry: Applications to Cytochrome c Oxidase

Lead Research Organisation:
University College London

Department Name: London Centre for Nanotechnology

### Abstract

Many of the important activities of biomolecules involve the breaking and making of chemical bonds between atoms or the transfer of electrons from one molecule to another. These are processes which are inherently quantum mechanical in their nature, and if we are to understand how and why they occur we must use quantum mechanics (QM). However, solving the QM equations exactly is impossible for systems larger than hydrogen, so a variety of computational techniques have been developed which calculate extremely accurate answers to the equations which can be systematically improved. The most successful of these, density functional theory (DFT), has been applied to a wide range of fields, including biochemistry, physics, chemistry, materials science and planetary science. However, the standard approaches to DFT have a computer effort which increases with the cube of the number of atoms considered. This puts an upper limit on the size of system which can be considered of a few hundred atoms, or possibly around a thousand atoms on very large, high performance computing (HPC) centres. This project will apply a different approach to DFT, which scales linearly with the number of atoms, to understanding how an important enzyme called cytochrome c oxidase transports hydrogen atoms through its structure. These linear scaling DFT methods can be applied to systems including up to 100,000 or 1,000,000 atoms when using HPC centres, which promises to produce a revolution in modelling of biomolecules. Cytochrome c oxidase is one of a set of enzymes that reside in the mitochondria (small structures inside cells which are responsible for energy production in the form of a molecule called ATP, among other roles). It it the final point of an electron transfer chain which turns oxygen into water, and pumps hydrogen ions from one side of a membrane to another; the hydrogen ions are then used elsewhere to create ATP, which powers many cellular processes. There are outstanding questions about how the hydrogen ions are transported across the membrane, and how this links to the oxygen chemistry. We will test and develop our linear scaling DFT code, Conquest, for biochemistry problems, and we will apply it to understanding the role of a central ring-like structure within cytochrome c oxidase. This will result in a new tool for studying the structure and function of biomolecules (linear scaling DFT) as well as an understanding of how the ring-like structure is involved in hydrogen transfer. We will make specific predictions which can be tested by experiments, and will aim to create follow-on projects which build on the results of this project to develop models for how the hydrogen ions and electrons are transported and used to turn oxygen into water.

### Technical Summary

The use of modelling in biochemistry at present encompasses molecular mechanics (MM) simulations based on force fields such as AMBER and CHARMM, as well as the use of quantum mechanical (QM) approaches typically implemented either as embedded QM/MM calculations or on isolated molecules. There are certain problems which require the use of QM, for instance calculations involving bond breaking or formation or electron transfer or excitation. These approaches have been remarkably successful, but there are inherent limitations on the size of the quantum mechanical system which come from the increase of computer effort with system size (at least with the cube of the number of atoms modelled). The most common QM approach is density functional theory (DFT). Over the last ten to fifteen years, a new approach to DFT calculations has been developed which scales linearly with the number of atoms: linear scaling DFT, which can now be applied to systems with 10,000-100,000 atoms using high performance computing (HPC) centres. One obvious target for these techniques is biochemistry problems, but this has proved challenging. In this grant, we will use the Conquest linear scaling DFT code which has been applied successfully to solid-state systems such as germanium growth on silicon surfaces to model problems related to proton transport in cytochrome c oxidase. We will test the accuracy of the code and characterise the important computational parameters (basis set, electronic localisation); we will implement important new functionality which will be important for modelling biochemistry problems (in particular, exchange and dispersion energies); and we will apply it to a set of problems identified by experiments as key in understanding the function of cytochrome c oxidase. We have chosen cytochrome c oxidase both because of its importance in the respiratory chain in mitochondria and because of the world-leading experimental expertise at UCL in the function of the complex.

### Planned Impact

The research is primarily basic science: applying a technique in common use in solid state physics (linear scaling DFT) to biochemistry problems, and elucidating certain aspects of the function of cytochrome c oxidase. As such, there is no clear short-term economic impact which can be identified. However, there are clear avenues which will open up for impact involving knowledge transfer, as well as the anticipation that advances in understanding of fundamental biochemistry could have an impact on medical sciences and hence both economic impact and improvement of quality of life. This research will also lead to significant knowledge transfer between the different disciplines involved: the PI (Dr Bowler) and PDRA (Dr Brazdova) will learn about both the basic biochemistry involved in cytochrome c oxidase and about the experiments which can be performed and how modelling can make predictions for testing by experiment as well as confirming experimental results or hypotheses. The PI and PDRA will also work with the co-I to share their expertise with HPC and QM; as the co-I has already started his own programme of QM calculations to predict IR spectra of isolated molecules, the collaboration will strengthen this work and increase the knowledge and use of HPC in biochemistry. One route to economic impact would be through consultancy and support services: while the Conquest code will be distributed freely, we will investigate the viability of offering either support for users of the code, or consultancy whereby we perform calculations on specific problems proposed by a client. This route to commercialisation of electronic structure calculations is a model which other researchers at UCL have followed, and we will draw on their experience with it when setting up our services. We will be following the standard practice for exploiting any opportunities that may arise during this research programme: filing disclosures, identifying market opportunities, seeking funds for prototyping, and then proceeding to exploitation via licensing and/or spin-out. The LCN has excellent facilities for supporting such knowledge transfer: the BioNanoCentre, which was spun out of the LCN, exists specifically to facilitate industrial transfer, and UCL Business provides a college-wide infrastructure for use of intellectual property. The LCN also employs a full-time business development manager, Dr. Thierry Bontoux. We will also use the expertise available in the London Technology Network.

### Publications

Arita M
(2014)

*Stable and Efficient Linear Scaling First-Principles Molecular Dynamics for 10000+ Atoms.*in Journal of chemical theory and computation
Arita M
(2014)

*Large-scale DFT simulations with a linear-scaling DFT code CONQUEST on K-computer*in Journal of Advanced Simulation in Science and Engineering
Hirakawa T
(2017)

*Canonical-ensemble extended Lagrangian Born-Oppenheimer molecular dynamics for the linear scaling density functional theory.*in Journal of physics. Condensed matter : an Institute of Physics journal
O'Rourke C
(2015)

*Linear scaling density matrix real time TDDFT: Propagator unitarity and matrix truncation.*in The Journal of chemical physics
Romero-MuĂ±iz C
(2018)

*High-accuracy large-scale DFT calculations using localized orbitals in complex electronic systems: the case of graphene-metal interfaces.*in Journal of physics. Condensed matter : an Institute of Physics journal
Truflandier L
(2016)

*Communication: Generalized canonical purification for density matrix minimization*in The Journal of Chemical PhysicsDescription | The implementation is now being made available to Conquest users, and we are writing a paper on our findings. |

First Year Of Impact | 2014 |

Title | Conquest |

Description | Conquest is a linear scaling electronic structure code that allows modelling of millions of atoms with ab initio accuracy. We added exact exchange to the code. |

Type Of Material | Improvements to research infrastructure |

Year Produced | 2012 |

Provided To Others? | Yes |

Impact | The code is available under beta testing |

URL | http://www.order-n.org/ |