## PhD Position: Protein NMR On A Chip

This position has been filled and is no longer available.

A 3-year PhD studentship is available in the group of Marcel Utz, supported by the Institute for Life Sciences (IfLS). The successful candidate should have a good degree in chemistry, biochemistry, physical chemistry, or biophysics and a special interest in nuclear magnetic resonance spectroscopy and/or microfluidic systems.

Nuclear magnetic resonance (NMR) spectroscopy is one of the most powerful analytical tools available to study the dynamics, structure, and interactions of proteins. In addition to detailed 3D structural information, NMR is particularly apt at providing information on dynamic processes, as well as binding interactions with peptides and other substrates. NMR is inherently non-invasive. In sharp contrast to other techniques such as x-ray diffraction, which require crystalline samples, high vacuum, and employ intense ionising radiation, NMR allows the study of proteins (and other systems) under very mild and realistic conditions, in some cases even directly in-vivo. The main aim of the present project is to bring this advantage to bear in the context of microfluidic lab-on-a chip devices.

The ability to perform meaningful NMR studies of protein systems on a chip would open interesting possibilities. For example, binding studies of a protein with an entire library of peptides could be efficiently integrated on a chip, offering considerable savings of cost and time.

Protein NMR almost universally relies on isotopically labelled samples. Most commonly, proteins are expressed in E. coli cultures fed with universally 15N and 13C labelled amino acids. This process is costly, and the ability to work with very small samples is therefore inherently attractive. Moreover, many proteins of interest are difficult to express in large quantities.

The present project is designed to explore quantitatively the technical challenges that need to be overcome to make microfluidic protein NMR possible. With the specific aim of carrying out a repeated dilution protein binding study, it is designed

to produce a convincing demonstration of the potential of this approach.

The magnetic resonance research section at the University of Southampton, UK, has access to a wide variety of state-of-the-art magnetic resonance instruments including NMR and EPR spectrometers, as well as hyperpolarization technologies such as dynamic nuclear polarization (DNP) and parahydrogen-induced polarization (PHIP).  In addition, Southampton provides an ideal environment for microfluidic technology, with several internationally renowned research groups active in this field.

The project welcomes applicants from the EU/UK who have or expect to obtain a first class degree in Chemistry, Physics or allied subjects/relevant disciplines. Funding will cover fees and a living allowance in line with RCUK guidelines (£14553 for 2017/2018).

Applications for a PhD in Chemistry should be submitted online at https://studentrecords.soton.ac.uk
Please ensure you select the academic session 2018-2019 in the academic year field and click on the Research radio button. Enter Chemistry in the search text field.

## Spin simulations in Julia

Julia is a programming language designed for numerical and scientific computation. It combined the convenience of an interpreted scripting language with the efficiency of compiled ones like C, Fortran, or C++. The goal of this effort is to provide a very simple and lightweight infrastructure for quick, but accurate, quantum mechanical simulations of small spin systems. NMR.jl represents spin operators in a Hilbert basis formed from the Kronecker
products of the individual $$|\alpha\rangle, |\beta\rangle,\dots$$ spin states. It uses sparse matrices wherever possible. In this way, simulations of up to ten spins 1/2 tend to run in a matter of minutes. Larger spin systems, up to about twenty spins or so, are possible, but require significant computational resources.

Here is an example of such a calculation. These commands are meant to be run either as a Julia script, line-by-line on the Julia command line, or, most usefully, as an IJulia notebook in a web browser. If you have not done so, install the current version of NMR.jl in your Julia environment by running the Julia command

Pkg.clone("https://github.com/marcel-utz/NMR.jl");


This will take a few moments. Once it’s done, you are ready to go.

First, we create a clean workspace and declare usage of the NMR modules SpinSim and PauliMatrix:

workspace();
using NMR.SpinSim;
using NMR.PauliMatrix;


Then, we need to define the properties of the spin system. In the present case, we are modelling hydroxy-ethyl propionate (HEP). The molecule looks like this:

There are five protons on the propionate side, three methyl (a) and two methylene (b), and two pairs of methylene protons on the ethyl (right) side (c) and (d). We assume the hydroxyl proton to be in fast exchange with the solvent. In addition, there is a 13C label at the carboxylate site (x). Therefore, we are simulating a ten spin system overall.
The parameters are

Jaa=-12.4;
Jab=7.5;
Jax=7.2;
Jbb=-10.8;
Jbx=-5.6;
Jcc=-10.8;
Jcd=7.5;
Jcx=3.2;
Jdd=-12.4;
Jdx=1.7;
δa=1.25;
δb=4.15;
δc=2.3;
δd=1.8;


The Zeeman Hamiltonian (in the rotating frame) is defined by taking into account the chemical shifts of the protons and the Z component of the spin operators:

Hz=δa*(SpinOp(10,Sz,1)+SpinOp(10,Sz,2)+SpinOp(10,Sz,3))+
δb*(SpinOp(10,Sz,4)+SpinOp(10,Sz,5))+
δc*(SpinOp(10,Sz,7)+SpinOp(10,Sz,8))+
δd*(SpinOp(10,Sz,9)+SpinOp(10,Sz,10)) ;


In addition, we need the J coupling Hamiltonian. We use strong coupling between chemically equivalent protons, and weak coupling in all other cases:

HJHHstrong=
2*pi*Jaa*(OpJstrong(10,1,2)+OpJstrong(10,2,3)+OpJstrong(10,1,3))+
2*pi*Jbb*OpJstrong(10,4,5)+
2*pi*Jcc*OpJstrong(10,7,8)+
2*pi*Jdd*OpJstrong(10,9,10);

HJHHweak=
2*pi*Jab*sum([OpJweak(10,k,l) for k=1:3,l=4:5])+
2*pi*Jcd*sum([OpJweak(10,k,l) for k=7:8,l=9:10]);


We also need some of the total spin operators, such as $$F_z$$ and $$F_y$$:

FzH=sum([SpinOp(10,Sz,k) for k=1:5])+sum([SpinOp(10,Sz,k) for k=7:10])
FyH=sum([SpinOp(10,Sy,k) for k=1:5])+sum([SpinOp(10,Sy,k) for k=7:10])
FmH=sum([SpinOp(10,Sm,k) for k=1:5])+sum([SpinOp(10,Sm,k) for k=7:10])
Fz=sum([SpinOp(10,Sz,k) for k=1:10])


Here, FzH is the $$F_z$$ operator for the protons only, where as Fz applies
to all spins, including 13C.

## Overview

The Utz lab is a research group within the School of Chemistry at the University of Southampton. It is one of five research groups that together make up the magnetic resonance research section at the University (MagRes@Soton).

Our research mainly concerns the study of live systems (cells, tissues, and small animals) by nuclear magnetic resonance. We are developing miniaturised “Lab-on-a-chip” devices for the culture of such biological systems, and integrate them with in-situ observation by nuclear magnetic resonance. This combination of microfluidic culture technology with advanced nuclear magnetic resonance techniques provides unique insight into the metabolic processes of life. Our work is motivated by applications across the life sciences, in particular in drug discovery and safety testing, and in the development of disease models.

Other research areas include the study of complex materials such as hydrogels, solid polymers, and composites. We are also actively contributing to an effort to develop a novel approach to neurostimulation of the spinal cord.