# EPSRC Summer Project

Project Title: The TSAR Mechanism: A Family of New Solid-State NMR Recoupling Techniques

Department: Physics

Research Group: Solid-State NMR

Supervisors: Dr Steven Brown and Dr Johanna Becker-Baldus

Funding: EPSRC

During the summer 2009, I undertook a 10 week research project at the world-leading magnetic resonance facility at Millburn House, under the supervision of Dr Steven Brown and Dr Johanna Becker-Baldus. As part of the dissemination of my work, I gave a presentation to the solid-state NMR group and this presentation file can be found here (9.6 MB) . I also produced an academic poster for the URSS student exhibition, which can be seen here (435 KB) .

## Introduction

Determining the structure of proteins has many important applications in areas of chemistry and biology. This has been accomplished many times by measuring internuclear distances using solution-state NMR. However, this is much harder to do using solid-state NMR since the spectral lines are greatly broadened by the strong coupling of hydrogen nuclei, hiding the distance information. To reduce this broadening we can decouple these interactions by physically spinning the sample, known as magic-angle spinning (MAS).

However, one of the interactions which the MAS removes is the dipolar interaction. This coupling is inversely proportional to the cube of the internuclear distance, and so can be used to measure the distances between the different nuclei. In order to determine the structure of proteins therefore, we must use recoupling techniques to re-introduce the dipolar couplings and get the distance information back.

Existing dipolar recoupling techniques each suffer from problems such as sample heating, poor sensitivity or dipolar truncation (weak long-distance dipolar couplings obscurred by stronger couplings), making them impractical for use with proteins. My project was to investigate two new recoupling sequences (one homonuclear and one heteronuclear), both based on a new mechanism which does not suffer from these problems.

## The TSAR Mechanism

Third spin assisted recoupling (TSAR) is a new magic-angle spinning dipolar recoupling mechanism developed by researchers at MIT and Université de Lyon [1]. It gives a polarisation transfer between spins B and C, assisted by a mediating heteronuclear spin A. It uses a second order cross term involving the dipolar couplings B-A and C-A.

We use protons as the mediating third spin A since they are highly abundant in proteins and have large gyromagnetic ratios, facilitating large polarisation transfers. For the case where B=C, we have homonuclear recoupling known as proton assisted recoupling (PAR). For the case where B≠C, we have heteronuclear recoupling known as proton assisted insensitive nuclei cross polarisation (PAIN-CP).

## PAR

This pulse sequence can be used to obtain a two-dimensional homonuclear correlation spectrum. The initial $\pi$/2 pulse rotates the hydrogen magnetisation into the transverse plane. Then cross polarisation (CP) pulses are used to transfer the magnetisation from the hydrogen nuclei (protons) to the less sensitive carbon nuclei. After an evolution time t1, a PAR mixing pulse is applied to both channels. The efficiency of the polarisation transfer during this recoupling period depends on the powers of the pulses applied to the two channels. The signal is then detected during the acquisition time t2.

In the original paper on PAR, the authors simulated the transfer efficiency as the power on each channels (which is related to the corresponding nucleus' nutation frequency) was varied in order to find optimum conditions for a very simple three-spin system [1]. One of the first things I did was to reproduce these results in order to gain an understanding of the PAR mechanism and how CP also plays a part in the optimisation maps. This optimisation map for 13C-13C transfer is shown below, and there is a clear optimisation region in a diagonal shape. Also a map for 13C-1H transfer is shown so that the conditions for CP (known as Hartmann-Hahn conditions) can be seen. These maps were simulated using a PAR mixing time of 3 ms.

Experimental 13C-13C spectra using the PAR sequence at optimum conditions were taken using a Bruker 500 MHz solid-state NMR magnet (as pictured on the ePortfolio homepage). We found that the optimum conditions were not difficult to locate experimentally. The integral of each peak on the 2D spectrum is proportional to the polarisation transfer between the two corresponding nuclei. In this way, several spectra at different mixing times were taken in order to measure how the polarisation transfer between each pair of nuclei varied with time, as shown below for tyrosine. These buildup curves were then simulated using quantum mechanical density matrix simulations [2] using the spin systems circled in red below each graph.

As seen above, the buildup curves were very accurately simulated with relatively small spin systems. This is very encouraging. In comparison, some competing techniques require much larger spin systems and yet produce buildup curves which differ from experiment by an order of magnitude! Also, we can see that as the internuclear distance increases (left to right) the peak in the buildup occurs at later times. This suggests how a PAR experiment could be used to measure distances within molecules.

## PAIN-CP

The PAIN-CP pulse sequence [3] can be used to obtain a two-dimensional heteronuclear correlation spectrum (e.g. between 15N and 13C). The initial $\pi$/2 pulse rotates the hydrogen magnetisation into the transverse plane. Then cross polarisation (CP) pulses are used to transfer the magnetisation from the protons to the less sensitive nitrogen nuclei. After an evolution time t1, a PAIN-CP mixing pulse is applied to the 1H, 13C and 15N channels. The efficiency of the polarisation transfer from the 15N nuclei to the 13C nuclei during this recoupling period depends on the powers applied to all three channels during this pulse. The signal is again detected during the acquisition time t2.

Since the PAIN-CP pulse is applied to three channels, the transfer efficiency depends on three different variables - namely the power on each of the channels. This means that, in contrast to those of PAR, the PAIN-CP optimisation maps are three dimensional. Since we desire optimum 13C-15N transfer, we utilise the 15N-13C Hartmann-Hahn (HH) conditions for good CP between these nuclei. These Hartmann-Hahn conditions each correspond to a specific relation between the 15N and 13C nutation frequencies, and so the 3D optimisation map has been condensed into a more managable 2D map.

Some PAIN-CP optimisation maps were simulated for a simple 7 spin system with one 15N nucleus, two 13C nuclei and four 1H nuclei. Three maps are shown below: two are using HH conditions and one is not, in order to demonstrate the importance of choosing HH conditions between the 15N and 13C channels.

 15N-13C n=0 HH condition 15N-13C n=1 HH condition Not a 15N-13C HH condition

## Conclusions

I have investigated two recoupling techniques for use in solid-state magic angle spinning NMR experiments. Unlike competing techniques, they can be used in high field and fast spinning regimes, enabling higher resolution spectra to be taken. Some advantages are the high transfer efficiency and the accuracy of the simulations. Also, their dipolar truncation is attenuated, making them ideal for protein structure determination.

## References

[1] G. De Paëpe, J. R. Lewandowski, A. Loquet, A. Böckmann and R. G. Griffin, J. Chem. Phys. 129, 245101 (2008)

[2] M. Veshtort, R. G. Griffin, J. Magn. Reson. 178, 248 (2006)

[3] J. R. Lewandowski, G. De Paëpe and R. G. Griffin, J. Am. Chem. Soc. 129, 728 (2007)

Dr Steven Brown

Research page

Email

### Collaborator:

Dr Johanna Becker-Baldus

Research page

Email