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A large variety of NMR experiments exists, to be chosen depending on the information we are seeking, on the nature of the sample and, of course, on the instruments available.

The most commonly used, and simplest, NMR experiments are the 1D proton and the 1D carbon spectra, routinely used in organic synthetic laboratories to quickly produce confirmation of structures of novel compounds. Further structural detail can be obtained by using more advanced 2D experiments such as NOESY, COSY or HSQC.

NMR measures not only carbon and hydrogen but basically any atom with a non-nul spin. The most commonly measured nuclides beside ¹³C and ¹H are ³¹P,¹⁹F,¹⁵N and

29Si.

5.1.3.1 Solid-state NMR spectroscopy

The main difference between solution-state and solid-state NMR is that in the liquid state the molecules tumble very quickly and many interactions get averaged during time (for instance, dipolar interactions average to zero and cannot be measured in this configuration). This gives for each atom one sharp signal. However, as the system of interest increases in size, the peaks get broader since the rotational diffusion slows down.

It is at this stage that solid NMR steps in.

Now that so many interactions became visible and measured very broad peaks are ob-tained, so in order to analyze the peaks the most common method is to artificially introduce an orientation and spin the sample around an axis very fast (several thousand times a second). In this way, many interactions get averaged again around the rotation axis. The coupling can be expressed in terms of cosine functions and they conveniently vanish while spinning at an angle θ_m = 54.74^◦ to the B₀ axis. This angle corresponds to the average of the x,y and z axes.

Since its invention, magic-angle spinning (MAS) has been used with a wide variety of compounds, including catalysts, polymers and biomolecules, especially membrane pro-teins [131]. MAS-NMR is mostly used for the analysis of native and model membranes, membrane proteins, and lipid/protein interactions [55,132]. The resonance peaks of the

MAS-NMR are similar to those of solution spectra and enable the analysis of proteins in complex environments [133]. Unlike solution-state spectroscopy, there is no upper limit to the molecular mass of proteins that can be analyzed. Despite the obvious advan-tage of being able to study a large variety of samples in various states, there are some drawbacks to the MAS technique. The resolution of the spectrum is lower than that obtained with solution-state NMR, and thus it requires greater amounts of sample due to the decrease in sensitivity. [134].

There may also be problems associated with localized heating of the sample due to high spinning speeds, and with non-uniform distribution of the sample due to high centrifugal forces. This problem may be overcome to a certain extent with the use of rotor inserts which help position a small amount of sample at the correct position in the NMR coils to achieve results with maximum efficiency. The signal-to-noise ratio found with MAS may be improved using the cross-polarization (CP) or the refocused INEPT techniques, which allow the transfer of polarization from abundant spins (such as protons) to rare spins (¹³Cor¹⁵N, for instance), thus improving detection of these rare nuclei [134]. The MAS experiment may be further improved by using high-power decoupling, which simplifies the spectrum by decoupling protons from rare nuclei. By spinning the sample, one loses information on lipid conformations and dynamics in the bilayer, due to the averaging out of anisotropic interactions. However, these interactions can be “recoupled”, as we will see below with the DROSS experiment.

Solid-state NMR spectroscopy enjoys an exceptional position in the field of membrane research [135]. The chemical shift measured by NMR is highly sensitive to hydrophobic and electrostatic interactions providing information about phase composition not acces-sible with other methodologies [136]. Additionally, the measurements of segmental order parameters obtained from the chemical shifts allow an estimation of domain sizes in the biomembranes (formed for example by lipids and cholesterol) system as a function of temperature and composition [135].

In the current study we present a novel application of MAS dipolar recoupling to record simultaneously the isotopic ¹³C chemical shifts (at natural isotopic abundance) and segmental order parameters for surfactant and lipid membranes doped with gramicidin at two temperatures: 30^◦C and 5^◦C. These temperatures were chosen based on the phase transition temperature in each corresponding phase diagram of the systems.

Dipolar Recoupling On-Axis with Scaling and Shape Preservation - DROSS is an NMR technique that measures¹³C−¹Hdipolar couplings in solids. The widths of the dipolar

couplings are used to produce order parameter measurements as follows:

SCH = W_CH^averaged

W_CH^static = W_CH^measured

χ×W_CH^static (5.7)

where SCH is the ¹³C−¹ H order parameter, W_CH^static , W_CH^averaged, W_CH^measured are the static, averaged and measured widths of the dipolar splitting, and χ is the DROSS scaling factor (equal to 0.393). W_CH^static is around 20 kHz, but another way to measure it is to use equation 5.7with W_CH^measured for a known SCH value (see below).

Equation 5.7is derived from the effective Hamiltonian equation [137] : H^{ef f} =

ω_D

2I_zS_z (5.8)

where

ωD

=πJCH+χ bCH

1

2(3cos²β−1) (5.9)

with β as the angle between the bilayer normal and the direction of the static mag-netic field, χ and are the scale factors (ranging from 0 to 0.393 and from 0.797 to 0 respectively) and

b_CH

=−b_CHS_CH (5.10)

as the motionally averaged heteronuclear dipolar coupling, where SCH = 1

2

3cos²θ−1

(5.11) is the¹³C−¹H dipolar order parameter, bCH = (µ0/4π)(γcγh~/r_CH³ ) is the rigid lattice dipolar coupling, andθis the average angle between the internuclear vector and motional axis [137].

5.1.3.2 Advantage of DROSS

There are a number of advantages to the use of DROSS over other methods: it has greater sensitivity than deuterium NMR, there is therefore no need for isotopic enrichment and it can be used to analyse natural abundance membranes, which is not possible for deuterium NMR [55,133,137]. It also yields the information for all the carbons at once, with straightforward assignment, whereas Deuterium NMR would require labelling of each deuteron at a time, since the resolution between two deuterons is very small.

However, the precision in the order parameter values calculated for deuterium NMR is

higher than the values calculated for DROSS because the ¹³C−¹H dipolar couplings are about an order of magnitude smaller than the deuterium quadrupolar coupling [138].

Last but not least, the possibility of obtaining, via a simple equation, the order parameter from the dipolar coupling width in Hz makes it a much easier NMR technique comparing to the others.

In principle, the DROSS experiments are implemented with a 4-πpulse sequence applied to either the¹³Cor the¹Hnuclei; however, it is found that the latter case yields distorted line shapes. Therefore, the 4-π pulse recoupling scheme is applied to the ¹³C nuclei as described in the Figure5.2.

Figure 5.2: Pulse timing diagram for the separated local field MAS experiment DROSS.

Sample preparation is the same as for the SAXS experiments, except for the use of D₂O instead ofH₂O. We prepared four different membrane systems doped with gram-icidin, denoted in the following by DMPC/gA, DLPC/gA, C12E4/gA and DDAO/gA.

All experiments on DMPC were performed at 30^◦C. This is 7^◦C above the gel to liquid-crystal phase transition of the lipid membrane. At this temperature, one is able to remove the strong (∼ 10 kHz) homonuclear ¹H - ¹H dipolar couplings revealing the residual homonuclear interaction, i.e. spinning sidebands, and isotopic chemical shifts of the center band.

5.1.3.3 NMR methods

NMR experiments with DMPC, DLPC and C₁₂E₄were performed with a Bruker AVANCE DMX400-WB NMR spectrometer (¹H resonance at 400 MHz,¹³C resonance at 100 MHz) using a Bruker 4-mm MAS probe. NMR experiments for DDAO were perfomed with a

Bruker AVANCE 300-WB spectrometer (¹H resonance at 300 MHz,¹³C resonance at 75 MHz) using a Bruker 4-mm MAS probe. All experiments were performed at 30^◦C and only DLPC was also performed at 5^◦C. Samples are loaded into 4 mm diameter rotors and fitted with finned caps. Spinning speeds are normally between 2.5 and 12 kHz.

The DROSS pulse sequence [137] with a scaling factorχ= 0.393 was used with carefully set pulse lengths and refocused insensitive nuclei enhanced by polarization transfer (IN-EPT) [137,138] with delays set to 1/8J and 1/4J and aJ value of 125 Hz. The spinning rate was set to 5 kHz, the typical pulse lengths were ¹³C (90^◦) = 3µs,¹H(90^◦) = 2.5µs and ¹H two-pulse phase-modulation (TPPM) decoupling at 50 kHz with a phase mod-ulation angle of 15^◦. For the 2D spectra, 64 free induction decays were acquired, with 64 to 512 scans summed, a recycle delay of 3 s, a spectral width of 32 kHz and 8,000 complex points. The total acquisition time was between 2 and 14 hours. The data were treated using the Bruker TopSpin 3.2 software.

5.2 Results