The program suite used in this chapter consists of several individual programs, which allow for a rapid identification of the most suitable set of symmetry numbers, in the large parameter space of possible combinations. The first routine in the program suite generates sets of symmetry numbers from a range of possible values specified by the user, iterating over all possible combinations. With a given set of symmetry numbers, the parameters for the simulation program SIMPSON are generated. The theory, which has been employed in the design of this testing algorithm, is discussed in [37] and briefly summarized in chapter 2. After the result is obtained, in the form of a buildup curve (magnetization on the hetero-nucleus over time), a second program performs an analysis, which consists of a check of the overall excitation efficiency and the time, after which the transfer maximum was reached. This routine is repeated, until the whole set of possible combinations is screened. When all symmetry sets have been computed, the results are output in form of a surface plot, giving the excitation efficiency over the symmetry numbers. Here, sequences not fulfilling the minimum limits in excitation efficiency and/or excitation profile can be excluded from the plot.
This plot is shown in Fig. 4.2.
From this plot, promising candidates can be selected by the user and be submitted to a program, which will automatically translate the symmetry numbers obtained into a Bruker pulse program.
This procedure makes it feasible to screen a large number of symmetries, which theoretically solve a given recoupling or decoupling problem.
Thus, this approach can be used to find any symmetry based recoupling (or de-coupling) sequence suited for a given experiment on one or more channels, as long as the target state is known and can be reliably evaluated by an automated routine.
4.2.1 Symmetry based heteronuclear transfer
To arrive at a set of sequences which fulfill the boundary conditions given above and to limit the number of sequences which have to be considered experimentally,
4.2. SIMULATIONS
Figure 4.2: Evaluation of the transfer efficiency of 63000 symmetry sets. Buildup curves were simulated using the SIMPSON software package and evaluated for all combinations of N (2-140), n (1-30) andν(1-30) as shown in a.1) Here, only the maxi-mum efficiency for all possible values ofνhas been plotted to reduce dimensionality to two, for sake of clarity. a.2) To arrive at a complete set of symmetry numbers, the slice indicated in a.1) is expanded alongνto find the sequence with the highest efficiency and complete the set of symmetry numbers. b.1) and b.2) are the same as a.1) and a.2) but with the additional selection criterion of a minimum of 0.75 maximal transfer and a RF power requirement of less than 10 xωr. The set of symmetry numbers for the sequenceR7016,166 is indicated in red. The spinning speed was set to 10 kHz for all simulations.
Figure 4.3: Simulated excitation curves for R7016,166 on a linear NH..H spinsystem using the same J-coupling (-92Hz) for each trace, but with scaled DD-couplings relative to the values used for the simulations shown in Fig.4.2. Full DD-coupling was used for the black solid trace, 0.6 x coupling for the red, broken trace and 0.2 x DD-coupling for the blue, dotted trace. It can be seen that dipolar couplings reduce
Figure 4.4: Excitation curves for a C-CH2group. Black are the traces for the carbon with attached protons, without (solid line) and with homo-nuclear J-coupling (dotted line) between the carbons. The traces for the carbon without directly bound protons are shown in red, without (solid line) and with homo-nuclear J-coupling (dotted line).
It is apparent that homo-nuclear13C-13C magnetization transfer occurs simultaneous to heteronuclear1H-13Ctransfer. Dipolar couplings were scaled by a factor of 0.1 for this simulation. Spinning speed was set to 10 kHz for all simulations.
symmetry numbers have to be chosen such that only the terms corresponding to the heteronuclear J-coupling in table 2.2 in chapter 2 are selected. All homo-nuclear terms should be suppressed, including the isotropic chemical shift, as it is desirable to suppress evolution during the transfer. This can be easily done for all interactions, save for the homo-nuclear J-coupling, which is always symmetry allowed, as can be seen from its space- and spin rank of 0. Therefore, the symmetries of interest would yield a multi interaction decoupling, while leaving the heteronuclear J-coupling intact.
Fortunately there are many sequences that exhibit this kind of recoupling profile.
Still the experimental performance of these sequences is not identical. The reason for this is, although the first order averaged Hamiltonian given in equations 2.119 and 2.120 in chapter 2 is a good indication to what terms will be symmetry allowed, second and higher order terms of the averaged Hamiltonian influence the experimental performance of a symmetry based sequence as well. Generally, there are many second and higher order terms which are symmetry allowed. This can lead to interference effects, degrading the experimental performance of the sequence, but the extent of these effects are difficult to predict. Therefore numerical simulations were conducted, to assess the transfer efficiency of all sequences in a range of symmetry numbers (N = 2-140, n = 1-30,ν = 1-30) using the SIMPSON simulation package [78], as outlined above. Simulations were performed for a simple linear spin system, in which a15N nucleus is directly bound to a proton and another distant, non bound proton is present.
The interaction strengths were set to typical values found in the literature (see Material and Methods for details). The evaluation of the resultant buildup curves for this spinsystem in presence of all heteronuclear interactions (J and DD) is shown in Fig.
4.2 a1). Here an efficiency landscape is plotted over the symmetry numbers N and n. Efficiency is defined here as the maximum15N magnetization obtained during the excitation time. For each point shown in Fig. 4.2 a1), only the the best efficiency for ν is plotted to keep the dimensionality to two, for sake of clarity. When a suitable set of N and n is chosen, a slice can be expanded along the chosen value of N, to yield the efficiency landscape in dependence ofν, as shown in Fig. 4.2 a2). Choosing an appropriateν finally yields a complete set of symmetry numbers. As can be seen from Fig. 4.2 a) there are many sequences that show efficient polarization transfer
4.2. SIMULATIONS
Figure 4.5: Transfer efficiency of the same symmetry sets numbers shown in Fig.4.2, but for aCH2 spinsystem derived from G35 in Ubiquitin. It is apparent, that for this spinsystem much stronger RF fields are required to yield good transfer, as compared to Fig.4.2. The spinning speed was set to 10kHz for all simulations.
from 1H to 15N, especially for sequences with higher RF-power requirements. This is expected, as symmetry based suppression of interactions only works reliably, if the radio frequency (RF) irradiation is much stronger than the interactions to be suppressed. If this is not the case, these interactions are still present to a certain degree, leading to attenuation of the transfer efficiency.
To identify the most suitable candidates for experimental implementation, limits were imposed on the radio frequency power requirement of the sequence (less than 10 x the MAS rate (ωr) ) and the transfer efficiency, where the maximum15N magneti-zation reached during the excitation time must be greater than 75% of the theoretical optimum. This was done to filter out sequences with unrealistically high demands on the hardware, and those in which competing interactions attenuate the through-bond polarization transfer.
These selection criteria lead to the reduced set of symmetry numbers shown in Fig. 4.2 b). To further differentiate between primarily J-coupling mediated and higher order coupling driven transfer, a variety of different homo- and heteronuclear DD-coupling strengths were simulated, keeping the J-DD-couplings fixed. This was done for the subset of symmetries which performed best in the first simulation run. Only sequences that showed minimal perturbation of the excitation profile with rising DD-coupling strength were considered for experimental evaluation. An example is shown in Fig.
4.3 forR7016,166 , which was identified as the most efficient and robust sequence of the parameter space investigated and which is used for the reminder of this chapter. Here, transfer is simulated in relation to dipolar coupling strength. For this, the J1N H coupling was left constant at a value of -92Hz, but all DD-couplings present were reduced by 40% (red curve) and 80% (blue curve). The reason for these simulations was to get an estimate of the effect of motional averaging on the sequence. Comparison of the curves shows that the maximum transfer of magnetization to15N is reduced by 25% under the full strength dipolar coupling, most likely by second order dipolar coupling terms present in the averaged Hamiltonian, for the spin system used.
To verify these results, spin systems with the orientations, distances and chemical
and non-protonated carbon (red), if no homo-nuclear J-coupling exists between the two carbons. As expected for a through bond polarization transfer, only the proto-nated carbon is polarized. The dotted lines show the magnetization buildup of the same spin system, upon introduction of a homo-nuclear J-coupling of 55Hz between the two carbons. A polarization buildup on the non-protonated carbon is apparent, which follows the polarization buildup of the protonated carbon with a certain lag.
Furthermore, the polarization of the protonated carbon is markedly reduced.
This strongly suggests that a relayed polarization transfer is possible between the two carbon nuclei, via the homo-nuclear J-coupling.
4.3 Materials and Methods
4.3.1 Samples
DMPC was bought from Avanti and used without further purification. A sample of 15 mg was rehydrated with 45µlD2O, freeze thawed via bath sonication three times and then packed into a 4mm MAS rotor using high resolution MAS inserts.
4.3.2 Computation
Simulations were performed using the SIMPSON package [78], with different spin systems. The initial set used in Fig. 4.2, consisted of a linear arrangement of a15N nucleus with a directly bound proton (HN) (J1N H= -92Hz, DD-coupling = 11146.6) and a distant proton (HD) (DD-coupling to 15N = 1393.32, DD-coupling to HN = -4925.27). For verification two additional spin-systems were calculated using SIMMOL [79] together with the pdb structure of ubiquitin (pdb: 1d3z). Relative orientations and distances for an amide group and a HCα were calculated for the backbone of the residue K6. Similarly a CH2 spin system was calculated from the geometry of the residue G35. The resultant buildup curves were evaluated with the help of the Tcl scripting language [24]. Graphs were plotted using Gnuplot 4.0. Processing of experimental spectra was done in Topspin 1.3 (Bruker, Karlsruhe). The programs used are given in the appendix.
4.3.3 NMR
Experiments were conducted on a Bruker Avance II 400 MHz Spectrometer using a 4mm DVT HXY probe. An MAS frequency of 5 kHz was used in all experiments. The temperature of the DMPC sample was varied between 270 and 310 K, as indicated in the figure captions. The pulse power used for all hard pulses and theR7016,166 mixing block was 58333 Hz , as given by the quotient of the symmetry numbers N/n and the MAS rate of 5 kHz. The excitation time was optimized to 6.52ms. Presaturation before theR7016,166 transfer was achieved with 8π/2 pulses spaced in intervals of 5ms.
The evolution delay for the heteronuclear J-coupling during refocused INEPT transfer