NMR relaxation dispersion experiments to study

The micro- to millisecond timescale dynamics are often relevant for small molecule binding events [63, 64]. The current view of proteins is that they exist in an ensemble of different states. In turn, ligand binding can shift the equilibrium of this conformational ensemble [65]. Thus, understanding the dynamics that govern the exchange between the states, as well as the structural information about the states, is needed to better understand the underlying biomolecular recognition events.

Provided that there is a difference in chemical shifts (∆ߜ) between the states and exchange between states is on the micro- to millisecond timescale, different peak patterns can be seen in the spectra, depending on the exchange regime (kex) between the states (Figure 1.8).

݇௘௫= ݇஺஻+ ݇஻஺ (eq. 4)

where kAB is the exchange rate constant from state A to B and kBA the exchange rate constant from B to A.

A single peak is observed when the exchange rate constant between the states is significantly faster than the chemical shift difference (∆ߜ) between the peaks corresponding to individual states (kex>>∆ߜ) (Figure 1.8). In this case, the observed peak position can be used to calculate the populations of individual states using the following equation (provided here for state A):

݌஺ = (ߜ௢௕௦− ߜ஺)/(ߜ஻− ߜ஺) (eq. 5)

Here pA is the population of state A, ߜobs the chemical shift for the observed peak andߜA,ߜBare the chemical shifts for states A and B respectively.

At the other end of spectrum, where the rate of exchange between two states is a lot slower than the difference in chemical shifts (kex<<∆ߜ) between the states, the spectra shows two peaks. For each peak, its height is proportional to the population of the corresponding state (Figure 1.8). Between the fast and slow exchange rates falls the intermediate range, where the exchange rate constant is roughly equal to the difference in chemical shifts between the two states (kex~∆ߜ). In this case, interconversion between state A and state B ‘interferes’ with the chemical shifts, resulting in ‘exchange broadening’ of the observed NMR peak.

In general, these differences in the peak pattern and peak width can be studied using line shape analysis. Line shape analysis can be used to estimate exchange rate constants and the population of individual states. However, for more careful quantitative analysis, relaxation dispersion measurements using the Carr-Purcell-Meiboom-Gill (CPMG) method are commonly used [30, 55].

Figure 1.8: Overview of NMR dynamics experiments using the classic two- site chemical exchange example. If the exchange between the two states (A and B) is slow, two peaks are observed where the height distribution reflects the population of each state. For fast exchange, only a single peak is visible with its the position based on the

population. Intermediate exchange, where the exchange between the two states is roughly equal to their chemical shift difference, results in a broad peak. (Figure modified from [55]).

The CPMG approach allows re-focusing the broad peaks caused by intermediate exchange. The basic idea behind these experiments is to quantify the effective line width of peaks as a function of number of refocusing pulses. Without refocusing, the line widths are broad due to dephasing of magnetisation caused by stochastically changing between two states (states A and B). In the absence of refocusing pulses, state A changes to state B

randomly, resulting in defocusing magnetisation in the XY plane. This causes a broadening of the resulting NMR peak (Figure 1.9, top). To re-focus magnetisation in XY plane, a variable number of 180° re-focusing pulses in the same delay period can be applied. As the refocusing pulses become more frequent, i.e. there is less time between 180° pulses, there is less of a chance for the state A to change to state B. The CPMG sequence can thus refocus magnetisation, and lead to sharper peaks (Figure 1.9). An elegant analogy of the CPMG experiment has also been suggested by Lewis Kay [66]. Here runners and walkers are used to describe the spins of the two different states (A and B), while differences in their speeds can be used to describe differences in chemical shifts between A and B. As states A and B can interchange, runners can start walking and walkers can start running. At the beginning of experiment runners and walkers are set off to run a lap around a field. In the absence of exchange (or if an exchange is very slow), there will be two populations of finishers; one group crosses the finish line first (runners) and another later (walkers). In this scenario, there will be two peaks in the NMR spectrum (one for state A and one for state B). If, on the other hand, the exchange rate constant is very fast (all runners became walkers many times over and vice versa), all the runners and walkers will finish together as one group, and here one peak is observed in the NMR spectrum. In the case of the intermediate exchange rate, some runners slow down to a walk once or twice, others five times and so on, during the lap of the field. As a result, all the runners and walkers finish at different times, and this would lead to a broad peak in the NMR spectrum. To refocus this group of runners and walkers, a CPMG experiment can be used. Here, the runners and walkers are again set off around the field, but this time, if a whistle is blown (representing the 180° pulse), all the runners and walkers will turn around. If there is no exchange (i.e. runners will keep running and walkers walking), two peaks are seen on the spectrum. If runners start randomly walking and walkers running, as in the case of intermediate exchange, if the whistle is blown, some of the runners may start walking back to start line and thus will not cover the same distance as they did on the way out. Here, not everyone will cross the start line at the same time. This would again lead to a broader peak in the NMR spectrum. However, if a larger number of whistles are blown to keep turning everyone

around again and again, the group should stay much less dispersed. As the period between whistles gets shorter, there is less time for runners to start walking and then running again. The distances covered running or walking are shorter and the participants are spread across a far smaller part of the field. This means that they are more likely to cross the finish line at the same time, equating to a sharper peak on the NMR spectra [66].

Figure 1.9: Schematic of a CPMG relaxation dispersion experiment peak re- focusing. If the two states of the system, A (in blue) and B (in red), interchange roughly at the same rate as their chemical shift difference, a broad peak is seen in spectra. The exchange between states A and B is shown as dashed red or blue line. The use of an increasing number of refocusing pulses (grey boxes) results in peak refocusing, as a peak from only one state is observed, as seen on the right panel. The bottom panel shows simulated data from CPMG experiments, where the peak is refocused when the CPMG frequency is increased. (Figure modified from [67] and [66])

Whilst CPMG experiments probe only µs-ms time scales, they have become a valued tool in studying ligand-protein binding, folding pathways and enzyme reactions [68-70]. To obtain exchange parameters such as the interconversion rate (kex) and the population of each state, as well as the chemical shift

differences between two interconverting states, relaxation dispersion experiments need to be recorded at multiple magnetic fields. These parameters provide information on global and local dynamics and the thermodynamics of the exchange process [66]. Moreover, this approach allows characterisations of minor populations (smaller than 1%) [71]. In turn, information about chemical shift differences between the major and minor conformations can be used to obtain insights into structure and dynamics of the minor (populated less than 1%) state, which is not possible by any other experimental method.

From the CPMG data, the transverse relaxation rates (R2eff) at different CPMG field strengths can be calculated from peak intensities using the following equation [72, 73]:

ܴ2

= −

ln

Here, TCPMG is the constant time used for the CPMG experiment, I the peak intensity and I0the reference peak intensity.

In this work the relaxation dispersion method is used to study the differences in µs-ms dynamics between the different Hsp90:inhibitor systems, and to allow comparison, and validation, of computer simulation data.