MD corroborates population shuffling

t A B

p _

 also shows no correlation with the accessibility to the solvent of these methyl groups (Appendix Figure 9) in which residues whose methyl groups are completely buried have p_{t A, B}

values between 0.06 to 0.19.

Nuclei p_{t A, B}

Val51 0.061 ± 0.002 Leu151 0.063 ± 0.001 Ile23 0.071 ± 0.002 Leu431 0.084 ± 0.001 Leu432 0.075 ± 0.002 Ile44 0.093 ± 0.002 Leu502 0.146 ± 0.001 Leu562 0.191 ± 0.001 Val702 0.055 ± 0.002 Leu712 0.042 ± 0.003

Table 3 The relative population differences between the trans rotamer from two different

conformers derived from methyl carbon motional amplitudes that report on population shuffling.

Calculated assuming a spectrometer field strength of 14.1 T.

4.6 MD corroborates population shuffling

Again, the above data does not support a model where rotameric interconversion occurs on the microsecond timescale. Instead, rotamer jumps occurring on a faster timescale (pico- to nanosecond) that experience different weighting between various ubiquitin conformations, or population shuffling, can account for the reduced ex values. In order examine this situation a collection of molecular dynamics (MD) simulations that were conducted with free ubiquitin and ubiquitin in complex with its various binding partners were considered [150].

70 MD simulations were taken from a recent report in which a 1 s simulation of unbound ubiquitin was compared to eleven simulations of ubiquitin in complex with different interaction partners [150]. An observation was made in which some binding partners constrict the sampling space of ubiquitin as compared to free ubiquitin across the same two major modes of motion (pincer-mode) [11] that was identified from the previous RDC based ensembles. The overall equilibration time of the MD trajectories are not on the same length of _ex, but the MD trajectories which were conducted up to 100 nanoseconds, could be used to asses the rotamer states assumed by a given ubiquitin conformation within each spatially restrained complex.

Figure 20 Comparison between free ubiquitin (blue points) and ubiquitin bound in complex (red points) show constriction in the sampled conformers. This restriction translates into large changes in the populations assumed by rotamer groups given by the plots displaying the density of a given

1 dihedral angle. Figure courtesy of Dr. Colin Smith (MPI-BPC, Dept. Theoretical and Computational Biophysics)

The determination of the RDC based structural ensembles highlighted that the largest structural variance occurs as a pincer like motion that involves the loop between first and second beta strands, the alpha helix and third beta strand, and the C-terminal tail of the helix in ubiquitin [11]. This is represented in PCA space (Figure 20) where the two largest modes, PCA 1 and 2 are plotted with respect to each other. Across these modes, free ubiquitin structures (Figure 20;

71 blue points) traverse between closed and open conformations. Two examples are given in Figure 20 in which a binding partner restricts the sampling of ubiquitin in either a closed (1NBF:C) [151] or open (1XD3:D) [152] conformational space. What can be surmised from this is that similar sites that display microsecond exchange also report on the largest redistribution in their rotamer populations (Figure 20; density plots between free ubiquitin (blue curve) and bound ubiquitin (red curve)). Given that rotamer redistribution occurs on a much faster timescale than the reorganization of the backbone and methyl nuclei a new model emerges in which depending on the fraction of openness that a ubiquitin conformer assumes, the backbone and methyl nuclei fluctuate in a concerted fashion that translates in a shuffling of the rotamer populations (Figure 21). Thus, the population shuffling between rotamers is predicated on the concerted microsecond backbone and side chain motion.

Figure 21 Proposed thermodynamic model. Structures are of free ubiquitin are from the two extremes between open (red) and closed (blue) free ubiquitin structures. Each ubiquitin conformer can contain different rotamer populations that occur on a timescale << ex.

72 4.7 Conclusion

We have compiled the most extensive RD data set using large amplitude spin-lock field R_1 for nuclei within ubiquitin (Figure 17 and Appendix Figure 7 and 8). In total thirty-one nuclei that span the sequence of ubiquitin display a common timescale of motion between 55-60 s at 277 K (Figure 18). Importantly, this motion which coexists for both backbone and side chain nuclei has not been experimentally observed before. The use of high powered RD experiments also narrows the kinetic regime where this motion takes place. Namely, with the current time resolution of 10 s and 4 s for ¹³C and ¹H, respectively, only a process between the 55-60 s could be detected. Insights into the meaning of this side chain motion at this timescale could not be reconciled with discrete processes assuming rotamer interconversion in the microsecond regime (Figure 19). Rather comparison of various binding partners (Figure 20) [150] revealed that the major mode of motion that has been attributed to the same timescale for backbone interconversion causes the population shuffling of rotameric states depending on the degree of openness for a given ubiquitin conformer. Further work is being pursued in order to optimize the various modes from the PCA analysis that are cross-validated with the RD data in hopes of attaining mechanistic insight into the direct structural changes due to this concerted motion.

Conformational sampling events within proteins have usually been limited to one set of nuclei [112,153]. However, the implications of this work can be far reaching where studying multiple types of nuclei can reveal a united behavior for the backbone and side chain moieties. However, the models required to describe the motion for each nuclei may be different. This work further extends our insight into the kinetics for conformational sampling in ubiquitin and potentially for other systems. The sampling of different conformers which for ubiquitin affects the binding to particular interaction partners appears to require a global concerted process that reorganizes the

73 backbone and side chain moieties differently. Additionally, the experimental and analytical tools laid out here should aid in establishing and/or quantitating this phenomenon for other systems of interest.

4.8 Materials and Methods