Protein dynamics and estimation of additional relaxation from 13C to measured 15N relaxation, diffusion tensor and overall rotational correlation time using uniformly 15N/13C-labeled NACI.

Studies of protein dynamics are mainly based on 15N relaxation data measured from a sample labeled by 15N only. For 15N/13C-labeled samples, contribution of additional relaxation from 13C to the 15N relaxation complicates studies of protein dynamics and model-free analysis. Here we present an optimization approach via correction of 15N-13Cα and 15N-13CO dipole-dipole interactions for 15N/13C-labeled NACI to determine correlation time and diffusion tensor and to correct measured R1 and R2 values for residues in which internal motion is restricted and chemical exchange is absent, by fitting the measured and theoretical R2/R1 ratios. The additional increased longitudinal and transverse relaxation rates via 15N-13C relaxation are determined as well by calculating 15N-13Cα and 15N-13CO dipole-dipole interactions. The estimated additional increased longitudinal and transverse relaxation rates via 15N-13C relaxation in the 15N/13C-labeled NACI are not constant over the protein, but different from residue to residue, and range between 0.124 s-1 and 0.132 s-1 for the additional increased transverse relaxation rate, corresponding to around 2 % increase of the transverse relaxation rate in the absence of 13C, and between 0.057 s-1 and 0.062 s-1 for the additional increased longitudinal relaxation rate, corresponding to around 3 % increase of the longitudinal relaxation rate in the absence of 13C. For the 15N/13C-labeled NACI with determined correlation time 5.0 ns, the measured R1 and R2, because of the increased relaxation in R2/R1 ratio close to 1, can be used directly as R2/R1 input into program 'r2r1_diffusion'. For verification of our approach, the measured R1 and R2 from the 15N/13C-labeled NACI were directly inputted into our approach and also into the program 'r2r1_diffusion' for comparison. The diffusion tensor obtained from the calculations of our approach is consistent with results derived from the program 'r2r1_diffusion', revealing that it is feasible to correct the effect of the additional relaxation on R1 and R2 values and to determine the correlation time and the diffusion tensor for the doubly 15N/13C-labeled NACI containing an additional long peptide from expression plasmid. When correlation time (from 3.5 to 30 ns) or magnetic field (from 500 to 800 MHz) increases, the contributions from the 13Cα and 13CO relative to 15N R1 and R2 without 13C labeling change only slightly and the changes in the additional increased percentages are very small; i.e., the additional increased percentages remain around 3 % increase in R1 and around 2 % increase in R2, and hence the additional increased percentages from the contribution of 13C to 15N could be considered approximately independent of both the correlation time (from 3.5 to 30 ns) and the magnetic field (from 500 to 800 MHz). For the diffusion parameters, such as correlation time and diffusion tensor, derived from using R2/R1 ratio, the contribution from carbon labeling is relatively very small and does not influence the fitting of the diffusion parameters. The reason is that the R2/R1 ratio is used, in which the 13C contribution effects are cancelled out each other via (1 + 3 %)/(1 + 2 %) in the R2/R1 ratio. But because the 3 % increase in R1 and the 2 % increase in R2, even though relatively small, do affect S2 values that are derived from the program 'Fast-Modelfree' using R1 and R2 individually, rather than using the R2/R1 ratio, and do make the S2 values higher by 0.2 % to 5.9 % (more rigid), the contribution from carbon labeling is hence not negligible for parameters fitted using individual R1 and R2 inputs. Overall, parameters fitted from R2/R1 ratio, in case of similar increased percentages, such as 3 % and 2 %, will not be influenced, whereas parameters, such as S2, fitted from using individual R1 and R2 will be influenced. Here, the corrections of the contributions from 13C to measured 15N relaxation are limited to those residues in which internal motion is restricted and chemical exchange is absent, and can be taken directly as R2NC,measured/R1NC,measured for input in the program 'r2r1_diffusion' or quantified as R1NC,measured/1.03 and R2NC,measured/1.02 for input in the program 'Fast-Modelfree'. In addition, relaxation data show significantly increased R2 values and R2/R1 ratios and hence suggest conformational exchange for assigned residues S13, C38, G39, G40 and N41 which are mainly confined to a region surrounding C14-C38 disulfide bond. S13 in the NACI experimentally shows temperature-dependent conformational exchange with reduced R1 value, significantly increased R2 value and R2/R1 ratio, and larger deviation of NOE, whereas P13 in BPTI lacks amide proton.