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Spin Diffusion and Cross Relaxation in CPMAS NMR of Proteins and Peptides.

Spin Diffusion and Cross Relaxation in CPMAS NMR of Proteins and Peptides. . Stowe Winter School, 2013. H. N. Using NMR relaxation in solid proteins to study molecular dynamics. 15 N T 1 (s ) vs. sequence. dynamics : straightforward separation of internal from overall motion.

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Spin Diffusion and Cross Relaxation in CPMAS NMR of Proteins and Peptides.

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  1. Spin Diffusion and Cross Relaxation in CPMAS NMR of Proteins and Peptides. Stowe Winter School, 2013

  2. H N Using NMR relaxation in solid proteins to study molecular dynamics 15N T1 (s) vs. sequence dynamics: straightforward separation of internal from overall motion activation parameters: wider accessible temperature range problem: spin diffusion in uniformly enriched proteins can mask most interesting dispersion in dynamics

  3. 240 200 160 120 80 40 0 ppm model for 15N-15N spin diffusion in a deuterated back-exchanged protein ala, leu amides T1 ~ 100 s GAL gly amine T1 ~ 0.4 s 15N1H3+ 15N—1H Zibby Fry

  4. 244 K 214 K 154 K 130 K 110 K 95 K 13C/15N glycyl-alanyl-leucine spectra vs. T CH CO CH2 CH3 H2O Zibby Fry ala CH3 leu CH3 synthesized u-15N, u-13C/15N and also u-13C/15N/2H 60 50 40 30 20 ppm 184 180 176 172 168 ppm 8000 4000 0 -4000 -8000 Hz 13C 13C 1H

  5. Isotropic shift difference δ truncates δ S1 S2 1H 15N2 15N1 1H when |d| << δ, S1S2 flip-flops are quenched

  6. spectral overlap un-truncates δ S2 S1 1H 15N2 15N1 1H δeff ~ 0 where lines overlap where δeff ~ 0, flip-flops are un-quenched

  7. δ S2 S1 1H 15N2 15N1 1H Heinrichs, Linder and Hewitt JCP (85), 1986, pgs. 7077-86 simple theory of spin diffusion overlap function where δeff ~ 0, flip-flops are un-quenched spin diffusion rate

  8. 2D spin diffusion experiment 15N t1 t t2 y x decouple decouple 1H +x -x y

  9. 2D spin diffusion experiment 15N t1 t t2 y x decouple decouple 1H +x -x y

  10. 2D spin diffusion experiment 15N t1 t t2 y x decouple decouple 1H +x -x y

  11. 2D spin diffusion experiment 15N t1 t t2 y x decouple decouple 1H +x -x y auto and cross peak intensities

  12. BB BA AA AB 15N-15N 2D spin diffusion measurements on u-15N GAL A B 15N1H3+ 15N—1H X BB peak intensity AA AB BA mixing time (s) 15N @ 80 MHz, νr = 18kHz

  13. BB AA AB BA 15N-15N 2D spin diffusion measurements on u-15N GAL A B 15N1H3+ 15N—1H X BB XX BA peak intensity XX AA XA AB XA mixing time (s) 15N @ 80 MHz, νr = 7 kHz

  14. TSD and T1 depend on MAS rate T1 decay TSD decay ln(AA+BB-AB-BB) ln(AA+BB+AB+BB) time (s) time (s)

  15. TSD and T1 depend on MAS rate 1/TSD vs. 1/ωr TSD decay RC (s-1) ln(AA+BB-AB-BB) time (s) 2π·103 /ωr (s) from initial slope

  16. TSD decay looks like classic diffusion barrier limited kinetics TSD decay TSD decay ln(AA+BB-AB-BB) ln(AA+BB+AB+BB) time (s) Root-time decay has same form as for nuclei relaxed by randomly distributed paramagnetic impurities Due to distribution of N-N vectors in rotor frame

  17. H H D D long CP H D short CP 138 134 130 126 122 118 ppm 34 32 30 28 26 ppm 3 4 3 3 3 2 3 1 3 0 2 9 2 8 2 7 2 6 p p m 1 3 8 1 3 6 1 3 4 1 3 2 1 3 0 1 2 8 1 2 6 1 2 4 1 2 2 1 2 0 1 1 8 1 1 6 p p m 15N spectra of gly-ala-leu 15N/13C/2Hcrystallized from D2O/H2O large secondary isotopic chemical shifts leu NH(D) gly NH3+(D) ala NH(D)

  18. Amide-Amide spin diffusion is 1H driven AH BH BD AD 120 121 122 123 124 125 126 127 128 129 2D 15N-15N 30 s spin exchange spectrum for 50/50 GAL AH-BH cross peaks 131 130 129 128 127 126 125 124 123 122 121 120 ppm

  19. Amide-Amide spin diffusion is 1H driven AH BH BD AD 120 121 122 123 124 125 126 127 128 129 2D 15N-15N 30 s spin exchange spectrum for 50/50 GAL AH-BD cross peaks 131 130 129 128 127 126 125 124 123 122 121 120 ppm

  20. Amide-Amide spin diffusion is 1H driven AH BH BD AD 120 121 122 123 124 125 126 127 128 129 2D 15N-15N 30 s spin exchange spectrum for 50/50 GAL AD-BH cross peaks 131 130 129 128 127 126 125 124 123 122 121 120 ppm

  21. Amide-Amide spin diffusion is 1H driven AH BH BD AD 120 121 122 123 124 125 126 127 128 129 x 2D 15N-15N 30 s spin exchange spectrum for 50/50 GAL No AD-BD cross peaks x 131 130 129 128 127 126 125 124 123 122 121 120 ppm

  22. 240 200 160 120 80 40 0 ppm 15N-15N spin diffusion should be detected in the 15N T1 relaxation ala, leu amides T1 ~ 100 s GAL gly amine T1 ~ 0.4 s 15N1H3+ 15N—1H

  23. 15N T1 independent of deuterium exchange T1 amine = 0.4 s T1 amide = 800 s as r  ∞

  24. Amide 15N T1 MAS independent if gly-15N is removed оala in 2-15N GAL оleu in 2-15N GAL T1 amine = 0.4 s T1 amide = 800 s as r  ∞

  25. Relaxation by spin diffusion to relaxation sinks Nuclear Cross-Relaxation Induced by Specimen Rotation E.R. Andrew et al, Physics Letters (4) 1963, pg 99-100 1H T1 and methyls - Slichter, Douglass ...... 13C T1 and methyls – White, Law ...... 2H T1 with relaxation sinks as CD3 – Gan, Wimperis..... 31P spectrum of PCl5

  26. CSA enabled 15N-15N spin diffusion amide amine 8000 Hz 12 kHz overlap ~ constant at slow MAS rates 5.0 kHz 2.2 kHz apparent R1fast MAS ~ R1 NH dipolar

  27. Fourier components of 2 4 0 2 0 0 1 6 0 1 2 0 8 0 4 0 0 p p m spin diffusion under MAS Suter and Ernst (32) 1985, 5608-27 Kubo and McDowell zero quantum lineshape powder sum zero quantum amplitudes are approximately the overlap integral for the amine line with the amide sidebands amine isotropic

  28. scaled overlap function fij Amide T1 TSD (s) T1 (s) vr (kHz) vr (kHz) T1 amine = 0.4 s T1 amide = 800 s as r  ∞

  29. T1 computed from amine overlap with  r,  2r sidebands of amide T1 amine = 0.4 s T1 amide = 800 s as r  ∞ amide linewidth ~2500 Hz

  30. increase overlap to decrease T1 15N trelax decouple 1H

  31. increase overlap to decrease T1 15N trelax decouple 1H ωr/2π = 7.0 kHz 0.0 0.1 0.2 0.5 1 2 5 10 50 100 200 400 1000 trelax (s)

  32. increase overlap to decrease T1 15N trelax decouple 1H ωr/2π = 20.0 kHz 0.0 0.1 0.2 0.5 1 2 5 10 50 100 400 1000 3000 trelax (s)

  33. WS Bo WI Wo 1H W2 WI WS 15N ◦ T1 T1 T1 time MAS and anisotropic relaxation

  34. Bo 1H 13C • Model like 13C T1 relaxation of a methyl group under MAS • internal rotation dominant • ii) temperature dependence of known D. Torchia and A. Szabo JMR 49, (1982) pg 107 Ottiger and Bax, JACS 121 (1999) pg 4690

  35. 1H 1H 15N H N dipolar T1 for a 15N-1H pair freely diffusing on surface of a cone

  36. 1H 1H 15N Bo 1H 15N amide in “fast” motion limit τc ~ 10-11s amine in “slow” motion limit τc ~ 10-7s R1 (s-1) or NOE log(τc)

  37. 13C T1 vs. MAS rate for 13C, 15N enriched GAL 150 ppm 13C O R1 enhancements for fast vs. slow MAS rates could be used to measure CH3 to CO rCC

  38. or… compare natural abundance with a single 13CH3 330 s 70 s 330 s 67 s 170 s 8 s

  39. or… compare natural abundance with a single 13CH3 303 s 111 s 2 s 21 s

  40. but some R1 enhancements are not so simple to explain 0.3 s 0.2 s 0.5 s 0.4 s 4 s 17 s 0.8 s 0.6 s

  41. coworkers: • Yale University • Van Phan • Zibby Fry • SuvrajitSengupta • Victoria Mooney • Lacey Ketzner • Shan Kuang • Josh Hernandez • Chris Bennett • Hannah Fuson • Catalina Espinosa • Josh Karli Funding: NSF Experimental Physical Chemistry Agilent Foundation

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