1 Introduction to solution NMR

Alexandre Bonvin

Bijvoet Center for Biomolecular Research

with thanks to Dr. Klaartje Houben

Bente%Vestergaard%

The NMR research group

Prof. Marc Baldus Prof. Rolf Boelens

SolutionSolution NMR:NMR: 950950(in, 900 progress)-cryo, 750, 900-cryo, 600-cryo, 750, 600US, 600-cryo, 2x500 600US, MHz 2017?:2x500 MHz1.2 GHz SolidSolid-state-state NMR:NMR: 800WB 800WB-DNP,-DNP, 400WB 400WB-DNP,-DNP, 700US,700US, 500WB500WB MHz MHz e-infrastructure: >1900 CPU cores + EGI grid (>110’000 CPU cores) 2017?: 1.2 GHz e-infrastructure: >1900 CPU cores + EGI grid (>100’000 CPU cores) Prof. Alexandre Bonvin

National andand EuropeanEuropean infrastructure http://www.uu.nl/nmr 5 6 NMR ‘journey’ Topics

• Why use NMR for structural biology...?

• The very basics

• Multidimensional NMR (intro)

• Resonance assignment (lecture Banci)

• Structure parameters & calculations (lecture Banci)

• NMR relaxation & dynamics

NMR & Structural biology

NATURE | Vol 462DYNAMICS| 19 November 2009 LETTERS

a F helices F helices

Why use NMR.... ? DBD

CBD

apo-CAP CAP-cAMP2 CAP-cAMP2-DNA

bc

Dynamic activation of an allosteric regulatory0.6 protein Tzeng 0.6 S-R & Kalodimos CG Nature (2009) (p.p.m.) (p.p.m.) 



Δ Δ

0.0 0.0

Figure 1 | Conformational states of CAP and effect of cAMP binding binding on the structure of WT-CAP (b) and CAP-S62F (c) as assessed by assessed by NMR. a, Structures of CAP in three ligation states: apo9, chemical shift mapping (Supplementary Fig. S4). Chemical shift difference 10 8 cAMP2-bound , and cAMP2-DNA-bound . The CBD, DBD and hinge (Dv; p.p.m.) values are mapped by continuous-scale colour onto the WT- region are coloured blue, magenta and yellow, respectively. cAMP and DNA CAP-cAMP2 structure. are displayed as grey and green sticks, respectively. b, c, Effect of cAMP

use distinct thermodynamic strategiestointeractstronglyandspecifi- DBD conformation of CAP-S62F-cAMP2, despite being so poorly cally with DNA. populated. Thus, the data indicate that DNA binding to CAP- 17 To better understand the mechanism by which CAP-S62F-cAMP2 S62F-cAMP2 proceeds with a population-shift mechanism . manages to bind strongly to DNA while adopting the DNA-binding Despite adopting predominantly the inactive conformation and inactive conformation, we performed a series of relaxation dispersion only very poorly the active one (,2%), CAP-S62F-cAMP2 binds to experiments (Fig. 3a). These experiments have the capacity to detect DNA as tightly as WT-CAP-cAMP2, driven by a large favourable and characterize low-populated conformations15,16. The results show binding entropy change, as measured experimentally by calorimetry that on binding of cAMP to CAP-S62F, DBD resonances become (Fig. 2a). The amount of surface that becomes buried on binding of broader, indicating the presence of exchange between conformations DNA to WT-CAP-cAMP2 and CAP-S62F-cAMP2 is very similar, on the micro-to-millisecond (ms–ms) time scale. Data fitting (see indicating that the hydrophobic effect is not the source of the large Methods) is indicative of a two-site exchange process, with the popu- entropy difference measured for the formation of the two DNA com- lation of the excited state being ,2% (Fig. 3a). The additional line plexes. To understand the origin of this large favourable change in broadening of NMR signals (Rex; Fig. 3c) caused by conformational entropy, we sought to determine the role of dynamics in the binding exchange between the ground (A) and an excited state (B) depends process. To assess the contribution of protein motions to the con- 18,19 on the relative populations of the exchanging species (pA and pB) and formational entropy of the system , we measured changes in N-H the chemical shift difference between the exchanging species bond order parameters for DNA binding to WT-CAP-cAMP2 and 15,16 15 (Dv) . The absolute N Dv values of DBD residues measured CAP-S62F-cAMP2 (Supplementary Figs 9–13). The order parameter, 2 between the apo-CAP and WT-CAP-cAMP2 (Figs 1b and 3b) clearly S , is a measure of the amplitude of internal motions on the ps–ns correlate with the Dv values between the major and the minor con- timescale and may vary from S2 5 1, for a bond vector having no formations of CAP-S62F-cAMP2 determined by relaxation disper- internal motion, to S2 5 0, for a bond vector rapidly sampling mul- 20 sion measurements (Dvdisp; Fig. 3d). Thus, the data provide strong tiple orientations . evidence that the excited state that DBD transiently populates in DNA binding to WT-CAP-cAMP2 results in widespread increase 2 CAP-S62F-cAMP2 closely resembles the active, DNA-binding com- in S , indicating a global rigidification of the protein (Fig. 2b and patible conformation. Because the affinity of the active DBD con- Supplementary Fig. 13c). Notably, DNA binding to CAP-S62F- formation for DNA (for example, in CAP-cAMP2) is many orders of cAMP2 causes a large number of residues to increase their motions magnitude higher than that of the inactive DBD conformation (for as evidenced by the corresponding decrease in their S2 values (Fig. 2b example in apo-CAP), DNA will preferentially bind to the active and Supplementary Fig. 13c). It is of interest to note that changes in 369 ©2009 Macmillan Publishers Limited. All rights reserved NMR & Structural biology NMR & Structural biology

•Allosteric regulation DYNAMICS Biomolecular interactions • Dynamic interaction between ligand-binding & DNA binding • Even weak and transient complexes can be studied site

Dynamic activation of an allosteric regulatory protein Tzeng S-R & Kalodimos CG Nature (2009)

11 12 NMR & Structural biology NMR & Structural biology MEMBRANE PROTEINS EXCITED STATES •Native like environment • Structural changes due to lipid environment

Shekhar & Kay PNAS 2013 van der Cruijsen, ..... & Baldus PNAS 2013 REPORTS

Fig. 2. Structure of the HET-s(218–289) fibrils. 13 14 The fibril axis is indicated by an arrow. (A)Side view of the five central NMR & Structuralmolecules of the lowest- biology NMR & Structural biology energy structure of the HET-s(218–289) hep- tamer calculated from the NMR restraints. (B) IN-CELL NMR AMYLOIDTop view of the central FIBRILS molecule from (A). b3 REPORTS and b4lieontopof b1andb2, respective- •Study proteins in their native cellular environment Fig. 2. Structure of the ly. A view orthogonal to HET-s(218–289) fibrils. the fibril axis is given in The fibril axis is indicated fig. S7. (C)NMRbundle: • Outermembrane protein in bacterial cell envelop by an arrow. (A)Side superposition on resi- view of the five central dues N226 to G242, molecules of the lowest- N262 to G278 of the energy structure of the 20 lowest-energy struc- HET-s(218–289) hep- tamer calculated from tures of a total of 200 the NMR restraints. (B) calculated HET-s(218– Top view of the central 289) structures. Only molecule from (A). b3 the central molecule of and b4lieontopof the heptamer is shown. b1andb2, respective- (D) Representation of ly. A view orthogonal to the well-defined central the fibril axis is given in core of the fibril (N226 on November 23, 2010 fig. S7. (C)NMRbundle: to G242, N262 to G278). superposition on resi- Hydrophobic residues are colored white, acidic residues red, basic residues to G278, displayed in (F)]. Abbreviations for the amino acid residues are as dues N226 to G242, blue, and others green (lowest-energy structure). (E and F) Schematic rep- follows: A, Ala; C, Cys; D, Asp; E, Glu; F, Phe; G, Gly; H, His; I, Ile; K, Lys; N262 to G278 of the resentations of the two windings in (D): the first winding [N226 to G242, L, Leu; M, Met; N, Asn; P, Pro; Q, Gln; R, Arg; S, Ser; T, Thr; V, Val; W, Trp; 20 lowest-energy struc- displayed in (E)] of the b solenoid is located beneath the second one [N262 and Y, Tyr. tures of a total ofAmyloid 200 Fibrils of the HET-s(218–289) Prion Form a β calculated HET-s(218Solenoid– with a Triangularproteins like filamentous Hydrophobic hemagglutinin Core (34)and Wasmer7. A. Balguerie C. et al .,alEMBO J. 22, 2071 (2003). 31. B. H. Toyama, M. J. S. Kelly, J. D. Gross, J. S. Weissman, 289) structures. Only the P22 tailspike protein (35). In contrast to HET- 8. C. Ritter et al., Nature 435, 844 (2005). Nature 449, 233 (2007). the central moleculeScience of (2008) 9. R. Tycko, Protein Pept. Lett. 13, 229 (2006). 32. A. V. Kajava, J. M. Squire, D. A. D. Parry, in Advances in

the heptamer is shown. s(218–289), these structures are not periodic, but 10. N. Ferguson et al., Proc. Natl. Acad. Sci. U.S.A. 103, Protein Chemistry (Academic Press,Renault New York, 2006), M, ..... & Balduswww.sciencemag.org PNAS 2012 (D) Representation of the geometry of the triangular core is quite 16248 (2006). vol. 73, pp. 1–15. the well-defined central similar. Furthermore, a b-solenoid fold has also 11. C. P. Jaroniec et al., Proc. Natl. Acad. Sci. U.S.A. 101, 33. N. D. Lazo, D. T. Downing, Biochemistry 37, 1731 core of the fibril (N226 been proposed for the prion state of the human 711 (2004). on November 23, 2010 (1998). to G242, N262 to G278). 12. H. Heise et al., Proc. Natl. Acad. Sci. U.S.A. 102, 15871 34. B. Clantin et al., Proc. Natl. Acad. Sci. U.S.A. 101, 6194 prion protein PrP on the basis of modeling and (2005). (2004). Hydrophobic residues are colored white, acidicelectron residues microscopy red, basic residues (36)andfortheyeastprionto G278, displayed in (F)]. Abbreviations for the amino acid residues are as blue, and others green (lowest-energy structure). (E and F) Schematic rep- follows: A, Ala; C, Cys; D,13. Asp; F. Shewmaker, E, Glu; F, R. Phe; B. Wickner, G, Gly; R. H, Tycko, His;Proc. I, Ile; Natl. K, Acad.Lys; 35. S. Steinbacher et al., Proc. Natl. Acad. Sci. U.S.A. 93, Sup35 (37, 38). Sci. U.S.A. 103, 19754 (2006). 10584 (1996). resentations of the two windings in (D): the first winding [N226 to G242, L, Leu; M, Met; N, Asn; P, Pro; Q, Gln; R, Arg; S, Ser; T, Thr; V, Val; W, Trp; The well-organized structure of the HET-s 14. A. T. Petkova, W. M. Yau, R. Tycko, Biochemistry 45, 498 36. C. Govaerts, H. Wille, S. B. Prusiner, F. E. Cohen, 16 displayed in (E)] of the b solenoid is located beneath the second one [N262 and Y, Tyr. (2006). Proc. Natl. Acad. Sci. U.S.A. 101, 8342 (2004). prion fibrils can explain the extraordinarily high Downloaded from 15. A. B. Siemer et al., J. Biomol. NMR 34, 75 (2006). 37. R. Krishnan, S. L. Lindquist, Nature 435, 765 (2005). 7. A. Balguerie et al., EMBO J. 22, 2071 (2003). 31. B. H. Toyama, M. J. S. Kelly, J. D. Gross, J. S. Weissman, proteins like filamentous hemagglutinin (34)andorder in these fibrils, as seen by NMR, as well as 16. A. B. Siemer et al., J. Am. Chem. Soc. 128, 13224 38. A. Kishimoto et al., Biochem. Biophys. Res. Commun. 8. C. Ritter et al., Nature 435, 844 (2005). Nature 449, 233 (2007). the P22 tailspike protein (35). In contrast to HET-the absence of polymorphism caused by different (2006). 315, 739 (2004). 9. R. Tycko, Protein Pept. Lett. 13, 229 (2006). 32. A. V. Kajava, J. M. Squire, D. A. D. Parry, in Advances in

www.sciencemag.org The NMR sample s(218–289), these structures are not periodic,underlying but 10. N. molecular Ferguson et al structures., Proc. Natl. at Acad. physiological Sci. U.S.A. 103, 17. A. Lange,Protein S. Chemistry Luca, M.(Academic Baldus, J. Press, Am. New Chem. York, Soc. 2006),124, 39. D. M. Fowler, A. V. Koulov, W. E. Balch, J. W. Kelly, the geometry of the triangular core is quitepH conditions,16248 because (2006). the specific nature of the 9704vol. (2002). 73, pp. 1–15. Trends Biochem. Sci. 32, 217 (2007). 18. A. Lange et al., Angew. Chem. Int. Ed. 44, 2089 40. We thank C. Ritter for support in producing the samples, similar. Furthermore, a b-solenoid fold has alsointeractions11. C. P. in Jaroniec the fibrilet al., Proc. excludes Natl. Acad. polymorphic Sci. U.S.A. 101, 33. N. D. Lazo, D. T. Downing, Biochemistry 37, 1731 been proposed for the prion state of the human 711 (2004). 2005).(1998). S. Saupe for scientific discussions, and the Swiss National molecular conformations with comparable stabil- 19. N. M. Szeverenyi, M. J. Sullivan, G. E. Maciel, J. Magn. Reson. Science Foundation and the TH-system of the ETH prion protein PrP on the basis of modeling and 12. H. Heise et al., Proc. Natl. Acad. Sci. U.S.A. 102, 15871 34. B. Clantin et al., Proc. Natl. Acad. Sci. U.S.A. 101, 6194 ity. The fibril(2005). structure of HET-s(218–289) ex- 47,(2004). 462 (1982). Zurich for financial support. H.V.M. acknowledges a electron microscopy (36)andfortheyeastprion emplifies13. the F. Shewmaker, well-defined R. B. Wickner,structure R. Tycko,of a functionalProc. Natl. Acad. 20.35. F. Castellani S. Steinbacheret alet., Nature al., Proc.420 Natl., 98 Acad. (2002). Sci. U.S.A. 93, stipend by the European Union (Marie Curie EIF,• FP6) Sup35 (37, 38). Sci. U.S.A. 103, 19754 (2006). 21. D. M.10584 LeMaster, (1996). D. M. Kushlan, J. Am. Chem. Soc. 118, and A.L. by the European Molecular Biology Organizationisotope labeling The well-organized structure of the HET-samyloid14. and A. T. illustrates Petkova, W. M. the Yau, interactions R. Tycko, Biochemistry that can45, 498 36.9255 C. Govaerts,(1996). H. Wille, S. B. Prusiner, F. E. Cohen, (EMBO). The bundle of 20 conformers representing the (2006). Proc. Natl. Acad. Sci. U.S.A. 101, 8342 (2004). 15 13 2 prion fibrils can explain the extraordinarily highstabilize their fold (39). 22. M. Etzkorn, A. Böckmann, A. Lange, M. Baldus, Downloaded from NMR structure has been deposited in the Protein Data– N, C, H 15. A. B. Siemer et al., J. Biomol. NMR 34, 75 (2006). 37. R. Krishnan, S. L. Lindquist, Nature 435, 765 (2005). order in these fibrils, as seen by NMR, as well as J. Am. Chem. Soc. 126, 14746 (2004). Bank with accession code 2RNM, and assignments have References16. A. B. Siemer and Noteset al., J. Am. Chem. Soc. 128, 13224 23.38. Materials A. Kishimoto and methodset al., Biochem. are available Biophys. as Res. supporting Commun. been deposited in the Biological Magnetic Resonance the absence of polymorphism caused by different (2006). 315, 739 (2004). – selective labeling (e.g. only methyl groups) 1. S. B. Prusiner, Science 216, 136 (1982). material on Science Online. Data Bank (ID 11028). 17. A. Lange, S. Luca, M. Baldus, J. Am. Chem. Soc. 124, 39. D. M. Fowler, A. V. Koulov, W. E. Balch, J. W. Kelly, underlying molecular structures at physiological2. G. A. H. Wells et al., Vet. Rec. 121, 419 (1987). 24. G. Cornilescu, F. Delaglio, A. Bax, J. Biomol. NMR 13, 9704 (2002). Trends Biochem. Sci. 32, 217 (2007). pH conditions, because the specific nature of the3. R. G. Will et al., Lancet 347, 921 (1996). 289 (1999). Supporting Online Material 18. A. Lange et al., Angew. Chem. Int. Ed. 44, 2089 40. We thank C. Ritter for support in producing the samples, – recombinant expression in E.coli 4. L. Benkemoun, S. J. Saupe, Fungal Genet. Biol. 43, 789 www.sciencemag.org/cgi/content/full/319/5869/1523/DC1 interactions in the fibrilThe excludes polymorphicvery 2005).basics of NMR25. A. SenS. Saupeet al., forJ. scientific Biol. Chem. discussions,282, 5545 and the (2007). Swiss National Materials and Methods molecular conformations with comparable stabil- (2006).19. N. M. Szeverenyi, M. J. Sullivan, G. E. Maciel, J. Magn. Reson. 26. P. Guntert,Science Foundation C. Mumenthaler, and the K. TH-system Wuthrich, ofJ. the Mol. ETH Biol. ity. The fibril structure of HET-s(218–289) ex-5. U. Baxa,47 T., 462Cassese, (1982). A. V. Kajava, A. C. Steven, in 273Zurich, 283 for (1997). financial support. H.V.M. acknowledges a Figs. S1 to S7 Advances in Protein Chemistry (Academic Press, New York, 27. R. Sabate et al., J. Mol. Biol. 370, 768 (2007). Tables S1 to S3 emplifies the well-defined structure of a functional 20. F. Castellani et al., Nature 420, 98 (2002). stipend by the European Union (Marie Curie EIF, FP6) 2006),21. vol. D. M. 73, LeMaster, pp. 125 D.–180. M. Kushlan, J. Am. Chem. Soc. 118, 28. M. D.and Yoder, A.L. by N. the T. European Keen, F. Molecular Jurnak, Science Biology260 Organization, 1503 References • sample amyloid and illustrates the interactions that can6. A. V. Kajava,9255 (1996).A. C. Steven, in Advances In Protein (1993).(EMBO). The bundle of 20 conformers representing the stabilize their fold (39). Chemistry22. M.(Academic Etzkorn, A. Press, Böckmann, New A. York, Lange, 2006), M. Baldus, vol. 73, 29. R. NelsonNMR structureet al., Nature has been435 deposited, 773 (2005). in the Protein Data 17 October 2007; accepted 6 February 2008 pp. 55–J.96. Am. Chem. Soc. 126, 14746 (2004). 30. M. R.Bank Sawaya with accessionet al., Nature code 2RNM,447, 453 and (2007).assignments have 10.1126/science.1151839 – pure, stable and high concentration References and Notes 23. Materials and methods are available as supporting been deposited in the Biological Magnetic Resonance 1. S. B. Prusiner, Science 216, 136 (1982). material on Science Online. Data Bank (ID 11028). • 500 uL of 0.5 mM solution -> ~ 5 mg per sample 2. G. A. H. Wells et al., Vet. Rec. 121, 419 (1987). 24. G. Cornilescu, F. Delaglio, A. Bax, J. Biomol. NMR 13, 3. R. G. Will et al., Lancet 347, 921 (1996).1526 289 (1999). 14 MARCH 2008Supporting VOL Online 319 MaterialSCIENCE www.sciencemag.org 4. L. Benkemoun, S. J. Saupe, Fungal Genet. Biol. 43, 789 25. A. Sen et al., J. Biol. Chem. 282, 5545 (2007). www.sciencemag.org/cgi/content/full/319/5869/1523/DC1 – preferably low salt, low pH (2006). 26. P. Guntert, C. Mumenthaler, K. Wuthrich, J. Mol. Biol. Materials and Methods 5. U. Baxa, T. Cassese, A. V. Kajava, A. C. Steven, in 273, 283 (1997). Figs. S1 to S7 Advances in Protein Chemistry (Academic Press, New York, 27. R. Sabate et al., J. Mol. Biol. 370, 768 (2007). Tables S1 to S3 – no additives 2006), vol. 73, pp. 125–180. 28. M. D. Yoder, N. T. Keen, F. Jurnak, Science 260, 1503 References 6. A. V. Kajava, A. C. Steven, in Advances In Protein (1993). Chemistry (Academic Press, New York, 2006), vol. 73, 29. R. Nelson et al., Nature 435, 773 (2005). 17 October 2007; accepted 6 February 2008 pp. 55–96. 30. M. R. Sawaya et al., Nature 447, 453 (2007). 10.1126/science.1151839

1526 14 MARCH 2008 VOL 319 SCIENCE www.sciencemag.org 17 18 Nuclear spin Nuclear spin precession

(rad . T-1 . s-1) E = µ B0

19 20 Nuclear spin Nuclear spin & radiowaves

•Nuclear magnetic resonance •NMR a non invasive technique • Only nuclei with non-zero spin quantum number are “magnets” • Low energy radiowaves • Commonly used spins are spin ½ nuclei: 1H, 13C, 15N, 31P etc.

quantum number I = ½ magnetic field strength

-½ β α ΔE = γħB0 B0 β ½ α

gyromagnetic ratio (different for each type of nucleus)

Larmor frequency ν = (γB0)/2π 21 22 Boltzman distribution Net magnetization

1 H m = -½

m = ½

Example - 20.001 spins - Only 1 more spin in lower energy state

24 Pulse Chemical shielding •Radio frequency pulses • Turn on an amplifier for a certain amount of time & certain amount of power (B1 field)

γ B0 B0 ν = (1−σ ) γ B 0 2π ν = 0 (1−σ ) 2π B γ B only rotation 1 ν = 1 B around B1 is γ 1 2π observed ν1 = 2π Local magnetic field is influenced by electronic environment rotating frame: observe with frequency ν0 ==> frequencies of nuclei will differ 25 26 Chemical shift The spectrometer shielding constant γ B ν = 0 (1−σ ) 2π

More conveniently expressed as part per million by comparison to a reference frequency: "# " != 106 ref " ref

27 28 Free induction decay (FID) FID: analogue vs digital

Free Induction Decay (FID)

29 30 Fourier Transform Relaxation

• NMR Relaxation

FT – Restores Boltzmann equilibrium Signal 0

Signal 0

0 25 50 75 100 125 150 175 200 time (ms) 0 5 10 15 20 25 30 35 40 freq. (s-1) • T2-relaxation (transverse relaxation)spin-spin) – disappearance of transverse (x,y) magnetization – contributions from spin-spin and T1 relaxation – 1/T2 ~ signal line-width

FT • T1-relaxation (longitudinal relaxation / spin-lattice) – build-up of longitudinal (z) magnetization – determines how long you should wait for the next experiment

31 32 Relaxation Relaxation •Restoring Boltzmann equilibrium •Restoring Boltzmann equilibrium

• T2 relaxation: disappearance of transverse (x,y) magnetization • T1 relaxation: build-up of longitudinal (z) magnetization

!! 1/T2 ~ signal line-width !! !! T1 determines when to start the next experiment !! 33 34 NMR spectral quality Scalar coupling / J-coupling

• Sensitivity – Signal to noise ratio (S/N) • Sample concentration • Field strength H3C - CH2 - Br • .. 3 • Resolution JHH – Peak separation • Line-width (T2) • Field strength • ..

35 Key concepts NMR

• Nuclear magnetic resonance • In a magnetic field magnetic nuclei will resonate with a specific frequency • FT-NMR Multidimensional NMR • Pulse, rotating frame, FID • Chemical shift • Electronic environment influences local magnetic field -> frequency • NMR relaxation • T1 & T2 • J-coupling 38 Why multidimensional NMR 2D NMR

•Resolve overlapping signals • observe signals from different nuclei separately •Correlate chemical shifts of different nuclei • needed for assignment of the chemical shifts

•Encoding structural and/or dynamical information • enables structure determination • enables study of dynamics

39 40 3D NMR nD experiment direct dimension 1D

t1 1 FID of N points preparation acquisition indirect dimensions

2D t1 N FIDs of N points t2 preparation evolution mixing acquisition

3D NxN FIDs of N points t1 t2 t3 preparation evolution mixing evolution mixing acquisition 41 42 Encoding information Magnetization transfer dipole-dipoleprecession interaction

• mixing/magnetization transfer E = µ B0 precession • Magnetic dipole interaction (NOE)

precession precession E = µ B – Nuclear Overhauser Effect 0 – through space – distance dependent (1/r6) E = B E = B µ 0 ???? µ 0 – NOESY -> distance restraints

• J-coupling interaction – through 3-4 bonds max. proton A proton B – chemical connectivities – assignment spin-spin interactions – also conformation dependent

43 homonuclear NMR 2D NOESY NOESY magnetic dipole • Uses dipolar interaction (NOE) to transfer t1 tm t2 interaction magnetization between protons crosspeak intensity ~1/r6 6 FID up to 5 Å – cross-peak intensity ~ 1/r – distances (r) < 5Å

COSY t1 t2 J-coupling interaction transfer over one J-coupling, i.e. FID max. 3-4 bonds diagonal HN

HN TOCSY t J-coupling interaction 1 t2 transfer over several J- mlev couplings, i.e. multiple steps cross-peak FID over max. 3-4 bonds

44 1J- and 2J-couplings in proteins 45 46 Homonuclear scalar coupling 2D COSY & TOCSY

2D COSY 2D TOCSY

Hβ Hβ

Hα Hα 3 JHαHβ ~ 3-12 Hz

HN HN 3 JHNHα ~ 2-10 Hz

precession 47 48 precession

E = B ~Å µ 0 E = B homonuclear NMR µ 0 heteronuclearprecession NMR precession

NOESY proton B t2 proton A t1 tm E = B E = B FID µ 0 µ 0

A A (ωA) A A (ωA) (F1,F2) = ωA, ωA

B B (ωB) (F1,F2) = ωA, ωB 1H 15N ωA ωB – measure frequencies of different nuclei; e.g. 1H, 15N, 13C – no diagonal peaks Diagonal – mixing not possible using NOE, only via J F1

ωA Cross-peak

F2 1J- and 2J-couplings in proteins 49 50 J coupling constants 15N HSQC – Backbone HN

– Side-chain NH and NH2

1JCbCg = 35 Hz

1JCbHb = 130 Hz

1JCaCb = 35 Hz

1 JCaC’ = 1JNC’ = 1JCaN = 55 Hz -15 Hz -11 Hz

1JCaHa = 140 Hz

1JHN = -92 Hz 2JCaN = 7 Hz 2JNC’ < 1 Hz

51 52 1H-15N HSQC: ‘protein fingerprint’ 1H-15N HSQC: ‘protein fingerprint’ 53 Key concepts multidimensional NMR • Resolve overlapping signals • Mixing/magnetization transfer

• NOESY, TOCSY, COSY Relaxation & dynamics • HSQC

• 3D NOESY-HSQC, 3D TOCSY-HSQC • Triple resonance

55 56 NMR relaxation Relaxation is caused by dynamics • Fluctuating magnetic fields • Return to equilibrium – Overall tumbling and local motions cause the local magnetic – Spin-lattice relaxation fields to fluctuate in time

– Longitudinal relaxation → T1 B0 relaxation B1 • Return to z-axis

– Spin-spin relaxation – Transversal relaxation → T2 B0 relaxation B0 • Dephasing of magnetization in the x/y B1 plane + return to z-axis

Bloc 57 58 Relaxation is caused by dynamics Local fluctuating magnetic fields • Fluctuating magnetic fields – Overall tumbling and local motions cause the local • Bloc(t) = Bloc[iso] + Bloc(t)[aniso] magnetic fields to fluctuate in time – Isotropic part is not time dependent – Bloc(t) is thus time dependent • chemical shift

– If Bloc(t) is fluctuating with frequency components near ω0 • J-coupling then transitions may be induced that bring the spins back – Only the anisotropic part is time dependent to equilibrium • chemical shift anisotropy (CSA) Molecular Motion and Relaxation – The efficiency of relaxation also depends on the amplitude • dipolar interaction (DD)

Interaction between 2of dipoles Bloc(t) Stationary random function, Bloc(t)

B 0 ez anisotropic 2 r 1 x 13 e C r12 • interactions (t) 0 t B0

ey loc B

ex CSA dipole-dipole 2 = 0 ≠ 0

3 2 E12 = (γ1γ2/r12)[I1•I2–3(I1•r12)(I2•r12)/r12] = γ2I2•Bloc What are the frequency components of Bloc(t)?

Bloc(t) = Σ An sin(nπt/T) (Fourier series) Molecular motions → time-varying local field: Bloc(t) n=1 = 1/2 Σ If Bloc(t) is fluctuating with frequency components near ω0, loc n=1 n then transitions may be induced that will bring the spins How is the total power distributed over ? back to equilibrium. The efficiency of relaxation also ω This is given by the Spectral Density, J(ω) depends on the amplitude of Bloc(t). 59 60 2 J(ω)∆ω = 1/2 Σ < n /T < + Local fluctuating ω magneticπ ω ∆ω fields Components of the local field

β • Bloc(t)•exy • Bloc(t) = Bloc[iso] + Bloc(t)[aniso] non-adiabatic – Transverse fluctuating fields – Isotropic part is not time dependent transitions – Non-adiabatic: exchange of energy between α • chemical shift the spin-system and the lattice [environment] • J-coupling – Only the anisotropic part is time dependent • chemical shift anisotropy (CSA) α • dipolar interaction (DD) transitions between states restore • Only Bloc(t)[aniso] can cause relaxation Boltzman equilibrium β – Transverse fluctuating fields: Bloc(t)•ex + Bloc(t)•ey – Longitudinal fluctuating fields: Bloc(t)•ez

T1 relaxation 61 62 Components of the local field Components of the local field

β • Bloc(t)•ez Bloc(t)•ez • Bloc(t)•exy non-adiabatic – Longitudinal fluctuating fields B – Transverse fluctuating fields transitions α – Adiabatic: NO exchange of energy 0 – Non-adiabatic: exchange of energy between the spin-system and the between the spin-system and the lattice lattice adiabatic [environment] The Spectral Density Function variations of – Effective field along z-axis varies ω0 • frequency ω0 varies variations of ω0 Bloc(t)•ez: frequency ω0 – Heisenberg’s uncertainty relationship: Time correlation function,varies due to C(localτ ) changes in B0 • shorter lifetimes ⇔ broadening of energy C(τ) = = levels loc loc Bloc(t)•elocxy: transitionsloc between states reduce phase coherence 1 2 C(0) = 0.8 T2 relaxation 0.6 C(τ) = exp(–τ/τ ) C(τ) c 0.4 2 63 0.2 C( ) = = 0 64 Correlation function Spectral density functionτ Statistical Description of RandomRandom ProcessesProcesses τc

• Describes the Stationary random function, B (t) Stationary random function, Blocloc(t) • Frequencies of the random fluctuating fields fluctuating magnetic Spectral density function, J(ω) – Spectral density function J(ω) is the Fourier transform of the x fields x (t)> == 00 e e loc

^ loc ^ • • correlation function C(τ) (t) (t) J( ) = d cos( ) C( ) – correlation function 0 tt ω τ ωτ τ loc loc B B 22 – 1e-08J(ω) describes if a certain frequency can induce relaxation and C(τ) decays (t)> ≠ 00 0 5 ns 10 ns whether it is efficient 20 ns exponentially with a J(0) = τ J(ω 8e-09) c characteristic time τc Time correlation function,function, C(C(ττ)) 2 2 6e-09 J(ω) = τc/(1+ω τc ) C(τ) = )> == <)> J(ω)

1 1 22 4e-09 C(0) == (t)> 0.8 τc 0.6 5 ns 0.6 C(ττ)) == exp(exp(––ττ//ττc)) C(τ) c 2e-09 10 ns 0.4 log(ω) 2 20 ns 0.2 C(∞) = 2= 0 C( ) = = 0 1/τc τ 0 τ τ 0 1e+08 2e+08 3e+08 4e+08 5e+08 6e+08 7e+08ω 8e+08 τc The Spectral Density Function

Time correlation function, C(τ)

C(τ) = =

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17 Frans Mulder Utrecht course 2007

Chapter 8: Experimental NMR relaxation methods II

The “standard set” of experiments to measure picosecond-nanosecond timescale dynamics in proteins:

15 N T1 measures decay of Nz

15 15 N T2 or N T1! measures decay of Nx,y

15N{1H} NOE measures the steady-state nitrogen magnetization in the absence and presence of 1H saturation.

69 70 Frans Mulder Utrecht course 2007

ProteinChapter 8 :backbone Experimental NMR dynamics relaxation methods II Protein backbone dynamics

The• “15standardN relaxation set” of to experiments describe ps-ns to measuredynamics • 15N relaxation to describe ps-ns dynamics picosecond-nanosecond timescale dynamics in proteins. – R1: longitudinal relaxation rate – R1: longitudinal relaxation rate The relationship between the rates, interaction – R2: transversal relaxation rate – R2: transversal relaxation rate constants and spectral densities: – hetero-nuclear NOE: {1H}-15N – hetero-nuclear NOE: {1H}-15N

• Measured as a 2D 1H-15N spectrum

– R1,R2: Repeat experiment several times with increasing relaxation- delay – Fit the signal intensity as a function of the relaxation delay

• I0. exp(-Rt) dipole interaction – {1H}-15N NOE: Intensity ratio between saturated and non-saturated chemical shift anisotropy experiment

Internal Motions in Macromolecules

1 71 6 Time correlation function, C(τ) Spectral density72 function, J(ω) Relaxation rates Lipari-SzaboC(τ) = /

1 effective logC(τ) internal motion, τinte J(ω) S2 overall rotation, τc

τ log(ω) 1

– Overall and local motion are considered to be 2 2 2 2 2 2 Time scale separation ( τ << τ ): J(ω) = S τc/(1+ω τc ) + (1–S )τe/(1+ω τe ) uncorrelated int c τe = 1/(1/τc + 1/τint) 2 – S F( =τ )order-parameter = F(τ) – int + int No internal motion: S2 = 1 fast slow Isotropic internal motion: S2 = 0

= < < (F(0)–int)(F(τ)–int)>int>rot + The order parameter corresponds to < intint >rot the residual anisotropy on the fast timescale: S ~ 2 2 int C(τ) = (1–S )Cint(τ) + S Crot(τ) Dynamics of Partly Unstructured Protein Dynamics of Partly Unstructured Protein 2835 2835

D26 (48), ATF-2 transactivation domainD26 (48),(49)), ATF-2 positive transactivationFitting of domain the relaxation (49)),positive data at a highFitting protein of concentra- the relaxation data at a high protein concentra- values, even up to 0.4, are regularlyvalues, found even (fibronectin up to 0.4,tion are using regularly the LS found model-free (fibronectin approach ledtion to using artificially the LS high model-free approach led to artificially high 2 2 binding protein (50), pro-peptide of subtilisinbinding (51), protein unfolded (50), pro-peptideorder parameters of subtilisin (Save (51),0 unfolded:93) and longorder internal parameters correlation (Save 0:93) and long internal correlation ubiquitin (52)). This indicates that theubiquitin positive (52)). hetNOEs This indicatestimes (. that400 the ps) positive for some¼ hetNOEs of the residuestimes in ( the.400 structured ps) for some¼ of the residues in the structured may, rather, be a result of an inherentmay, property rather, beof thea resultpart. of an These inherent features property are clearly of the relatedpart. to These the observed features are clearly related to the observed individual nature of the amino acidsindividual along the sequence. nature of theaggregation amino acids (26), along which the is sequence. not taken intoaggregation account by (26), the LSwhich is not taken into account by the LS Indeed, a high percentage of large and chargedIndeed, side a high chains percentage is model of large and and is charged only implicitly side chains parameterized is model in and an increasedis only implicitly parameterized in an increased present in the N-subdomain of PX, and thepresent stretch in the(470–498) N-subdomainoverall of PX, correlation and the stretch time (470–498)(8.9 ns). The relaxationoverall correlation rates at the time (8.9 ns). The relaxation rates at the that has positive hetNOE values lacksthat both has Ala positive and Gly hetNOElow values protein lacks concentration both Ala andcould, Gly however,low be protein analyzed concentration with could, however, be analyzed with residues, which evidently slightly restrictsresidues, the amplitudes which evidently of the slightly model-free restricts approach the amplitudes (Fig. 4). of For thethe structured model-free part, approach an (Fig. 4). For the structured part, an Introduction fast motions. The region that containsfast a series motions. of relatively The regionisotropic that contains diffusion a series model, of relatively using a tc isotropicof 7.3 ns, diffusion was con- model, using a tc of 7.3 ns, was con- small residues (A-504, S-505, N-506,small A-507, residues S-508) (A-504, does S-505,sidered N-506, acceptable A-507, since S-508)Dpar/D doesper was foundsidered to acceptablebe only 1.15. sinceXFMM
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τ S c = 7.3 ns rotational correlation time tc. Isotropic rotational correlation time tc. Isotropic rotational diffusion with a correlation rotational diffusion with a correlation domain motions time of 7.3 ns was assumed for the time of 7.3 ns was assumed for the structured part (519–568), whereas a structured part (519–568), whereasloop a motions local diffusion model was used for local diffusion model was used for residues in the unstructured part. (B) residues in theside unstructured chain motions part. (B) 2 2 Product of order parameters for fast (Sf ) Product of order parameters for fast (Sf ) 2 2 and slow (Ss ) internal motions. An protein dynamics and slow (Ss ) internal motions. An 2 bond vibrations overall2 tumbling enzyme catalysis; allosterics extended model including Ss was only extended model including Ss was only used for T-567 (S2 0:79) and N-568 used for T-567 (S2 0:79) and N-568 s ¼ s ¼ (S2 0:68). (C) Local correlation time (S2 0:68). (C) Local correlation time s ¼ fs s ¼ ps ns Ms ms s (te) for internal motion. (D) Rex contri- (te) for internal motion. (D) Rex contri- bution to the R2 relaxation rates. bution to the R2 relaxation rates. R1,R2,NOE relaxation dispersion real time NMR

NMR J-couplings H/D exchange RDC

Biophysical Journal 93(8) 2830–2844'JHVSF
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17

75 76 Conformational exchange Conformational exchange

• Causes line-broadening of the signals

–R2,eff = R2 + Rex 77 78 H/D exchange Key concepts relaxation

• time scales

Lac headpiece • fluctuating magnetic fields Kalodimos et al. Science • correlation function, spectral density function

• molecular motions • rotational correlation time (ns)

protected in the free state • fast time scale flexibility (ps-ns) protected only in the DNA-bound state • slow time scale (μs-ms): conformational exchange

The End

Thank you for your attention!