NMR-spectroscopy of proteins in solution. Peter Schmieder

Transcription

1 NMR-spectroscopy of proteins in solution

2 Basic aspects of NMR-Spektroskopie

3 Basic aspects of NMR-spectroscopy 3/84 Prerequisite for NMR-spectroscopy is a nuclear spin that can be thought of as a mixture of a gyroscope and a little magnet

4 Basic aspects of NMR-spectroscopy 4/84 A gyroscope has an angular momentum that is firmly oriented in space

5 Basic aspects of NMR-spectroscopy 5/84 Orientation of the little nuclear magnet is prevented by its gyroscopic properties, the nucleus starts a precessional motion.

6 Basic aspects of NMR-spectroscopy 6/84 The resonance frequency of the spins (here the proton spins) is determined by the strength of the magnetic field B 0 [Tesla] [MHz]

7 Basic aspects of NMR-spectroscopy 7/84 But we are dealing with quantum mechanical phenomenon, in the case that we are interested in (high resolution NMR) there are two possible orientations ( and ) for the gyroscope/magnet=spin E = ћ B 0

8 Basic aspects of NMR-spectroscopy 8/84 We will then have a Boltzmann-distribution N /N = exp(- E/kT) = exp(- h B 0 / 2 kt) At 600 MHz frequency we get N /N = This extremely small difference is the reason for the low sensitivity of NMR spectroscopy

9 Basic aspects of NMR-spectroscopy 9/84 Without an external magnetic field all orientations are equal and the spins are randomly oriented

10 Basic aspects of NMR-spectroscopy 10/84 With an external magnetic field the resulting orientation yields a small magnetic moment, a small macroscopic magnet, the axis is called the z-axis. This magnetic moment is quite small and it is not easy to extract frequencies from it.

11 Basic aspects of NMR-spectroscopy 11/84 Therefore RF pulses are used to rotate the spins, they are tunes such that each spin rotes by 90.

12 Das rotierende Koordinatensystem 12/84 This results in a rotation of the magnetic moment into the x,yplane, no z-magnetization is left

13 Basic aspects of NMR-spectroscopy 13/84 After the RF pulse the precession is still going on and induces a current in the detection coil which is then digitized

14 Basic aspects of NMR-spectroscopy 14/84 The detected time signal (the FID) is converted into a frequency spectrum by Fourier transform FT

15 Basic aspects of NMR-spectroscopy 15/84 Thus the simplest NMR experiment consists of the application of an RF pulse and the detection of an FID. To get better signal-to-noise it is repeated several times.

16 Basic aspects of NMR-spectroscopy 16/84 Magnetic properties of some NMR nuclei Kern I natürliche Häufigkeit gyromagnetisches Verhältnis 1 H 1/ % C % 0 13 C 1/ % N % N 1/ % F 1/2 100 % P 1/2 100 % Cd 1/ % -5.96

17 NMR-Parameter (1)

18 NMR-parameter 18/84 Chemical Shift The electrons around the nucleus shield it from the external magnetic field, the more electrons there are the less field reaches the nucleus B eff = (1 - ) B 0 = (1 - ) B 0 = ( ref ) / 0 x 10 6 = ( ref ) x 10 6

19 NMR-parameter 19/84 Chemical shift ArOH -CHO olefinic ROH RNH 2 aromatic CH -O n acetylenic CH nch -N CH 2 CH 3 -C n -CO CH -Ar 3 CH -C=C 3 TMS 1 ( H)/ppm

20 NMR-parameter 20/84 Assignment means to find the nucleus to each line in the spectrum OHs ppm

21 NMR-parameter 21/84 Scalar or J-coupling The electrons surrounding the nuclei do also establish an interaction between the nuclei

22 NMR-parameter 22/84 RCH - CH 2 3 Scalar or J- coupling J = 8 Hz

23 NMR-spectroscopy of proteins (1)

24 NMR-spectroscopy of proteins 24/84 The principal problem of NMR-spectra of proteins result from the fact that a protein is a polymer, i.e. a repetition of identical units. We still get one line per atom but contrary to e.g. typical natural products all atoms are in similar environments

25 NMR-spectroscopy of proteins 25/84 (-)-Menthol ppm

26 NMR-spectroscopy of proteins 26/84 cyclic hexapeptid aromatic protons H N -protons H -protons aliphatic protons Indol-H N ppm

27 NMR-spectroscopy of proteins 27/84 1 H NMR-spectrum of a protein Aromaten aromatic Aromaten Aliphaten Aliphaten aliphatic H N H N H H CH CH 3 3

28 NMR-spectroscopy of proteins 28/84 Differences in the chemical shifts result from defined elements of secondary structure

29 NMR-spectroscopy of proteins 29/84 1 H NMR-spectrum of an unfolded protein ppm

30 DO2 HO2 NMR-spectroscopy of proteins 30/84 13 C NMR-spectrum of a protein

31 DO2 HO2 NMR-spectroscopy of proteins 31/84 15 N NMR-spectrum of a protein

32 DO2 HO2 NMR-spectroscopy of proteins 32/84 NMR-spectra of proteins are thus not that much different from spectra of small molecules and show similar features (chemical shift, j-coupling etc.). But because of the large number of nuclei contributing to the spectrum, the fact that they are polymers and their size, the spectra are just far more crowded than that of smaller molecules and more complicated to assign. One-dimensional spectra are therefore not sufficient and we need to use multidimensional ones.

33 Multidimensional NMR-spectroscopy

34 Multidimensional NMR-spectroscopy 34/84 The two most important advantages of multidimensional spectra are: Improved resolution: The signals are distributed over an area (2D) or a space (3D, 4D) rather than a line (1D) Transfer of magnetization: The resulting signals indicate the interaction between nuclei. These can be interactions via bonds (J-coupling) or through space (NOE) but for an assignment mainly experiments utilizing scalar coupling are used. Taken together this enables an easier assignment and interpretation of spectra and a more straightforward extraction of information.

35 Multidimensional NMR-spectroscopy 35/84 While a 1D-NMR experiment consists of a preparation period in which the nuclei relax and are sometimes prepared for detection by special pulse sequences, 2D-NMR experiments usually consist of more pulses contain two new elements: evolution time and mixing time preparation evolution mixing detection (t 1 ) (t 2 ) evolution time: creation of a further frequency axis by indirect detection mixing time: transfer of magnetization via spinspin interactions

36 Multidimensional NMR-spectroscopy 36/84 Evolution time The indirect detection of the frequency is performed by a systematic variation of a time interval thereby creating a twodimensional surface of data points...

37 Multidimensional NMR-spectroscopy 37/84... a two-dimensional FID

38 Multidimensional NMR-spectroscopy 38/84 a first FT results in an interferogram

39 Multidimensional NMR-spectroscopy 39/84 a second FT yields the two-dimensional spectrum

40 Multidimensional NMR-spectroscopy 40/84 To analyze the spectra they are viewed as contour-plots, in which intensities are display as contour levels Note: There are many different spectra possible now, not just one per type of nucleus!!

41 Multidimensional NMR-spectroscopy 41/84 homonuclear spectra Here the transfer of magnetization takes place between nuclei of the same type. Both frequency axes then show the same type of chemical shift. If there is a transfer this results in two different chemical shifts in both dimensions: Crosspeak If there is no transfer the chemical shift in both dimensions is identical: Diagonalpeak Diagonalpeak Crosspeak

42 Multidimensional NMR-spectroscopy 42/84 heteronuclear spectra Here the transfer takes place between different types of nuclei und thus both axes exhibit different chemical shifts. If there is no transfer then there will be no peak, but if there is, the peak appears at the intersection of the chemical shifts of the two nuclei involved.

43 Multidimensional NMR-spectroscopy 43/84 3D-NMR

44 Multidimensional NMR-spectroscopy 44/84 3D-NMR

45 NMR-spectroscopy of proteins (2)

46 NMR-spectroscopy of proteins 46/84 H, N-HSQC 1 15 H, C-HSQC H, 15 N and 1 H, 13 C HSQC-spectra of proteins (schematic) 1 H, 15 N HSQC 1 H, 13 C HSQC

47 NMR-spectroscopy of proteins 47/84 As with all other molecules the first step of an extraction of information is the assignment of resonances but we have that polymer-problem. This problem can be solved by using sequence specific assignment

48 NMR-spectroscopy of proteins 48/84 There are several strategies to obtain a sequence specific assignment, either based on homonuclear spectra (NOESY,TOCSY) or triple resonance experiments. The goal always is an assignment of as many resonances as possible SH3 from - spectrin Assignment

49 NMR-spectroscopy of proteins 49/84 1 H, 15 N HSQC-spectra are fingerprints of proteins and assigned HSQCs are the prerequisite for every NMR analysis (relaxation, interaction, structural parameters)

50 NMR-Parameter (2)

51 NMR-parameter 51/84 Dipol-Dipol Interaction This mutual interaction is working through-space and results in an interaction network of spins. The size of the dipol-dipol coupling constant is much larger than that a scalar coupling and distant dependent r D HH = Hz for r = 200 pm

52 NMR-parameter 52/84 While the dipol-dipol coupling constant is only dependent on the distance between the spins the size of the interaction does also depend on the orientation between the vector between the spins and the magnetic field. D ~ (3 cos 2 jk 1)

53 NMR-parameter 53/84 Chemical shift anisotropy (CSA) When we first discussed chemical shift we assumed that the electrons would surround the nucleus spherically. This is usually not the case and the electrons create different additional field in each direction

54 NMR-parameter 54/84 In a solid this results in a complicated pattern called a powder spectrum. In solution, the rapid reorientation of all molecules averages the effect of CSA and results in a single isotropic chemical shift

55 Exchange and NMR-spectroscopy 55/84 D ~ (3 cos 2 jk 1) 0 π dθjk sinθ jk (3 cos 2 θ jk -1) = 0 The same averaging takes places for the dipol-dipol-interaction. There is a distribution of orientations with many possibilities perpendicular to the field and only two with the field. Adding up all interactions leads to their cancelation.

56 NMR-parameter 56/84 Relaxation Relaxation is the process during which the nuclei get rid of the energy transferred to the system by the RF pulse Contrary to other types of spectroscopy there are not many ways to create the necessary fluctuating magnetic field, except the movement of the molecule itself. Thats why NMR-states are fairly long-lived! If the dynamics of the molecule are the reason for relaxation, then we can learn something about the dynamics from analyzing relaxation

57 NMR-parameter 57/84 The movements can be within the molecule are of the molecule as a whole. They will be on different time scales in the range between picoseconds and milliseconds, sometimes even longer (seconds)

58 NMR-parameter 58/84 Larger Molecules move differently from smaller ones, they have other correlation times c. That s why they will have different relaxation properties

59 NMR-parameter 59/84 A description of the dynamics of even a simple molecule can be quite complicated since there are many different motions. This is usually attempted using the concept of spectral densities which can be thought of an estimate which frequencies are provided by the molecule. J( ) = c 1 + ( c ) 2 The overall correlation time of proteins is in the range of several nanoseconds

60 NMR-parameter 60/84 Dipolar coupling (DD) and Chemical Shift Anisotropy (CSA) are the main sources of relaxation. Even though they are averaged out for the sum of all molecules, locally they are active in creating fluctuating fields via the reorientation of the molecules DD CSA

61 NMR-parameter 61/84 Relaxation is described phenomenologically by two processes. The term longitudinal relaxation is used to describe the return of the changed occupation of the energy levels to their thermal equilibrium, i.e. the return of the z-component of the magnetization to its original position. The term transverse relaxation is used to describe the disappearance of the coherence between spins and thus any measurable magnetization.

62 NMR-parameter 62/84 Both can be described using exponential functions with characteristic time constants which are called longitudinal relaxation time T 1 and a transvers relaxation time T 2. Starting point of every experiment is the sample in thermal equilibrium sitting in the magnetic field.

63 NMR-parameter 63/84 Pulses disturb that equilibrium, a 90 -pulse turns the net magnetization in the x,y-plane, a 180 pulse inverts it. A 90 pulse also creates a coherent relationship between spins

64 NMR-parameter 64/84 longitudinal relaxation (T 1 ) M z (t) = M z (t 0 ) [ 1 2 exp(-t/t 1 )]

65 NMR-parameter 65/84 transverse relaxation (T 2 ) M x (t) = M x (t 0 ) exp(-t/t 2 ) So longitudinal relaxation describes the return to equilibrium by transitions caused by local fields while transverse relaxation the loss of synchronization of identical spins due to different frequencies caused by local fields

66 NMR-parameter 66/84 T 2 is necessarily always shorter than T 1, it determines the line width while T 1 determines how long the time between scans needs to be. Different situations are possible, T 2 can be long, the signal will then decay slowly, this will be the case for small molecules. Or T 2 is short, then the signal will have decayed long before the equilibrium has been reestablished. This will be the case for large molecules

67 NMR-parameter 67/84 Simple experiments can be used to determine the time constants for small molecules: k 180 n 90 T 1 is determined using an inversion recovery experiment using a series of 1Ds. T 2 is determined using a CPMG -experiment using also a series of 1Ds

68 NMR-parameter 68/84 Because of the dense network of spins the relaxation times often depend on complicated interactions with many spins and are thus difficult to analyse, in particular in proteins. =H-N There is, however, one good possibility: the H-N pair of spins. Because both spins are so close together the relaxation of the nitrogen is mainly dictated by their interaction and can be described assuming simple motional models.

69 NMR-parameter 69/84 The formulas are based on the Redfield relaxation theory and can be used together with a further experiment, the heteronuclear NOE, to test the suitability of certain simple motional models. c J( ) = 1 + ( c ) 2

70 NMR-parameter 70/84 A determination of the relaxations times of individual nitrogens in a protein is not possible using 1Ds, so the experiments are embedded in the HSQC-experiment and a series of 2Ds is recorded. The intensity of the peaks in the HSQC changes according to the relaxation time with can be determined using exponential fits.

71 NMR-parameter 71/84 A typical display of the results for a folded protein shows almost uniform but nevertheless fluctuation values for the relaxation parameters. The N- and C-terminus are often more flexible as can be easily seen from all relaxation parameters

72 NMR-parameter 72/84 If proteins were rigid entities the relaxation times would have to be the same for all H-N pairs since a single correlation time c would determine the movement of the spins. This is, however, not the case and the data are analyzed using the Lipari-Szabo approach, which introduces a second, local correlation time weighted J( ) = S 2 c (1-S 2 ) + -1 = -1 c + -1 e 1 + ( c ) ( ) 2 S is called the generalized order parameter that gives a measure for the rigidity of the region of the H-N spin pair. If S 2 = 1 for all spin pairs the molecule the molecule is completely rigid.

73 NMR-parameter 73/84 This is rarely the case and the typical values for a folded protein of 60 amino acids are S 2 = 0.8 and values for c = 5 nsec and e = 0.05 nsec 14 C 30 C An extended formula with two instead of one extra correlation times has also been proposed and several software packages for a full analysis using an extended set of motional models are available.

74 Exchange and NMR

75 Exchange and NMR-spectroscopy 75/84 Exchange NMR-spectroscopy is well suited to observe and analyze exchange phaenomena (either chemical or conformational exchange or exchange in protein-ligand interactions) at atomic resolution. In favorable cases kinetic constants can be extracted, an influence of exchange phenomena on the appearance of spectra is always visible. O H N CH 3 CH 3 O H N CH 3 CH 3 A k k B

76 Exchange and NMR-spectroscopy 76/84 If we consider a simple two-site exchange then there are two possible situations (A and B) that give rise to different chemical shifts. Of importance is the difference in chemical shift for the two situations: = A - B A B A k < /2 k > /2 A B A B A A B A B A A B A k decreases ms SLOW INTERMEDIATE EXCHANGE s FAST INTERMEDIATE EXCHANGE k k increases A 0 t 1 ms B Lineshape Perturbations

77 Exchange and NMR-spectroscopy 77/84 If the exchange is extremely slow we will obtain two signals, if it is extremely fast, one averaged signal of similar lineshape as for the two line in the other extreme. Inbetween we find a peculiar effect that leads to motional broadening: the detected frequency changes depending on the state, if many molecules are averaged this leads to an increased apparent decay and thus to broader lines. A B A B A t t t

78 Exchange and NMR-spectroscopy 78/ k = 0.2 x 10-3 s s k = 1.0 x 10-3 s s -1 cross-over 3-1 k = 6.3 x s s -1 k = x 10-3 s s -1 k = 50 x s s -1 t -3 khz 0 +3 khz

79 Exchange and NMR-spectroscopy 79/84 O CH 3 O CH 3 N N H CH 3 H CH 3 Note that considerable temperature differences may be necessary to go from fast exchange to slow exchange JACS 106, 2451 (1984)

80 Exchange and NMR-spectroscopy 80/84 slow fast In two-dimensional spectra, where the transfer of magentisation via scalar coupling takes a certain amount of time, the apparent faster decay will lead to signal attenuation, in extreme cases to the disapperance of peaks

81 Exchange and NMR-spectroscopy 81/84 If the two states are of different energy and thus the rates different, fast exchange will not lead to a centered average but the signal will be shifted towards the position of the higher populated state. B Energy k' k A SLOW EXCHANGE A B FAST EXCHANGE

82 Exchange and NMR-spectroscopy 82/84 An example is the interface between 2m and the heavy chain in an MHC-I complex. Peaks in 2 m shift and show weak intensity with different peptides and subtypes 33S 57S 52S 53D 61S 3R 64L 65L 4T 62F 2Q Comparison of the spectra of 2 m B2709/B2705 Beerbaum M. et al. (2013) J. Biomolec. NMR 57,

83 Exchange and NMR-spectroscopy 83/84 D524 L479 Note that depending A579 L474 V468 A526 M521 on the difference in shift between the endpoints of the A513 R508 K581 W522 A N-DnaGC 600 MHz, 297 K 325 M + SSB-ct-peptide 15 N-SOFAST-HMQC no peptide titration (no peptide and 300 M peptide) the signal of the middle concentration A peptide 300 M peptide (100 M peptide) is visible or not

84 84/84 That s it