Biochemistry 530 NMR Theory and Practice Gabriele Varani Department of Biochemistry and Department of Chemistry University of Washington
Lecturer: Gabriele Varani Biochemistry and Chemistry Room J479 and Bagley 63 Phone: 543 7113 Email: varani@chem.washington.edu Office Hours by arrangement Lecture 1: Basic Principles of NMR Lecture 2: 2D NMR Lecture 3: NMR assignments/structure determination Lecture 4: 2D and 3D heteronuclear NMR
Recommended NMR Textbooks Derome, A. E. (1987) Modern NMR Techniques for Chemistry Research, Pergamon Press Wüthrich, K. (1986) NMR of Proteins and Nucleic Acids, John Wiley and Sons Roberts, G. C. K. (1993) NMR of Macromolecules: A Practical Approach, Oxford Univ. Press Cavanagh, J., et al. (1996) Protein NMR Spectroscopy, Principles and Practice, Academic Press Evans, J. N. S. (1999) Biomolecular NMR Spectroscopy, Oxford Univ. Press
Useful websites http://www.ch.ic.ac.uk/local/organic/nmr.html NMR Spectroscopy. Principles and Application. Six second year lectures given at Imperial College, U.K. http://uic.unl.edu/nmr_theory.html http://www.shu.ac.uk/schools/sci/chem/tutorials/molspec/n mr1.htm Theoretical principles of NMR Courtesy of Sheffield Hallam University, U.K. http://www.nature.com/nsb/wilma/v4n10.875828203.html links to various NMR and structural biology web sites simulation and analysis software; NMR research groups, etc.
NMR spectrum of a protein: hundreds of individual resonances resolved 1D spectrum amides NH 2 H a Side chain CH 2 Side chain CH 3
Fourier-transform NMR (Ernst, 1965) Signal - FID (time domain) Spectrum (frequency domain)
2D NMR spectrum of a protein 2D projection representation 2D contour representation
1 ( 13 C Methyl ) [ppm] 13 C methyl HMQC on selectively labeled protein RRM1 RRM2 ω 2 ( 1 H Methyl ) [ppm]
1 ( 13 C Methyl ) [ppm] 13 C methyl HMQC on protein-rna complex RRM1 RRM2 ω 2 ( 1 H Methyl ) [ppm]
1 ( 13 C Methyl ) [ppm] 13 C methyl HMQC on 300 kda complex I222d1 Rna14 V217g1 I228d1 I313d1 V247g2 RRM1 RRM2 Rna15 V185g2 V300g2 V175g2 V297g2 L274d1 L205d2 ω 2 ( 1 H Methyl ) [ppm]
Define and identify protein interaction sites in large complexes Rna14 Hrp1 180 RNA Rna15
Ultrafast acquisition of NMR spectra Standard (10 min) 156 50 100 150 200 250 Ultrafast NMR (2-3s) U28 U82 U16,U70 U71 U68 U17 50 100 150 200 250 50 158 160 150 100 162 200 164 14 13 12 11 250 Bound riboswitch U39 U31 156 50 U82 U47 158 100 U16,U70 U74 U68 U40 U34 U22 U17 U77 U25 U71 U41 U49 160 162 164 250 200 150 14 13 12 11
Conformation changes in real time 149 144 12 12.2 12.4 12.6 12.8 13 13.2 13.4 13.6 144 G14 G57 145 146 148 G81 G59 G43 G44 G72 G78 148 147 146 150 150 151 t = 0 sec 13 12
Conformation changes in real time 150 144 145 147 148 146 12 12.2 12.4 12.6 12.8 13 13.2 13.4 13.6 G57 G14 G43 G44 G78 G59 149 151 G81 t = 16 sec
Conformation changes in real time 144 145 146 147 12 12.2 12.4 12.6 12.8 13 13.2 13.4 13.6 G57 G14 G32 G43 G78 G37 G38,G59 G44 148 G81 G46 149 150 151 t = 28 sec
Conformation changes in real time 144 150 145 146 147 148 12 12.2 12.4 12.6 12.8 13 13.2 13.4 13.6 G14 G32 G37 G43 G44 G57 G78 G38,G59 149 151 G81 t = 58 sec
The Spectrometer: 1. A powerful magnet Magnet sample PROBE PRE-AMP 499,995,000 < o < 500,005,000 Hz RECEIVER DETECTOR +- o- = +-5,000 Hz A D C BINARY NUMBERS TO COM PUTERS TRANSMITTER = 500 MHz = 500,000,000 Hz CONTINUOUS REF ERENCE
The Spectrometer: 2 A Radio station The transmitter generates short (<0.1 ms) RF pulses to the probe RF pulses stimulate nuclear spin transitions in the sample The emitted signal is measured by the receiver and digitized RF signals arising from the sample are all in the region of 500 MHz, differing only by the chemical shift range present Magnet For protons this is typically 10 ppm or 5000 Hz at 500 Mhz PROBE sample PRE-AMP TRANSMITTER 499,995,000 < o < 500,005,000 Hz RECEIVER = 500 MHz = 500,000,000 Hz CONTINUOUS REFERENCE DETECTOR +- o- = +-5,000 Hz A D C BINARY NUMBERS TO COMPUTERS If we subtract some reference frequency ( = 500 MHz) from the signal, we only digitize the chemical shifts ( o - ) (audiofrequencies)
Spectrometer performance: sensitivity and stability The probe is in many ways the heart of the spectrometer: it determines s/n (e.g. cryoprobes) PROBE Magnet sample PRE-AMP TRANSMITTER 499,995,000 < o < 500,005,000 Hz RECEIVER = 500 MHz = 500,000,000 Hz CONTINUOUS REFERENCE DETECTOR +- o- = +-5,000 Hz A D C BINARY NUMBERS TO COMPUTERS Magnet homogeneity and long term stability determine resolution (1 part in 10 9 ) Stability of RF amplifier/signal preamplifier/frequency generation units determine artifacts (1 part in 10 9 )
Spectrometer performance: Magnetic field strength provides increased resolution 500 Mhz (1 peak?) 750 Mhz (2 peaks?) 800 Mhz (2 peaks!)
The chemical shift scale The frequency of absorption of the NMR signal depends on the external field as we have seen n 0 = g B 0 /2p Let us now introduce a quantity that describes the fact that different nuclei in the sample experience slightly different magnetic fields because of chemical structure and conformation n = (1-s) g B 0 Finally, let us introduce a scale that is field-independent, so that we can compare directly data recorded on different spectrometers: d=(n-n o )/n 0 x10 6 We use a standard sample (e.g. DSS) to reference all of our spectra, so that we can report the resonance frequency for our proton in a universal, field-independent manner
The NMR Signal and Spectrum Signal - FID (time domain) Spectrum (frequency domain)
The NMR Signal and Spectrum The emission signals are oscillatory and physically damped (damped harmonic oscillations) This signal is called the Free Induction Decay or FID The actual spectrum is recovered from the FID via Fourier transformation, which transforms the time interferogram into a frequency spectrum Without FT NMR, it would take the square of the time to obtain an equivalent signal/noise ration
Example: FID and a 1D spectrum FID Fourier Transform 1D spectrum
Origin of the NMR signal Nuclear subatomic particles have spin 1. If the number of neutrons and protons are both even the nucleus has 0 spin i.e. 12 C (6 neutrons + 6 protons = 12) has I = Ø spin 2. If the number of neutrons plus protons is odd the nucleus has a half-integer spin (1/2, 3/2, 5/2) i.e. 13 C (7 neutrons + 6 protons = 13) has I = 1/2 spin 3. If the number of neutrons and protons are both odd then the nucleus has an integer spin (1, 2, 3) i.e. 14 N (7 neutrons + 7 protons = 14) has I = 1 spin; spin 1 nuclei are quadrupolar (relax fast) For high resolution applications, we use spin ½ nuclei ( 1 H, 13 C, 15 N, 31 P in biology);
Nuclear spins and the energy levels in a magnetic field A nucleus of spin I has 2I + 1 possible orientations (a nucleus with spin 1/2 has 2 possible orientations) Each level is given a magnetic quantum number m The energy levels for a 1 H nucleus are referred to as: a (m = +1/2) and b (m = -1/2) In the absence of an external magnetic field, these orientations have equal energy; if a magnetic field is applied, energy levels are split The a state is the energetically preferred orientation (magnetic moment parallel with the applied magnetic field) The b state has higher energy (magnetic moment anti-parallel to the applied magnetic field)
Nuclear spins and the energy levels in a magnetic field The energy of a particular level is given by: E = g h m B o where: g is the the gyromagnetic ratio, a nuclear property (a measure of the polarizability of the nucleus) h is Planck's constant divided by 2p (h = h/2p ) B o is the strength of the magnetic field The difference in energy between levels (the transition energy) DE = g h B o If the magnetic field is increased, so is DE (as DE increases, so does sensitivity)
NMR properties of nuclei of common use in biology Isotope Spin Abundance Magnetogyric ratio NMR frequenc (I) g/10 7 rad T -1 s -1 MHz (2.3 T magnet) 1 H 1/2 99.985 % 26.7519 100.000000 2 H 1 0.015 4.1066 15.351 13 C 1/2 1.108 6.7283 25.145 14 N 1 99.63 1.9338 7.228 15 N 1/2 0.37-2.712 10.136783 17 O 5/2 0.037-3.6279 13.561 19 F 1/2 100 25.181 94.094003 23 Na 3/2 100 7.08013 26.466 31 P 1/2 100 10.841 40.480737 113 Cd 1/2 12.26-5.9550 22.193173
Nuclear precession in a magnetic field: semiclassical description Bo z y The nucleus has a positive charge and spins This generates a small magnetic field x The nucleus possesses a magnetic moment m proportional to its spin I In a magnetic field, the axis of rotation will precess about the magnetic field B o The frequency of precession ( o Larmor frequency) is identical to the transition frequency ( o = -gb o ) The precession may be clockwise or anticlockwise depending on the sign of the gyromagnetic ratio (+g or -g)
Origin of a macroscopic (observable) NMR signal Bo x z Mo y Out of a large collection of moments, a surplus have their z component aligned with the applied field, so the sample becomes magnetized in the direction of the main field B o The parallel orientation is of lower energy than the antiparallel At equilibrium, spins will be distributed according to Boltzmann distribution between the two energy states A net magnetization parallel to the applied magnetic field arises because of the small population difference between states
Sensitivity of NMR experiment Nuclei populate energy levels according to Boltzmann distribution n 1 /n 2 = exp (-DE/kT) If we irradiate the system on resonance (DE=hn), the probability of signal absorption will be proportional to the population difference: n 2 -n 1 If DE>>kT (e.g. optical spectroscopy) then all dipoles are in the ground state If DE<kT (NMR), then the net absorption of energy will be small because n 2 =n 1 and stimulated emission/absorption are equally probable The only thing you can do is increase the magnetic field, because DE = g h B o
S/N in NMR is poor because energy levels are so close According to Boltzmann distribution: n ( E E ) / kt n 2 e 1 1 2 If the system is exposed to a frequency: then the energy absorbed is proportional to the difference v E 2 h E 1 if DE kt n2 n 1 (as is the case for optical spectroscopy), then essentially all the molecules will be in their ground state configuration
S/N in NMR is poor because energy levels are so close n ( E E ) / kt n 2 e 1 1 2 If instead DE kt n1 n2 (as is the case for NMR spectroscopy), then the net absorption of energy will be very small because the rate of upward transitions is equal to the rate of downward transitions For this reason, we use magnets of increasing strength to separate energy level more and increase the sensitivity of the experiment