This project received funding by the European Commission under the GA n° 2019-1-IT02-KA203-063391 innocore-project@unitn.it www.innocore-project.eu Core Technologies for Education and Innovation in Life Sciences NMR Spectroscopy Basics by Radovan Fiala, Karel Kubicek, and Pavel Kaderavek CEITEC, Masaryk University Nuclear spin Atomic nuclei consist of protons and neutrons (nucleons) Protons and neutrons have spin ½ Spins tend to compensate each other but often not completely Resulting spin quantum number of the nucleus is I = k * ½ k is integer 0, 1, 2 …. A close up of a necklace Description automatically generated Proton Neutron Magnetic spin quantum number – number of possible spin states m = -I, -I+1, -I+2 ……I-2, I-1, I Examples I = ½, m = -½, +½ 2 spin states example: 1H I = 1, m = - 1, 0, 1 3 spin states example: 2H Magnetic moment No magnetic field In magnetic field B0 Only nuclei with non-zero spins have magnetic moments and are active in NMR Magnetic moment ħ=h/2p h Planck’s constant g magnetogyric ratio, specific to isotopes Isotopes differ by the number of neutrons and have generally different spins. In NMR, we refer to isotopes rather than elements, e.g. 1H (proton) or 13C instead of hydrogen and carbon Spins in magnetic field E = hgB0/2 B0 external magnetic field n= gB0/2 n h = 6,626.10-34 J.s h is Planck’s constant gMagnetogyric ratio, specific for each isotope g For 1H g = 42 494 369 s-1.T-1 For 100 MHz resonance frequency you need magnet B0 = 100 s-1 /42.494 s-1.T-1 @ 2.35 T g E B0 E = h S = 1/2 Research grade NMR spectrometers are produced usually with 1H resonance frequencies in multiples of 100 MHz, currently from 400 MHz up to 1,200 MHz (1.2 GHz), corresponding to magnets from 9.4 T to 28.2 T. For protein studies, high-field spectrometers with resonance frequencies 600 MHz or higher are commonly used. On Earth, spins are always subject to a magnetic field, but the magnetic field of Earth is only about 50 µT. NMR and electromagnetic spectrum NMR 107 Noninvasive Low sensitivity Chemical shift  0 5 10 A picture containing game Description automatically generated Nuclei do not experience the external magnetic field B0 only, But also the fields of other particles, especially electrons. Net magnetic field at a nucleus B = B0 (1 - s) s nuclear shielding Resonance frequencies differ slightly depending on the location of the nucleus in the molecule. Resonance frequencies are field dependent, which is impractical – values are not comparable between different spectrometers. Chemical shift – frequency difference relative to a suitable standard, expressed in ppm. d = 106 (u - uref) / uref For 1H, TMS (tetramethylsilane) is a common reference compound Spin-spin interactions Dipolar coupling Direct interaction between nuclear spins Depends on the orientation of the internuclear vector with respect to external magnetic field Important in solid-state spektra In liquids manifests itself only through relaxation phenomena Scalar / J-coupling Interaction of nuclei through the cloud of electrons Does not depend on the external magnetic field Causes splitting of signals (doublets for spins ½) Scalar interaction constant J (in Hz, no dependence on B0) I S B0 ris Textové pole: q q Reaching the resonance - CW Continuous wave (CW) Irradiation frequency is changed (swept) over the range. When resonance occurs, the irradiation energy is absorbed which is recorded as a signal. The resulting record of intensities vs. frequency is the spectrum. To get undistorted spectrum the process must be SLOW (minutes) 1pulse spectrum f1 Hz f2 frequency sweep ppm Reaching the resonance - PFT Pulsed with Fourier Transform The spin system is irradiated by a single short high intensity pulse. This is equivalent to irradiating a range of frequencies. The shorter and more intense the pulse is, the broader range of frequencies is affected. After the pulse, the response of the spin system is recorded as a function of time. The record is FID (Free Induction Decay). The spectrum is produced by Fourier Transform of an FID. FID 1pulse FT FID – time domain Spectrum - frequency domain RF pulse 90° ppm t Relaxation Spin-lattice relaxation - T1 Transferring the energy into surroundings (solvent/’lattice’). The spin system returns into equilibrium. Spin-spin relaxation - T2 The intensity of the signal in FID is dropping with time (Free Induction Decay) due to loss of coherence. The energy is still in the spin system but randomly oriented nuclear magnetic moment average to zero. Exponential decay exp(-t/T2) EB300Ac.jpg Resolution EB600c.jpg 300 MHz 600 MHz Position of signals is given by the chemical shift (relative number) The with of 1 ppm in Hz (absolute scale) depends on magnetic field: at 500 MHz, 1 ppm = 500 Hz, at 1000 MHz, 1 ppm = 1,000 Hz If the linewidth is the same, signal appear farther from each other at higher field. Resolution and sensitivity increase linearly with magnetic field Aromatic part of ethylbenzene spectrum Sensitivity Energy difference between spin levels are very small. Boltzmann distribution Na = Nb .exp(-DE/kBT) E = h, h Planck’s constant, kB Boltzmann constant Na, Nb – polulations of the spin states For protons at 500 MHz and 303 K, the population difference between the ernergy levels is less than 0.01%! We work with a small fraction od nuclei – sensitivity of NMR is inherently low For proteins, you need about 0.5 ml of sample with 0.5 mM concentration. Improving sensitivity by signal accumulation – more scans Signal-to-noise ratio increases with square root of number of scans: S/N ~ √ns Increasing Resolution Biopolymers: repetition of identical units (nucleotides, amino acids) High resolution is needed High magnetic field Increasing number of dimensions NMR Spectrometer Major parts Spectrometer1.jpg Spectrometer2.jpg NMR Spectrometer - Scheme Signal - sl(t)=S sl(t) l The Magnet Adjusting the magnetic field homogeneity Magnet2.jpg B0 The Probe Houses the sample Changes electric current into magnetic field and back. Must be tuned for best sensitivity Inverse probes, X-nuclei detection probes Room temperature probes, cryoprobes Probe.jpg Sonda2_sm.jpg Electronics •Frequency synthesis & signal processing •Computer (real-time control) • •Power amplifiers • •Magnet control • sample insert & eject • shimming • temperature control Console2.jpg 19 How the NMR Spectrometer Works !!!!!!!!B1 ~ I ~ P1/2 (P=RI2)!!!!!!!! Lp = [dB] Transmitter – power vs. rf field induction Relative power ratio expressed in decibel 1 dB: P1/P2 = 1.2589254 Relative rf field ratio ex-pressed in decibel 1 dB: w1/w2 = 1.120185 20 How the NMR Spectrometer Works Transmitter – phase shifted pulses 21 How the NMR Spectrometer Works A/D converter n=6 bits 64 levels n=8 bits 256 levels 3bit A/D converter (8 levels) 2n = 8 A/D converter typically 16 bits i.e. 65 536 levels 32 bits i.e. 4 294 967 296 levels 22 How the NMR Spectrometer Works A/D converter – sampling frequency Nyquist frequency fmax = 1 kHz => D = 500 ms 23 How the NMR Spectrometer Works A/D-converter – signal folding 24 How the NMR Spectrometer Works Receiver NMR signal Local oscilator Intermediate frequency A/D converters 25 How the NMR Spectrometer Works Quadrature detection mixer cosA.cosB=1/2(cos(A+B) + cos(A-B)) cosA.sinB=1/2(sin(A+B) - sin(A-B)) ( ) 26 How the NMR Spectrometer Works Quadrature detection Intermediate frequence Frequency wo+wrx removed by filter 27 How the NMR Spectrometer Works Quadrature detection – time vs. frequency Spectral width fsw Acqusition time tacq N – number of acquisition points D – sampling interval 28 How the NMR Spectrometer Works Pulse programmer INEPT with refocusing 29 How the NMR Spectrometer Works Pulse programmer ;ineptrd ;avance-version (02/05/31) ;INEPT for non-selective polarization transfer ;with decoupling during acquisition #include "p2=p1*2" "p4=p3*2" "d3=1s/(cnst2*cnst11)" "d4=1s/(cnst2*4)" "d12=20u" 1 ze 2 30m do:f2 d1 d12 pl2:f2 (p3 ph1):f2 d4 (center (p4 ph2):f2 (p2 ph4) ) d4 (p3 ph3):f2 (p1 ph5) d3 (center (p4 ph2):f2 (p2 ph6) ) d3 pl12:f2 go=2 ph31 cpd2:f2 30m do:f2 mc #0 to 2 F0(zd) exit ph1=0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 ph2=0 2 ph3=1 1 3 3 ph4=0 2 ph5=0 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3 ph6=0 2 0 2 1 3 1 3 ph31=0 0 2 2 1 1 3 3 ;pl1 : f1 channel - power level for pulse (default) ;pl2 : f2 channel - power level for pulse (default) ;pl12: f2 channel - power level for CPD/BB decoupling ;p1 : f1 channel - 90 degree high power pulse ;p2 : f1 channel - 180 degree high power pulse ;p3 : f2 channel - 90 degree high power pulse ;p4 : f2 channel - 180 degree high power pulse ;d1 : relaxation delay; 1-5 * T1 ;d3 : 1/(6J(XH)) XH, XH2, XH3 positive ; 1/(4J(XH)) XH only ; 1/(3J(XH)) XH, XH3 positive, XH2 negative ;d4 : 1/(4J(XH)) ;d12: delay for power switching [20 usec] ;cnst2: = J(XH) ;cnst11: 6 XH, XH2, XH3 positive ; 4 XH only ; 3 XH, XH3 positive, XH2 negative ;NS: 4 * n, total number of scans: NS * TD0 ;DS: 16 ;cpd2: decoupling according to sequence defined by cpdprg2 ;pcpd2: f2 channel - 90 degree pulse for decoupling sequence ;$Id: ineptrd,v 1.8 2002/06/12 09:05:00 ber Exp $ 23.10.2012 CID-15N-HSQC_JCh.png Screen Shot 2013-10-09 at 9.53.04 AM.png 1D proton spectrum of a protein 1H 1D, Cavanagh et al., Protein NMR Spectroscopy, 2007 Examples 1H-15N HSQC of a well folded protein at 293 K with approximately 155 amino acids, 600MHz Additional reading Keeler-2002-Understanding_NMR_Spectroscopy.pdf (cam.ac.uk) YouTube videos NMR Spectroscopy Visualized Introduction to NMR spectroscopy Part 1, Part 2 This project received funding by the European Commission under the GA n° 2019-1-IT02-KA203-063391 innocore-project@unitn.it www.innocore-project.eu Core Technologies for Education and Innovation in Life Sciences The End Questions, comments? radovan.fiala@ceitec.muni.cz