(NMR) Spectroscopy

Nuclear Magnetic Resonance (NMR) Spectroscopy

Felix Bloch & Edward Purcell Richard Ernst Kurt Wuthrich Physics-1952 Chemistry -1991 Chemistry-2002

Paul Lauterbur & Peter Mansﬁeld Brian Sykes Lewis Kay Medicine-2003 Principles of NMR Protein Spectroscopy

What does NMR tell us ? 1) Primary structure characterization 2) Dynamics - psec-sec timescales 3) Equilibrium binding 4) Folding/Unfolding 5) Three dimensional structure Some Advantages 1) Solution based 2) Non-destructive 3) Residue speciﬁc information Principles of NMR Protein Spectroscopy

Wavelength (nm) X-rays Radio waves

10 100 1000 104 105 106 107 108 109 Crystallography IR NMR UV/Vis

Electron Nuclear spin transitions transitions Principles of NMR Protein Spectroscopy

Nucleus I # Protons # Neutrons 1H 1/2 1 0 12C 0 6 6 13C 1/2 6 7 14N 1 7 7 15N 1/2 7 8 Absorption of energy by nucleus - depends on nuclear spin (I) = sum of unpaired protons + neutrons (spin 1/2) I≠0 - NMR observed - spin will have magnetic moment µ=γI For proteins 1H, 13C, 15N (31P) Principles of NMR Protein Spectroscopy

N N S

S N m = -1/2 mI = +1/2 I α β S

m=(-I, -I+1 ….I-1, I) Principles of NMR Protein Spectroscopy

Normal Magnetic Field (Bo) z

µ=-γIz

x y Bo Principles of Protein NMR Spectroscopy

So how does this give us an “NMR signal” ?

N N S β

S N m = +1/2 m = -1/2 I I α S α β Principles of Protein NMR Spectroscopy

This occurs for all 1H, 13C, 15N in magnetic ﬁeld

β γ (∗107 rad / T sec) 1H 26.75 13C 6.73 α 15N -2.72

B0 Principles of Protein NMR Spectroscopy

ΔE = γhB0 = hν ν = γB0 (Hz) ω = γB0 (rad) 2π α Larmor Precession

Nucleus γ (∗107 rad / T sec) ν at 14.09 T 1H 26.75 600.00 13C 6.73 150.87 15N -2.71 60.82 Principles of Protein NMR Spectroscopy

NMR is an insensitive method 1H N=106 11.75T 18.79T β 499,980 499,968

α 500,020 500,032 Principles of Protein NMR Spectroscopy

Sensitivity

nα-nβ = Δn = NγhBo 2kT 2 Mo=nαµzα + nβµzβ = Δnµzα= 1 γhΔn = 1 N (γh) Bo 2 4kT z z

x x y y Bo Bo Principles of Protein NMR Spectroscopy

Net Magnetization

z z

x x y y ωo Bo Bo

Rotating Frame Principles of Protein NMR Spectroscopy

How is the NMR Signal Obtained ? -employ a rf pulse at ν of desired nucleus

z z θ Mo

x “rf pulse” x Bo y y B1 B1 Principles of Protein NMR Spectroscopy

z z

Mo π/2 = /2 x θ π x Bo y y B1 B1

pw = 6 µsec γB1 = 41 kHz rf on off Principles of Protein NMR Spectroscopy

z z z Mo π/2

x x x Bo y y receiver y B1 B1 B1 rf FT on off time ν Principles of Protein NMR Spectroscopy

z -t/T Mz(t) = Mo(1-e 1) z x T1 y B1 x z y receiver B1 T2

x y -t/T off B1 My(t) = My(0)*e 2 time Principles of Protein NMR Spectroscopy

T1, T2 (sec) Linewidths 100 T1 10

0.1 T 0.01 2

0.001 0.5 Hz 10 Hz 100 10 1 0.1 0.01 0.001

Correlation Time, τc (nsec) MW 100 MW 20,000 Molecular Weight Principles of Protein NMR Spectroscopy

NMR Instrumentation

Magnet - Bo 18.79 T

vacuum

N2(l)

He(l)

magnet

22.31 T (2006) probe Principles of Protein NMR Spectroscopy

Magnet Technology Principles of Protein NMR Spectroscopy

Probe Technology

B1 Bo Principles of Protein NMR Spectroscopy

Cold “Cryogenic” Probe

1/2 S/N ~ 1/{Rs*(Ts+Tpa)+(Rc*(Tc +Tpa)}

Tpa, Tc - lowered 298˚K 20˚K

Rs, Ts - near 298˚K 3-4 time more sensitive 500 MHz + cold probe = 1.6x S/N 800 MHz Principles of Protein NMR Spectroscopy

Block Diagram of NMR Spectrometer

Probe

obs, dec, lk obs, lk Duplexer

Transmitter Preampliﬁer

obs, lk CPU Receiver

Computer