high resolution nmr

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BSB 512 Nuclear Magnetic Resonance Spectroscopy TTh 2:20 - 3:25 pm Lecture notes available at http://sos.bio.sunysb.edu/bsb512 Lecture 1: Basics Lecture 2-4: Protein structure determination Lecture 5: Relaxation and dynamics Lecture 6: Lab Session: Sample preparation. Pulse Programs Probe selection. Tuning. Shimming Pulse calibration. Data collection.

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References http://www.cis.rit.edu/htbooks/nmr Books Wuthrich, K. NMR of Proteins and Nucleic Acids Levitt, MH Spin Dynamics Cavanagh J. et al. Protein NMR Spectroscopy Ernst, R. et al. Principles of NMR in One and Two Dimensions Bax, A Two dimensional NMR in Liquids

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NMR Spectroscopy: Some history 1915 Einstein and de Hass - Correlation between magnetic moment and spin angular momentum 1922 Stern and Gerlach - Spins are quantized 1946 Bloch and Purcell - First NMR experiment Richard Ernst - Fourier transformations Jean Jeener - Two dimensional NMR - COSY 1976 Richard Ernst - First two dimensional NMR experiment 1986 Kurt Wuthrich - First independent NMR - X-ray comparison

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High resolution solution NMR of proteins Observe protons (1H) This differs from x-ray diffraction where one determines structure based on the electron density from the electron rich atoms (C, N, O). Protein is solubilized in water.

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High resolution solution NMR of proteins Observe protons Assign proton resonances to indivdual amino acids. Proton resonances are often resolved by differences in chemical shifts. Measure intra-residue and inter-residue proton to proton distances through dipolar couplings. Measure torsion angles through J-couplings. Use distance and torsion angle constraints to determine secondary and tertiary structure.

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High resolution solution NMR of proteins Protons have a property called spin angular momentum. They behave like small bar magnets and align with or against a magnetic field. These small magnets interact with each other. Bo S N S N

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13C and 15N also have spin angular momentum and “interact” with 1H

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Bo N H C H C C H H H Magnetization can be transferred between 1H, 13C and 15N to establish connectivities Chemical Shifts J-couplings (through bond) Dipolar couplings (through space)

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N H C H C C H H H Magnetization can be transferred between 1H, 13C and 15N to establish connectivities HNCA HNCOCA HNCOCACB etc HSQC-TOCSY They all use INEPT tranfers Chemical Shifts J-couplings (through bond) Dipolar couplings (through space) N H C H C C H H H N H C H C C H H H N H C H C C H H H 3D HSQC - NOESY for Inter-residue contacts

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Concept 1: Some nuclei have non-zero spin quantum numbers. Nuclei with odd mass numbers have half-integer spin quantum numbers. i.e. 13C, 1H, 31P are spin I = 1/2 17O is spin I = 5/2 Nuclei with an even mass number and an even charge number have spin quantum numbers of zero. ie. 12C Nuclei with an even mass number and an odd charge number have integer spin quantum numbers. i.e. 2H is spin I = 1 Electrons also have a spin quantum number of 1/2

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e- e- Concept 2: Current passed through a coil induces a magnetic field. e- e- Concept 3: A changing magnetic field in a coil induces a current.

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Mz Classical picture Concept 4: Placing nuclei with spin I = 1/2 into a magnetic field leads to a net magnetization aligned along the magnetic field axis.

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Bo Large external magnet Net magnetization aligned along Z-axis of the magnetic field

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Bo B 1 Net magnetization aligned along x-axis of the magnetic field after application of B1 field. The B1 field is produced by a small coil in the NMR probe which is placed in the bore of the large external magnet.

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Bo B 1 NMR probe NMR magnet. e- e-

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Concept 5: When the B1 field is turned on, the net magnetization rotates down into the XY plane Bo z x y

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Concept 6: When the B1 field is turned off, the net magnetization relaxes back to the Z axis with the time constant T1 T1 is the “longitudinal” relaxation time constant which results from “spin-lattice” relaxation

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Exponential Functions y = e -x/t y x y = 1- e -x/t y x Mz = Mo (1- e -t/T1 ) Mz t

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z x y Bo Concept 7: Individual spins precess about the magnetic field axis. Precession frequency = Larmor frequency wo = -g Bo (MHz)

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Concept 8: After magnetization is rotated into the xy plane by the B1 field produced from a pulse through the coil, it will precess in the xy plane. Bo z x y x y

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Concept 9: The individual magnetization vectors whirling around in the xy plane represent a changing magnetic field and will induce a current in the sample coil which has its axis along the x-axis. y x y

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Concept 10: NMR signal is a Fourier transform of the oscillating current induced in the sample coil y y x - y - x time frequency

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Chemical Shifts

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Concept 12: Nuclear spins produce small magnetic fields

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Concept 13: Electrons are spin I =1/2 particles. They produce small magnetic fields which oppose the external magnetic field. 1H has a small chemical shift range (15 ppm). 113Cd has a large chemical shift range (300 ppm).

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What is a ppm? Ppm = part per million 1H has a small chemical shift range (15 ppm). 1H 13C 15N 400 MHz 100 MHz 30 MHz 1 ppm = 400 Hz 15 ppm = 6000 Hz 15 ppm

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a b CH3 C-OH Concept 14: The surrounding electrons shield the nuclear spins from the larger external Bo field. This results in a reduction in the energy spacing of the two energy levels and a lower Larmor frequency. This is the chemical shift. CH3 C-OH frequency

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Concept 11: In a frame of reference that ROTATES at the Larmor (precession) frequency, magnetization that is placed along the x-axis does not move. (It simply relaxes back to the z-axis via T1 processes.)

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a b a b CH3 C-OH 100,010,000 Hz 100,000,000 Hz Reference or carrier = 100,005,000 Hz

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Concept 15: The nuclei with different chemical shifts and Larmor frequencies will rotate around the z-axis at different speeds. T2 is the time constant for the magnetization vectors to "dephase" in the xy plane. CH3 C-OH frequency reference frequency

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N H C H C C H H H Chemical Shifts J-couplings (through bond) Dipolar couplings (through space) T1 relaxation T2 relaxation Structure Dynamics

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Acquire General One Dimensional Experiment Fourier Transform t1 -> f1 f1 t1

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Acquire General One Dimensional Experiment Fourier Transform t1 -> f1 f1 t1

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Acquire General One Dimensional Experiment Fourier Transform t1 -> f1 f1 t1 Fourier Transformation resolves multiple frequencies that overlap in the time domain

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Acquire General Two Dimensional Experiment Fourier Transform t1 -> f1 and t2 -> f2 f2 t1 t2 f1

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Acquire General Two Dimensional Experiment t1 t2 Acquire t1 t2 Acquire t1 t2 Vary t1 Collect a series of 1D spectra

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General Two Dimensional Experiment t1 f2 Vary t1 Collect a series of 1D spectra Here, the intensities of and do not change as a function of the t1 evolution time

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General Two Dimensional Experiment t1 f2 Vary t1 Collect a series of 1D spectra Whereas here, the intensity of is modulated as a function of the t1 evolution time

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General Two Dimensional Experiment t1 f2 Transpose and then Fourier transform in t1 dimension

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General Two Dimensional Experiment t1 f2 Transpose and then Fourier transform in t1 dimension

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General Two Dimensional Experiment f1 f2 Projection on f2 gives original chemical shifts

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General Two Dimensional Experiment f1 f2 Projection on f1 yields new information

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General Two Dimensional Experiment 1H chemical shift J coupling 1H chemical shift Dipolar coupling 1H chemical shift 13C chemical shift 1H chemical shift 1H chemical shift

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