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1 Modern Approaches to Protein structure Determination (6 lectures) Dr Matthew Crump

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2 Two types of angular momentum Normal or extrinsic angular momentum (due to rotational or orbital motion) Intrinsic or spin angular momentum (a property of fundamental particles -- cannot be visualized). use your right hand to figure out the way the angular momentum vector points the direction of the spin angular momentum is indicated by an arrow.

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3 The gyromagnetic ratio determines the ratio of the nuclear magnetic moment to the nuclear spin. It is a fundamental property of each nuclear isotope Fundamental symmetry theorems predict that spin and magnetic moment are co-linear Gyromagnetic ratio (1) The gyromagnetic ratio is also known as the magnetogyric ratio = I This equation tells us how much magnetism we get for a given spin.

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4 Quantum Angular Momentum If we specify an I value, quantum mechanics restricts us as well to specifying the projection of this vector along only one of the three Cartesian components of I. By convention the z-axis is chosen and I z is given by where m is a second quantum number which can take values m=-I,-I+1,-I+2,..,I. Therefore I z has 2I+1 values. In quantum mechanics, angular momentum is quantized. The total angular momentum of particles with spin takes the values of the form

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5 the energy of the state with quantum number I z is given by Zeeman splitting Energy ground state; no field ground state; with field Zeeman splitting h B/2π Planck constant gyromagnetic ratio Energy of interaction is given by E=-.B in a magnetic field B. The dot product tells us the energy depends on the size and relative orientation of B and. We take B to be along the Z axis, so the dot product becomes E=- z B z (I.e. x B z and y B z = 0 m=-1/2 m=+1/2 m=-1 m=+1 m= 0

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6 m=-1/2 m=+1/2 I=1/2 m=-1 m=+1 I=1 m= 0 The Zeeman splitting is therefore

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7 The gyromagnetic ratio determines how rapidly the Zeeman splitting increases when the magnetic field is increased. Gryomagnetic ratio (2) 1H1H 15 N 27 Al Note the ordering of the energy levels ( is negative for 15 N) Note the ordering of the energy levels ( is positive for 1 H)

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8 Spins I and gyromagnetic ratios for some common nuclear isotopes: Gyromagnetic ratio (3)

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9 A compass in a magnetic field

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10 A nuclear spin precesses in a magnetic field the circulating motion of the spin angular momentum is called precession Nuclear spins precess because: they are magnetic they have angular momentum this arrow denotes the direction of the spin angular momentum

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11 Precession frequency = Larmor frequency 0 = - B z /2π Larmor frequency in Hz (= cycles per second) gyromagnetic ratio in rad s –1 T – 1 magnetic field in Tesla (T) Compare with Zeeman Splitting

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12 Larmor frequency and Zeeman splitting Zeeman splitting E = h 0

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13 Positive negative precession Negative positive precession

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14 Precession frequencies for different isotopes the Larmor frequency is proportional to the field

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15 Generation of the NMR spectrum Fourier transform The NMR spectrum

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16 The sense of the frequency axis more rapid precession increasing | | less rapid precession the sense of the precession is ignored

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17 Chemical Shifts The molecular environment distorts the magnetic field on a microscopic scale

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18 Mechanism of Chemical Shift The magnetic field causes the electrons to circulate The circulating electrons generate an additional magnetic field which is sensed by the nuclei.This is called the induced field. It is proportional to the applied field. The electrons in a molecule cause the local magnetic fields to vary on a submolecular distance scale 2 steps… 1 2

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19 Proton Chemical Shifts Chemical shifts correlate well with molecular structure and functional groups shielding : magnetic field at nucleus reduced by molecular environment deshielding : magnetic field at nucleus enhanced by molecular environment chemical shift

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20 This definition is used because it is field-independent Definition of Chemical Shift chemical shift chemical shift of site j Larmor frequency of site j, ignoring the sign Larmor frequency of spins in a reference compound, ignoring the sign By convention the spectrum is plotted with increasing from right to left. The result is usually quoted in units of ppm (parts per million), where 1 ppm =

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21 A common reference compound: TMS (Tetramethylsilane) chemical shift chemical shift of TMS protons

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22 Ethanol proton spectrum chemical shift of TMS protons = 0 CH 2 protons; = 3.7 ppm OH proton; = 2.6 ppm CH 3 protons; = 1.2 ppm chemical shift

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23 Cholesterol proton spectrum chemical shift of TMS protons = 0

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24 Chemical equivalence Two spins are chemically equivalent if there is a molecular symmetry operation that exchanges their positions, or there is a dynamic process between two or more energetically equivalent conformations, in which the positions of the two nuclei are exchanged. Chemically equivalent spins have the same chemical shift.

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25 Examples of chemical equivalence

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26 An example of chemical inequivalence chiral centre the rotation around the C- C bond exchanges the protons but the onformations are not equivalent (different energies and different chemical shifts)

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27 Chemical inequivalence in amino acids: L-phenylalanine chiral centre chemically inequivalent CH 2 protons

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28 Spin-spin couplings Direct DD coupling (averages to zero in ordinary liquids) Indirect DD coupling or J– coupling (doesnt average to zero in ordinary liquids) electrons

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29 J-couplings cause splittings chemical shift ethanol proton spectrum multiplet structure caused by J-couplings multiplet structures caused by homonuclear J-couplings between protons

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30 J-multiplets J-coupling to N magnetically equivalent spins-1/2 splits the spectrum into N+1 multiplet components 1 coupling partner: doublet 2 coupling partners: triplet 3 coupling partners: quartet

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