Presentation on theme: "Modern Approaches to Protein structure Determination (6 lectures)"— Presentation transcript:
1 Modern Approaches to Protein structure Determination (6 lectures) Dr Matthew Crump
2 Two types of angular momentum “Normal” or “extrinsic” angular momentum (due to rotational or orbital motion)use your right hand to figure out the way the angular momentum vector points“Intrinsic” or “spin angular momentum” (a property of fundamental particles -- cannot be visualized).the direction of the spin angular momentum is indicated by an arrow.
3 This equation tells us how much magnetism we get for a given spin. Gyromagnetic ratio (1)The gyromagnetic ratio g determines the ratio of the nuclear magnetic moment to the nuclear spin.It is a fundamental property of each nuclear isotopeFundamental symmetry theorems predict that spin and magnetic moment are co-linearmm =gIThe gyromagnetic ratio is also known as the magnetogyric ratioThis equation tells us how much magnetism we get for a given spin.
4 Quantum Angular Momentum In quantum mechanics, angular momentum is quantized.The total angular momentum of particles with spin takes the values of the formIf 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 Iz is given bywhere m is a second quantum number which can take values m=-I,-I+1,-I+2,..,I. Therefore Iz has 2I+1 values.
5 Zeeman splittingEnergy of interaction is given by E=-m.B in a magnetic field B. The dot product tells us the energy depends on the size and relative orientation of B and m.We take B to be along the Z axis, so the dot product becomes E=-mzBz (I.e. mxBz and myBz = 0the energy of the state with quantum number Iz is given byPlanck constantgyromagnetic ratioEnergym=-1/2m=-1m= 0m=+1/2m=+1ground state; no fieldZeeman splitting h g B/2πground state; with field
7 Gryomagnetic ratio (2)The gyromagnetic ratio g determines how rapidly the Zeeman splitting increases when the magnetic field is increased.1H15N27AlNote the ordering of the energy levels (g is positive for 1H)Note the ordering of the energy levels (g is negative for 15N)
8 Gyromagnetic ratio (3)Spins I and gyromagnetic ratios g for some common nuclear isotopes:
10 A nuclear spin precesses in a magnetic field the circulating motion of the spin angular momentum is called precessionthis arrow denotes the direction of the spin angular momentumNuclear spins precess because:they are magneticthey have angular momentum
11 Precession frequency = Larmor frequency n0 = - g Bz/2πmagnetic field inTesla (T)Larmor frequency in Hz (= cycles per second)gyromagnetic ratio in rad s–1 T–1Compare with Zeeman Splitting
12 Larmor frequency and Zeeman splitting DE = h n0
13 Positive g negative precession Negative g positive precession
14 Precession frequencies for different isotopes the Larmor frequency is proportional to the field
15 Generation of the NMR spectrum FouriertransformThe NMR spectrum
16 The sense of the frequency axis less rapid precessionmore rapid precessionincreasing | n |the sense of the precession is ignored
17 Chemical Shifts The molecular environment distorts the magnetic field on a microscopic scale
18 Mechanism of Chemical Shift The electrons in a molecule cause the localmagnetic fields to vary on a submolecular distancescale2 steps…12The 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 magnetic field causes the electrons to circulate
19 Proton Chemical Shifts chemical shift d“deshielding” : magnetic field at nucleus enhanced by molecular environment“shielding” : magnetic field at nucleus reduced by molecular environmentChemical shifts correlate wellwith molecular structure and functional groups
20 Definition of Chemical Shift Larmor frequency of site j, ignoring the signchemical shift of site jLarmor frequency of spins in a reference compound, ignoring the signchemical shift dBy convention the spectrum is plotted with d increasing from right to left.The result is usually quoted in units of ppm (parts per million), where 1 ppm = 10-6This definition is used because it is field-independent
21 A common reference compound: TMS (Tetramethylsilane) chemical shift of TMS protonschemical shift dd = 0
22 Ethanol proton spectrum CH3 protons; d = 1.2 ppmOH proton; d = 2.6 ppmCH2 protons; d = 3.7 ppmchemical shift dchemical shift of TMS protons d = 0
23 Cholesterol proton spectrum chemical shift of TMS protons d = 0
24 Chemical equivalence Two spins are chemically equivalent if there is a molecular symmetry operation that exchanges their positions, orthere 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.
26 An example of chemical inequivalence chiral centrethe rotation around the C-C bond exchanges the protons but the onformations are not equivalent (different energies and different chemical shifts)
27 Chemical inequivalence in amino acids: L-phenylalanine chiral centrechemically inequivalent CH2 protons
28 Direct DD coupling (averages to zero in ordinary liquids) Spin-spin couplingsDirect DD coupling (averages to zero in ordinary liquids)Indirect DD coupling or J–coupling (doesn’t average to zero in ordinary liquids)electrons
29 J-couplings cause splittings ethanol proton spectrumchemical shift dmultiplet structures caused by homonuclear J-couplings between protonsmultiplet structure caused by J-couplings
30 J-multipletsJ-coupling to N magnetically equivalent spins-1/2 splits the spectrum into N+1 multiplet components1 coupling partner:doublet2 coupling partners:triplet3 coupling partners:quartet