NMR
The Structural Biology Continuum Today s lecture: NMR Lots of slides adapted from Levitt, Spin Dynamics; Creighton, Proteins; And Andy Rawlinson
There are three types of particles in the universe Quarks at least 6 different types, form protons and neutrons Leptons Force particles again at least 6 different types, including the electron photons, gluons, vector bosons
Particles can have 1. Mass(/energy) 2. Charge 3. Spin We know what mass and charge are, but what is spin?
Spin Intrinsic (leptons and quarks have spin 1/2, photons spin 1) Independent of history Not due to rotational motion-exists even at absolute zero-but makes some sense to think of it as rotation Concept forced upon theorists by experimental evidence Dictates steps between available total angular momentum Doesn t make it into the macroscopic world - a strictly quantum mechanical concept When two fundamental particles like electrons with spin come together, they can combine in such a way that the net spin is either zero ( antiparallel ) or the sum ( parallel ).
Neutrons for instance are composed of 3 quarks (a proton is similarly three quarks, but ends up with charge +1)
Spin produces a magnetic moment u = γ S where gamma is the magnetogyric ratio of that nucleus Each electron in an atom has a spin 1/2, so when they are together in shells they minimize spin by being one-up, one-down, like we learned in chemistry (1s, 2s, 2p, 3s, 3p, 3d, etc. orbitals)
When neutrons and protons are together, the spin relationships are not so simple: some nuclei have net spin in their ground state, others don t Used in protein NMR
Normally, nuclear magnetic moments are randomly aligned, so there is no net macroscopic magnetic moment
If an external magnetic field is introduced, nuclear magnetic moments cannot simply align themselves with it like a compass needle because they must conserve angular momentum. Instead they precess, like a top. The Larmor frequency is given by ω = γ β Note the frequency depends on the magnetogyric ratio, and so thus is different for different nuclei. The angle of the precession cone depends only on the initial direction of the spin angular momentum. This angle is stable to translations, rotations, and collisions of the molecule
11 Paul Callaghan:http://www.youtube.com/watch?v=7aRKAXD4dAg
Nevertheless, because the local magnetic field varies slightly because of the tiny, moving magnetic moments of particles in the immediate vicinity, the precession angle wanders over the course of seconds Because being aligned with the external magnetic field is slightly energetically favorable, 1 in about every 10 4 or 10 5 nuclear magnetic moments become aligned, producing a stable (equilibrium), macroscopic, longitudinal magnetic moment
A radiofrequency pulse is introduced along x, which rotates individual magnetic moments away from z and they start precessing. Now think of the linearly-polarized pulse as the superposition of a left- and rightcircularly polarized wave. If the pulse is of the same, resonant frequency as the Larmor frequency, one of these will pull the magnetic moment down towards the xy plane, or even beyond, depending on the duration of the pulse.
Linearly polarized waves can be thought of as the superposition of a left-circularlypolarized and a right-circularly-polarized wave 15
Oscillating current around the transverse coil produces a horizontal, linearly polarized oscillating magnetic field - equivalent to the superposition of a left-circularlypolarized and a right-circularly-polarized magnetic field. in horizontal plane 16
These precess in phase (like so many clocks) until perturbations gradually restore the equilibrium (longitudinal) net magnetic moment B 0 M z z y O M transverse x
The precession of this transverse net magnetic moment can be measured ω = γ B 0 M z Coil No signal ω = γ B 0 Coil Signal M transverse NMR Signal
Pulse sequences are followed by detection Can be multi-channel to induce and detect signals in different nuclei Each signal has a unique frequency and decay constant pattern called free induction decay, or FID spectrum obtained through Fourier transformation
H 13 C 29 Si Consider tetramethylsilane
Inhomogeneous broadening leads to MRI http://www.qedata.se/e_gr-design_bakgrund.htm Introduce external magnetic field that varies linearly over the field of view Result is a projection of the resonator density Record projections in different directions, merge into 3D reconstruction
Chemical shift CH3 CH2 Since electrons are magnetic, the nuclear Larmor frequency depends on the local electronic environment, introducing chemical shift
Typical shifts of protons in different chemical groups found in proteins
Sometimes multiple pulses are given, with variable delays between them
Systematically varying the time delay results in a two-dimensional array of data FT Pulse sequence Free-induction decay signals Spectrum
The 2-D Fourier transform can then reveal geometric and chemical relationships between nuclei through magnetization transfer : through-bond Jcoupling 2D COSY spectrum through-space nuclear Overhauser effect (NOE) http://www.chemistry.ccsu.edu/glagovich/teaching/472/nmr/cosy.html
Magnetization transfer Through-bond J couplings Give information about dihedral angles Through-space NOE couplings Peak volume proportional to 1/d 6 Practically useful only for protons < 5Å apart Can be drained by other close protons Neither very accurate-rely on redundancy
Spin systems for each amino acid are identified by patterns in their chemical shifts and cross-peaks Alanine
Gly Try glycine
Now try valine Valine Taken from Creighton, Proteins
Once individual spin systems are identified by amino acid type, their relative positions within the protein sequence are determined. This is done, for instance, by noting that the amide proton of each residue is certain to be within ~3Å from at least one of the protons of the last residue. Secondary structure is usually also apparent from the strong NOEs used to make these assignments. Strong NOEs exist, for instance, in alpha helices between NHi and NH(i+1), and between C-betaH(i) and NH(i+1), but not between CalphaH(i) and NH(i+1). B-strands have a different pattern. Taken from Creighton, Proteins
Next, regions of secondary structure are detected through predicted NOEs
NMR protein structure determination overview Only hydrogen atoms are observed Find connectivity using through-bond cross peaks Find spin systems in spectra Assign spin systems to specific amino acids in the sequence, peaks to specific protons Measure some or all of the following constraints : Distances between certain protons (< 5Å) Which protons are involved in hydrogen bonds Dihedral angles Likely relative orientation of N-H vectors if you deliberately orient the molecules with dense phage or something Start with randomized structure, gradually adjust to match constraints, repeat in hopes that a consistent family of structures will emerge
Structure modeling Start with a random conformation Impose secondary structure Fold to satisfy NOE constraints and other knowns Satisfy dihedral angle measurements as well as possible Optimize with MD
Example ribbon diagram of NMR structure
http://en.wikipedia.org/wiki/nuclear_magnetic_resonance
Superconducting coils are used to produce the magnetic field
A single perpendicular coil is used both to introduce radiofrequency pulses and capture the NMR signal
3-D NMR spectrum 1H 13C 1H Could alternatively use 2 H, 15 N, or even two together for a 4-D spectrum
Real pulse sequences can get complicated
Applications/Limitations Advantages/Disadvantages Gives solution structure Non-damaging Not bothered by disordered regions Can see which hydrogens are exchanging Can see if certain side chains are rotating rapidly Can see if buffer/ligands and environmental conditions induce folding Can identify binding sites for small molecules or other macromolecules Requires high concentrations Requires long data collection periods (up to weeks or months) Many proteins not stable under those conditions for that long Size limited by complexity of spectrum to ~50 kda Expensive equipment requiring expert use--we have 600 MHz (~14 T) instrument, best are 900 MHz (~21 T)
Prestegard et al. Biochemistry 40:8677
no Ca 2+ with Ca 2+ Smoothness reveals foldedness Prestegard et al. Biochemistry 40:8677
Equipment and activities at Caltech Field trip Watch Paul Callaghan videos! http://www.youtube.com/watch?v=7arkaxd4dag See also Khan academy videos https://www.youtube.com/watch? v=jjchzutgwxk&index=1&list=pl0pjuwki0yczryrgkq HXZ0XCIu11afbJ8