Imaging
The Nobel Prize in Physiology or Medicine 2003
"for their discoveries concerning magnetic resonance imaging"
Paul C. Lauterbur
Sir Peter Mansfield
Imaging System: 7T160 mm
Magnets are often horizontal bore Coils built to order
RF coils are quite
Intermediates Detection and
Hydrogen Exchange
NMR methods for detecting intermediates and
excited states
Amide exchange
Methods for detecting Amide Exchange
Application of Amide Exchange to proteins
NMR Dynamic Experiments
CPMG and PRE are sensitive t
BCMB/CHEM 8190
Data Acquisition and Processing
Fourier Transformation
Fourier Transformation
My
FT
time (t)
Frequency ()
S() = S(t) exp(it) dt = S(t) (cos(t) i sin(t)dt


N1
S(k/(dtN) =
S(jdt) exp(i2j (k/dtN), N/2 < j < N/2
J=0
Visualization of FT
M
Drug Discovery Small Molecule
Binding by NMR
BCMB/CHEM 8190
SAR by NMR
Shuker, Hajduk, Meadows, Fesik, Science, 274, 1531 (1996)
KA
KB
GAB = GA + GB, RTln(K) =  GAB ,
KAB
KAB = KAx KB
KA = 2 x 103, KB = 5 x 103 , KAB = 1 x 107
Me Mannose Bound to MBP
Ad
Dipolar Coupling and Solids NMR
BCMB/CHEM 8190
Liquids v. Solids
One can collect similar spectra
but some tricks are required
13C
solution, satd glucose, 8 min
13C
CPMAS, 30 mg cellulose, 9 min
The Classical DipoleDipole Interaction:
z
"
B0
1
r
"
r
2
x
Density Matrix Description of NMR
BCMB/CHEM 8190
Some Sequences Need Quantum Explanations
For example: the INEPT and HSQC Experiments
Solution: density matrix and product operator descriptions
1H
90x
180y
90y
15N
z
x
z
J>
yx
z
z
90x z
yx
z
y
J>
x
yx
yx
COSY and TOCSY
BCMB/CHEM 8190
COSY for an AX Spin System
90x
d1 (recover)
90x (mix)
t1 (evolve)
t2 (observe)
Hamiltonian: H = B0(1A)IZA B0(1X)IZX + 2 J IZA IZX
chemical shift
Basis set : (, , )
Using product operator transformation tables,
or Kanters
http:/cnsonline.org/v1.21/
Structure Calculation using CNS
DO THE FOLLOWING, IF YOU HAVE NOT ALREADY DONE SO:
First, look in your home directory to see if there is a subdirectory named cns:
[[email protected] ~]$ pwd
/home/yourusername
[youruse
Classical simulations with PJNMR
BCMB/CHEM LAB
The program PJNMR was written by PaulJean Letourneau as a joint project between the
PENCE & NANUC projects in Canada. It rotates vectors representing spin magnetization
Effects of Chemical Exchange on NMR Spectra
Effects of Chemical Exchange on NMR Spectra
Chemical exchange refers to any process in which a nucleus
exchanges between two or more environments in which its NMR
parameters (e.g. chemical shift, scalar coupling
Pulse and FT NMR
In practice bulk magnetization is observed
For isolated spins behavior is according to
classical Bloch equations
dM/dt = M X B (Mz M0) (1/T1) Mx,y (1/T2)
Precession in a Static Field
Torque on system with angular momentum (J)
causes prece
An s;wef\g.
Name:      
BCMB/CHEM 8190, B IOMOLECULAR N MR
M IDTERM  02/29/08
I nstructions: This is an open book, limited time, exam. You may use notes you have
from class and any text book you find useful. You may also use a calculator. You will
4) P roto n l in e w idth s for n onexchangin g amide p roton s in m yoglobi n are a pproximatel y 15 Hz.
Hemoglobi n is a t etrame r of s ubunit s that are a pproximatel y the same size as m yoglobin . W ha t
woul d you expect for l in e w idth s of n o
BCMB/CHEM 8190
Problem Set 6
1) A NOESY experiment is conducted on a small protein using a short mixing time
(50ms). Crosspeaks are observed and integrated for a glycine residue. Using the distance
between the two alpha protons in this amino acid (0.175nm
BCMB/CHEM 8190
PROBLEM SET 5
1) Use density matrix methods to examine magnetization for a pair of spin 1/2 nuclei in a
magnetic field Bo along the z axis. The first spin listed oscillates at A and the second
at X. Assume the scalar coupling is small and c
BCMB/CHEM 8190
PROBLEM SET 4
1) A dilute protein solution at 330K gave rise to 13C alpha resonances with spin lattice
relaxation times of 30ms when examined at a spectrometer frequency of 15MHz. A
full negative NOE was also observed (W0 more effective tha
BCMB/CHEM 8190
ANSWERS TO PROBLEM SET 4
1)
2) The separation between outer lines will give the coupling constant
for an AB system (this is not true for all splittings in more complex
systems ie ABC or ABX). Here 5.325.35 = 0.03ppm. At 500 MHz this
is 500
BCMB/CHEM 8190
PROBLEM SET 3
1) Couplings between 5' and 5' protons and the phosphate phosphorus in a 5' nucleotide
are observed to be 6.0 and 8.0 Hz, respectively. Using the formula JPH = 21 x cos()2
2.25, and assuming idealized rotomer geometries about
BCMB/CHEM 8190
ANSWERS TO PROBLEM SET 3
1)
2)
Assuming adenine H2s have the sixmembered ring of other adenines 3A above and
below, each would shift the H2 upfield by 0.75 ppm. (one can find this number on the
plots from BothnerBys article, or by using t
PROBLEM SET 2 BCMB 8190
1) The following amplitudes of a water resonance are observed at the indicated delay
times in an inversion recovery experiment. What is the T1 for water? t=0.1s, 28; t=
0.5s, 23s; t=2.5s, 2; 12.5s, 27; 60s, 30.
2) It is frequent
BCMB/CHEM 8190
ANSWERS TO PROBLEM SET 2
1) The easiest way to approach this problem is to linearize the equation we gave in class
and either graph the data, or use your favorite linear least squares program. The equation
after rearranging and taking the l
*BCMB/CHEM 8190*
*ANSWERS TO PROBLEM SET 1*
1) Receptivities given in the table are reduced by abundances (except 3H).
Divide by abundance to get receptivity for equal number of nuclei. The
dependence on gamma can be seen by equating the ratio of the gamm
BCMB/CHEM 8190
PROBLEM SET 9
1) In an SAR by NMR experiment two ligands, A and B, are found to perturb
resonances in an HSQC experiment that belong to sites that are within 6 A of one
another. Ligand A has a dissociation constant of 2 X 10*4 and ligand B
BCMB/CHEM 8190
PROBLEM SET 8
1) Below is a 15N1H HSQC spectrum of an RNA duplex. How many Gs and how many
Us are in the molecule?
2) Below is a 1H1H NOESY spectrum of a selfcomplementary DNA decamer
(GCGAATTCGC). A starting point is given. See if you c
BCMB/CHEM 8190
PROBLEM SET 7
1) The following are planes from HNCA and NHCO experiments taken at the same 15N
chemical shift.
a) add the residue number to the peaks in the HNCA spectrum
b) why are the upfield peaks in each pair weaker?
c) will the weaker
BCMB/CHEM 8190
PROBLEM SET 1
1) Using a table of nuclear properties such as found at
http:/bouman.chem.georgetown.edu/NMRpt/NMRPerTab.html look through the
elements in the first three rows of the periodic table and find all the spin isotopes.
What are the
BCMB/CHEM 8190 ANSWERS
PROBLEM SET 9
1)
Dissociation constant = 2X10^4 X 5X10^6 = 1X10^9
2) The relative rate of buildup of NOEs will be 300,000/2000. A 20% contribution
from the free NOE would occur with a free to bound ratio of X/(X1) where X*2)/(1
BCMB/CHEM 8190
Answers, Problem Set 8
1) There are 9 Gs and 3 Us
2)
3)
a) negative
b) positive
c) yes and no
4)
a) Assuming polarization of the electron is still in the linear limit of the Boltzmann factor
DNP enhancement is proportional to e / C. Using e