Name:
BCMB/CHEM 8190, BIOMOLECULAR NMR
FINAL EXAM-5/5/10
Instructions: 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. The exam is intended to
take about 2 hours, but you may use the full exam period (8-11) if you wish. Write your
answers and name on the exam; turn it in at the end of the period.
Part I (100 pts). Give short answers to the following:
1) The four lines of a proton AB spectrum are at the following frequencies: 1032.5, 1037.0,
1041.0, 1045.5. What can you say about the size of the scalar coupling between A and B?
H
2) In a recent publication, Arora et al. (Nat. Struct. Biol. 8, 334-338 (2001)), determined the
three-dimensional fold (low resolution structure) of a membrane protein (19 kDa, 177 amino
acids) in micelles. The protein (transmembrane domain of OmpA) that they used was nearly
completely (-98%) deuterated at nonexchangeable sites. Why, in general, are proteins
sometimes deuterated for NMR studies?
5ypp / i
3) We collect a ID proton spectrum on a natural product and find typical line widths to be 3 Hz.
There are several poorly resolved overlapping peaks and we decide to improve the resolution
by multiplying the original FID by an exponential function exp(t/0.21). On Fourier
transforming the resultant FID what line width would you observe? Would the resolution
have improved?
4) In a ' C, N enriched protein which do you expect to have the larger (magnitude) scalar
coupling, carbonyl carbon to amide nitrogen or alpha carbon to amide nitrogen, and why?
5) How would your answer in 4 enter into the relative sensitivity of the following two
experiments: HN(CO)CACB and HNCACB? (Which would you expect to give the better
signal to noise ratio?)
MfixbCUk.
Am^. 3 / ' S . _ ^-A/
6) A TROSY version of an 15 N- ! H HSQC spectrum is collected on a large macromolecule. How
do the positions of peaks in this spectrum relate to positions in a normal HSQC?
7) The chemical shift range for 19F (y = 25.1815 x 107 rad Tesla"1 s"1) is quite large; -1300 ppm.
For a static magnetic field strength of 9.4 Tesla, what is the frequency difference between two
19F signals separated by 1300 ppm?
8) Using
SAR by NMR three ligands with binding constants of 2.0 x 103, 5.0 x 102, and 7.0 x
•5
10 are found to bind in spatially proximate sites on the surface of a protein. If we
successfully link them in a rigid framework that doesn't perturb their individual binding, what
might you expect for a binding constant of the new ligand?
Q
7* SO**
7x /O
9) Protein structures calculated using distance geometry methods followed by regularization and
minimization often have high energies. How might you improve (decrease) the energies of
these structures or improve the ratio of low/high energy structures calculated?
u
10) Proton line widths for non-exchanging amide protons in myoglobin are approximately 15
Hz. Hemoglobin is a tetramer of subunits that are approximately the same size as myoglobin.
What would you expect for line widths of non-exchangeable amide protons in hemoglobin?
11) A common solvent for collecting H and C spectra of organic
molecules is deuterated benzene (Ce He). An expansion of a
region of a ' J C spectrum near 130 ppm is shown to the right.
are there three peaks? Why are they of equal intensity?
small
Why
/
12) A variety of constraints are typically applied in the NMR-based structure determination of a
protein. What types of data lead to constraints on v|/ and fy torsional angles?
13) Five seconds after application of a 90° pulse, only 10% of the original (equilibrium)
magnetization has returned to z. What is the approximate T\n time constant?
-=0*114) We have interpreted 15N TI, T2, and 1H-15N NOE measurements in terms of the "model free"
description of the power spectral density function. Most amide H-N pairs in a protein give
square order parameters of (S2) of 0.8. Several residues in a loop give S2 values of 0.6
indicating more internal motion. If we model the motion as jumps between equally populated
states with H-N angles of 0 and 6, what is the value of the angle 0?
?)>^s
/-J:
15) A NOESY-HSQC of an 15N labeled protein shows strong HN-HN connections between
sequential residues and Ha-HN connections between i -> i +1 and i -> i + 3 residues. What
type of secondary structure does this part of the protein have?
16) Ribose ring puckers are sometimes 2' endo and sometimes 3' endo. What measurement
would you make to help decide the preferred conformer in a small RNA molecule?
/ -2
- 5/
17) The H2 and H6 protons on a tyrosine ring in a protein give discrete resonances separated by
100 Hz at 500 MHz and 5°C. As temperature is raised the resonances broaden, coalesce, and
sharpen. This is due to 180° ring flips about the Cp-C Y bond. At 45°C a single resonance, 30
Hz full width at half height, is observed. Given that most other resonances are lOHz in width
at this temperature, what is the exchange rate?
HO
NH
AUJ
f> b *-"
M//5 -t
2^)
=
/
(/0t?xzrt)'*
C=
0,0013
H5
1 8) In solids NMR cross-polarization is used to transfer magnetization from a high gamma
nucleus like protons to a low gamma nucleus like carbon- 13. Suppose we have fluorinated
polymer like Teflon and we want to detect carbon- 13 with high sensitivity. Our spectrometer
operating at 300 MHz for protons is set up for cross polarization from protons. The gamma
for fluorine is 2.518 x 10 rad Tesla" s"and that for a proton is 2.7 x 10 rad Tesla"1 s"1
What frequency would you choose for your high gamma nucleus spin-lock? By what fraction
would you change the BI spin-lock field strength for fluorine?
19) The following chemical shift anisotropy powder pattern is seen for an amide nitrogen
resonance in a 1?N labeled amino acid using a 300 MHz (proton frequency) spectrometer to
observe a static sample. How fast will you have to spin the sample in a magic angle spinning
experiment to see a single high resolution line?
250
200
150
100 50 PPM
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20) We run an HNCACB experiment on a protein and observe the following set of peaks on a
column connected to a single 1H-I5N cross-peak: 55.2, 45.2, 23.5. We know the cross-peak
must belong to an amino acid in the sequence: HIQGAFIYLSP. What amino acid is it?
A
Part II (24 points)
An imaging experiment is run with a contrast reagent that shortens T2 spin relaxation times for
water protons in regions occupied by the reagent from 1.5s to 0.5s. We use the echo-planar pulse
sequence sketched below. We plan to inset an element into the sequence that would allow T2
decay to affect the amplitude of signals coming from various parts of the image.
90x
c3
(2
1
t2
t2
t2
t2
'
t1
dw-1
dw-2
dw-3
dw-4
dw-5
a) Suppose the element allows decay for an additional Is. What would the relative signal
amplitudes be for signals coming from the two regions?
^79
b) Indicate a suitable place in the sequence to put a T2 filter element.
r
-£=*-
c) Sketch a pulse sequence element that you could use for the filter.
f
:t
Part III (24 pts)
We measure at pH 6 and 25 C the disappearance of two cross-peaks in a 15 N,'H HSQC spectrum
of a small protein. They belong to alanines in sites with sequences RGAD and GADK
respectively. The first exchanges with a half time of 2 days and the second with a half time of 5
hours.
a) Can you say anything about the relative stability of the secondary structure elements in which
the sites exist? If you can, make it more quantitative by predicting a difference in the free energy
of opening of the secondary structure element.
IZ-
-s
b) What can you say about the first site relative to the second site in terms of solvent
accessibility?
c) What do you expect the half times to be at pH 7?
Part IV (24 pts)
We are collecting 3N- H residual dipolar coupling data on a small protein containing
three helices. The following table presents splittings measured in an HSQC experiment.
Residue #
3
4
5
6
Isotropic splitting
94.5
94.0
94.0
95.0
Oriented splitting
105.5
105.5
105.0
106.0
11
12
13
94.5
95.5
94.5
89.5
89.0
89.0
22
23
24
25
95.0
94.0
94.5
94.5
105.0
104.5
104.5
105.0
RDC?
-lt,0
- n, T
- ;/, o
- //. n
4 5-7,0
^ c-
*-£•,<-
— /o<o
-/o, r
-to ,o
-/0,h
a) Fill in the RDC column in the table with the proper sign for the RDCs
b) Given that the protein is nearly axially symmetric in shape and the RDCs for residues 3-6 are
among the largest in magnitude for any seen in the protein, what can you say about the preferred
orientation of the 3-6 helix axis relative to the magnetic field?
c) What can you say about the orientation of the 3-6 helix relative to the other two helices?
Part V (28 pts). Answer the following showing your work.
We have managed to excite double quantum coherence between a proton spin (I) and a carbon
spin (S). In product operator form this is described as 2IxSx#2IySy.
a) Write this in density matrix form. What spin states (aa, ap,pa, or PP) are connected by the
finite elements in the matrix?
. /
-> frh
o
f?
0
o
I
O
O
/ 0 O 0
OOO - 2.
OO I O
o ioo
ooo |
O O OO
o> o o o
I o oo
b) Using matrix methods to extract an observable, show that there is no observable Mx
magnetization for the system represented by this density matrix.
I 00
A
I
c) Using product operator representations and the transformations caused bV a single 90 pulse
(of your choosing) show how you would convert the original density matrix tcKme
observable SStSrmagnetization.
/fthMs^sMjW^
j^/tfT/l ^ /)
d) Sketch the spectrum that would be observed after collection of an FID and Fourier
transformation.
Additional useful tables: (Note: J in footnote is in radians. Normally J is in Hz. In this case
coefficient is sin(TiJt). ^
'/ 2 E
Ilz
I2z
2 IlzI2z
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0 - 1 0 0
0
0
1
0
0
0
0
1
2 0 0 - 1 0
0
0
0
0
1
0
1
0
0
0
1/2 i
0
0
i
0
0
0
0
0
0
0
0
-i
0
0
0
1/2 1 0 0 0
0
0
0 - 1 0 0
0
-i
0
0
1
0
0
1
0
0
1
0
0
0
0
0
i
0
0
0
0
1
0
0
0
-i
0 0 0 - 1
0
0
1
0
0
0
i
0
0 0 - 1 0
0
0
0
0
0
1
0
1/2
0
-i
0
0
0
0
i
i
0
0
0
0
-i
0
0
0
-i
0
0
i
0
0
0
0
0
0
i
0
0
-i
0
/2
/2
2IlyI2y
2IlxI2y
2IlyI2x
1
0 0 0 - 1
0 0
0
-i
0
0
0
-i
0
0
1
0
0
i
0
0
0
-i
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1/2
1/2
- 1 0 0 0
0
0 -i
0
0
i
0
0
0
1/2
0
i
0
0
i
0
0
0
Transformations Caused by Various Evolution Operators
Product Oper.
l/2E
0
2 11 zI2y
0
!/2
0
0 0 - 1 0
2IlzI2x
0
0
2
0 0 0 - 1
1
0
t
0
0
2IlxI2x
1
0 - 1 0 0
2IlyI2z
-i
I2y
I2x
1
0
2IlxI2z
1
0
1
Ily
0
0
0
0
0 0 0 - 1
0
1
0
0 0 0 - 1
Ilx
0
2 0
0
Ilx
Ily
Ilz+I2z
2 IlzI2z
&E
>/ 2 E
'/ 2 E
!/2E
Ilz
-Ily
Ilx
Ilz
Ilz
I2z
I2z
I2z
I2z
I2z
2IlzI2z
-2IlyI2z
2IlxI2z
2IlzI2z
2IlzI2x
Ilx
Ilx
-Ilz
Ily
2IlyI2z
Ily
Ilz
Ily
-Ilx
-2IlxI2z
I2x
I2x
I2x
I2y
2IlzI2x
12y
I2y
I2y
-I2x
-2IlzI2x
211x122
2 IlxI2z
-2IlzI2z
2IlyI2z
Ily
2IlyI2z
2IlzI2z
2IlyI2z
-211x122
-Ilx
2 IlzI2x
-2Ilyl2x
2IlxI2x
2 IlzI2y
I2y
2IlzI2y
-2IlyI2y
2IlxI2y
2IlxI2x
2 IlxI2x
-2IlzI2x
-2IlzI2x
...
2 IlxI2x
2IlyI2x
2IlzI2x
2 IlyI2x
...
2IlyI2x
2 IlxI2y
2 IlxI2y
-2 IlzI2y
...
2 IlxI2y
2IlyI2y
2IlzI2y
2IlyI2y
...
2IlyI2y
-I2x
Evolution is to 2, 4( ), or more —. Coefficient is sin of /3, '/2 Jt, or wt.
10
Table 1.2 A selection oi nuclear isotopes and their properties. A complete listing of nuclear spins, gyromagnetic
ratios and Larmor frequencies (omitting the sign) may be found on the website www. web elements , con.
Isotope
:H
-H
3H
IOB
11 B
BC
1; N
«N
17O
ivp
Na
27 A 1
•""Si
27
Mp
»ci
*a
"Cu
6X"u
P 7 AK
'*Ag
n ' J Xe
Ground -state
spin
Natural
abundance/%
Gyromagnetic ratio
Y/UT rads'1!'1
NMR frequency at 11.74T
(o»°/23r)/MHz
1/2
1
1/2
3
3/2
1/2
1
1/2
5/2
1/2
3/2
5/2
1/2
1/2
3/2
-100
0.013
267.522
41.066
285.349
28.747
85.847
67.283
-500.000
-76.753
- 533.320
-53.718
- 160.420
-125.725
-36.132
+50.684
+67.782
470.470
-1.32.259
-130.285
+99.336
-202.606
-48.990
-40.779
-132.577
-142.018
+20.239
+23.268
+ 139.045
-104.603
a/2
3/2
3/2
1/2
1 /2
1/2
Xffpb
1/2
~C
"O
0
0
0
19.9
80.1
1.1
99.0
0,37
0.04
19338
-.27.126
-36.281
251.815
70.808
69.763
-53.190
108.394
10.610
8,832
71.118
76.044
-10.889
-12.518
-74.521
55805
-100
-100
-100
4.7
-100
75.77
24.23
69,17
30. S3
51.84
48.16
24.4
22.1
98.9
--1C0
*t*
7
R,
h.
fiU/t
11