Name:

BCMB/CHEM 8190, BIOMOLECULAR NMRFINAL EXAM-5/5/10

Instructions: This is an open book, limited time, exam. You may use notes you have from classand any text book you find useful. You may also use a calculator. The exam is intended totake about 2 hours, but you may use the full exam period (8-11) if you wish. Write youranswers 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?

H2) 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 aminoacids) in micelles. The protein (transmembrane domain of OmpA) that they used was nearlycompletely (-98%) deuterated at nonexchangeable sites. Why, in general, are proteinssometimes deuterated for NMR studies?

5 p / iyp

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 resolutionby multiplying the original FID by an exponential function exp(t/0.21). On Fouriertransforming the resultant FID what line width would you observe? Would the resolutionhave improved?

4) In a ' C, N enriched protein which do you expect to have the larger (magnitude) scalarcoupling, 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 twoexperiments: HN(CO)CACB and HNCACB? (Which would you expect to give the bettersignal to noise ratio?)

MfixbCUk. Am^. 3/'S. _ ̂ -A/

6) A TROSY version of an 15N-!H HSQC spectrum is collected on a large macromolecule. Howdo 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 two19F 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 wesuccessfully link them in a rigid framework that doesn't perturb their individual binding, whatmight 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 andminimization often have high energies. How might you improve (decrease) the energies ofthese 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 15Hz. 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 organicmolecules is deuterated benzene (Ce He). An expansion of aregion of a 'JC spectrum near 130 ppm is shown to the right.are there three peaks? Why are they of equal intensity? /

smallWhy

12) A variety of constraints are typically applied in the NMR-based structure determination of aprotein. 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*1-

14) 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 givesquare order parameters of (S2) of 0.8. Several residues in a loop give S2 values of 0.6indicating more internal motion. If we model the motion as jumps between equally populatedstates 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 betweensequential residues and Ha-HN connections between i -> i +1 and i -> i + 3 residues. Whattype of secondary structure does this part of the protein have?

16) Ribose ring puckers are sometimes 2' endo and sometimes 3' endo. What measurementwould 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 by100 Hz at 500 MHz and 5°C. As temperature is raised the resonances broaden, coalesce, andsharpen. This is due to 180° ring flips about the Cp-CY bond. At 45°C a single resonance, 30Hz full width at half height, is observed. Given that most other resonances are lOHz in widthat this temperature, what is the exchange rate?

f> b *-"M//5 -t

AUJHO NH

2^) = / (/0t?xzrt)'* C= 0,0013 H5

1 8) In solids NMR cross-polarization is used to transfer magnetization from a high gammanucleus like protons to a low gamma nucleus like carbon- 13. Suppose we have fluorinatedpolymer like Teflon and we want to detect carbon- 13 with high sensitivity. Our spectrometeroperating at 300 MHz for protons is set up for cross polarization from protons. The gamma

"1 s"1for fluorine is 2.518 x 10 rad Tesla" s"and that for a proton is 2.7 x 10 rad TeslaWhat frequency would you choose for your high gamma nucleus spin-lock? By what fractionwould you change the BI spin-lock field strength for fluorine?

19) The following chemical shift anisotropy powder pattern is seen for an amide nitrogenresonance in a 1?N labeled amino acid using a 300 MHz (proton frequency) spectrometer toobserve a static sample. How fast will you have to spin the sample in a magic angle spinningexperiment to see a single high resolution line?

>250 200 150 100 50 PPM

20) We run an HNCACB experiment on a protein and observe the following set of peaks on acolumn connected to a single 1H-I5N cross-peak: 55.2, 45.2, 23.5. We know the cross-peakmust 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 forwater protons in regions occupied by the reagent from 1.5s to 0.5s. We use the echo-planar pulsesequence sketched below. We plan to inset an element into the sequence that would allow T2decay to affect the amplitude of signals coming from various parts of the image.

90x

c3 (2

1 '

dw-1

t2

dw-2

t2

t1

dw-3

t2

dw-4

t2

dw-5

a) Suppose the element allows decay for an additional Is. What would the relative signalamplitudes be for signals coming from the two regions?

^79 f: t

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.

Part III (24 pts)

We measure at pH 6 and 25 C the disappearance of two cross-peaks in a 15N,'H HSQC spectrumof a small protein. They belong to alanines in sites with sequences RGAD and GADKrespectively. The first exchanges with a half time of 2 days and the second with a half time of 5hours.

a) Can you say anything about the relative stability of the secondary structure elements in whichthe sites exist? If you can, make it more quantitative by predicting a difference in the free energyof opening of the secondary structure element.

IZ-

-sb) What can you say about the first site relative to the second site in terms of solventaccessibility?

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 containingthree helices. The following table presents splittings measured in an HSQC experiment.

Residue #3456

111213

22232425

Isotropic splitting94.594.094.095.0

94.595.594.5

95.094.094.594.5

Oriented splitting105.5105.5105.0106.0

89.589.089.0

105.0104.5104.5105.0

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 areamong the largest in magnitude for any seen in the protein, what can you say about the preferredorientation 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.

f?

A

We have managed to excite double quantum coherence between a proton spin (I) and a carbonspin (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 thefinite elements in the matrix?

o0o

I OO

/ 0 O 0

OOO - 2.

OO I Oo i o o

o o o |

O O O Oo> o o oI o o o

. / -> frh

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 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 tcKmeobservable SStSrmagnetization. /fthMs^sMjW^ j^/tfT/l ^ /)

d) Sketch the spectrum that would be observed after collection of an FID and Fouriertransformation.

Additional useful tables: (Note: J in footnote is in radians. Normally J is in Hz. In this casecoefficient is sin(TiJt). ̂

'/2E I l z I2z 2 I l z I2z

1 0 0 0

0 1 0 0

0 0 1 0

0 0 0 1

2

1 0 0 0

0 1 0 0

0 0 - 1 0

0 0 0 - 1

2

1 0 0 0

0 - 1 0 0

0 0 1 0

0 0 0 - 1

t2

1 0 0 0

0 - 1 0 0

0 0 - 1 0

0 0 0 1

I l x I l y 2 I l x I 2 z 2 I l y I 2 z

0 0 1 0

0 0 0 1

1 0 0 0

0 1 0 0

1/2

0 0 -i 0

0 0 0 -i

i 0 0 0

0 i 0 0

1/2

0 0 1 0

0 0 0 - 1

1 0 0 0

0 - 1 0 0

1/2

0 0 -i 0

0 0 0 i

i 0 0 0

0 -i 0 0

I2x I2y 2I lzI2x 2 11 zI2y

0 1 0 0

1 0 0 0

0 0 0 1

0 0 1 0

!/2

0 -i 0 0

i 0 0 0

0 0 0 -i

0 0 i 0

/2

0 1 0 0

1 0 0 0

0 0 0 - 1

0 0 - 1 0

/2

0 -i 0 0

i 0 0 0

0 0 0 i

0 0 -i 0

2 I l x I 2 x 2 I ly I2y 2 I l x I 2 y 2 I l y I 2 x

0 0 0 1

0 0 1 0

0 1 0 0

1 0 0 0

1/2

0 0 0 - 1

0 0 1 0

0 1 0 0

- 1 0 0 0

1/2

0 0 0 -i

0 0 i 0

0 -i 0 0

i 0 0 0

1/2

0 0 0 -i

0 0 -i 0

0 i 0 0

i 0 0 0

Transformations Caused by Various Evolution OperatorsProduct Oper. Ilx Ily Ilz+I2z 2 IlzI2z

l/2E

Ilz

I2z

2IlzI2z

Ilx

Ily

I2x

12y

211x122

2IlyI2z

2 IlzI2x

2IlzI2y

2IlxI2x

2IlyI2x

2 IlxI2y

2I lyI2y

&E

-Ily

I2z

-2IlyI2z

Ilx

Ilz

I2x

I2y

2 IlxI2z

2IlzI2z

-2Ilyl2x

-2IlyI2y

2 IlxI2x

2IlzI2x

2 IlxI2y

2IlzI2y

>/2E

Ilx

I2z

2IlxI2z

-Ilz

Ily

I2x

I2y

-2IlzI2z

2IlyI2z

2IlxI2x

2IlxI2y

-2IlzI2x

2 IlyI2x

-2 IlzI2y

2I lyI2y

'/2E

Ilz

I2z

2IlzI2z

Ily

-Ilx

I2y

-I2x

2IlyI2z

-211x122

2 IlzI2y

-2IlzI2x

...

...

...

...

!/2E

Ilz

I2z

2IlzI2x

2IlyI2z

-2IlxI2z

2IlzI2x

-2IlzI2x

Ily

-Ilx

I2y

-I2x

2 IlxI2x

2IlyI2x

2 IlxI2y

2IlyI2y

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, gyromagneticratios and Larmor frequencies (omitting the sign) may be found on the website www. web elements , con.

Ground -stateIsotope

:H

-H3HIOB

11 BBC1;N«N17Oivp

27 Na27 A 1•""SiMp

»ci*a"Cu6X"uP7AK'*Agn'JXeXffpb

~C"O

spin

1/21

1/23

3/21/2

11/25/21/23/25/21/21/23/2a/2

3/23/21/21 /21/21/200

Naturalabundance/%

-1000.013

019.980.11.1

99.00,370.04-100-100-1004.7

-10075.7724.2369,1730. S351.8448.1624.422.198.9--1C0

Gyromagnetic ratioY/UT rads'1!'1

267.52241.066

285.34928.74785.84767.28319338

-.27.126-36.281251.815

70.80869.763

-53.190108.394

10.6108,832

71.11876.044

-10.889-12.518-74.521

55805

NMR frequency at 11.74T(o»°/23r)/MHz

-500.000-76.753

- 533.320-53.718

- 160.420-125.725-36.132+50.684+67.782470.470

-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

*t*R,h.

7

fiU/t

11