BioNMR2008FinalKey - Name: BCMBICHEM 8190, BIOMOLECULAR NMR...

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Unformatted text preview: Name: BCMBICHEM 8190, BIOMOLECULAR NMR Final — 04f30f08 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. I) (20 pts) A 3D TOCSY-HSQC is run on a protein sample with a pulse sequence that has a four step phase cycle, quadrature in all dimensions, and an average recycle time (including recovery and evolution times) of 2.05. The first proton dimension has crosspeaks falling between 9.0 and 1.0 ppm and we want to have a raw resolution (spectral sampling per point without linear prediction or zero- fiIling) of 0.08 ppm. The nitrogen dimension has peaks falling between }OO and 130 Ppm and we want to have a raw resolution of 1.0 ppm. 1' so}??? 7" ‘ ,3 '1 a) How many increments in the t1 and t2 dimensions would you have to acquire? 2'1. I: X ’2‘ “" if " NU “A?” ._-'-'-"-."-Z ‘-- 30 - - .. v- r u“ " - .u l I. ' I IX- ‘ I. r If H. (,- b) What would the dwell time (increment in evolution time) be for the first two dimensions? arr-.9. ‘ ‘ C’s-“TKY‘. " -- - '- ’- ‘ri- -1 , 7- /r_m;' -‘ - " 290 " 'r’ r d) How would you improve the apparent resolution in the indirect dimensions without collecting more points? . - ; ._ 1 I _.I “Ir‘lf‘ I f: .I! , A . - . ‘ La 4' ‘ _i. ",1 I, I. r .J - ‘ f 2) (24 pts) The TROSY effect comes from interference between two relaxation mechanisms, at dipole-dipole mechanism and a CSA mechanism. Can you predict which of the two peaks of an amide nitrogen would be the broadest; the upfield (low frequency) peak or the downfield (high frequency) peak? a) The unique shielding axis of the CSA tensor for the nitrogen is nearly along the N-H bond. Considering that the bond to the carbon is partly a double bond (remember our discussion of ethylene chemical shifts) do you suspect a field applied along the NH bond to be more shielded or less shielded than the average isotropic shielding? I ;. -"L f l | ‘2». . \-n——/- b) Draw an amide bond with the laboratory field along the NH bond. Add a symbol for the moment of a proton in the or state (m = '/z ) . Sketch the field linesfrom this moment. Do they add or subtract from the laboratory field at the nitrogen? Do they add or subtract from the shielding contribution of r the C SA tensor? ax Jr . I _. ; -+si? Ma r ; 9, r .H i‘ x ..g'“ .! r' . I -_ _r i ‘ ‘z 4‘. I' I. ‘_ \ \ .- . '1‘. l 1t c) Sketch a doublet for the proton coupled nitrogen. Indicate the high field and low field direction on the plot. Considering the ys for the nuclei and the fact that the one bond coupling mechanism adds to the energy when the coupled nuclear moments are parallel, label the peaks coming fi‘om molecules with the proton in the (I and [3 states. ,. .Y . , " fl. . \ ..\ fl. r . f“ .I’II“ , ._—__.. 3) (24 points) We design the following homonuclear NMR experiment and apply it to an AX spin system in which the spins are coupled with coupling constant I. The pulses affect both spins equally. 90y 180y I I t1/2 I I t1/2 t2 3 I! 4 - I '_ I. ' | __ '-t' 3.) Using product operators and starting with the system at equilibrium describe the state of the system after the 90° pulse, before the 180° pulse when t] is set to zero, after the 180° pulse when t] is set to zero, and at the beginning of t; when t; is set to zero. Jr"; '75] :1ch 4 e1)! r.-,ri'\l.7l.-" “\EK , )It 4 if? V r a . ' " 14-f- rfig; ~~IJK w_ 2; l 3”” '“"""f cf it “’ .~ J): v .72)? b) What two types of operators are active during the periods t1f2 and t2? .- ' ._ . \ I' .' J} E II f . ‘ fl rail 'II {I 1:?! '3‘ f9"; J-* i**-'-“' ."fl-‘ri ,i-i ‘f 31‘ “F ""5"!" 5 I J { T"?! " 0) Which operator in b do you expect to have contributed to evolution of the system at the end of the second t1f2 period? In terms of product operators give an expression for the t] time dependence of the system at the end of the second t1 period. “ ' f /7»* a _ ,4 [I / .fi , {ii ’1" Fri 5“” If t" 2}" r‘i‘ .r . k f H r :1“ /'r‘” t *n‘ f”- r,- (-f' {3; x} —- [(2, rt 4 .4“ \‘\ :h H \‘\ - - If. 31 .7“ ‘- I - I - 54 h p5? ( J! 5’3/ afflx) ‘3' x 4 .Z/z} gm o _ J ‘— f3 "m (7‘7 .3} d) Sketch what you would expect to observe for this experiment after Fourier transformation in both dimensions in the form of a 2D contour map. 4) (25 pts) Below is a structural representation of uridine monophosphate, one of the building books of RNA. We conduct a series of experiments designed to assign Spectra. These include proton COSY, proton TOCSY, carbon-proton HSQC, carbon-proton HMBC, and proton-proton NOESY. Assuming we analyze only a column emanating from the H1. proton, what major crosspeak connectivities would you expect to see for each of the experiments? You can assume that scalar couplings are near average values for various through-bond couplings and that you do not need to consider the effects of Karplus relationships. You can assume that the mixing time for the TOCSY experiment is long (100ms), and the mixing time for the NOESY experiment is short (50ms). b) TOCSY c) NOESY d) 9" ‘5' 5) (24 pts) N—acetylproline undergoes interchange between two conformers, one with a cis-amide and one with a trans-amide bond. At 50°C it has an 800 MHz proton NMR spectrum with two Lorenzian lines in the acetyl methyl region separated by 150 Hz. The one associated with the trans conformer has a width at half height of 12 Hz and a height of 10 and the one associated with the cis conformer has a width at halfheight of6 Hz and a height of 50. 0 H°\/ ’ a r O N-acetylproline a) What are the relative populations of the cis and trans conformers? - ' 1 w - 15-w- Ct.-.'.":1_ .' - :' .' I-v - 5 ' - -" " p . ‘ _ "-l _. _\ . ‘ _r'\ b) What are the relative life times in the two states? If ir‘ i‘T "J c) What is the exchange cpntr’ibution (in Hz) to the line width of each peak? u“? «in . . r J Xxx/)1. ,9". ’ t k .3; f1») 3 ' '7 " ' :4 ., HF . \ ._r ‘- _\ _,_ w“ ‘ .. \I- ‘ . J ; ' l' - a" 1‘91}? :- / O y a” a " 7 d) What are the actual life times of the two states (in seconds)? I. -- v ‘. " "’1'". . I") I], “A- K {i ..I,. - =er \I” H L] . I". _.5_ (I. In _: _ «I I“ 6) (16 pts) The maximum dipolar coupling (8 = 0) between a 13 C and 3 directly bonded proton in a methyl group when all motion is stopped is 64500 Hz. In real solids, at most temperatures, methyl groups rotate very rapidly and interactions are projected onto the methyl rotation axis. For a methyl group in an amorphous solid, that is deuterated at two positions leaving just one proton, the following 13 C powder pattern is observed under conditions where deuteriums are decoupled and chemical shift anisotropy effects are small. 11,000 Hz ‘_———p a) What angle relative to the laboratory field does the methyl rotation axis make for molecules contributing to the maximum intensity parts of the pattern? .: :,—.._ ¢"'_' _ . ~ " \ I“. t A. t |' In:- ‘t .1. . . . . ._ a - l2"} 2' I’; i \_ I: '2 i lill I _.r‘ )3 "-1 \v - ‘ \ II 1. f v {If} g"; / “I 5) f1“ [ .I K“ _.‘ \ 'I A W -\- 1 - .l 4!... _L '1"! +_ f“ -. ' -' _ . M a .5 7) (12 points) Estimate the magnitudes of the three bond IH, 'H coupling constants (3JHH) for the pairs of hydro gens labeled “A” and “B” in each of the compounds below. Justify your values with an brief explanation. Assume that the rings are rigid. HA HA HA EH3 CH3 CH3 CH3—(13 HE ens—d! (ma—(ll Ha CH3 CH3 HE CH3 , ‘x I x . _. . ,\._] fl, m {r 1;. a a: "-3 I. ‘1"! .l t , .. / 8) (15 points) In the initial INEPT element in the HSQC pulse sequence, a 2: gradient pulse is often inserted between the 90y (1H) and 90x (UN) pulses, which otherwise are applied simultaneously. 1H (I) “l? T [Note: following the second delay (second tau period, where 1803, 90x r=1f(4J;1,N)), a product operator treatment indicates antiphase 'I-l 15N (S) I I magnetization (2foz)]. a) What product operator describes an ideally behaving coupled Gz—‘_ two spin system at the point after the 90y pulse? 90x 180y 90y b) What is the effect of the gradient on this operator? . i f‘ I. ." .'- _ y" /\“l a .3». . r . ya I I c) What is the purpose of the gradient? _ ‘L- fl ' .. K 1 _ ._.F .- ' -. - ' . ' -’ ' - j I; ,5. _1 . ' .2 9) (10 pts) We conduct an imaging experiment in which a 10 mT (milli Tesla) x’ cm gradient is applied at right angles to the axes of two narrow tubes filled with water (a phantom). An FID is collected and after transformation two peaks appear in the frequency domain offset by -300 and + 700 Hz from our reference frequency. What is the distance between the tubes in the particular projection sampled? 10) (10 points) A transferred NOE experiment is conducted on a disaccharide (molecular weight 360 Da) binding to a 36 kDa lectin (protein). In the absence of the protein two NOEs involving the internal anomeric proton are seen; one to a protou in the same sugar ring and one to a proton in the second sugar ring (across the glycosidic bond). They are weakly positive NOES and their intensities are in the ratio of 8:1. In the presence of the protein the NOES are strongly negative and the ratio of internal to trans-glycosidic NOEs is 4: 1. 3) Assuming the rings are rigid and the molecules effectively spherical in shape, what is the ratio of the distances between the intra-rin g and trans-glycosidic pairs in the absence of the protein? 1 I \ {I i _ _ J. (“I ‘\ to ,1,“ . f\__,_ I . J ' _ r’) ‘” r) s,» x .J ll.” * W/L’ L. b) Is the distance between the trans-glycosidic pair longer or shorter in the presence of the protein? / -4L_-. _J _ “,5, 4.41! l. e.” L. Lt;- \H 11) (10 points) Dihedral angle information is often used for restraining backbone dihedral angles (phi and psi) during structure calculations. This information can be derived experimentally by measuring coupling constants. In lieu of coupling constant data, what information might be useful for providing backbone phi and psi angle restraints? Explain the basis for your answer. . I' I .- _i I- ‘9 , , we R. r K .- I . . .- --: . .r ‘ - . I x “If r" . a - . r—v _ -. ' » - J _. x (’1‘ if \ _I' II I-. r f1 : . -‘ ,1 i I — ._. g d _ . . . 1’ fl if I . I I t I. I I I. H. Li. k: _ I ,4 I . t .,. _r / ‘ r . __ ._ , I I, 3‘ I E r. . .. ‘ A .x ,- .r _.- ‘. . J - . . g _, _ . . I. I .- . _. , . . a}: x l t . - . - ‘ . l \ . H I_ t 1 . r! I; t l t. .l I l l -_- , f- \ - . ‘ '1: a - ' i I I' 4- T‘ cf;"nL_ 12) (10 points) The one bond lSN-UCQ coupling constant in a peptide is 7 Hz. What do you expect the 15N=13C one bond coupling constant in a histidine sidechain ring to be? _a" A ' y - I. IA 1" _k t J _ \ {I _ ’1, I w) '3 I1 1 ~ '- (—a t“ ’H l I" ~ " fa 1' f“ 'r 2,’ / 31.3.” x "/5 L ' ’ .f «I! .--~. ' a .5 ' K.“ k\ l ¥ t/l; {.7 I_ g l x a. r) :r l ‘i r :1 t.- I-e a .._ # '_.‘° (1? "l ______:_ "x - fil r 1 ___._I _ _.f.‘ ,L . f)?“ , 2‘ , h- J C0 " '7’ --' '2 .\. ’ . . \- I. \ rm) a .- .—o" l \_ " ,J - Ar "'— ( . ll: 8 Additional useful tables and constants: (Note: J in the table footnote is in radians. IN is in Hz the coefficient would be sin(th). 7,, = 2.675 x 108 rad s'1 T'l, h = 6.62 )1 1044.15, k = 1.38 x 10‘23 J K‘1 V: E 112 122 211212: 1000 1000 1000 1000 I{0100V111011 y0—100I/0-100 20010 200-10 20010 ’00-10 0001 000-1 000.1 0001 1111 My ZleIZZ ZIlyIZZ 0010 00-10 0010 00—10 0001 1100-1 000.1 0 01 "31000151000 lA1000 I“51000 0100 0100 0.100 0400 [2x 12y 211212): 2111,12)! 0100 0-100 0100 0-100 1000 1000 1000 1000 V2 5/: 1/1 V2 1 0001 000.. 000.1 0001 0010 00.0 00.10 0040 2llx12x 211y12y 211x12y 2113/12): 0001 000-1 000.: 000.1 0010 0010 00.0 00-10 150100 720100 I“30.100 '40100 1000 -1000 1000 1000 Transformations Caused by Various Evolution Operators Product Opcr. II x + l2x Ily +1231 112 +122 2112121 _ _ — _ Evolution is to 2, 4( ), or more ---. Coefficient is sin offi, V211, or (01. ...
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This note was uploaded on 11/07/2011 for the course CHEM 8853R taught by Professor Gelbaum during the Fall '11 term at Georgia Institute of Technology.

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BioNMR2008FinalKey - Name: BCMBICHEM 8190, BIOMOLECULAR NMR...

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