1. A few weeks ago you recorded one of the two NMR spectra below. Explain briefly the necessary procedure to record such beautiful spectra!

Transcription

1 llowed aids: en/encil, eraser, ruler, calculator You may answer in English or Swedish. few weeks ago you recorded one of the two NMR sectra below. Exlain briefly the necessary rocedure to record such beautiful sectra!. oth sectra above clearly show folded roteins. Yet they differ in imortant regards. a) Which of the structures below is more likely to give rise to the sectrum to the left? Protein Protein b) The eaks in the sectrum to the left are of aroximately the same intensity, which is not true for the eaks in the sectrum to the right. Suggest a ossible roerty of the rotein in the latter case that exlains the difference in eak intensities!

2 3. Shown below are the structures of the two amino acids glutamate and tyrosine. Order the 3 C nuclei of the amino acids in order of increasing chemical shift and exlain your reasoning! [The nuclei are called (from right to left): CO, Cα, Cβ, Cγ, Cδ, Cε (Tyr only), Cξ (Tyr only)] 4. Discuss, and illustrate with a figure, a good strategy to assign the NMR signals to various nuclei in a rotein! 5. The NMR active nuclei in a certain molecule can be described as MX YZ. ll of them are 3 C. Their resonance frequencies are ν > ν M > ν X > ν Y > ν Z. is scalar couled to M with couling constant J M. M is additionally scalar couled with X with the couling constant J MX (J MX >> J M ). Y and Z are scalar couled with the couling constant J YZ. a) Sketch the one dimensional 3 C NMR sectrum for the molecule! b) Sketch the two dimensional 3 C TOCSY sectrum for the molecule! Here you may disregard from any multilet structure. 6. rotein is exchanging between two conformations with a global (same for all nuclei) rate constant. Shown below are the NMR sectra for two nuclei of the rotein at two different temeratures. a) What can you say about the chemical exchange for the two different nuclei? If you think there is difference, exlain what causes this difference! b) Which of the two nuclei is more likely to exerience the largest structural fluctuations due to exchange? Exlain!

3 3 7. a) List several reasons why NMR alications to rotein are facilitated by two dimensional exeriments! b) Exlain how two dimensional sectroscoy works! 8. The rotein TPMT tumbles with a correlation time of 5 ns at a magnetic field of 8.8 T. The average of the square of the fluctuations of the magnetic field is s -. a) What is the NMR line width for a 5 N nucleus with an order arameter of.? b) Would the line width increase or decrease for a nucleus with an order arameter of.5 in the same rotein under the same conditions? c) For which arts of roteins, regular secondary structure elements or loos, do you exect the narrowest signals? 9. nucleus in a rotein is in fast chemical exchange between two states. You haen to know that the exchange rate is s - and the difference in resonance frequencies for the nucleus in the two states is Hz. In a sectrum you measure that the line broadening due to chemical exchange is 5.97 Hz. a) Calculate the oulations for the two states! b) Calculate the energy difference between the two states!

4 4. Consider a H nucleus that is scalar couled to a 5 N nucleus. The resonance frequency of H in the absence of the scalar couling is ν H and the size of the scalar couling is J NH. a) Sketch the NMR sectrum of H considering the scalar couling to 5 N! b) t the start of the ulse sequence below, the magnetization of H is aligned along the x-axis. Sketch the hase(s) of the magnetization for H! The hase is defined as φ(t) π ν t. The 8 ulses on 5 N do not touch H. c) Now imagine that you aly hundreds of 8 ulses on 5 N during the same interval. Sketch the hase(s) and NMR sectrum of H under these conditions and exlain what you have achieved! Hay Holidays!

5 5 Tables and collection of equations Isotoe I γ (T - s - ) H / H C - 3 C / N / O - 7 O 5/ F / I [ I( I + ) ] / I {, ½,, ½,, } I z m m {-I, -I+,, I-, I}.5 γ I E m 34 kg m µ γm z s k k ki LW i π E ν γ γ γ π ω uer E / k T k lower e.38 γ ( σ ) ν π -3 J K 4πδν LW k + k T T J ( ω ) τ J(ω) c + ω τ c ( J () + J ( ω )) δν ν - ν ν ν δ ν v ref ref 6 m γ ( σ ) π X J X m X J(ω) S τ c + ω τ + ( S )τ e c + ω τ e LW πt