IChO 2009, Теория — Задача 3. Theoretical problem3 — Protein Folding
41st International Chemistry Olympiad — Cambridge2009 — Theoretical problems (Volume3 collection edition2014)
Внимание: Бележка към темата
Source edition: The Competition Problems from the International Chemistry Olympiads, Volume 3, edited by Anton Sirota, IUVENTA / IChO International Information Centre, Bratislava, 2014. The collection normalizes task numbering and omits some original grading points, practical instructions and data-dependent key material. Every item actually printed in this Cambridge 2009 section is retained. The referenced practical answer booklet, TLC template and Practical 1 carbon NMR spectrum were not obtained. Reproduced for teaching purposes with the printed Volume 3 attribution and rights notice; commercial publication/distribution requires permission from the copyright holder.
Collection edition and native section
The Competition Problems from the International Chemistry Olympiads, Volume3,41st–45th IChO2009–2013. Edited by Anton Sirota. IUVENTA–Slovak Youth Institute, Bratislava2014. This scoped paper preserves only the41st International Chemistry Olympiad,18–27July2009, Cambridge, United Kingdom.

Native rights statement and archive qualification
You are free to copy, distribute, transmit or adapt this publication or its parts for unlimited teaching purposes, you are obliged, however, to attribute your copies, transmissions or adaptations with a reference to "The Competition Problems from the International Chemistry Olympiads, Volume 3" as it is commonly required in the chemical literature. The problems copied cannot be published and distributed for commercial proposes. The above conditions can only be waived if you get permission from the copyright holder.
Copyright2014IUVENTA–IChO International Information Centre; ISBN978-80-8072-154-1. Attribution: The Competition Problems from the International Chemistry Olympiads, Volume3, edited by Anton Sirota, Bratislava2014.
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Issued by IUVENTA – Slovak Youth Institute in 2014 with the financial support of the Ministry of Education of the Slovak Republic. Number of copies: 250. Not for sale.
International Chemistry Olympiad, International Information Centre, IUVENTA – Slovak Youth Institute, Búdková 2, SK 811 04 Bratislava 1, Slovakia. E-mail: anton.sirota@stuba.sk. Web: www.icho.sk.
Full native editorial preface
Preface This publication contains 39 theoretical and 14 practical competition problems from the 41st – 45th International Chemistry Olympiads (IChO) organized in the years 2009 – 2013. It has been published by the IChO International Information Centre in Bratislava (Slovakia) as a continuation of the preceding Volumes 1 and 2 published on the occasion of the 40th anniversary of the IChO with the titles: • The competition problems from the International Chemistry Olympiads, Volume 1, 1st – 20th IChO, 1968 – 1988 (IUVENTA, Bratislava, 2008). • The competition problems from the International Chemistry Olympiads, Volume 2, 21st – 40th IChO, 1989 – 2008 (IUVENTA, Bratislava, 2009). Not less than 318 theoretical and 110 practical problems were set in the IChO during the forty-five years of its existence. In the elaboration of this collection the editor had to face certain difficulties because the aim was not only to make use of past recordings but also to give them such a form that they may be used in practice and further chemical education. Consequently, it was necessary to make some corrections in order to unify the form of the problems (numbering the tasks of the particular problems, solution inserted immediately after the text of the problem, solutions without grading points and special graphs used for grading of practical problems). Nevertheless, the mentioned corrections and changes do not concern the contents and language of the competition problems. The practical problems set in the IChO competitions, contain as a rule some instructions, list of apparatuses available, chemicals on each desk and those available in the laboratory, and the risk and safety phrases with regard to the chemicals used. All of these items are important for the competitors during the competition but less important for those who are going to read the competition tasks of this collection and thus, they are omitted. Some parts of the solutions of practical problems are also left out since they require the experimental data which could be obtained by experiments during the practical part of the IChO competition. In this publication SI quantities and units are preferred. Only some exceptions have been made when, in an effort to preserve the original text, the quantities and units have been used that are not SI. Although the numbers of significant figures in the results of some solutions do not obey the criteria generally accepted, they were left without change.
Unfortunately, the authors of the particular competition problems are not known and due to the procedure of creation of the IChO competition problems, it is impossible to assign any author's name to a particular problem. Nevertheless, responsibility for the scientific content and language of the problems lies exclusively with the organizers of the particular International Chemistry Olympiads. This review of the competition problems from the 41st – 45th IChO should serve to both competitors and their teachers as a source of further ideas in their preparation for this difficult competition. For those who have taken part in some of these International Chemistry Olympiads the collection of the problems could be of help as archival and documentary material. In the previous forty-five years many known and unknown people - teachers, authors, pupils, and organizers proved their abilities and knowledge and contributed to the success of this already well known and world-wide competition. We wish to all who will organize and attend the future International Chemistry Olympiads, success and happiness. Bratislava, July 2014 Anton Sirota, editor
Source note: The preface describes general editorial omissions. This Cambridge section nevertheless prints practical chemical lists, procedures and selected grading graphs, all retained. Missing original answer-booklet/NMR material is not invented.
Условие
The unfolding reaction for many small proteins can be represented by the equilibrium:
You may assume that the protein folding reaction takes place in a single step. The position of this equilibrium changes with temperature; the melting temperature Tₘ is defined as the temperature at which half of the molecules are unfolded and half are folded.
The intensity of the fluorescence signal at a wavelength of356nm of a1.0μM(M=mol dm⁻³) sample of the protein Chymotrypsin Inhibitor2(CI2) was measured as a function of temperature over the range58to66°C:
| Temperature / °C | 58 | 60 | 62 | 64 | 66 |
|---|---|---|---|---|---|
| Fluorescence intensity(arbitrary units) | 27 | 30 | 34 | 37 | 40 |
A1.0μM sample in which all of the protein molecules are folded gives a fluorescence signal of21units at356nm. A1.0μM sample in which all of the protein molecules are unfolded gives a fluorescence signal of43units.
3.1 Assuming that the fluorescence intensity from each species is directly proportional to its concentration, calculate the fraction, x, of unfolded molecules present at each temperature.
3.2 Give an expression for the equilibrium constant, K, in terms of x, and hence calculate the value of K at each temperature.
3.3 Estimate the value of Tm for this protein (to the nearest 1 °C).
Assuming that the values of ΔH° and ΔS° for the protein unfolding reaction are constant with temperature then:
where C is a constant.
3.4 Plot a suitable graph and hence determine the values of ΔH° and ΔS° for the protein unfolding reaction. [If you have been unable to calculate values for ∆Ho and ∆So, you should use the following incorrect values for the subsequent parts of the problem: ∆Ho = 130 kJ mol⁻¹; ∆So = 250 J K⁻¹ mol⁻¹.]
3.5 Calculate the equilibrium constant for the unfolding reaction at 25 °C. [If you have been unable to calculate a value for K, you should use the following incorrect value for the subsequent parts of the problem: K = ]
The first order rate constant for the CI2 protein folding reaction can be determined by following the fluorescence intensity when a sample of unfolded protein is allowed to refold(typically the pH of the solution is changed). The concentration of protein when a1.0μM sample of unfolded CI2 was allowed to refold was measured at a temperature of25°C:
| time / ms | 0 | 10 | 20 | 30 | 40 |
|---|---|---|---|---|---|
| concentration / μM | 1 | 0.64 | 0.36 | 0.23 | 0.14 |
3.6 Plot a suitable graph and hence determine the value of the rate constant for the protein folding reaction, kf, at 25 °C. [If you have been unable to calculate the value for kf, you should use the following incorrect value for the subsequent parts of the question: kf = 60 s⁻¹.]
3.7 Determine the value of the rate constant for the protein unfolding reaction, ku, at 25 °C.
3.8 At 20 °C the rate constant for the protein folding reaction is 33 s⁻¹. Calculate the activation energy for the protein folding reaction.
Решение
3.1
| Temp / °C | 58 | 60 | 62 | 64 | 66 |
|---|---|---|---|---|---|
| x | 0.27 | 0.41 | 0.59 | 0.73 | 0.86 |
3.2
| Temp / °C | 58 | 60 | 62 | 64 | 66 |
|---|---|---|---|---|---|
| K | 0.38 | 0.69 | 1.4 | 2.7 | 6.3 |
3.3 Answer:Tₘ=61°C.
3.4

Answers:ΔH°=330kJ mol⁻¹;ΔS°=980J mol⁻¹ K⁻¹.
3.5 ΔH°=330000J mol⁻¹ andΔS°=980J mol⁻¹ K⁻¹ thenΔG°=30500J mol⁻¹ at25°C,hence .
3.6

Answer:Rate constant for the protein folding reaction,kf=50s⁻¹.
3.7 Answer:Rate constant for the protein unfolding reaction,.
3.8 Answer:Activation energy=61kJ mol⁻¹.
Source note: The native page21 image printsΔG°=30500J mol⁻¹, although its text layer reads35000. The actual printed30500 is retained. These rounded thermodynamic quantities and K do not agree exactly with direct recomputation; no revised values are invented.
Оригинал в Архива: IChO 41st-45th.pdf · решение от архива: IChO 41st-45th.pdf · допълнителни данни: IChO 41st-45th.pdf