72 lines
2.1 KiB
Markdown
72 lines
2.1 KiB
Markdown
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---
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id: 5900f49a1000cf542c50ffac
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challengeType: 5
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title: 'Problem 300: Protein folding'
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---
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## Description
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<section id='description'>
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In a very simplified form, we can consider proteins as strings consisting of hydrophobic (H) and polar (P) elements, e.g. HHPPHHHPHHPH.
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For this problem, the orientation of a protein is important; e.g. HPP is considered distinct from PPH. Thus, there are 2n distinct proteins consisting of n elements.
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When one encounters these strings in nature, they are always folded in such a way that the number of H-H contact points is as large as possible, since this is energetically advantageous.
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As a result, the H-elements tend to accumulate in the inner part, with the P-elements on the outside.
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Natural proteins are folded in three dimensions of course, but we will only consider protein folding in two dimensions.
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The figure below shows two possible ways that our example protein could be folded (H-H contact points are shown with red dots).
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The folding on the left has only six H-H contact points, thus it would never occur naturally.
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On the other hand, the folding on the right has nine H-H contact points, which is optimal for this string.
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Assuming that H and P elements are equally likely to occur in any position along the string, the average number of H-H contact points in an optimal folding of a random protein string of length 8 turns out to be 850 / 28=3.3203125.
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What is the average number of H-H contact points in an optimal folding of a random protein string of length 15?
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Give your answer using as many decimal places as necessary for an exact result.
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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- text: <code>euler300()</code> should return 8.0540771484375.
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testString: 'assert.strictEqual(euler300(), 8.0540771484375, "<code>euler300()</code> should return 8.0540771484375.");'
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function euler300() {
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// Good luck!
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return true;
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}
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euler300();
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// solution required
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```
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</section>
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