Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A small protein has 50 links in its chain, and each link can sit in 3 positions. Suppose that the chain could test shapes every second, one after another.
Folding is driven by the hydrophobic effect and held by hydrogen bonds, salt bridges and disulphide bridges. Heat, pH, urea and thiols denature a protein, but its peptide bonds stay whole. The isoelectric point, pI, is the pH of zero net charge: the average of the two pK values on either side of the neutral form.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The shapes. .
Step 2. The time. seconds. A year has seconds, so the time is years.
Step 3. The meaning. A chain that tries every shape would need thousands of years. Real chains fold in about a second, so they do not search at random. Folding runs downhill through a few steps, with the hydrophobic collapse early on.
Answer: shapes (7.18e23); about 2275 years; folding is guided, not a random search.
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