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Physics/probability question

E

Eeezee

Diamond Member
I had a question on a test recently that went as follows

"A protein consists of 1000 linked amino acids. There are 20 naturally occurring amino acids. How many different proteins can you amek from those 20 amino acids?

The answer is 20^1000, with a note

Note: The answer is actually approximately 20^1000 / 2. The first 5 students to tell me why there is a factor of 2 will receive +3 points on their exame. The first 3 to explain why it's approximately and not exactly (20^2000) / 2 will receive an additional +3, and these students need not necessarily be part of the original 5.

Help me out here! Why is it approximately 20^1000 / 2?
 
Seriously, extra credit FTW, although I don't know the answer. Give me a hand here!

If you can explain to me what a start/stop codon is that might help. This is probably purely a probability question though, since we really don't study proteins in this class.
 
Originally posted by: Eeezee
I had a question on a test recently that went as follows

"A protein consists of 1000 linked amino acids. There are 20 naturally occurring amino acids. How many different proteins can you amek from those 20 amino acids?

The answer is 20^1000, with a note

Note: The answer is actually approximately 20^1000 / 2. The first 5 students to tell me why there is a factor of 2 will receive +3 points on their exame. The first 3 to explain why it's approximately and not exactly (20^2000) / 2 will receive an additional +3, and these students need not necessarily be part of the original 5.

Help me out here! Why is it approximately 20^1000 / 2?
Click to expand...

You divide by 2 cause the protein could be the same backwards and forwards.
For example, if you had the link ABC, it would be the same as the link CBA.

It's not exact when you divide by 2 because sometimes you can have "palindrome" proteins.
For example, ABA is the same backwards and forwards.
 
Originally posted by: chuckywang
Originally posted by: Eeezee
I had a question on a test recently that went as follows

"A protein consists of 1000 linked amino acids. There are 20 naturally occurring amino acids. How many different proteins can you amek from those 20 amino acids?

The answer is 20^1000, with a note

Note: The answer is actually approximately 20^1000 / 2. The first 5 students to tell me why there is a factor of 2 will receive +3 points on their exame. The first 3 to explain why it's approximately and not exactly (20^2000) / 2 will receive an additional +3, and these students need not necessarily be part of the original 5.

Help me out here! Why is it approximately 20^1000 / 2?
Click to expand...

You divide by 2 cause the protein could be the same backwards and forwards.
For example, if you had the link ABC, it would be the same as the link BCA.

It's not exact when you divide by 2 because sometimes you can have "palindrome" proteins.
For example, ABA is the same backwards and forwards.
Click to expand...

you HAD to go and spoil it!
 
Originally posted by: StevenYoo
Originally posted by: chuckywang
Originally posted by: Eeezee
I had a question on a test recently that went as follows

"A protein consists of 1000 linked amino acids. There are 20 naturally occurring amino acids. How many different proteins can you amek from those 20 amino acids?

The answer is 20^1000, with a note

Note: The answer is actually approximately 20^1000 / 2. The first 5 students to tell me why there is a factor of 2 will receive +3 points on their exame. The first 3 to explain why it's approximately and not exactly (20^2000) / 2 will receive an additional +3, and these students need not necessarily be part of the original 5.

Help me out here! Why is it approximately 20^1000 / 2?
Click to expand...

You divide by 2 cause the protein could be the same backwards and forwards.
For example, if you had the link ABC, it would be the same as the link BCA.

It's not exact when you divide by 2 because sometimes you can have "palindrome" proteins.
For example, ABA is the same backwards and forwards.
Click to expand...

you HAD to go and spoil it!
Click to expand...

Geez, I can do basic probability/counting but I can't even copy words down backwards. Edited my mistake in my post.
 
Originally posted by: StevenYoo
Originally posted by: chuckywang
Originally posted by: Eeezee
I had a question on a test recently that went as follows

"A protein consists of 1000 linked amino acids. There are 20 naturally occurring amino acids. How many different proteins can you amek from those 20 amino acids?

The answer is 20^1000, with a note

Note: The answer is actually approximately 20^1000 / 2. The first 5 students to tell me why there is a factor of 2 will receive +3 points on their exame. The first 3 to explain why it's approximately and not exactly (20^2000) / 2 will receive an additional +3, and these students need not necessarily be part of the original 5.

Help me out here! Why is it approximately 20^1000 / 2?
Click to expand...

You divide by 2 cause the protein could be the same backwards and forwards.
For example, if you had the link ABC, it would be the same as the link BCA.

It's not exact when you divide by 2 because sometimes you can have "palindrome" proteins.
For example, ABA is the same backwards and forwards.
Click to expand...

you HAD to go and spoil it!
Click to expand...

I don't quite understand that first part. Dividing by 2 eliminates this problem?

Edit: Nevermind, I understand now that your very very helpful post was edited. Thanks! :cookie:
 
Originally posted by: Eeezee
Originally posted by: StevenYoo
Originally posted by: chuckywang
Originally posted by: Eeezee
I had a question on a test recently that went as follows

"A protein consists of 1000 linked amino acids. There are 20 naturally occurring amino acids. How many different proteins can you amek from those 20 amino acids?

The answer is 20^1000, with a note

Note: The answer is actually approximately 20^1000 / 2. The first 5 students to tell me why there is a factor of 2 will receive +3 points on their exame. The first 3 to explain why it's approximately and not exactly (20^2000) / 2 will receive an additional +3, and these students need not necessarily be part of the original 5.

Help me out here! Why is it approximately 20^1000 / 2?
Click to expand...

You divide by 2 cause the protein could be the same backwards and forwards.
For example, if you had the link ABC, it would be the same as the link BCA.

It's not exact when you divide by 2 because sometimes you can have "palindrome" proteins.
For example, ABA is the same backwards and forwards.
Click to expand...

you HAD to go and spoil it!
Click to expand...

I don't quite understand that first part. Dividing by 2 eliminates this problem?
Click to expand...

123 = 321

Those are two probabilities, but the same number in physical form.

Not sure if your teacher will do something like this, but "start/stop codons" are basically sequences of amino acids that begin and end all proteins. This is more biology, though, so that might not be of any relevance to what your professor wants.
 
Originally posted by: Eeezee
I wish I knew more about protein links :embarrassed;
Click to expand...

it's not a matter of knowing about proteins, it's a permutation problem.

the same problem can be made with a 1000 letter string, using only the first 20 letters of the alphabet, or 20 different symbols or something.
 
Originally posted by: JayHu
How many points for saying exactly the number?
Click to expand...

Do you have exactly the number? I don't think there's anything extra, but I'm sure a quick computer program could calculate it (I'm not sure why someone would bother in this case though...)
 
Man, how do you people come up with this stuff? I'm just barely getting into probability, so I'm a little slow at it
 
Originally posted by: Eeezee
Man, how do you people come up with this stuff? I'm just barely getting into probability, so I'm a little slow at it
Click to expand...

Answer had nothing to do with prob. and everything to do with group theory. So I wouldn't worry about knowing how the answer came around, just see what you can get for it 🙂


Originally posted by: TuxDave
Originally posted by: JayHu
I believe the answer in this case is..

1/2*(20^1000 + 20^500)
Click to expand...

Sounds right to me
Click to expand...

Excellent, my skills are not yet dull 😀
 
Originally posted by: Eeezee
Ah, but how did you come upon that answer? I'm really curious
Click to expand...

I'm glad to know you're curious, but really the idea is fairly difficult to understand without group theory knowledge. Just to throw out a few key ideas though : groups acting on sets, Cauchy-Frobenius thm and the polya-burnside method. That's basically what you'll need to know to understand it.

I'm also sure that if you were good at enumeration (ie counting) you could come up with the same result, but it would take a lot longer.
 
I'll do some google searching to see if I can better understand it. It sounds fairly complicated. Thanks for your help 🙂
 
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