Possible Disulfide Combinations in Proinsulin

Introduction:
Proinsulin is an 84 residue polypeptide with six cysteines. The disulfide bonds formed between the cysteine residues are critical for the correct folding and function of the protein. The number of possible disulfide combinations in proinsulin can be calculated using a combinatorial approach.

Method:
The number of possible disulfide combinations can be calculated using the formula:

nCr = n! / r! (n-r)!

Where n is the total number of cysteine residues and r is the number of disulfide bonds formed.

Calculation:
In proinsulin, there are six cysteine residues. To determine the number of possible disulfide combinations, we need to consider the number of disulfide bonds that can be formed.

- Number of disulfide bonds = 0: There is only one possible combination where all cysteine residues remain unpaired.

- Number of disulfide bonds = 1: There are six possible combinations where one cysteine residue pairs with another cysteine residue.

- Number of disulfide bonds = 2: There are 15 possible combinations where two cysteine residues each pair with another cysteine residue.

- Number of disulfide bonds = 3: There are 20 possible combinations where three cysteine residues each pair with another cysteine residue.

- Number of disulfide bonds = 4: There are 15 possible combinations where four cysteine residues each pair with another cysteine residue.

- Number of disulfide bonds = 5: There are six possible combinations where five cysteine residues each pair with another cysteine residue.

- Number of disulfide bonds = 6: There is only one possible combination where all cysteine residues pair with another cysteine residue.

Result:
The total number of possible disulfide combinations in proinsulin can be calculated by adding up the number of combinations for each possible number of disulfide bonds:

1 + 6 + 15 + 20 + 15 + 6 + 1 = 64

However, since the disulfide bonds in proinsulin are formed in pairs, we need to divide this number by two to get the total number of unique disulfide combinations:

64 / 2 = 32

Therefore, the correct answer is '15 to 15'.