# Proinsulin is an 84 residue polypeptide with six cysteines. How many different disulfide combinations are possible?

Generally cysteine residues form disulfide linkages - so how many combinations are possible out of (say) six residues. Also can cysteine form bonds with all the residues?

• I suggested some minor changes to the text of the question, but did not want to alter the second sentence : do you mean something like "can all these disulphide links be created"? – gilleain Oct 13 '20 at 13:31
• The Biology.SE community has agreed that questions that show little or no prior research effort are off-topic on this site unless you have shown your attempt at an answer. Please edit your question and tell us where you've looked for answers, what you do know about the topic, and where exactly you still have questions. Unresearched questions may be subject to down-voting and closure. – MattDMo Oct 13 '20 at 16:10
• yes, actually i wanted to ask can all disulfide links be created? – arkadeep Oct 14 '20 at 6:49

This is a mathematical problem rather than biological.

see this

the refined question would be this : we have 6 items and we want to pack them in 3 groups of 2.(We assume that all six cysteines do form a disulfide bond with each other and none of them are ungrouped or left out.Let me know if you have the question about the latter situation.) How many different sorting are possible?

Disclaimer: I am terrible at these types of mathematics . but I believe I have found the right answer.

Method A :

Write all of them!

six items are called A,B,C,D,E,F respectively

Fix A.

## AF/BC/DE AF/BE/DC AF/BD/CE

Method B:

you could also use C(n,r) function for better understanding but I'm going with this:

we have 6 items. Split them into 3 groups of 2. Group 1 ,group 2 , group 3.

calculate number of different combinations.

group 1 : 6 * 5 /2 = 15 (you can reverse the order of the first 2 objects and the group would still remain the same)

group 2 : 4 * 3 /2 =6 (you can reverse the order of the first 2 objects and the group would still remain the same) (Two of the items are used in the previous group)

group 3 : 2 * 1 /2 =1

(you can reverse the order of the first 2 objects and the group would still remain the same) (Four of the items are used in the previous groups)

You have to multiply these numbers . But do not forget that combination between group 1,2,3 does not matter(you can call any of them 1 , any of them 2 ,etc and the result would NOT change. It is just naming.)

3!=6

we have 6 repetitious/same groups counted in each unique combination . Therefore devide the whole amount by 6

15 * 6 * 1 / 6 = 15

About the second question the answer is no. Cysteine form disulfide bonds only with itself as far as I know

• If the question is mathematical it is probably off-topic as it bears no relationship to the reality of biology. Even assuming a random chain finding different combinations, rather than the chain folding in a manner governed by the amino acid sequence) the possibility of a second disulphide bond forming after one has formed would depend on their relative location. In fact the protein probably forms first and then oxidation occurs. So the answer is 1. – David Nov 5 '20 at 12:02
• the nascent protein translocates into the ER then it is oxidized to form S-S bonds. Suppose our protein has 6 cysteines. A biochemical procedure occurs by Ero1 and DPI which oxidizes the sulfurs exactly one after another ( i.e. cys1 is bound to cys2 and cys 3 to cys4 and cys 5 to cys 6) . This intermediate might be thermodynamically-instable . So here comes PDI again to REARRANGE the incorrect disulfide bonds , Literally testing each combination of S-S until it gets the most stable combination/conformation. So in theory there might be all different combinations of disulfide bonds...... – Sam Nov 5 '20 at 13:54
• The less stable combinations are later degraded . Here's the references: Molecular Cell Biology Lodish et al 8th ed chapter 13 figure 13-19 . Also take a look at M. M. Lyles and H. F. Gilbert, 1991, Biochemistry 30:619. – Sam Nov 5 '20 at 13:54