Q.46 Proinsulin is an 84 residue polypeptide with six cysteines. How many different disulfide
combinations are possible?
Proinsulin with six cysteines can form 15 different disulfide combinations. This calculation arises from the combinatorial ways to pair all six cysteines into three disulfide bonds, a key concept in protein folding relevant for CSIR NET Life Sciences.
Disulfide Bond Basics
Disulfide bonds form between the thiol groups of two cysteine residues, stabilizing protein structures like proinsulin, an 84-residue precursor to insulin with exactly six cysteines. These bonds include two interchain (B7-A7, B19-A20) and one intrachain (A6-A11) in the native form, but mispairing during folding creates non-native isomers. With six cysteines, random pairing yields multiple possibilities beyond the functional one.
Calculation Method
The number of ways to form k=n/2 disulfide bonds from n=6 cysteines follows the double factorial formula: (2k−1)!!, where n!!=n×(n−2)×⋯×1. Compute as: 5!!=5×3×1=15.
Step-by-step pairing logic:
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Pair first cysteine with any of 5 others: 5 choices.
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Pair next unpaired with any of 3 remaining: 3 choices.
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Last two pair automatically: 1 choice.
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Divide by 3!=6 (order of bond formation): 5×3×1/6=15.
Verification for smaller cases confirms: 2 cysteines yield 1 way; 4 yield 3 ways (AB/CD, AB/CE/DF wait no: for 4: 1-2/3-4, 1-3/2-4, 1-4/2-3).
All Possible Combinations
Label cysteines 1-6 sequentially. The 15 unique pairings are:
| Pattern Type | Examples |
|---|---|
| Non-crossing | 12/34/56, 12/35/46, 13/24/56, 14/23/56, 16/23/45 |
| Crossing | 13/25/46, 14/25/36, 15/24/36, 15/26/34, 23/14/56 wait structured: actually full list via formula yields exactly 15 distinct topologies. |
In vitro studies observe only 2-3 major isomers due to folding kinetics favoring native paths, not all 15 equally.
Proinsulin six cysteines disulfide combinations puzzle students preparing for CSIR NET Life Sciences, as this 84-residue polypeptide’s folding hinges on correct cysteine pairing. With six cysteines forming three disulfide bonds, exactly 15 different disulfide combinations are possible, computed via the double factorial (5!!=15). This count underscores why proinsulin misfolding disrupts insulin production in diabetes.
Why 15 Combinations Matter
Random pairing explodes possibilities: for 6 cysteines, the formula (2n−1)!! with n=3 bonds gives 15, far more than simpler proteins. Native proinsulin selects B7-A7, B19-A20, A6-A11 amid kinetic traps. CSIR NET questions test this combinatorics to assess protein biochemistry grasp.
CSIR NET Exam Tips
Expect variants like “intra-chain bonds in proinsulin” (answer: 1) or full count. Practice verifies 4 cysteines: 3 ways; scales to 15 for six. Misfolding links to ER stress in beta-cells.
