Question

If a protein contains four different SH groups, how many different disulfide bonds are possible if only a single disulfide bond is formed? How many different disulfides are possible if two disulfide bonds are formed?

Short answer

Answer: If there is only a single disulfide bond formed, 6 different disulfide bonds are possible. If there are two disulfide bonds formed, there is 1 different combination possible.

Step-by-step solution

Understanding Disulfide Bond Formation

A disulfide bond is formed when two SH groups react and create a sulfur-sulfur (S-S) bond. In this exercise, there are four different SH groups (SH1, SH2, SH3, and SH4).

Find the Number of Single Disulfide Bonds Possible

As we are given four different SH groups, we'll have to determine the combination of any two groups in the form of pairs. In this case, we'll use the concept of combinations without repetition, which can be calculated using the formula: Number of combinations = \(\binom{n}{r} = \frac{n!}{r!(n-r)!}\) Where "n" is the total number of SH groups, and "r" is the number of SH groups to be combined (2 for a disulfide bond). In our case, n = 4 and r = 2. We'll plug these values into the formula to find the number of single disulfide bonds possible: Number of single disulfide bonds = \(\binom{4}{2} = \frac{4!}{2!(4-2)!} = \frac{4!}{2!2!} = \frac{4*3*2*1}{(2*1)(2*1)} = \frac{24}{4} = 6\) So, there are 6 different ways to form a single disulfide bond.

Find the Number of Disulfides Possible with Two Disulfide Bonds

As there should be two disulfide bonds formed from the given four SH groups, there's only one possible combination - a pair of two bonds (SH1-SH2 and SH3-SH4). It's easy to verify that the bonds forming the pairs are distinct, and no SH group is left unbound. Thus, for two disulfide bonds, there are 1 different combination possible. To conclude, if there is only a single disulfide bond formed, 6 different disulfide bonds are possible. If there are two disulfide bonds formed, there is 1 different combination possible.