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: There are 6 different disulfide bonds possible when only a single disulfide bond is formed, and 1 possible arrangement of disulfide bonds when two disulfide bonds are formed.

Step-by-step solution

Understand the concept of combinations

In this step, we need to understand the concept of combinations. A combination is a way of selecting items from a larger set, where the order of selection does not matter. In this case, we want to find the number of possible disulfide bonds that can be formed by choosing two SH groups from a set of four. The formula for combinations is given by: C(n, k) = n! / (k!(n-k)!) where n is the total number of items, k is the number of items to choose, and ! denotes the factorial of a number.

Calculate the number of possible disulfide bonds when only a single bond is formed

To calculate the number of possible disulfide bonds when only a single bond is formed, we need to choose two SH groups from the set of four. Using the combination formula, we can calculate the number of ways to choose two SH groups from a set of four: C(4, 2) = 4! / (2!(4-2)!) = (4 * 3 * 2 * 1) / (2 * 1 * 2 * 1) = 6 Therefore, there are 6 possible different disulfide bonds when only a single bond is formed.

Calculate the number of possible disulfide bonds when two bonds are formed

When two disulfide bonds are formed, all four SH groups will be bonded. To calculate the number of possible disulfide bonds in this case, we need to divide the total number of SH groups by the number of groups in each bond, and then calculate the combination: Number of bonds formed = Total number of SH groups / Number of groups in each bond = 4 / 2 = 2 Now, we need to find the number of ways to choose two bonds from a set of two: C(2, 2) = 2! / (2!(2-2)!) = (2 * 1) / (2 * 1 * 1) = 1 Therefore, there is only 1 possible arrangement of disulfide bonds when two bonds are formed.

Conclusion

In conclusion, there are 6 different disulfide bonds possible when only a single disulfide bond is formed, and there is only 1 possible arrangement of disulfide bonds when two disulfide bonds are formed.