## Assume a protein is composed of 105 amino acid residues and that each amino acid can have three possible orientations. How many total possible orientations are there for the protein?

### 4.17×1049 orientations Explanation: Each possible orientation of an amino acid is due to rotation about a bond. Since there are two terminal amino acids, there will be one fewer peptide bond compared to the number of amino acids. Since there are three possible selections at each point of rotation, the number of combinations would be calculated by raising 3 to the power of 105−1.

To calculate the number of total possible orientations for a protein composed of 105 amino acid residues, we need to use the multiplication principle of counting.

There are three possible orientations for each amino acid residue, so we can think of each residue as having three choices.

Using the multiplication principle, we need to multiply the number of choices for each residue (3) by itself for the number of residues in the protein (105).

Therefore, the total possible orientations for the protein is 3^105, which is approximately 1.26 x 10^50. This is an extremely large number, highlighting the vast structural diversity that is possible for proteins.

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