How many different tripeptides can be formed from two molecules of glycine and one molecule of cysteine? Write all the structures by using the three-letter codes Gly and Cys.

Peptides are small chains of amino acids linked by peptide bonds. These bonds form between the carboxyl group of one amino acid and the amino group of another.
The sequence of amino acids in a peptide, including tripeptides, is crucial as it determines the peptide's properties and function.
The simplest form of a peptide is a dipeptide, which contains two amino acids. A tripeptide is the next level, containing three linked amino acids.
Peptides are named by listing the amino acids in the order they appear, starting from the N-terminus (which has a free amino group) to the C-terminus (which has a free carboxyl group).
In our example, we are considering a tripeptide formed using two molecules of glycine (Gly) and one molecule of cysteine (Cys). Therefore, the task is to find all the different ways to arrange these three amino acids to form unique tripeptides.

The arrangement of amino acids in a peptide is called its primary structure. This arrangement is vital because it affects the peptide's biological function and properties.
When arranging amino acids, we pay attention to their specific sequence, as different sequences can result in entirely different peptides.
Considering two identical molecules of glycine (Gly) and one molecule of cysteine (Cys), our goal is to list every unique order they can form a tripeptide.
One way to understand this is by visualizing our task as trying to arrange the set {Gly, Gly, Cys}.

• The possible sequences we need to explore are:
• Gly-Gly-Cys
• Gly-Cys-Gly
• Cys-Gly-Gly

The sequences considered here are unique and distinct in the context of peptide chemistry.

To determine how many unique tripeptides can be formed from our amino acids, we use permutations.
Permutations represent the different ways of arranging a set of items. In our case, we need the permutations of two glycine (Gly) molecules and one cysteine (Cys) molecule.
Since we have repeated elements (two Gly molecules), we use the permutation formula for multisets:\[ \frac{n!}{n1! \times n2! \times ... \times nk!} \]
Here, n is the total number of items, and each n_i represents the frequency of each distinct item.
In our example:\textarea \text{Gly} \text{Gly} \text{Cys}, n = 3 (total amino acids), Gly = 2 times, Cys = 1 time. Substituting these values:\[ \frac{3!}{2! \times 1!} = \frac{6}{2} = 3 \]

So there are 3 unique permutations:

{Gly, Gly, Cys}

{Gly, Cys, Gly}

{Cys, Gly, Gly}

This tells us that we can form three distinct tripeptides given the specified amino acids.
Understanding permutations is fundamental in biochemistry as it helps in predicting the number of unique sequences and structures possible with any set of amino acids.