Question

How many different tripeptides can be formed by lysine and alanine?

Short answer

8 different tripeptides can be formed.

Step-by-step solution

Understanding Tripeptides

A tripeptide is formed by connecting three amino acids in a specific order. Each position in the tripeptide can be filled with either lysine (K) or alanine (A). The order of these amino acids in the sequence is crucial, as differently ordered sequences represent different peptides.

Calculating Possible Combinations

For each of the three positions in the tripeptide sequence, you have two options (lysine or alanine). This results in multiple combinations. The number of different combinations can be represented by the formula for permutations with repetition: \[ 2^3 \]where 2 represents the number of amino acids available (lysine or alanine) and 3 represents the positions in the tripeptide.

Performing the Calculation

We have determined the formula to find how many different tripeptides can be formed is \(2^3\). Perform the calculation:\[ 2^3 = 2 \times 2 \times 2 = 8 \]

Conclusion

There are 8 different tripeptides that can be formed using lysine and alanine. Each tripeptide is a unique sequence of the three amino acids.

Key concepts

Amino Acids

Amino acids are the building blocks of proteins. They are organic compounds made up of an amino group \((NH_2)\), a carboxyl group \((COOH)\), and a unique side chain. This unique side chain determines the properties and function of each amino acid. There are 20 standard amino acids that play a vital role in almost all biological processes.
Amino acids link together to form peptide chains, which in turn fold into functional proteins. The order and number of amino acids in these chains determine the protein's properties.

• They serve as intermediates in metabolism.
• Some amino acids are essential, meaning humans must get them from their diet.

Overall, amino acids are crucial for life as they are involved in fundamental processes like neurotransmitter transport, biosynthesis, and cellular signaling.

Lysine

Lysine is one of the 20 essential amino acids, which means it cannot be synthesized by the human body and must be obtained from the diet. It has the unique characteristic of an \(( ext{NH}_3^+)\) side group which is positively charged at physiological pH. This contributes to lysine's role in protein structure and function.
Lysine plays a significant role in several functions within the body including:

• Protein synthesis, providing molecules necessary for building new proteins.
• Calcium absorption and bone health, working to increase the intestinal absorption of calcium.
• It also supports immune system function by helping the synthesis of antibodies.

As an amino acid, lysine is crucial in the formation of collagen, a protein necessary for skin elasticity and tissue repair.

Alanine

Alanine is another standard amino acid, known for its simple structure with a \((CH_3)\) methyl group as its side chain. This simplicity plays a functional role in metabolism and energy production. Alanine is classified as a non-essential amino acid because it can be synthesized by the body.
Some roles of alanine include:

• Providing energy for muscles and the central nervous system.
• Promoting a stable glucose level in the blood.
• Boosting the immune system by playing a part in generating T cells.

Alanine is often involved in converting energy stored in the muscle tissue back into glucose in the liver, providing a significant energy boost during physical activities.

Peptide Sequence

A peptide sequence refers to a specific order of amino acids linked together through peptide bonds. The sequence and arrangement of these amino acids determine the properties and function of the resulting peptide or protein.
Each position in the sequence can drastically alter the structure and function of the resulting molecule. A small peptide, such as a tripeptide, consists of three amino acids, and even these short chains can have diverse structural and functional roles.

• Significance lies in specific interactions between amino acids that can affect the overall 3D structure.
• Even a single change in an amino acid can lead to a completely different function or malfunction of the peptide.

Understanding peptide sequences helps in synthesizing proteins with desired functions and applications in biotechnology and medicine.

Permutations with Repetition

Permutations with repetition are a mathematical concept used to determine how many different sequences can be formed when certain elements can be repeated. This principle applies when calculating the possible arrangements of amino acids to form tripeptides.
In the case of tripeptides formed from lysine and alanine, each of the three positions in the peptide can contain either amino acid.
The formula to calculate the number of different permutations is: \[2^3 = 8\]

• "2" represents the number of different amino acids (lysine and alanine).
• "3" denotes the number of positions in the sequence (as each position can be filled independently).

This formula helps us find that there are 8 possible tripeptide sequences, showcasing permutations' importance in understanding potential biological outcomes.