Question

The codons (words) in DNA (that specify which amino acid should be at a particular point in a protein) are three bases long. How many such three- letter words can be made from the four bases adenine, cytosine, guanine, and thymine?

Short answer

There are 64 different possible codons (three-letter words) that can be made using the four bases adenine, cytosine, guanine, and thymine. This is calculated by applying the counting principle to the 4 choices for each of the 3 positions in the codon: \(4 \times 4 \times 4 = 64\).

Step-by-step solution

Identify the number of choices at each position

There are four bases: adenine (A), cytosine (C), guanine (G), and thymine (T). Each position in the three-letter codon can be occupied by any one of these bases. Therefore, there are 4 choices for each of the 3 positions in the codon.

Apply the counting principle

According to the counting principle, if there are m ways to do one thing and n ways to do another, then there are m × n ways to do both. Since there are 4 choices for each of the 3 positions in the codon, we can determine the total number of possible codons by multiplying the number of choices for each position: Total number of codons = (Number of choices for position 1) × (Number of choices for position 2) × (Number of choices for position 3)

Calculate the total number of codons

Substitute the number of choices for each position in the equation: Total number of codons = 4 × 4 × 4 Total number of codons = 64 There are 64 different possible codons (three-letter words) that can be made using the four bases adenine, cytosine, guanine, and thymine.

Key concepts

DNA Base Pairs

In the fascinating world of genetics, DNA base pairs form the language of life. DNA, or deoxyribonucleic acid, is the blueprint for every organism, carrying instructions for the development, functioning, growth, and reproduction of all known living organisms and many viruses.

DNA is composed of two strands that coil around each other to form a double helix. Each strand is made up of a long chain of nucleotide units. Each nucleotide consists of a sugar molecule, a phosphate group, and one of four types of nitrogen bases: adenine (A), thymine (T), cytosine (C), or guanine (G). The nitrogen bases on one strand pair with the bases on another strand: adenine pairs with thymine, and cytosine pairs with guanine. This pairing is due to the hydrogen bonding between the bases. The order of these bases along a strand is what determines the genetic information.

Complementary Base Pairing

Complementary base pairing is critical for DNA replication and transcription. During DNA replication, the strands separate and serve as templates for creating two new double helices. Each original strand's nitrogen bases are used to pair new complementary bases, which ensures that the genetic information is copied accurately.

In transcription, the process where DNA is used to create messenger RNA (mRNA), the same base pairing rules apply, except that uracil (U) replaces thymine when RNA is synthesized. Understanding DNA base pairing is crucial for grasping concepts such as genetic coding and mutations that can affect protein synthesis.

Protein Synthesis

Protein synthesis is a complex, two-part process consisting of transcription and translation, through which the genetic code within DNA is used to produce proteins. Proteins perform a multitude of functions within organisms, including catalyzing metabolic reactions, replicating DNA, and responding to stimuli.

Transcription: From DNA to RNA

During transcription, a specific segment of DNA is decoded into mRNA, mirroring the complementary base pairs of DNA—except that uracil (U) is used in place of thymine (T). This mRNA molecule then exits the nucleus and enters the cytoplasm of the cell.

Translation: From RNA to Protein

In translation, the mRNA is read by a ribosome in sets of three nucleotides known as codons. Each codon corresponds to a specific amino acid or a stop signal for the growing polypeptide chain. Transfer RNA (tRNA) molecules carry amino acids to the ribosome, matching the anticodons on the tRNA with the codons on the mRNA to ensure the correct amino acid sequence for the protein.

The order of the three-letter codons on the mRNA determines the sequence of amino acids in the protein, and this, in turn, determines the protein's structure and function. Therefore, the precise arrangement of nucleotide bases in DNA is ultimately responsible for the diversity and complexity of life.

Counting Principle in Genetics

The counting principle in genetics is a fundamental concept that enables us to calculate the probable outcomes of genetic combinations, such as during gamete formation or predicting the genetic makeup of offspring.

When applying the counting principle to the genetic codons, as shown in the exercise, it is important to understand that each position in the codon can be thought of as a separate event with multiple possible outcomes. In this case, there are four possible nucleotides that can occupy each position in a three-base long codon. According to the counting principle, if one event can occur in 'm' ways and another independent event can occur in 'n' ways, then there are 'm' times 'n' total possible ways these events can occur together.

For the three-letter genetic codons formed by four bases (A, C, G, T), the counting principle tells us to multiply the number of possibilities for each base:

1. First position: 4 possible nucleotides (A, C, G, T)
2. Second position: 4 possible nucleotides (A, C, G, T)
3. Third position: 4 possible nucleotides (A, C, G, T)

Using the formula, we find that the total number of possible codons is 4 × 4 × 4, which equals 64. This mathematical understanding is vital for geneticists when decoding genetic information, predicting patterns of inheritance, and understanding how mutations can affect genetic variation within populations.

Through the simple application of the counting principle, we see how the diversity of life is supported by a surprisingly manageable number of genetic combinations, showcasing the efficiency and elegance of the genetic language.