Problem 113 - Arihant Objective Approach to Organic Chemistry for IIT JEE and NEET all Medical Entrances Part 4

Question

The number of possible different codons is : (a) 16 (b) 64 (c) 32 (d) 48

Step-by-Step Solution

Answer

The number of possible different codons is 64.

Step 1: Understanding Codons

A codon consists of a sequence of three nucleotides, and each position in the sequence can be occupied by one of the four nucleotides: Adenine (A), Thymine (T), Guanine (G), or Cytosine (C). Thus, there are four possible choices for each position in the codon.

Step 2: Calculate Total Combinations

The total number of different codons can be calculated by considering all the combinations of nucleotide sequences for the three positions. Since each position can be filled in 4 different ways, the calculation is as follows: \[ ext{Total Codons} = 4 imes 4 imes 4 = 4^3 \]

Step 3: Perform the Calculation

Now let's perform the calculation: \[ 4^3 = 4 imes 4 imes 4 = 64 \] So, there are 64 possible different codons.

Key Concepts

Codons

In the world of genetics, a **codon** is an essential concept. It is a sequence of three nucleotides that corresponds to a specific amino acid or a start/stop signal in protein synthesis.
Codons are part of the genetic code used by living organisms to translate genetic information into proteins. Each three-nucleotide sequence, or triplet, plays a crucial role in determining which amino acids are added during protein synthesis.
This universality is why understanding codons is foundational in fields like genetics, molecular biology, and bioinformatics.

Nucleotides

Nucleotides are the building blocks of DNA and RNA, which constitute the genetic material of organisms. Each nucleotide consists of three parts:

• A nitrogenous base (Adenine, Thymine, Guanine, Cytosine in DNA; Adenine, Uracil, Guanine, Cytosine in RNA)
• A five-carbon sugar (deoxyribose in DNA and ribose in RNA)
• A phosphate group

These components link together to form the DNA double helix or RNA single strand.
In the context of codons, nucleotides are specifically the letters that make up the three-letter codon sequence, dictating protein synthesis.

Combinatorial Mathematics

Combinatorial mathematics is crucial in understanding how different genetic sequences can be formed. The concept of combinations—how many ways a set of items can be arranged—applies directly to codons and nucleotides.
To calculate the number of possible codons, we utilize combinatorials. With four nucleotides possible at each of the three positions in a codon, the calculation is as follows:
Choose one of 4 nucleotides for the first position;
Then choose again among the 4 nucleotides for the second position;
Finally, choose once more among 4 nucleotides for the third position.
This results in a total of \(4 \times 4 \times 4 = 4^3 = 64\)
possible combinations. This mathematical process explains why there are 64 unique codons in the genetic code.