The problem describes the synthesis of proteins involving ribosomes moving along an mRNA molecule (ARNm). We are given that one mRNA molecule has 900 nucleotides. During protein synthesis, four ribosomes move along the mRNA at equal speeds, without turning back. The distance between each ribosome is 18 nm, and the total time taken is 4 minutes. We need to calculate: a) The number of protein molecules synthesized. b) The total number of amino acids in all protein molecules. c) The speed of movement of the ribosomes along the mRNA molecule.

1. Problem Description

The problem describes the synthesis of proteins involving ribosomes moving along an mRNA molecule (ARNm). We are given that one mRNA molecule has 900 nucleotides. During protein synthesis, four ribosomes move along the mRNA at equal speeds, without turning back. The distance between each ribosome is 18 nm, and the total time taken is 4 minutes. We need to calculate:

a) The number of protein molecules synthesized.

b) The total number of amino acids in all protein molecules.

c) The speed of movement of the ribosomes along the mRNA molecule.

2. Solution Steps

a) Number of protein molecules synthesized:

Since there are four ribosomes moving along the mRNA, and each ribosome synthesizes one protein molecule, the number of protein molecules synthesized is

4.

b) Total number of amino acids:

We know that one mRNA molecule has 900 nucleotides. Each codon consists of 3 nucleotides, and each codon codes for one amino acid (assuming all codons code for an amino acid).

Number of codons = Total nucleotides / Nucleotides per codon

Number of codons = $900 / 3 = 300$

Therefore, each protein molecule contains 300 amino acids. Since 4 protein molecules are synthesized, the total number of amino acids is:

Total amino acids = Amino acids per protein * Number of proteins

Total amino acids = $300 * 4 = 1200$

c) Speed of ribosome movement:

We know the distance between each ribosome is 18 nm. Since there are four ribosomes, there are three gaps between them. The total distance spanned by the four ribosomes is the distance occupied by the first ribosome to the last ribosome. We'll estimate how many nucleotide bases are covered by each ribosome separation distance.

First find the total distance covered by three ribosomal gaps.

Total Ribosome Distance = $(3) * (18 \, nm) = 54 \, nm$

We need to find the conversion factor from nm to nucleotides:

1 nucleotide pair length is approximately $0.34 \, nm$.

Number of nucleotides covered by ribosomes = $54 \, nm / 0.34 \, nm/nucleotide = 158.82 \approx 159$ nucleotides.

The total number of nucleotides on ARNm is

9

0

0. After the ribosome covers $\approx$ 159 nucleotides, the proteins are released.

Since it takes 4 minutes to complete the synthesis:

$time = 4 \, minutes = 4*60 \, seconds = 240 \, seconds$

The ARNm is approximately $900 * 0.34 nm = 306 nm$.

The speed is $distance / time$

$speed = 306 nm / 240 s = 1.275 nm/s$.

Another approach:

Four ribosomes work to produce protein in 4 minutes (240 seconds). Each moves 900 bases.

Length of nucleotide = $0.34 nm$

Length = 900 * 0.34 nm = 306 nm

$speed = 306 nm / 240 seconds = 1.275 nm/s$

3. Final Answer

a) The number of protein molecules synthesized is

4. b) The total number of amino acids in all protein molecules is

1

2

0

0. c) The speed of movement of the ribosomes along the mRNA molecule is 1.275 nm/s.