The problem describes an mRNA molecule (ARNm) consisting of 1800 ribonucleotides. This mRNA is used to synthesize a protein, with ribosomes moving along the mRNA molecule at a speed of 6.8 nm/second. The problem consists of three parts: a) Calculate the number of amino acids in the protein molecule. b) The ARNm molecule is synthesized from a gene that has 300 fewer A nucleotides than C nucleotides. Calculate the number of each type of nucleotide in the gene. c) How long does the protein synthesis take?

1. Problem Description

The problem describes an mRNA molecule (ARNm) consisting of 1800 ribonucleotides. This mRNA is used to synthesize a protein, with ribosomes moving along the mRNA molecule at a speed of 6.8 nm/second. The problem consists of three parts:

a) Calculate the number of amino acids in the protein molecule.

b) The ARNm molecule is synthesized from a gene that has 300 fewer A nucleotides than C nucleotides. Calculate the number of each type of nucleotide in the gene.

c) How long does the protein synthesis take?

2. Solution Steps

a) Calculating the number of amino acids in the protein:

Each codon (a sequence of 3 nucleotides) codes for one amino acid. Therefore, to find the number of amino acids, we need to divide the total number of nucleotides by

3. Number of amino acids = Total number of nucleotides / 3

Number of amino acids = 1800 / 3 = 600

b) Calculating the number of each type of nucleotide in the gene:

Let A, T, G, and C represent the number of adenine, thymine, guanine, and cytosine nucleotides in the gene, respectively. Since the ARNm comes from one strand of the DNA, we can consider one strand of the DNA molecule.

We know that the total number of nucleotides in the mRNA precursor(or a strand of the DNA) is not explicitly given, we assume here that the mRNA molecule corresponds exactly to the gene length considered. Moreover, because DNA has two strands, the total number of bases in the gene is twice the length of the mRNA, 1800*2=

3

6

0

0. The problem states there are 300 fewer A nucleotides than C nucleotides, so $A = C - 300$.

Also, for a double-stranded DNA molecule, A = T and C = G. So, $A + T + C + G = 2(A + C) = 3600$.

Therefore, $A + C = 1800$. Substituting $A = C - 300$, we get $(C - 300) + C = 1800$, which means $2C = 2100$, so $C = 1050$.

Since $A = C - 300$, $A = 1050 - 300 = 750$.

So, $A = T = 750$ and $C = G = 1050$.

c) Calculating the time taken for protein synthesis:

The length of the mRNA molecule needs to be known to calculate the time. We know there are 1800 nucleotides, and the ribosome moves at a speed of 6.8 nm/second. We are missing the length of each nucleotide. Since we do not have any other information about the mRNA molecule length, we can assume the length of each nucleotide in the mRNA is 0.34 nm, which is the distance between base pairs in DNA.

Total length of mRNA = Number of nucleotides * Length per nucleotide

Total length of mRNA = $1800 * 0.34 nm = 612 nm$

Time = Distance / Speed

Time = $612 nm / 6.8 nm/second = 90 seconds$

3. Final Answer

a) The number of amino acids in the protein molecule is

6

0

0. b) The number of each type of nucleotide in the gene is: A = 750, T = 750, C = 1050, G =

1

0

5

0. c) The time taken for protein synthesis is 90 seconds.