Probability and ribonucleotides

[Yann]

There's question in Hardt's Essential Genetics that bugs me, because I'm not sure if the answer is very simple or if I just don't get the question right. If you have a sequence of 4 ribonucleotides (with equal frequency), what is the probability to have a start codon/stop codon and what would be the average distance between stop codons in a DNA sequence...

The probability of a start codon is 1/64, it's 3/64 for stop codons (of course it depends on the organism but in this case it must be the "convenctional" start/stop codons). A codon is made of 3, not 4 nucleotides. Within a sequence of 4 codons, there could be 2 codons (XXXY or YXXX), so it seems the probability would be 2/64 and 6/64, but I'm not sure if it's that simple...

For the average distance it's easier; 64/3 codons or 64 nucleotides.

 

[farful]

The probability of codon frequency is dependent on the GC content. To make life easier, suppose GC content is 50%. Then, the probability of a stop codon is indeed 3/64. Asking for the probability of a start codon is a dumb question and is dependent on the locations of the stop codon. Even the naive approach to gene finding first choose the longest regions without stop codons, then look for the start codon.

A codon is made of 3, not 4 nucleotides. Within a sequence of 4 codons, there could be 2 codons (XXXY or YXXX)

That made no sense. Within a sequence of 4 codons, there are four codons - not two. If you meant that within a sequence of 4 nucleotides, there are two codons, that's not true either - there are four. Two in the 5' to 3' direction and two in the 3' to 5' direction.

As for average distance, assuming a GC content of 50%, I agree with your answer.

 

[quicknote]

Your question is a valid one and it shows that you are thinking critically about the problem. The answer is not as simple as just dividing the number of possible codon combinations by 64. The reason for this is that the start and stop codons are specific sequences that are necessary for proper protein synthesis. In most organisms, the start codon is AUG and the stop codons are UAA, UAG, and UGA. This means that out of the 64 possible codon combinations, only 1 out of 64 will be a start codon and 3 out of 64 will be stop codons. Therefore, the probability of having a start codon in a sequence of 4 codons is 1/64 and the probability of having a stop codon is 3/64.

To calculate the average distance between stop codons in a DNA sequence, we need to consider the fact that there can be multiple stop codons in a sequence. For example, in a sequence of 12 codons, there could be 3 stop codons (UAG, UAA, and UGA) which would result in an average distance of 4 codons between each stop codon. However, in a sequence of 12 codons, there could also be just 1 stop codon (UAA) resulting in an average distance of 12 codons between stop codons. Therefore, the average distance between stop codons in a DNA sequence cannot be determined without knowing the specific sequence of codons.

In summary, the probability of having a start codon and stop codon in a sequence of 4 ribonucleotides is 1/64 and 3/64 respectively. However, the average distance between stop codons cannot be determined without knowing the specific sequence of codons. Keep questioning and exploring these concepts, it will only deepen your understanding of genetics and probability.