Question

Suppose that in the use of polynucleotide phosphorylase, nucleotides A and C are added in a ratio of 1A:5C. What is the probability that an AAA sequence will occur?

Short answer

Answer: The probability of an AAA sequence occurring in this reaction is 1/216.

Step-by-step solution

Calculate probabilities of A and C being added

Given the ratio of 1A:5C, we can find the probability of each nucleotide being added by dividing the frequency of each nucleotide by the total frequency of nucleotides. The total frequency of nucleotides is 1A + 5C = 6. The probability of A being added is 1/6, and the probability of C being added is 5/6.

Calculate the probability of each nucleotide in the AAA sequence

To find the probability of the AAA sequence occurring, we need to calculate the probability of each A nucleotide in the sequence. Since these events are independent, we can find the probability for each A in the sequence separately: - Probability of first A: 1/6. - Probability of second A: 1/6. - Probability of third A: 1/6.

Calculate the combined probability of the AAA sequence

Now that we have the probability of each A in the sequence, we can find the probability of the entire AAA sequence occurring by multiplying the probabilities of each nucleotide together: (1/6) * (1/6) * (1/6) = 1/216. So, the probability that an AAA sequence will occur is 1/216.

Key concepts

Nucleotide Ratios

Nucleotide ratios are key when determining the occurrence of specific genetic sequences. In the genetic exercise above, the nucleotides A (adenine) and C (cytosine) are added in a specific ratio of 1A : 5C. This means for every adenine, there are five cytosines. Ratios help predict which nucleotide is more likely to be incorporated into a sequence.
To determine the probability of a nucleotide's addition, you first calculate the total sum of the numbers in the ratio. In this case, totaling 1 + 5 = 6.
The probability of a single nucleotide being added is calculated by dividing its frequency by the total sum:

• The probability of A being added: 1/6.
• The probability of C being added: 5/6.

This basic arithmetic provides a clear understanding of how often each nucleotide might occur in a sample, aiding in sequence probability predictions.

Polynucleotide Phosphorylase

Polynucleotide phosphorylase is an enzyme capable of synthesizing RNA sequences without a template DNA. This means it can randomly assemble nucleotides into strands. The randomness hinges on the relative concentration of available nucleotides. As such, given specific ratios or concentrations of nucleotides — like 1A : 5C — the enzyme generates sequences based on these probabilities.
This enzyme's properties are crucial for studying genetic sequences independent of DNA templates. By manipulating nucleotide concentrations, researchers can discern how different ratios result in varied RNA sequences. Thus, polynucleotide phosphorylase not only assists in generating RNA but also provides insights into sequence probability when particular nucleotide ratios are known.

Genetic Sequence Probability

Understanding genetic sequence probability starts with identifying the likelihood of individual nucleotides appearing. For example, in our exercise, knowing the probability of each nucleotide impacts how we calculate the chance of sequences like AAA occurring.
With nucleotides added at a probability of 1/6 for A and 5/6 for C, calculating an AAA sequence involves independent probabilities. Each A being added is separate from others, making probabilities multiplicative. Hence:

• Probability of first A: 1/6
• Probability of second A: 1/6
• Probability of third A: 1/6

All these are multiplied: \((1/6) \times (1/6) \times (1/6) = 1/216\).
Thus, the complete sequence of AAA has a probability of 1/216. Recognizing these probabilities allows for predicting how often certain sequences occur, crucial for genetic research and applications.