Final answer:
To determine the unique DNA sequence length in humans, we must find a sequence length n such that there are more possible sequences of that length than there are places in the genome. Calculating this using the formula n = ceil(log4(3 x 10^9)) gives the answer, as you cannot have fractional nucleotides. The sequence length that comes from this calculation is the minimum length expected to be unique.
Step-by-step explanation:
Estimating the Unique DNA Sequence Length in Humans
The question is asking for the minimum length of a DNA sequence that will likely appear only once in the human genome, assuming that the four nucleotides (A, C, G, and T) are equally likely to occur.
Given that the human genome contains approximately 3 billion nucleotides, and there are four possible nucleotides at each position, we can calculate the probability of any specific sequence of length n occurring more than once.
To find a sequence that only occurs once, we'll need a sequence that has more combinations than there are places in the genome for it to start. The total number of unique sequences of length n can be calculated as 4^n. Since there are 3 billion places to start a sequence, we want 4^n to be just over 3 billion.
Thus, log4(3 billion) gives us the minimum length of the sequence when rounded up to the nearest whole number, as we cannot have fractions of nucleotides.
In mathematical terms, the equation would be n = ceil(log4(3 x 10^9)). Calculating this value would give us the minimum length of a DNA sequence expected to be unique within the human genome, on one strand.