There are about 300,000,000 US citizens. If we wanted to assign each person a unique
identifier, using DNA sequences, how long a DNA sequence would we need? (Here’s
another way of phrasing the question: How many bases of DNA are required for there to be
at least 300 million different possible DNA sequence of that length?)
To determine the length of DNA sequence needed to assign a unique identifier to each of the approximately 300,000,000 US citizens, we can make use of the concept of combinatorics.
In DNA, there are four different bases: adenine (A), thymine (T), cytosine (C), and guanine (G). Each base can be represented by 2 bits. Therefore, we have 2^2 = 4 possible combinations for a single base.
To calculate the length of the DNA sequence required, we need to find the number of combinations that can be formed with 4 bases for at least 300 million unique sequences.
The formula to calculate the number of combinations is given by:
Number of combinations = 4^N
Where N represents the length of the DNA sequence in bases.
Now, we need to solve for N in the equation:
4^N >= 300,000,000
Taking the logarithm of both sides (base 4), we get:
N >= log(300,000,000) / log(4)
Calculating this expression, we find:
N >= 14.5238
Therefore, we need a DNA sequence with a length of at least 15 bases to provide at least 300 million different possible DNA sequences.
To calculate the length of the DNA sequence needed to assign a unique identifier to 300 million US citizens, we need to determine the minimum number of bases required to achieve at least 300 million different DNA sequences.
In DNA, there are four different bases: adenine (A), cytosine (C), guanine (G), and thymine (T). Each base can be thought of as a digit in a numbering system.
The total number of possible unique DNA sequences of a given length can be calculated using the formula 4^n, where n is the number of bases in the sequence. This is because for each position in the sequence, we have four choices (A, C, G, or T).
Using this formula, we can solve for the number of bases needed:
4^n >= 300 million
Taking the logarithm of both sides of the equation to isolate n, we get:
n >= log(300 million) / log(4)
Now, let's calculate the value of n:
n >= log(300,000,000) / log(4)
n >= 8.86155
Since we cannot have a fractional number of bases, we round up to the nearest whole number. Therefore, we would need a DNA sequence length of at least 9 bases to ensure there are at least 300 million different possible DNA sequences.
Please note that this calculation assumes that each DNA sequence is truly unique and that there are no restrictions or limitations on the sequence composition. In reality, additional factors such as genetic variations and sequence constraints may affect the uniqueness of DNA sequences.