Question

Your book contains about 2 million characters (letters, spaces, and punctuation marks). If you could type with the accuracy with which the prokaryote \(E\), coli incorporates, proofreads, and repairs bases in replication (about one uncorrected error in \(\left.10^{9} \text { to } 10^{10} \text { bases }\right),\) how many such books would you have to type before an uncorrected error is "permitted"? (Assume that the error rate is one in \(10^{10}\) bases.

Short answer

5000 books

Step-by-step solution

Understand the Given Information

The book contains about 2 million characters, which is equivalent to 2 x 10^6 characters. The error rate during replication is given as one uncorrected error in 10^10 bases.

Calculate the Number of Characters per Book

Since the book has 2 million characters, we convert this to scientific notation as follows:2 million characters = 2 x 10^6 characters.

Determine How Many Books Before an Error

The rate of error is one uncorrected error per 10^10 bases. We need to find out how many books (each with 2 x 10^6 characters) are needed to reach 10^10 characters. This can be found by dividing 10^10 by the number of characters per book:\[\text{Number of books} = \frac{10^{10}}{2 \times 10^6}\]

Perform the Division

Now divide 10^10 by 2 x 10^6:\[\frac{10^{10}}{2 \times 10^6} = \frac{10^{10}}{2 \times 10^6} = \frac{10^4}{2} = 5000 \text{ books}\]

Conclusion

Therefore, you would need to type 5000 such books before an uncorrected error is 'permitted.'

Key concepts

error rate in DNA replication

DNA replication is the process by which a cell makes a copy of its genetic material. This process is critical for cell division and overall organism growth. The accuracy of DNA replication is essential because errors can lead to mutations.
In prokaryotic organisms like _E. coli_, the error rate is remarkably low, at about one uncorrected error in every 10 billion bases, or \(10^{10}\) bases. This means that the replication machinery must accurately copy an enormous amount of genetic information with minimal errors.
To put this into perspective, if DNA replication were as error-prone as our book typing example, errors would be rare—occurring only once in 5000 books of 2 million characters each. This incredible fidelity is due to various proofreading and repair mechanisms that correct most errors before they become permanent mutations.

prokaryotic replication fidelity

Replication fidelity in prokaryotes is high due to several mechanisms:

• **Proofreading:** The DNA polymerase has a proofreading function that checks for and corrects errors immediately during DNA synthesis.
• **Mismatch Repair:** Any errors missed by the proofreading function are later corrected by the mismatch repair system.

These combined processes ensure the low error rate of one in 10 billion bases. The high fidelity of prokaryotic replication is essential for maintaining genetic stability, which is especially crucial given the rapid rate of cell division in prokaryotes. Without such high accuracy, prokaryotes would accumulate harmful mutations quickly.

scientific notation in calculations

Scientific notation is a way to express very large or very small numbers conveniently. It’s particularly useful when dealing with biological data, which often involve large quantities.
In our exercise, we expressed the number of characters in the book and the error rate in scientific notation:

• 2 million characters is written as \(2 \times 10^6\).
• The error rate is one error in \(10^{10}\) bases.

This format simplifies calculations by allowing us to work with exponents. For example, to find out how many books would be needed to reach 10 billion characters, we divided \(10^{10}\) by \(2 \times 10^6\), simplifying the calculation to \(10^4 / 2 = 5000\). Using scientific notation ensures that we can handle these large numbers easily and minimizes the chance of errors in our calculations.

base incorporation accuracy

Base incorporation accuracy refers to how correctly nucleotides are added during DNA replication. High base incorporation accuracy is crucial for preventing mutations, which can lead to diseases like cancer.
The DNA polymerase enzyme is responsible for adding new nucleotides. It does so with high accuracy due to its structure, which checks whether the correct nucleotide is being added by forming hydrogen bonds with the template strand.
Even when errors occur, the cell has mechanisms to correct them, enhancing the overall accuracy. Given the low error rate of one in \(10^{10}\) bases, it’s clear that the combination of correct base incorporation and effective proofreading and repair systems makes DNA replication remarkably reliable. This accuracy is key to ensuring that genetic information is passed on correctly during cell division.