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,andrepairsbasesinreplication (aboutoneuncorrected 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 Error Rate

The error rate is given as one error for every \[10^{10}\] bases. This means there is one error in every \[10^{10}\] characters.

Determine the Number of Characters Per Book

The book contains about 2 million characters, which we can write as \[2 \times 10^6\] characters.

Calculate the Number of Books Per Error

To find how many books you need to type before encountering an error, divide the total number of characters that can be typed (\[10^{10}\]) by the number of characters in one book (\[2 \times 10^6\]). This gives: \[\frac{10^{10}}{2 \times 10^6} = \frac{10^{10}}{2 \times 10^6} = 5 \times 10^3 = 5000\] books.

Key concepts

Prokaryote Replication

Prokaryote replication refers to the process by which prokaryotic cells, such as bacteria, duplicate their DNA. It’s a vital part of cell division, ensuring that each new cell inherits a complete set of genetic information. Unlike eukaryotes, prokaryotes have a singular, circular chromosome that is relatively simple but highly efficient. The replication process involves several steps: initiation, where replication begins at the origin of replication; elongation, where the DNA polymerase synthesizes new DNA strands using the original strands as templates; and termination, where the replication process concludes and the new DNA molecules separate. This process is rapid and typically more accurate, thanks to advanced proofreading mechanisms.

Error Rate Calculation

Error rate calculation in DNA replication involves determining the frequency of base-pair mismatches that are not corrected during the replication process. An error rate is usually expressed as the number of errors per number of bases replicated. For prokaryotes like E. coli, this is notably low, at about one error per 10 billion (10^10) bases. To find the number of books you would need to type before encountering an error, given a book has 2 million characters, you would divide the total number of characters that can be typed without an error by the number of characters in one book: 10 billion (10^10) / 2 million (2 x 10^6), which equals 5000 books.

Proofreading in DNA Replication

Proofreading in DNA replication is a crucial mechanism that enhances the accuracy of DNA synthesis. DNA polymerase, the enzyme responsible for adding nucleotides, has an intrinsic proofreading activity. As it adds each nucleotide, it checks whether the previous nucleotide pair is correct. If an incorrect nucleotide is detected, the enzyme pauses, removes the incorrect nucleotide via exonuclease activity, and then resumes adding the correct nucleotide. This proofreading function dramatically reduces the error rate, ensuring that errors are caught and corrected immediately, thus maintaining genetic fidelity across generations.

E. coli Replication Accuracy

Escherichia coli (E. coli) is a model organism for studying DNA replication because of its high replication accuracy. E. coli's DNA polymerase can incorporate, proofread, and repair bases with remarkable precision, resulting in an error rate as low as one mistake per 10 billion (10^10) bases. This high fidelity is achieved through a combination of accurate nucleotide selection, effective proofreading, and efficient mismatch repair systems. The low error rate is essential for minimizing mutations and ensuring the stability of the genetic code.

Character Count in Text

When considering the accuracy of DNA replication in relation to character count in text, it becomes easier to conceptualize. If a book contains about 2 million characters, and the error rate is one mistake per 10 billion (10^10) bases, you can calculate how many such books you would need to type before an uncorrected error might occur. By dividing the error threshold (10^10 characters) by the character count of one book (2 x 10^6 characters), you get approximately 5000 books. This analogy helps in understanding just how accurate DNA replication can be, even more accurate than typing out thousands of books without a single mistake.