In prokaryotes, the error rate in protein synthesis may be...

In prokaryotes, the error rate in protein synthesis may be as high as $5 \times 10^{-4}$ per codon. What fraction of polypeptides containing
(a) 500 residues or
(b) 2000 residues would you expect to contain at least one amino acid substitution?

Key Concepts

Error Rate in Protein Synthesis

This concept refers to the frequency at which mistakes occur during the translation of genetic information into proteins. It characterizes the likelihood that an incorrect amino acid is incorporated at any given codon position, which is crucial in understanding the overall fidelity of protein synthesis processes in biological systems.

Complementary Probability

This is the probability that an event will occur calculated by subtracting the probability of its complement (the event not occurring) from one. In the context of protein synthesis errors, it is used to determine the likelihood that a polypeptide contains at least one error by subtracting the probability of it being completely error?free from one.

Binomial Distribution

The binomial distribution is a probability distribution that summarizes the likelihood of a given number of successes in a fixed number of independent experiments, each with the same probability of success. In protein synthesis, each codon represents an independent trial with a small fixed error probability, making the binomial model a natural choice for calculating the distribution of errors among residues.

Exponential Approximation

For processes involving a large number of independent events with a small probability of error per event, the binomial probability can be approximated using an exponential function. This approximation simplifies calculations when determining the probability of having no errors in a long polypeptide, which is then used to compute the probability of having at least one error.

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