Question

Thank you angels its an example problem

4.2 Binomial distribution The genome of the HIV-1 virus, like any genome, is a string of "letters" (basepai an "alphabet"containing only four letters. The message for HIV is rather rs) in short, just 101 letters in all. Because any of the letters can mutat choices, there's a total of 30 000 possible distinct one-letter mutations. e to any of the three other In 1995, A. Perelson and D. Ho found that every day about 101° new virus par are formed in an asymptomatic HIV patient. They further estimated that about 1% of these virus particles proceed to infect new white blood cells. It was already known that the error rate in duplicating the HIV genome was about one error for every 3. 10" letters" copied. Thus the number of newly infected white cells receiving a copy of the ticles viral genome with one mutation is roughly 1010 0.01x (104/(3. 104)) 3-107 per day. This number is much larger than the total 30000 possible 1-letter mutations, o every possible mutation will be generated many times per day. a. How many distinct two-base mutations are there? b. You can work out the probability P2 that a given viral particle has two bases copied inaccurately from the previous generation by using the sum and product rules of probability. Let P = 1/(3-104) be the probability that any given base is copied incorrectly. Then the probability of exactly two errors is P2, times the probability that the remaining 9998 letters don't get copied inaccurately, times the number o distinct ways to choose which two letters get copied inaccurately. Find P2 Random Walks, Friction, and Diffusion c. Find the expected number of two-letter mutant viruses infecting new white cells per day and compare to your answer to (a). Suppose that an antiviral drug attacks some part of HIV but that the virus can vade the drug's effects by making one particular, single to the preceding information, the virus will very quickly stumble upon the right mutation-the drug isn't effective for very long. Why do you suppose an effective HIV therapy involves a combination of three different antiviral drugs administered simultaneously? d. Repeat (a-c) for three independent mutations

Answer 1