Restriction enzymes recognize specific sequences in DNA and cut the DNA within or near those sites. Many restriction enzymes recognize 6-bp sequences. How many possible combinations of 6 nt sequences are there?
At what frequency would you expect to find a binding site for a particular restriction enzyme that recognizes a 6 bp sequence? Note: Restriction enzymes usually recognize a palindromic sequence, so you don’t need to worry about looking on both strands.
What is the average length of a fragment produced by a 6-cutter?
The EcoR1 enzyme cuts the sequence “GAATTC”. How many different sequences could be made out of this set of nucleotides (assume that you treat each A and T as distinct individuals)?
You are interested in synthesizing a bunch of random oligonucleotides for a SELEX experiment. How many possible oligos of length 22 are there?
How many ways could you make a sequence of 6 nt by grabbing them at random from a bag of 12 nucleotides (assuming each base is treated as a distinct unique entity, and you can only pick each nt once)? This is an example of “random sampling without replacement”.
How many combinations of 6nt are there in a set of 12 random nucleotides? (That is, pick any group of 6 nt, where each one is treated as unique, and you don’t care about the sequence in which you pick them.)
How are your answers in parts e and f related?
The frequency of a minor allele at the CFTR gene was found to be 0.17. What is the probability that any allele chosen at random from the population will NOT be that same allele?
Consider a genome in which the four bases \(A,C,G,T\) are present in equal proportions (this is actually rather uncommon, but let’s go with it for now).
For the following questions, think of them as “What is the probability of X and not Y?” (So, you are asking a binary question about one possible outcome vs. all others.)
If you were to pick a sequence of 10 nt completely at random, what is the chance that exactly 3 bases will be an \(A\) (or any other homopolymer)?
What is the chance that you will find less than 5 \(G\)s (i.e. 4 or fewer)?
What is the chance that you will find between 2 and 4 \(T\)s?
The quantile function qbinom(p, size, prob) returns the smallest value of \(q\) such that \(Pr(X \le q) \ge p\). The quantile is defined as the smallest value \(x\) such that \(F(x) \ge p\). For example, \(F(x) \ge 0.75\) means that 75% of the distribution is less than \(x\).
What is the maximum number of any single base you would expect to find in 75% of 10-mers picked at random from the genome?
What is the maximum number of any single base you would expect to find in 99% of random 10-mers?
Say you are analyzing the GC content across different regions of the genome and you find a region of 100 bases upstream of your favorite gene that has 63% CG content. How likely is it that this region has no significant CG bias?
First use the pbinom() function to get a p-value, and then perform a two-sided test using binom.test().
# pbinom
# binom.testAre the results the same?