# Obtaining Overrepresented Motifs in DNA Sequences, Part 1

Changing gears now, leaving behind Pfam alignments. I decided to start a new series of posts based on the conversion of some small C++ programs I developed in the past. These small programs (I call them modules because they were part of a larger application) were used to count motifs, short nucleotide words up to 10-12 base pairs, and then calculate statistical overrepresentation of these words by comparing a foreground set of DNA sequences against a background set.

We will start comparing the different approaches of the C++ and the Python codes and point out advantages and disadvantages of doing it in one language or the other.

First thing we need to do is to count the motifs in all sequences from our foreground and background sets. For the project I was working on, the ideal word length was 10 nucleotides. Basically our C++ approach to increase speed was to transform the character DNA sequences into numbers and then, while sliding a window with the desired word length, hash the base-four numbers into base 10 and increment a vector position, previously initialized with 0. For four nucleotides and a word size of 10 there are 1,048,576 permutations possible, from `AAAAAAAAAA` to `TTTTTTTTTT`. Initially the C++ program would do

reading all sequences and pushing an figure for each nucleotide in a vector, and then sliding a window on this vector and hashing the base-four number

The whole C++ code has about 400 lines, including all the possible output formatting and printing. Timing with `time` the C++ executable takes a little bit less than 2 seconds to read, count and output different files. For Python, we will use a different approach and gain a lot in code simplicity. As we want to count the number of times size-10 words appear in all sequences, we first need to generate all possible permutations (with replacement) of four nucleotides. This can be easily accomplished by using generator functions. Regular functions run until completion and the return a value. For instance, a function that calculates the factorial of 10 will return the last value only, after multiplying 10.9.8.7.6.5.4.3.2.

A generator function runs until a value is available to return, `yielding` it and then suspending its operation until called again. The yielding part was emphasized because `yield` is the command used by Python to return the value and suspend the function until further notice. In the factorial function, a generator would return the intermediary factorial values up to 10. To generate all 1 million plus permutations of 4 nucleotides we need a function similar to the one below (modified from here)

Basically, what this generator function does is to combine all four nucleotides in words of size 10. This is a recursive function “Recursion (computer science)”), where the result of the function is dependent on the n-1 value calculated by the function until n equals 0. The first `for` loop over the items that we want to permute (the nucleotides) and the second `for` recursively calls `permutations starting with the initial n` passed (10) until we reach 0. Debugging this function we will see that `i` is constant for each iteration of the second loop and only `n` changes from 10 to 0, while one by one nucleotides are joined to form a motif. It starts with `AAAAAAAAAA`, then `AAAAAAAAAC`, then `AAAAAAAAAG`, until it gets to a poly-T. Our final code would look like the one below

where we read the input sequence(s), merge them in one long string and as we generate all possible combinations we count the number of times they appear. This code running on the same input file used on the C++ executable is 60 times slower, taking in average one full minute to count motifs in 8 500 bp DNA sequences. The slowest section is the count, as the generation of all possible combinations is straightforward. We lose some speed, but gain a lot on code simplicity and clarity. Next we will modify this code to output different counts needed for the statistical analysis.