Suffix Arrays

In our quest to win a million dollars, we're trying to Index the Human Genome. A typical index, like in the back of a book, is composed of an entry, say "Sheep", and a list of page numbers, say "88,121,265". But when we went to try this idea on the 3,000,000,000 characters in the genome, we found that it took up significantly more space than the genome itself, which was unworkable. Surely we can find a more efficient solution to the problem. (Or, we could throw up our hands, call it "Big Data", and put a supercomputer to work on it. Let's not do that.)

Actually, there's a fair amount of redundancy in an index. If there are three instances of the word "Sheep" in our book, and we add a fourth instance of it to the index, we're increased the number of sheep, so to speak, by 33%. If we do that for every word in the book we'll add a significant chunk to the overall size.

But suppose, rather than just give the user the page numbers where the word "Sheep" is, we provided them with with the line and word numbers as well. "Sheep" is on page 88, line 14, word six. Now, the index is in alphabetical order of course, so what we can do is simply eliminate all those redundant words from the index. So the index entry for "Sheep" would just say "88,14,6". Say readers want to find the word "Streams". They would go and find an entry "88,14,6" and look up the word in the book. Finding that it's "Sheep", they realize the word is later in the index, since "Streams" is alphabetically after "Sheep". They go to the next entry in the index, maybe "81,19,11", and look up that word in the book. It's "Streams", so they've found their word, and the index didn't require any of those annoying, redundant words in it!

Sheep. By a stream.

OK, not a very simple operation for a human reader. But easy enough for a computer. And since our genome doesn't have pages or lines, we could simply record the location of each individual 20-mer and put the locations in alphabetical order. We can even take it one step further: since 20 is just an arbitrary length that we chose, we'll remove it from the solution and just say that we'll take as many characters as we need to get a unique ordering of all of the strings. Notice that you might need to take all of the remaining characters of the genome to alphabetize it correctly, and if you do, you have a suffix of the genome. If you don't need all the characters, it doesn't matter if you add them or not, so you might as well, and therefore we have an array of the suffixes of the genome. A suffix array.

I won't go into the details of how to create such an index right now, but it can be done in relatively few lines of code. (One easy-to-use library is called SAIS.) Now, the simplest way to write out a suffix array is a text file of the alphabetized suffix indices, in ASCII format, one number per line. This, unfortunately, brings us straight back to the size problem - let's say eight bytes on average, per line, with one line per character in the genome, and we end up with 24 gigabytes worth of index. But at least it's a workable index. If we split the index into several files to keep it manageable, it even suggests a refinement of our attack on the overall problem. We'll see how another time.

(Update: I wrote an article on suffix array algorithms.)

Part I: A Million Dollars Up For Grabs
Part II: Analyzing DNA with BWA
Part III: Analyzing DNA Programmatically
Part IV: Indexing the Human Genome
Part V: Suffix Arrays

Indexing the human genome

Last time I had decided that to efficiently analyze the reads, we had to make an index of the human genome. So how do we go about that?

Indexing at the Library of Congress

What we need is an efficient way to access any given substring in the genome. It's not quite the same as indexing a book; rather than determining the locations of "dynamo", "father", and "pseudopodia" in the book, we need to be able to find the location of EVERY substring. It's as if, in our book, we had to find instances of "dynamo", "ynamo", "namo" and so on. Not only that, but if the book had the sentence, "A dynamo has unlimited duration." we have to find instances of "namo h", "namo ha" "namo has" and so on.

So we can't just split the genome by word boundaries like we would for a book. Can we split it into even-sized chunks and index those? For example, could we choose a chunk size of five and split every ten characters into two index entries?

It won't work. For example, if the genome was "AGACTTGCTG", we might choose to index every five characters (called a 5-mer). This would give us two strings, "AGACT" and "TGCTG", which is fine, but if we come along later and try to search for "CTTGC", we're out of luck - that's not in our index. But it is in the string.

So we have to choose an index size and go through the genome character by character. In our ten-character genome, indexing by 5-mer, we get the strings:

AGACT
GACTT
ACTTG
CTTGC
TTGCT
TGCTG

(and a few shorter strings at the end, if we so desire.)

To be useful, we'll have to store our index as a dictionary of 5-mers to an array of integers, representing the locations in the genome where that string was found. For our sample, we have 30 characters worth of 5-mers, and just six integers to save, for a total of 54 bytes. What happens when we index the whole genome?

It's a fair assumption that every possible string will be in the genome, so we'll have 4⁵ or 1024 entries in our index. The number of values, though...we have to have an index value for every single character in the genome. If our genome was the book Moby Dick, we'd have around a million characters to index. Each index value would have, on average, about 1000 items in it. If we're really hoping to match all of our reads to each item in the index, we're going to go through 1000 entries for each read, which might be a bit slow. Unfortunately, our genome isn't Moby Dick. It's roughly the size of 6,000 Moby Dicks. Each index is going to be in just about six million locations. It can't possibly read all those at the speed we require.

Okay, so if we have too many items per index value, we just have to make our index larger. What if we do 10-mers, or even 20-mers? Well, 10-mers gives us 4¹⁰ entries - call it a million. That means each index will be found in about 6,000 locations. Kind of a lot, but maybe doable. If we do 20-mers - well, 4²⁰ is 1,099,511,627,776. This is more on the lines of what we need in an index - it's well beyond the number of characters in the genome, so each index shouldn't show up in more than one or two locations. There's just one small problem: We now have six billion entries with twenty-character identifiers, and the space our index needs is now up to 120 gigabytes!

Maybe we could tweak and tune and find a sweet spot, but instead we'll try a different approach entirely to indexing. Next time.

Part I: A Million Dollars Up For Grabs
Part II: Analyzing DNA with BWA
Part III: Analyzing DNA Programmatically
Part IV: Indexing the Human Genome

Analyzing DNA programmatically

Last time I discussed using a program called BWA to try to determine if a given sequence was part of the human genome or not. It didn't seem to do a great job. How do we approach it programmatically?

Let's review the problem first. You have a machine that has analyzed some DNA, and it's given you some sequences it's found. Roughly 300,000 of them. Some with maybe only five characters, some with a few hundred. We call them "reads".

Recall that a DNA sequence, from a programming standpoint, consists of any number of any of four characters: A,C,G, and T. A human genome, in the end, is just a DNA sequence. So if the human sequence was "AAGGTTTCC" and your sequence is "AGGT", bing! You've got a match.

Now, here's the catch: a read, instead of being four characters, is reasonably a minimum of fifty characters. The human genome, instead of being nine characters, is roughly six billion characters. 6,000,000,000 characters. If your first thought is to fire up a text editor and do a search, you had better make sure that (a) the editor is capable of handling a six gigabyte file, and (b) that your computer has six gigs available to throw around (In 2013, a high-end laptop will probably have eight gigs, so just barely enough space to hold the genome and run a couple of other programs.)

Another, minor issue is that most genome files are formatted with sixty-character lines. If your sequence is split across two lines, a simple text search won't find it. You can preprocess the file to remove all the carriage returns, but if you do, your text editor had better be able to handle one line with 6 billion characters on it!

Your next idea: grep. Will grep find a 50-character match in a genome? I couldn't find a good way to do it reliably, since, again, genome files tend to be formatted into 60-character lines, and grep isn't really capable of finding a string that breaks across a line. Moreover, grep is a line-based tool, so odds are if you try preprocessing the line, grep will think (rightly) that you have a file with one six-billion character line in it, try to read in the line, and run out of memory.

Here's the other catch: Suppose you could get grep to work, and it managed to search the whole genome in three seconds. But we have 300,000 reads to get through! That's about 250 hours worth of search time and we're under a three-hour deadline. So we can't really afford to search the entire genome for each read.

So we'll write a script. A good processing plan might be this: index the genome, index the reads, then march down the two together to find our list of best prefixes. Sounds great!

But it turns out that even indexing a file the size of the human genome is a pain. I'll think about why next time.

Also see: A Million Dollars Up For Grabs

Analyzing DNA with BWA

Last time I discussed a million-dollar challenge posted by Innocenture. The challenge is to analyze a series of DNA reads and determine the source. My professor suggested using a program named BWA, a Burrows-Wheeler Aligner. Burrows-Wheeler alignment is an algorithm for matching up two sequences which may not be the same length. Perhaps one sequence has two extra nucleotides in the middle but the entire rest of the sequences match. These kinds of sequences are very difficult to find naively, and which match is better can come down to a judgment call.

So the goal is to align each sequence in the example file to the human genome. BWA, for speed, asks that you index the target genome - the human genome, in this case - which takes a fair amount of time. Then, you pass it each sequence on the command line, with a command something like:

>bwa align AAGCTCTA human_genome

and it does its magic and returns the location in the genome of the best several matches.

So I worked up a Python script to analyze the input file and pass each sequence to BWA in that format, and let it run for a few hours. (I'm never sure how many because I never remember to change the machine's power settings to not switch itself off after a few minutes of no UI activity). But it eventually completed. I went to look at the results, and I found them very intriguiing. Although, according to the challenge, no less than 90% of the DNA was human, the BWA program only managed to match about 50%, about 150,000 reads.

I took a closer look at the BWA manual, and found this option:

-o INT

Maximum number of gap opens [1]

If I understand this correctly, it means that if the alignment has more than one gap in it, BWA will discard it as not being a match. You can change the value of this parameter, but when I did, it seemed to slow down the analysis quite a bit. I didn't let it complete, but based on the portions I did run I suspect it would have gone over the three-hour limitation - at least on my workstation, which I'm sure is underpowered compared to the target hardware.

So I started to think about what sort of coding would need to be done to meet this challenge. Next time I'll think about Analyzing DNA Programmatically

A million dollars up for grabs

Of course, you have to do a few things to earn it. Innocenture is running a challenge, with a million dollar prize, for the ability to take a DNA read, analyze it, and determine the precise species of each read. Here's the kicker: it has to be done rapidly.

They have some examples available. The input is in a large XML file that contains the DNA reads and some information on the quality of the reads, and they provide you with the output file they would be looking for. One example has a little more that 300,000 reads of between 50 and 200 nucleotides, putatively taken from a human. According to the output, at least 90% of the reads are from human DNA.

So how do we duplicate this output file? There's a program called BLAST available on the web for bioinformatic analysis - you give it a sequence of DNA and it almost immediately comes back with the closest matches across their entire, huge DNA database.

So, we might be able to slam that database with the reads and get back the results. There's just one problem - notice I said 300,000 reads? Suppose we could get back each one in one tenth of a second. That makes 30,000 seconds, or a total of eight hours and 20 minutes of runtime. Sadly, the million dollars probably won't be given away unless you can get the reads done in under three hours. Oh, and did I mention the application won't actually have internet access?

So the BLAST site is out, which is unfortunate, because it really does an amazing job at matching sequences. What do we do instead?

Due to the nature of science in the United States - "publish or perish" - there are a whole lot of little bioinformatics applications around. Mostly, people will write one, publish a paper about it, and then forget about it. There's no point in maintaining it or going back and improving it since there's no chance of writing another paper about it unless you change the algorithms significantly.

Still, a few of these applications manage to have some shelf life. I'll look at Analyzing DNA with BWA next.

Also see:
Analyzing DNA Programmatically

RNA Polymerase ||| and the RIG-I pathway

A little story about immune responses in cells.

Type-I interferons (IFNs) are important for antiviral and autoimmune responses.  They interfere with viruses as the viruses try to borrow the cell's replication mechanism to reproduce themselves.

The cell will produce interferons due to a couple of proteins: the retinoic acid induced gene I (RIG-I) and mitochondrial antiviral signaling (MAVS) proteins.

These, in turn, start the production process when cytosolic double-stranded RNA or single-stranded RNA containing 5′-triphosphate (5′-ppp) are nearby.

Here's a surprising thing: Cytosolic B-form double-stranded DNA can also induce IFN-β. For example, a DNA sequence of repeating AT can induce it (It’s known as poly(dA-dT). But no one knew how. Until a paper came out in 2009 by Yu-Hsin Chiu and a couple of other people. It turned out that inside the cell, the poly(dA-DT) was actually being converted into 5′-ppp. 

But how? It turns out that an enzyme uses the poly(dA-dT) as a template to synthesizes 5′-ppp RNA. The enzyme is DNA-dependent RNA polymerase III (Pol-III). This was interesting because it was known that the Pol-III had a role in the nucleus of the cell, but not that it had to do with the immune system.

If you inhibit the working of Pol-III in a cell, and then introduce a bacteria like Legionella pneumophil, the bacteria grows in the cell. The implication is that Pol-III senses the DNA of the bacteria and triggers the IFN process.

How did they do it? 

In a cell, they attached a luciferase reporter to the IFN-β promoter, so if the cell creates IFN-β, it would bioluminesce.

Then, they put different things in the cell. Of all the things tested, only poly(dA-dT) activated the IRF3.

To ensure that there wasn’t something going on at another step in the path, some other things were tried: A silencing RNA strand was introduced into the cell that would stop the production of RIG-I and MAVS. No IFN-β was produced. DNASE-I is an enzyme that breaks down DNA. When that was introduced, no IFN-β was produced. On the other hand, IFN-β was produced in the presence of RNASE-I, so breaking down RNA had no effect.

Nucleic acids from the poly(dA-dT) cells were able to induce IFN- β, even in the presence of DNase I, so it wasn’t DNA that was causing it. Production stopped in the presence of RNase I though, so it must have been RNA that was being produced.

Similar tests were done to determine the exact length of the poly. As few as 30 base pairs were able to trigger the IFN. But, longer sequences with G’s and C have failed to trigger anything.

RNA Characteristics

 Two enzymes, polynucleotide kinase (PNK) and shrimp alkaline phosphatase (SAP) are used by chemists: the former adds a phosphate group to a DNA or RNA molecule, the latter removes one. A third enzyme, Terminator Exonuclease, or Ter Ex, breaks apart RNA with exactly one phosphate at the 5’ end.

When the SAP was used to remove the phosphate, the RNA no longer induced IFN- β (the PNK had no effect). Even when the PNK was used to add back the phosphate that was removed, there was still no induction, implying that a single phosphate was inadequate. Similarly, treating the RNA with Ter Ex also made no difference.

Another pair of RNase enzymes break apart specifically single stranded RNA (ssRNA) or double stranded RNA (dsRNA). RNase III breaks apart dsRNA, while RNase T1 breaks apart ssRNA. RNase III turned out to inhibit the IFN- β, indicating that dsRNA was required.

Put all these together and it seems that the trigger is dsRNA with multiple phosphate groups attached.

So the chain takes you from the poly(dA-dT) to a 5′-ppp.

Conclusion

Other tests bring you to the conclusion that Pol-III is the enzyme that triggers this conversion. Thus, Poly-III, in the cytoplasm of a cell, actually acts as a DNA sensor that will trigger an immune response. An entirely different function from the one it has inside the cell nucleus. Quite a surprise!