What happens after the purification step in Hi-C sequencing?

Question

I am a statistician reading an article on Hi-C, and I am trying to better understand one of the steps in the DNA isolation and sequencing process.

Since I'm a statistician, please try to avoid too much jargon in your answers, and if you must use jargon, please define/explain it.


Specifically, I am confused about the isolation and shearing step. To explain myself, I will make reference to the following images, labeled 1 through 4.

Image 1)




Image 2)
_{(source: nature.com)}





Image 3)
_{(source: babraham.ac.uk)}



Image 4)
_{(source: nature.com)}



I understand that the DNA is cut up with restriction enzymes, producing a cloud of DNA fragments, some crosslinked and other not. When these pieces are attached with biotin and ligated in a dilute mixture, it is highly likely that these pieces will ligate with themselves, resulting in either; 1) a ring from strands that were NOT crosslinked (as in the third drawing in Image 3 marked "self-ligation"), or 2) figure-eights from strands that ARE crosslinked (as in the fourth drawing in Image 1).

Now, the following is what I find confusing:

1. The pull-down step draws down the rings containing biotin, but Image 1 and Image 4 make it seem as though only the crosslinked bits are pulled down, and not the solo rings. Don't both have biotin? And thus would both be drawn into the pulled-down sample? Or does the pull-down process rely on a molecule having 2 biotins? If not, can one discern whether a pulled-down piece of DNA is the result of a cross-linked or solo piece of DNA?

2. Why aren't all of the loose ends of the DNA ligated in Image 2? Incomplete digestion? Does this affect the biotin linkage?

3. My next question. Assuming that the pull-down process only selects the figure-eights that are crosslinked, then purified (i.e. the cross-linking protein or formaldehyde is removed) forming a ring that is composed of two strands of ligated DNA (as in the upper-right corner of Image 4). The process then records a genome-wide contact matrix $m_{ij}$, the number of "ligation products" between locus $i$ and locus $j$. What is a "ligation product"?

Sorry, I know the above is a lot, but I want to understand the nature of the data before I analyze it. Thank you for your help.

Answer 1

So, after the restriction digestion, the sample consists of DNA fragments with 5' overhangs. These are filled in by Klenow DNA polymerase, adding biotin-dCTP to both ends of each fragment. Then the fragments are ligated under conditions (ie low DNA concentration) such that ligation between non-crosslinked DNA is less likely. This reduced ligation efficiency (which is already lessened by the use of blunt end fragments) means that all crosslinked fragments may not be ligated, which I imagine is what they are showing in Image 2. Any two molecules which become joined by this reaction are called ligation products (ie they are the products of the ligation reaction).

After this step, the sample is treated with T4 DNA polymerase which, as well as having polymerase activity (obviously), also has 3'->5' exonuclease activity. Thus, any free DNA ends which have not been ligated will be trimmed, removing the biotin. After this step, biotin will mostly be present at ligation junctions, and these molecules can be selectively pulled down by the beads. I say mostly because some of these so-called dangling ends will still retain biotin, but these can be distinguished during mapping (see image below).

As for self circles: because they have been ligated, they will contain biotin and be pulled down with the crosslinked DNA. However, since this DNA is from the same genomic locus, they can also be distinguished from valid interacting pairs during mapping:

[source]

Finally, a quick note on the pull-down mechanism. The beads are coated with a protein called streptavidin (or avidin), which just binds to biotin very tightly. Only one biotin need be attached to any molecule (such as DNA) for it to be captured.