Modeling correspondences among Hox genes and their resultant structures

PZ Myers has another great biological post this morning (I know, that's redundant). It's about how the interactions among Hox genes create structures. As he writes, "The message of which I try to always remind myself (not always successfully) is that genes don't make things, interactions between collections of genes and the environment make things. Biology arises out of the processes, not the structures; it's the reactions, not the end-product."--in other words, there is not a 1:1 correspondence between genes and products, nor between genotype and phenotype.

This is where my a big part of my research lies--I'm essentially trying to represent comparative anatomy 1) in a way the computer can understand, while 2) not misrepresenting the subject through oversimplification in doing so. There's a lifetime of fascinating research questions in undertaking this task.

So up to now, we've explored what we are comparing (referents), and on what basis (homology). While we haven't yet gotten into the details of how we compare them, PZ's post provides a great excuse for one of my favorite examples of a modeling problem. Like PZ's post, it deals with structures resulting from Hox genes, but the species I am looking at are more familiar to most of us: the mouse and the chick.

Like us, mice and chicken are vertebrates; we have a spinal column made up of vertebrae surrounding and protecting a major part of the nervous system. This high-level abstract similarity among all three species is part of what the old anatomists called the vertebrate Bauplan, or "building plan". From the 30,000-foot point of view, we all have a dorsal vertebral column bisecting the body, with a head at one end, a tail (admittedly vestigial in our case) at the other, and two limbs off either side in between.

That is the kind of thing we mean by anatomical similarity. But when we look at it more closely, differences emerge as well. Here, we will take our vestigial tails and leave the discussion, to focus more specifically on the mouse and the chick.

One of the differences we notice right away is that although they both have vertebrae, they are distributed differently: the chicken has a long neck, while the mouse has a short one; conversely, the mouse has a long tail, while the chicken's is very short. Although we are not comparing them quantitatively, qualitative differences such as "long" and "short" are exactly the kind of thing we will be looking at.

To avoid a perceptual confusion, though, let us first do one thing with our model that, sadly, PZ cannot do in his lab: we normalize the chicken and mouse to the same size.



The reason we do this is so that the vertebrae we are comparing will also be the same size, and so we know that many vertebrae in a line will be longer than fewer vertebrae. Otherwise, we could have a situation where many tiny mouse vertebrae are still shorter than fewer chicken vertebrae. By normalizing the size of our models, we have now robustly connected relative length of chain of vertebrae to number of vertebrae.

On our mouse and chicken, we now draw their vertebrae, indicating each different region with a different color.



The red line segment is the cervical (neck) vertebrate; green is thoracic (chest); pink is lumbar (lower back); dark blue is sacral (sacrum); and light blue is coccygeal or caudal (tail).

Now we drag our line segments off the drawings and juxtapose them to compare them directly to each other.



We see that while the chicken's neck is much longer than the mouse's, the mouse has a much longer tail segment, thoracic segment, and lumbar segment, while the sacral segments are pretty similar. Because of the step where we normalized the size of the models, we know that that means that the chicken has a greater number of vertebrae in the neck than the mouse does, while the mouse has a greater number of vertebrae in the tail, and so forth. However, the overall number of vertebrae (disregarding the segment they belong in) appears to be roughly comparable.

So it would seem that, rather than having lots more vertebrae to have several longer sections, the mouse and the chick have roughly the same number of vertebrae, and these vertebrae are distributed differently.

Let's check out that idea. In order to do so, we go back to the embryological structure from which vertebrae arise, the somite. The drawing below shows the correspondence between somites in the chick (yellow circles) and the mouse (gray circles). The two-headed arrows indicate the correspondence across species.



At this point, we (rightly) cannot see a lot of difference, except for species. The somite has the potential to become any different kind of vertebra; what kind of vertebra it will become depends on the interaction among the Hox genes. And indeed, the mouse and the chick both have the same (stipulating different species) Hox genes (again, yellow for chick and gray for mouse).



To be totally consistent, this drawing should have two-headed arrows between the Hox genes across species as well. However, it is about to get out of control real fast anyway without them, so we'll just say right up front that for the sake of simplicity, we are leaving out some relationships from the drawing.

What kind of vertebrae somites become is not controlled on a one-to-one basis by the Hox genes, but rather by their interactions. (Actually, there is not even a one-to-one correspondence between somites and vertebrae; the back half of one somite joins with the front half of the somite behind it to become one vertebra.)



While Hox 5 controls the development of cervical vertebrae, the interaction of Hox 6 and Hox 9 control the development of thoracic vertebrae, and Hox 10 controls the development of lumbar, sacral, and caudal vertebrae--hardly a one-to-one correspondence. Additionally, the Hox genes have to coordinate with each other to "know" where one set of interactions leaves off and the next begins. It is a real challenge to represent this complexity on a 2D sheet of paper (or in a computer, for that matter), and these diagrams are greatly simplified.



Ok, for the space allowed in a post, this drawing now seems to be too complex to get all the details in. We do note, however, that between somites and vertebrae (colored squares), there are two correspondence lines, indicating that a vertebra develops from neighboring halves of two somites. Additionally, all the vertebrae across species are connected by a simple black line, indicating that the correspondence is no longer exact--in terms of vertebra number it is similar, maybe even the same, but in terms of what segment it belongs to, it can be very different.

And this is only a simplified representation of the relationships; there are many more that were left out of the drawings. This is the raison d'être of my work: there is so much emerging information in biology, and the relationships are so complex, that computers are necessary to manage the sheer volume of data. Peter Karp asks what happens when an idea is too big for one human to grasp--that is why we need computers in biology.

At the same time, computers are stupid, or perhaps it is fairer to say "overly literal". To represent these ideas in a form the computer can understand, we run a real risk of oversimplifying them. There is an Italian proverb "Traduttore, traditore", or, "who translates, betrays". If, to get the biology into the computer, we misrepresent it--betraying it--not only have we not advanced knowledge, we have even set it back. My research concerns how we can take such complex work, and represent it truly and meaningfully for the computer to be able to manage it.

PZ finishes his post with "Evo-devo is really moving fast to leave the ghosts of molecular preformationism behind, and our vision of how developmental biology works is becoming progressively more strange and abstract. Give us a few more years, and developmental biology is going to be as weird and mind-bending as modern physics.". That is so true and totally cool that nothing I say can add to it, except maybe just that I am thrilled to be involved in my research at such an exciting time in biology.

(this post is based on a couple of animated PowerPoint slides from my thesis defense, and the material on which I developed the slides came out of notes from my comparative vertebrate embryology class. I need to go back to primary sources to get some references for this post, and will do so, modulo time constraints in getting ready to move; I was just so excited to see PZ's post on this topic this morning that I couldn't wait to write it.)