Protein of the Day #10: TRPV1

Mmmmm...spicy food. Wouldn't be as nice if we didn't have TRPV1, which responds to the capsaicin from hot peppers. Here is the predicted domain structure from the SMART database, with the transmembrane domains picked out (along with some ankyrin repeats):

Wordle Malaria

Wordle is a fun little site; I fed the OMIM entry for malaria susceptibility into it and got:

Protein of the Day #9: Retrocyclin

The defensins are an interesting protein family that is important in mammalian immune systems. It now seems that most mammals have some versions of the alpha- and beta-defensins, but only some primates have theta-defensins. In the human, there is a pseudo-gene for a theta-defensin that is post-translationally processed into a cyclic peptide called retrocyclin. It is possible that our loss of a functional retrocyclin contributes to our susceptibility to HIV and AIDS; its an interesting avenue for future gene therapy.

I can't find out too much about retrocyclin; since you pretty much have to use rhesus monkeys to study it, there isn't a lot out there yet. A good place to start is the OMIM entry for the alpha-defensins, and the paper by Cole et al.

Schlegel and the 600 cell

I just wrote a patch to do Schlegel diagrams (a sort of projection) of 4D polytopes in Sage. The 4D regular polytopes are an awful lot of fun to think about; below is a picture of the 600 cell as rendered by my new code. Its much more fun to play with it interactively - check it out.

Protein of the Day #8: Hemoglobin

So I should have called it "Protein of the Week". Ah well. Its the protein of the day, just not every day...

Hemoglobin: its a classic! Don't think that makes it boring. On the contrary, I think it remains a fascinating protein.

Its possible that it deserves the title of most-studied protein. Right now there are 4820 hemoglobin sequences at NCBI. It was discovered in 1851, and the structure solved in 1959 - I think that was the first protein structure found by x-ray crystallography. I could go on and on...

One of my interests in it at the moment is that hemoglobin is the food for the Plasmodium species that cause malaria. Amazingly, they synthesize their own heme groups. Hemoglobin is a funny food though, because of dealing with all those heme units, and Plasmodium has to accumulate hemozoin garbage.

Protein of the Day #7: Enolase

Mammals have three enolases. A more descriptive name is "phosphopyruvate hydratase" - they catalyze the conversion of 2-phospho-D-glycerate to phosphoenolpyruvate.

In Plasmodium falciparum, there is still some controversy about their enolase. It appears that at least part of it comes from a migration from the apicoplast genome into the nuclear genome, but it may be a hybrid. Here's the telltale insertion that matches up with plants (in this case rice, but the apicoplast probably came from a red algae ancestor endosymbiont):

Movie of a Groebner fan

This summer I spent some time thinking about animation and visualizing algebraic and geometric information. I have a longer to-do list than accomplishments but I have made some progress.

One of pilot project ideas was to take a 5-variable polynomial ideal and:
1) compute the Groebner fan using Sage and Gfan,
2) intersect it with a hyperplane (so now we're down to 4 dimensions)
3) slowly rotate the resulting polyhedral complex in 4 dimensions, rendering it using Tachyon/Sage
4) animate the resulting set of frames.

For step 4, I initially wanted to use Blender, but that was really overkill for what I needed and I didn't want to figure out how to get Sage and Blender using the same copy of Python (although someone should). In the end I used ffmpeg to get my movie.

Check out my current best effort.

My next goal in this direction is to do something with Sage's @interact command and JMol to highlight pieces of the fan, since the movie isn't really informative (more art than math I think).

Protein of the Day #6: CD36/Fatty acid translocase

CD36 is a great example of the complexity of biology.

After some modification, it is the same thing as "platelet glycoprotein IV", an important protein in platelets and clotting - thrombospondin binds to it. Its also important in malaria, since Plasmodium infected erythrocytes can bind to CD36, and mutations in it can result in varying severity of malaria.

But its also "fatty acid translocase" and its a receptor for low density lipoprotein (LDL). Its been associated with a number of effects on the immune system, reaction to hyperglycemia, and oxidant stress.

Both these roles make it interesing in the context of mammalian hibernation, where the clotting reactions must be suppressed and metabolism switched to using ketone bodies derived from lipid stores.

Free Stanford!

...just a little joke, no one is repressing it. But the Stanford Engineering school has done something extremely nice, namely put up entire course materials online for computer programming, AI, and some electrical engineering courses. Looks very well done. I really like the transcripts of the video lectures, since I like reading more than listening. I don't think MIT's OpenCourseWare does that, but that is another very nice open access project.

I am a little envious of today's self-motivated youth, it would be pretty easy to teach yourself almost anything these days. When I was a teenager I taught myself basic calculus from an old 1940s book (it was called something funny like Calculus for the Everyman, I can't remember exactly). It had nice line drawings but geez, being able to virtually sit in on MIT classes would have helped I think.

Protein of the Day #5: Aldehyde dehydrogenase 2

Aldehyde dehydrogenase 2, or ALHD2, is the highlight of an article in Science this week showing it is related to mechanisms for protecting the heart from ischemia (lack of blood, which results in lack of oxygen (hypoxia)). There are cytosolic and mitochondrial versions; since this protein is important in metabolizing alcohol, having both versions seems to clear alcohol faster, although I can't find a definitive reference for that fact.

Protein of the Day #4: apical membrane antigen 1 (AMA1)

In the Plasmodium species that cause malaria, the merozoite stage must invade red blood cells. It does this using the strange apicoplast organelle, which is a much-warped descendent of a chloroplast. Apicoplast:chloroplast as Gollum:Hobbit. Anyway, one of the proteins that helps this invasion is the apical membrane antigen 1, although like most Plasmodial proteins not that much is known about it.

Eloquent Javascript

Because of my interest in Sage and eventually helping more with the notebook interface, I've been trying to learn some Javascript. Recently I found a fantastic online book that's a joy to use, partly because it has an interactive Javascript console and all code examples can be run within that framework: check out Eloquent Javascript.

Protein of the Day #3: Bone morphogenic protein 7

In this week's Nature there is some exciting news about what makes brown adipose tissue, or "brown fat". It turns out that brown fat actually comes from muscle precursor cells, not fat cells, and bone morphogenic protein 7 (Bmp7) can induce the transformation.

Brown fat is very important in hibernation as it can generate heat by short-circuiting the mitochondrial proton pump. At very low temperatures, animals cannot shiver so they need other heat generating mechanisms. Its also important for infant mammals, including humans.

Bmp7 is part of the TGF-beta superfamily (transforming growth factors). In the human its on chromosome 20. 7 exons, very typical gene in that respect.

Brown fat has generated a lot of controversy over the years (since 1551!); this discovery seems like a big step forward.

Protein of the Day #2: Clathrin

Clathrin is a very cool protein. It forms polyhedral lattices that help cells in endocytosis. Your synapses are using a lot of clathrin right now.

Protein of the Day #1: Alpha-2 Macroglobulin

Long time no post. I've decided to try a "Protein of the Day" post mostly to help myself remember some of them.

For protein #1, I've picked alpha-2 macroglobulin, a serum protease inhibitor. NCBI's Online Mendelian Inheritance in Man (OMIM) is a nice curated resource for protein/gene information and its where I often turn first. Wikipedia has a nice entry too - the quality of wikipedia articles in biochemistry is usually excellent in my experience so far.

Its a glycoprotein, so there are some extra carbohydrates attached. There are four subunits held together by SS bonds. The gene structure is relatively complicated, with 36 exons (same number in human and mouse. It is thought to be evolutionarily related to the C3 and C4 proteins.

My interest in it mainly stems from the fact that it is important in mammalian hibernation. Among many other effects, it inhibits coagulation and fibrinolysis.

Anders Jensen's nonregular Groebner fan in 3D

The only example of a non-regular Groebner fan that I am aware of is the following one from Anders Jensen's 2007 thesis, here plotted in 3D with Sage and gfan:

R4. = PolynomialRing(QQ,4)
idnp = R4.ideal([x*y*z+x^2*z-x*y,x*w^2-z,x*w^4+x*z])
gfnp = idnp.groebner_fan()
show(gfnp.render3d(), frame = False)

You have to follow the link for the plot since I am not sure how to include JMol applets on a blogger post.

OpenWetWare and Sage

After reading a nice article by Julius Lucks on OpenWetWare, about python, biopython and SWIG, I suggested he check out Sage. He in turn suggested I write something up on OpenWetWare, and so I have. Hopefully this will lead to some more biology and bioinformatics interest in Sage.

Back from Lausanne

Last week I went to a very nice conference at the Bernoulli Center, on real algebraic and tropical geometry. I gave a talk on some problems on finiteness and bounds on the real solution of polynomial systems coming from the n-body problem; Sage was featured in a variety of ways during my talk. Here's an animation of a 4-body central configuration (couldn't seem to upload it to the blog directly; maybe its too big).

making tracks

I've finally added a feature to Sage that I've wanted for a long time: tracking the solution paths of polynomial systems through a homotopy continuation (using Jan Verschelde's phcpack). I am cleaning up my code for formal inclusion, but it seems to work pretty well. The picture below tracks 87 of 99 solutions of the Albouy-Chenciner equations for the three-body problem (in the complex plane). The initial solutions (small blue dots) are for masses m1 = 1, m2 = 2, and m3 = 3. The final solutions are for m1 = 1/100, m2 = 1/10, and m3 = 3. Some of the solutions are moving off to infinity: the mixed volume for the system with m1=m2=0 is only 18, so 81 solutions have to coalesce or move out to infinity. (Why only 87 of the 99? The other twelve are somewhat degenerate, and their solution paths are a little jumpy). Alex Jokela helped a lot with writing the parser for the phcpack path-tracking output.

color me gfan, now in rgb

Various improvements to the gfan interface in sage are in the works; one of the minor things I've had fun doing is adding more flexible color functions to the render function. Here's the Groebner fan of the 3-vortex problem relative equilibria equations, where the color is determined by the polynomial in each reduced Groebner basis which has the highest degree in any one variable - the degrees of the polynomial are converted to RGB values.