Sage at the joint math meetings

Live from DC, we're halfway throught the joint mathematics meetings. This is the second year that Sage has had a booth in the exhibit hall.

Our location is not as good as last year's, but we are still getting a good amount of foot traffic - enough to occupy most of the people here most of the time. David Harvey, David Joyner, Robert Miller and I have been manning it most of time. Jason Grout helped out this afternoon quite a bit. I may be forgetting some folks because I'm a little frazzled.

The word of mouth about Sage is increasing, many people stopping by have tried it or at least heard about it. I think its very encouraging for the future. Several people expressed interest in how to become developers.

We had an MAA panel session today on open-source software in the undergraduate curriculum. Four speakers, two of which (David Joyner and Robert Miller) talked about Sage (others on R and WeBWork).

Overall, so far the booth has been another success in raising awareness and enthusiasm for Sage. Talking to different people has made me enthused about all sorts of development projects, enough to keep me busy for at least the next year...

Protein of the Day #15: Adropin

Recently in Cell Metabolism there was a very interesting article on the newly characterized peptide Adropin. Adropin seems quite important in regulating the balance between sugar and lipid use as fuels; its one of several promising avenues to understanding and treating diabetes that have come out in the last year or two. The peptide is cleaved from the product of the gene Enho (energy homoestasis associated). Its extremely well conserved in mammals - for most species the amino acid sequence is 100% identical (a few ungulates have 1 amino acid difference). Here is a picture of the conservation from UCSC's genome browser:

Coloring book reject

The image below is a Groebner fan that is just too complicated to put in the coloring book, buts I think its pretty impressive:



The ideal generating this is from what I call the "super three-vortex problem", the equations for the central configurations of a 1/r^2 potential:



I am mainly interested in the nonzero solutions of this system. To get at those, we can saturate the ideal - or in practical terms we can introduce a new variable, w, and add the equation w*s12*s13*s23 - 1 = 0 to the ideal. The 3D Groebner fan of the resulting system can be seen here.

A mathematical coloring book

I've been working on a mathematical coloring book, with the pictures created using Sage. It still needs some work but I've put a preliminary version up at lulu.com. (I am not making any money on it, the cost is what lulu.com charges to print it.) I have also made the download freely available. I would appreciate feedback, especially from people with kids who try it out.

Protein of the Day #14: XP_001352106

The genome of the malaria-causing Plasmodium falciparum is bizarre in a number of ways - the most striking feature being the extremely high (over 80%) A+T content. Looking on the protein level, there seem to be many proteins with long asparagine inserts. These asparagine inserts must serve some sort of purpose but it is unclear what it is. They do tend to confuse sequence-alignment and similarity searches, which is one reason so many of the proteins remain uncharacterized.
An extreme case of this is XP_001352106, which has a run of 83 asparagines in a row. It does have some similarity to a subunit of cyclin kinase but not enough to be very confident about its identity.

Symmetric Venn Diagram

This was the start of a small industry of making symmetric Venn diagrams, which Branko Grunbaum found in 1975. I have been working on making a mathematical coloring book (first edition should be - needs to be - done by the holidays, so more details on that soon). I've been trying to making some symmetric Venn diagrams for it, this is a by-product of my first attempts:

Protein of the Day #13: ATP synthase, beta chain

One of my students is doing a comparative genomics study of Plasmodium falciparum (with an ultimate goal of developing better alignment algorithms for organisms with extreme genomes), and I was curious about what the most conserved protein is relative to a model organism such as yeast. Turns out its ATP synthase; not too surprising but one might guess some other things too. The wikipedia entry is pretty good, although perhaps not as good as it could be. It does have a nice cartoon of the structure:

Protein of the Day #12: V1rf3

V1rf3 vomeronasal 1 receptor, F3, as its called in mice, appears well-conserved in a variety of mammals, as shown below (sometimes under slightly different names). The vomeronasal system is distinct from the usual olfactory system for smelling, and can be sensitive to very different compounds. In mice the vomeronasal system is important for pheromones. It remains unclear whether humans have any sort of functional vomeronasal at all; my guess is that most of us do not, but perhaps a few people still do.

Permutohedron mirrors

The image below is from a viewpoint in a mirror-faced 3D permutohedron (truncated cuboctahedron). It should link to a larger (1920x1200) version. This image was produced with Sage (using the Tachyon raytracer and some new code for polytopes that I've been working on).

Slices of the 600-cell

Over the last 6 months or so I've been doing some work on visualizing polytopes, Groebner fans, and other geometric/algebraic objects. I gave a presentation last week about some of that, which forced me to finish up some projects. One of those was a movie of the 600-cell being sliced by 3-planes.

Protein of the Day #11: cystathionine gamma-lyase (CTH)

In a recent article in Science, Yang et al found that cystathionine gamma-lyase can produce hydrogen sulfide gas in mice, and that this seems to help control blood pressure. Since I'm interested in mammalian hibernation, this made me wonder about connections with another Science article from 2005 which showed that a torpor-like state of lowered body temperature can be induced in mice by a particular level of H2S exposure. This protein is very well conserved; below is an alignment with the mouse version with some mammals and the chicken. Normally it is involved in cysteine metabolism and presumably does not create H2S; there are some splice variants and perhaps the variants are important in this respect.

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.