The things we never knew we never knew

We were walking along seminary avenue on a rainy afternoon when Brown stopped to look at the leaves of a tree by the sidewalk. Seeing some math in the pattern, she said, “I wonder why the leaves have that pattern?” That night I spent hours in a whirlwind search that culminated in me pulling down our encyclopedia to look up the entry “nitrogen fixation.”

This week’s seminar speaker was a young professor from Sydney who got up and said, “We work on the genetics behind branching patterns in plants.” That (or the accent) got me to the edge of my seat. He puzzled about how he was seeing analogous variation in grass species on branching, but couldn’t explain it. Analogous variation is a rare evolutionary occurrence where two species that diverged long ago look more similar to each other than to their closer relatives. The mechanisms behind it are poorly understood. Now, this is supposition, but then again it’s not peer-reviewed.

Think like a plant. You can’t move, nor can your offspring select their home. From seed you have to adapt to conditions completely beyond your control. Say there’s a 10 year drought, or rainy period, or a micro-climate shift. Your kids aren’t going anywhere in that time either. But suppose your development is controlled by combining many mathematical patterns. Like a fourier transform on wave functions, or, analogously, like the addition of numerous harmonics that make a flute’s C sound like a flute. Very simple changes to one of those patterns could alter the entire branching plan because fourier-like systems can be mathematically chaotic. That would let your kids change their response to conditions rapidly to turn your flute sound into a trombone. If all plants shared a similar mathematical hierarchy, with different harmonics, you would expect to see similar genetic alterations based on similar climate shifts, so a plant in Nevada would revert back to the same type of patterns that a plant in Palestine would have, even if they were hundreds of millions of years removed. That would be analogous variation.

After his talk, I told him my supposition. We talked for 30 minutes when he said he was very interested, but was applying for a position here and had to go to interviews, but would love to continue if I had time for dinner. I took him to an Italian restaurant. We started with simple analyses he could apply to the data he had already collected, and what new parameters he should include in the data he collects from now on. I advised him to enlist the aid of a real mathematician, cause apparently it interests them too. Then he told me about his research, and taught me more about plant genetics than I would have learned in a semester. For example, almost the only difference between maize and its ancestor teosinte is in a single gene controlling branching, and weeds undergo analogous variation to look like maize to keep from getting weeded. Or that development is regulated by small interfering RNAs. I leapt to a conclusion and got excited that a system would use an intron from one gene to target another gene while making a protein. It would be lightning fast and perfectly efficient. But he just smiled and said “No introns, what you say would be a good system, but these are their own elements. They don’t code for proteins at all. Nobody knows how they evolved. The sole purpose of making the RNA is to destroy an RNA the cell already took the trouble to make. Seems wasteful, right?” All I could think to say was “I wonder why?”

The ocean is so big, and my boat so small.