The Polyheligon Model

I today’s post I make a revelation. I decided to take the easy way and not try to explain the mechanism of reflective gravity at all in my first manuscript on the topic. Or more precisely, I realized that I could introduce the concept of reflective gravity in my long-awaited manuscript on my proposal for the structure of lignin.

Lignin is a name that I’ve bandied around a bit, but it’s been almost two years since I last really posted on it (not counting later references to these posts). As I was thinking about my vacuum bubble hypothesis, I realized that I can apply the mathematics I’ve been developing into explaining the motion of monolignols, by applying an analogy of the Ouroboros model of August Kekulé to them.

Kekulé dreamed this model originally to explain the structure of the benzene molecule. Kekulé said:

“that he had discovered the ring shape of the benzene molecule after having a reverie or day-dream of a snake seizing its own tail”

I had had my own day-dream of a hollow tube of monolignol molecules eating its tail already over five years ago. But it wasn’t until these past few days that I realized how to add motion to this model. Or more precisely, I had lived under the impression that the motion of the monolignols would be a bit like throwing a ball into a pipe: mostly linear, but with a bit of rotation caused by not throwing the ball exactly parallel to the pipe. But trying to making this model work, I was constantly hitting the wall of the conservation of the angular momentum.

It's quite difficult to explain the problem in simple terms, but it revolved around keeping a set of helices moving at the same speed, allowing the slinky-like toroidosomes structure of monolignols to maintain  its shape at all times. But if the problem was a bit hard to explain, the solution is at least somewhat easier. You see, if we consider the possibility that monolignols move along the loops of the ‘monolignol slinky’, the speed of each molecule will be identical regardless of where along the toroidosome path they are. Although for a second, I thought there would be a problem: the curvature of the structure would create tiny fluctuations to the speeds of the molecules.  Again, it’s quite hard to explain why, but the solution was dead simple: I consider the path continuous, but its function changing after each turn. This concept involves in converting the initial helical torus of the toroidosome into a structure that I call a polyheligon.

I find the structure easier to illustrate if I make a torus where I reduce the number of major segments to just six, as in the model below. This no longer illustrates monolignol toroidosomes properly, but allows one an unobstructed access to each turn of the helix in the structure. In each segment the motion comprises of two components: firstly the linear component along the side of the cylindrical segments, and secondly the rotational component around it.

And if you place the beginning and the start of the helix at the outer rim of the polyheligon, it doesn’t matter that the cylinders are diagonally cut at the edges.

One might still ask, why would the monolignol molecules not fly apart from this rapidly revolving structure? To this, the easy (and hopefully correct) answer is hydrogen bonding. While the neighboring molecules aren’t covalently bonded into a large polymer, the strength of hydrogen bonding is apparently sufficient to keep the closed loop of molecules in a sufficiently polymer-like configuration that it remains at least relatively stable.

While this model is still to some extent hypothetical, I think I can at least introduce in the supplementary information of my upcoming lignin adhesive article. One might ask why I wouldn’t publish this as a separate paper. The problem is its still somewhat hypothetical nature. In chemistry (or physics), you don’t really have respectable journals on major new hypotheses. That is, not unless you manage to piggyback the hypothesis into the paper alongside experimental data.