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Folding a Rainbow

There are so many outstanding challenges regarding the genetic code it is hard to know where to begin or what to do. What is the genetic code? What does it do and how? And to me the most fascinating and mystical question is where did it come from?

Since we do not have all that great of a handle on the first few questions - the ones that we can actually observe in today’s world - there is no way to have any real confidence in the last question. The base for any viable scenario, I think, must be founded in emergence. Emergence is a very difficult concept to define precisely, but it is the companion or dual concept of complexity. Each leads to the other. I will let someone far more qualified than I weigh in on the definition of emergence. (Italics are the author’s.)

Emergence is above all a product of coupled, context-dependent interactions. Technically these interactions, and the resulting systems, are nonlinear: The behavior of the overall system cannot be obtained by summing the behaviors of its constituent parts. We can no more truly understand strategies in a board game by compiling statistics of the movements of its pieces than we can understand the behavior of an ant colony in terms of averages. Under these conditions, the whole is indeed more than the sum of its parts. However, we can reduce the behavior of the whole to the lawful behavior of its parts, if we take the nonlinear interactions into account.

John H. Holland
Emergence, From chaos to Order

The most stunning aspect of protein synthesis, in my mind, is that it is a sequential process. I think this aspect is almost universally misinterpreted as “linear” because of the superficial similarities between sequential nucleotides and lines. To me, the first big hurdle that life had to clear was in coming up with a sequential molecular mechanism so that significant amounts of molecular information could be algorithmically handled.

Cairns-Smith makes two indispensable points in thinking about the origins of life. First, the original molecules of life, organic molecules, could not have been organic molecules by today’s standards. Second, layers of inorganic molecules are capable of storing sequential molecular information.

Given this mix of ideas, I see a value to understanding how today’s code could be visualized in terms of inorganic forces. The primary force that shapes life is water, and the ideal form driving the structure of all organic processes is a dodecahedron. Actually I think of life as an inherently spherical system, because I think that life represents a perfect dynamic balance of physical molecular forces. But the dodecahedron is the largest possible form of perfectly balanced forces. Twenty is the most possible points that can be evenly spaced on a sphere, and if you connect all these points they will form a dodecahedron.

So I see, somewhere in the mix of molecular history, there was a need to fold up layers, or a sequence of molecules within a hierarchy of water affinities. The original organic material could have been no more than some form of carbon sludge, and I see the process as some emergence of gazillions of instances of progressively more complex dynamic crystalline structures. I think this calls to mind an iterative process of concentrating structures by repeated cycles of hydration and dehydration of little sludge globules.

If the freezing or crystallization occurs within pockets of pockets of sludge. The dehydration process can partition itself in sections of sludge, and gradients are formed. The grand orchestration can split between the easy access of tetrahedrons and the more complex circumstances of dodecahedrons. With separation and gradients come interfaces and transitions. This is where the real drama rages, at the interfaces, the interface of chemicals, shapes and order.

This drama is a process not an event. The process involves large amounts of repetition sprinkled with the essential spice of constant change. We mark the milestones in the process historically with the crowning of champions, symbolic kings of survival. But these inaugurations are chimera existing only in our mental models of complex, repetitious events, historical events with no special features during the times of their own existence. They carry the titles of “last common ancestor” and “origin of this” or “origin of that”. They are the pyric victories of posthumous coronations for detached, historical champions. The drama emerges not from imagining something improbable and isolated, but in imagining a process ubiquitous and inevitable.

Enough goth, let’s splash some color into our scene. Here’s a sludge globule.

Pretty unimpressive, but we can imagine some simple sludge properties for this globule to set it up for some sludge tricks. If we consider that there are natural properties of sludge, such as its ability to get along with water, then sludge placed in a dynamic setting might entertain us. If sludge is not perfectly copasetic among water, then it will segregate itself into globules. If these globules are not homogenous sludge, then they will create gradients according to water affinity. The water-loving sludge will hang around the perimeter, and the water hating sludge will squirrel itself as far from water as it can.

Of course no sludge is an island, so water will continue to be a part of sludge’s life to some degree or another. It is only through dehydration, or the exclusion of water, that sludge can crystallize into a solid of its own. This process will follow a path as diverse as the number of sludge globules one can imagine. In general, the crystallization process will make sludge smaller, so we can imagine sludge columns forming within the water matrix. This is simpler to visualize if we start with a sludge layer on top of water.

Now we have a new sludge-water interface as the stratified sludge begins to crystallize, which is a happy circumstance because new gradients can form, and we love gradients.

The most concentrated water-hating sludge should be found at the core of the sludge crystals. This process is just as true with sludge globules as sludge layers. Perhaps it is a combination of the two, where sludge spicules form and aggregate into sludge clusters, much like lipid layers are known to do.

It is the core of these crystals and aggregations of crystals that I imagine environments for carbon crystallization much like a freezing pond. The specifics are beyond me by many orders of magnitude, but I generally sense that the process of carbon jostling for crystalline position will be multileveled, complex, and interesting. Sludge at the core will be presented with different environments than sludge at the watered periphery, it will chose different strategies, and there will be an interface between strategies. We now have imagined a carbon sludge crystal that is stratified with a strategy predicated on water affinity. We can imagine this beast in bazillions of instances with bazillions of different strategies.

It is at this rudimentary level that the true dynamics of the drama can kick in. They invite new players called combination and aggregation. Complexity, network science, universality, chaos, emergence are all playgrounds for these new players. Simple things combine to form complex things. Things aggregate and accumulate, but these combinations do not become big versions of little things, they become different versions of new things. More is not more, more is different.

I view a living cell as a colony of molecules. They are not sentient beings, but they interact in a molecular dance no less complex than a modern city. More perplexing, these molecules have a language and can communicate information. On what physical principle could such information and such a language be founded?

In this new world of social mingling and sludge spicule accumulation it would be a useful trick for sludge to learn a measure of independence. If talented spicules figured out how to ball-up, they could travel from aggregate to aggregate and form new connections, a crystal network can evolve and complexity will emerge.

Buckminster Fuller teaches us the simplest way to ball up a spicule or rod; it’s called a tetrahedron. This is the lowest energy folding strategy for a column, practically just two folds and a splice.

In the real world of sludge spicules the splice is a bitch, and the folds are no cake either. If these sludge regions actually wanted to get together they would have gotten together in the first place. They are apart because they prefer to be that way, so they will need special sludge chaperones, or glue to keep them together. The region of most desperate conflict is the space between water loving and water hating, blue and red, so we will put a firewall in as a splice.

The other regions between the hydrophobic and hydrophilic poles of the folded structure will require creative arrangements to maintain a happy structure. We can represent the finessing of the balance at these junctions with some special sludge icons.

This is a quite fanciful representation of a mythical sludge spicule strategically built to form and travel in water. Such a beast could probably never exist on this planet, but it is starting to look like a pattern we’ve seen before.

The spicule is mythical, but the map, or globe of the genetic code is not. The pattern demonstrated by that structure is self-generated. Even if you reject the notion that there is meaning embedded in the genetic code, you cannot deny the pedagogic value of studying this object. It is exponentially more powerful to comprehend codons on this globe compared to anything approaching linear. Assignments, properties, such as water affinities, similarities and differences of all parameters in the system can be illustrated relative to one another. It is the natural habitat of nature’s data. These study tricks are founded on many of the principles we used to imagine the folded spicule. It is possibly a coincidence that these parallels are even possible, but the intellectual utility of this genetic globe is striking.

Just as our fanciful crystal spicules can aggregate, so too can crystal particles. These rough, imprecise seedlings will be polar, and they will cluster in water. This form of spontaneous aggregation or assembly is particularly interesting in light of the many modern homologs in biochemistry, viruses being a major example. In cases where aggregation of subunits is a major growth strategy dodecahedral and icosahedral symmetries are common.

As seed crystals, these large mythical beasts are now in a position to fold a diverse collection of smaller beasts - proteins - based on any and all platonic forms. Empiric evidence suggests that this is exactly how proteins fold. Is this the clue to a fundamental law of folding?

But are crystal spicules common, and what relationship would they have to dodecahedrons? Crystal spicules are fairly common phenomena, but dodecahedrons are not. Dodecahedrons are very rare in natural crystal systems because that symmetry is an awkward way to make an interconnected lattice. Consequently, inorganic crystals demonstrating the five-fold symmetries of dodecahedrons are unusual, but five-fold symmetry is the rule rather than the exception in living systems. What would a dodecahedral spicule look like?

Again, merely a fanciful illustration of a dodecahedral crystal spicule, intentionally designed for a demonstrative reason. I am not aware of any natural crystals that spontaneously form in this type of dodecahedral structure. I aligned dodecahedrons sequentially and proportioned them so that their complimentary faces can be colored and the cores removed:

I am not aware of any structure in nature like this, except…well…DNA, but that’s not really a crystal, is it? Another interesting foray can be found in tiling a plane with a dodecahedron.

There is another artist named Mark Curtis in Britain who has been bitten by the bug of geometric principles behind life’s little crystalline tricks. You should visit his website and see how he feels about the geometry of DNA.

This is the exact proportion of the double helix in DNA, which also demonstrates dodecahedral symmetry. It has a major and minor grove, complimentarity, the same pitch, the same number of faces per rotation. It is not meaningful in any sense other than as a fanciful parallel between DNA and a sequence of dodecahedrons. This is not a typically useful crystallization strategy for carbon, which will generally take one of two pure forms in nature: graphite and diamond. The precise form taken, and therefore the symmetry employed is a function of the environment in which it crystallizes. The following diagrams are from my college minerology textbook, Dr. Klein’s. I’m sure he won’t mind.

In low pressure environments, such as at earth’s surface, carbon will crystallize into the six-fold sheeted symmetry of graphite. At higher pressures carbon crystallizes into the tetrahedral symmetry of diamond.

Graphite

Diamond

The differences in physical properties between these two structures are dramatic. Color, luster, cleavage and hardness are quite disparate, and they form the basis of widely differing commercial value. The environment produced the structure, and the structure produces the utility. An environment where regular crystallization is not an option will favor strategies that embrace irregularity. These are the type of strategies that demonstrate emergence. They are agent-based strategies, where simple agents are acting on simple laws in huge numbers. It is only through context and combination that more complex behavior begins to emerge from the system.

Grandma

The theory of Babbage accounts with great probability for the rise of ground in the vicinity of volcanos, and Herschel’s theory accounts, perhaps, for the subsidence of deltas and other places where great accumulation of sediment occurs; and this latter theory has the additional advantage of accounting for metamorphism, and perhaps, also, for volcanic phenomena. But it is evident that some other and more general theory is necessary to account for those great inequalities of the earth’s crust which form land and sea-bottom.

Joseph Le Conte
Elements of Geology – 1898


Life is a cascade of networked precursors. Flesh, bone, talent, ideas, culture, it all moves along with time, propagating from one network to the next. We like to see linear relationships in the process, but I doubt that the linearity is more than an illusion.

My last living Grandparent just died, Naomi. I learned a lot of things about her only after she died. She was a special lady on many counts, but she had horrendous handwriting - of course I knew that before she died. What I didn’t know was how beautiful her husband’s handwriting was, Grandpa’s. She always wrote everything for the pair, but you could never read a damn word she wrote. Grandpa could write like nobody’s business, but I never saw a thing he wrote until after they both died. My Dad got his mother’s handwriting, which he didn’t give to me, because I have no handwriting at all, so I print, or I use my computer. I can’t really decide which of my four grandparents is to blame for that lexic defect.

Naomi attended the university of Chicago before girls generally went off to college, and she took geology classes. My brother was a geology student as well, neither of us knew that Grandma had preceded us in the study of geology. After she died, we found some of her projects and textbooks. Based on that material, she was clearly a better student and geologist than I ever was or ever will be. The above quote was from one of her books. It is remarkable for two reasons. First, they had no clue whatsoever in 1898 about plate techtonics. We now know that the crust of the earth is wandering around the surface, but without that little tidbit of information there are a lot of facts that are absolute head-scratchers. For instance, an ancient shoreline can somehow be located at the peak of a contemporary mountain. They struggled valiantly to make sense of that, but in the end they were debating the dance patterns of fairies on the head of a pin. Second, the statement is remarkable for the following line:

But it is evident that some other and more general theory is necessary to account for those great inequalities of the earth’s crust which form land and sea-bottom.

They knew what they didn’t know, and they were willing to withhold final judgment on the theory in lieu of better ideas to come. In other words, knowing something about something isn’t the same as knowing everything about something. We seem to have forgotten this. Conversely They did not vex their cultural descendants with dogmatic insistence on one theory or another. Apparently the excitement of bigger ideas outweighed the fear of no ideas at all. To them, the interpretation of the earth’s crust without plate techtonics was like the interpretation of the genetic code without a dodecahedron. It shouldn’t be done.

Differential settling was eventually replaced with a model of techtonics, but it was not an unreasonable guess, because heavy things sink. The really heavy stuff in the earth is toward the center, and it gets hotter from pressure as we descend to the core. Toward the periphery are left the lighter elements, the most interesting of which are carbon, oxygen, nitrogen, and of course hydrogen. The most interesting interaction of these elements at the surface of the earth - in the universe - is the interaction of hydrogen and oxygen to form water. The properties of water are oddball in innumerable ways, but without them Life is improbable.

Seventy percent of the surface of the earth is water. The atmosphere is full of it. H2O exists on the periphery of earth in many forms, gas, liquid, ice, and in that most interesting of all forms, the semi-solid carbon slushy form of Life. About seventy percent of Life is water. Life is like a continuous crystalline outer crust on the surface of the earth. What possible mechanism could get this crystal started all those billions of years ago?


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