Merge Left

The Off Topic series continues and this time it is chemical. More precisely, the discussion begins with thermodynamics and this Gibb’s Free Energy diagram.

It seems strangely appropriate to mention that the phrase “Free Energy” was the first thing about academic chemistry that resonated with my childlike entrancement with nature. What more could an Anarchist want? But that’s another story.

There are 2 key aspects to the energy diagram, 1) the relative position of the left and right hand states (pun fully intended) and 2) the shape/height of the transition between them. (this video explains in more detail).

Gibb's Free Energy Diagram

The diagram distinguishes the relative amount of free energy, that is, the difference between the energies of the stable states. Going downhill from left to right is the spontaneous direction and the transition releases energy (in one form or another). To go from right to left require free energy be transferred to the system undergoing transition. The other aspect of the diagram is the energy pathway between stable states, which may involve much larger energies than the difference between them. Activation energy is the barrier between stable states. Just as the diagram implies, the higher the barrier, the less likely it is that the entities described by the stable states will have acquired sufficient energy to reach the peak, the activation state, where it becomes possible to roll down hill into a new stable state. The deeper the fall-off, the more likely the entity will roll down it, but it’s a statistics game and we left out entropy for the moment.

The energy pathway between states determines how fast the “reactants” are converted to “products”. Catalysts accelerate reactions because they lower the activation energy and “push” the transition state toward the desired products, even if the right hand stable state is at higher free energy. Biological catalysts, best represented by enzymes, are very good at these “biosynthetic” mechanisms (but that’s another story). One way to conceive of how enzymes operate at the molecular level is by ratcheting the products up to the transition state by creating a set of smaller “sub-states” and guiding the transition state to particular products. The transition between stable states of (roughly) equal free energy should not be underappreciated (not covered in video).

The Free Energy diagram is intimately related to the image of bistability in my previous diary (Stability and Change) in which the two states are of equivalent free energy. A transportation analogy reflects situation quite nicely. The distance between any two destinations is determined by geography while the rate at which one can move between the states is determined by individual modes transportation. There are a lot of ways to get to San Jose and each pathway (reaction diagram) has an associated free energy profile, but all of them connect A to B. Crawl, walk, run, fly or teleport we still move between the same two cities. The 2 dimensional depiction of bistability is likely an over simplification of the multifaceted “real world”, but I opt for graphical simplicity and encourage the reader to visualize the multidimensional version of the diagram.

Levels of Biological Organization

The depiction of the biological scales emphasizes the nestedness of the more complex levels. That is, each system is a part of the next more complex and thereby included in all others. An analogy might be found in this symbol. Specifically, the small pieces of the opposing part of the duality that each contains, imagined as a multiplicity, where each level contains a piece of all “lesser” levels. Nesting preserves the value of the less complex systems because each has critical functions within the more complex levels. For example, molecular hormones operate within the context of the multicellular, multiorgan human physiology. Likewise, the individual biological entity that bears the germline DNA is not demeaned by the more complex structures within which in which it lives. Each of us, like any other animal or plant, is simultaneously whole and part. That we can conceive of the situation and comment upon it is (part of) what makes us human. But that particular digression is beyond the scope of this installment.

The scale diagram implies a systems science approach. A sense of the systems perspective is provided by considering how many molecules comprise any given level of organization. In order to manifest the entire biome of the planet and to maintain it over time, all of those molecules are organized. One way these are organized, or coordinated, is by physically nesting them into cells, tissues, organs, individuals, etc. How does the whole become greater than the sum of its parts? By organizing of course, only by coordinated interaction between the parts will the little bit extra that characterizes the whole be manifest. Non-interaction is so sum of the parts! Time is also a biological scale, in the evolutionary sense if no other, and is also nested. More visually, the concept may be encompassed by the full circles within opposing semi-circles the Yin Yang, but rendered in multiple dimensions and shades of grey. Each full circle a remnant of the closed levels within the open level beyond which no one can yet conceive of something larger. What can hold the universe? The tails, too, where light dissolves into dark and shadow melds with light, is something like the point at the top of the scale diagram where all the (sub)systems intersect. After all, Einstein, matter is energy in the end.