Re: [Fis] ON MOLECULAR BIONETWORKS (IV) On Number

Dear Jerry,

I will answer "my part" in green:

Igor writes (vol. 488, 6)

  A cell mechanism A adapts (measures) to the cell environment, which it is part of. During this adaptation it increases its complexity and changes (by its very presence) the cell environment, which thus also increases its complexity. Given that there are many such mechanisms (enzyme catalyzed chemical reactions, organelles, membranes, etc), each mechanism increases its complexity by reflecting on the presence of the totality of the other mechanisms.

  JLRC:
  Reading your words from a 'big picture' frame of mind, I concur.

  I would prefer to express the concepts in terms of the flow of electrical particles...

      It may be flow of electric particles, e.g. "measurement" as exchange of electrons or radicals in chemical reactions, which leads to saturations of concentrations of products and thus changes the environment;
      It may be flow of photons, e.g. photosyntetic apparatus of green plants "measures" the incident light by producing flow of protons further used in ATP production and flow of electrons for NADPH production. These flows change, for example, the pH in certain parts of chloroplast, which, in turn, changes the flows themselves, including the available photon flow by, for example, epoxydation/deepoxydation of xantofills, "screening" photosystems from light;
      It may be flow of ions (changes in the state of the neuron through activity of calcium and potassium channels
      It may be flow of genetic information, e.g. transcription of RNA as a reaction to change in the cell environment, which leads to production of enzymes, which, in turn, modify this cell environment (e.g. reaction to heat shock or to strong light)

  Many more examples possible...

  In all these cases change, occuring as a reaction to a certain flow, is a measurement of this flow, and it, in turn, forces the changes to this flow.

  Yes, one may say that most of these phenomena deal with either flows of charged particles or photons. This is, however, trivial. Indeed, there exist only 4 force fields -- electromagnetic, gravity, strong and weak. In case of living matter, at the level of description of biomolecular networks, we deal only with the first one, with electromagnetic field. Hence, the only material objects that really matter are those which interact with the electromagnetic field or are produced by it, i.e. photons and charges (ions and electrons)

  The term "mechanism" can be used in either a mathematical sense, a chemical sense, or a general sense. In what sense is it being used in this paragraph?

  When I say "mechanism" I mean:
       a chemical system of interactions between the biomolecules, ions and quanta, NECESSARILY in the structural context, i.e. in the organelles and compartments, where such interaction happen.
       a mathematical abstraction in the form of system of equations for the biochemical networks, that represents our understanding of the above.

  Nature as such does not know equations and networks, these are means of our interpretation of what happens out there. I think that this is more or less in line with Robert Rosen's views.

  More specifically, in the narrative you provide, how does one create relations between electrical particles and the dynamics of bionetworks? Although only a small number of different electrical particles exist, how does one create the range of organisms in an ecosystem?
      
  As it is known from the theory of systems (examples being Lorentz attractor and other strange attractors, swarm theory, fractal structures, and many many more), it is quite possible to develop very complex systems from very small number of simple elements. The source of this complexity is the nonlinearity and instability of the system, or, in a more mathematical sense, the positive Lyapunov exponential in a finite and bounded phase space. It is, for example, known, that all possible patterns on the sea shells may be reproduced in modeling by means of a system of two simple nonlinear equations (this was in Journal of Theoretical Biology some time in 1987). Please also refer to the works of Karl Simms ("virtual creatures") and works in experimental mathematics of evolution by Chris Langton and other guys from Santa Fe institute.

  Another argument: One needs only 0 and 1 values for the bit to convey in a string of bits as much information as one needs to.

  How can we make such concepts EXACT such that they become a meaningful method of scientific prediction? This is the challenge for bionetworks at all levels of perplexity. How does individuality arise from such a narrative?

  The problem is that we are oftentimes dealing here with the unstable non-equilibrium systems which are deterministic but unpredictable. This means that we cannot predict their behavior but can explain it afterwards. A good example is the game of pool. It is absolutely impossible to predict (before the stroke is made) exactly where each ball lands after the first stroke made into the "triangle" of balls. However, all the interactions, of course, obey Newtonian laws, and backward reconstruction of the process is possible. Same with evolution of biological systems and, in a way, with bionetworks. Only general features of it may be probabilistically predicted. And this is exactly how the individuality comes into picture. Had it not been for these instabilities and extreme sensitivity to small variations in initial and boundary conditions, we would have been all alike and all the same.

  Igor

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Received on Sun Dec 25 17:34:51 2005