[Fis] TR: some notes
Sungchul Ji
sji at pharmacy.rutgers.edu
Tue Nov 14 04:36:53 CET 2017
Pedro wrote:
"3. About logics in the pre-science, Joseph is quite right demanding that
discussion to accompany principles or basic problems. Actually
principles, rules, theories, etc. are interconnected or should be by a
logic (or several logics?) in order to give validity and coherence to
the different combinations of elements. For instance, in the
biomolecular realm there is a fascinating interplay of activation and
inhibition among the participating molecular partners (enzymes and
proteins) as active elements. I am not aware that classical ideas from
Jacob (La Logique du vivant) have been sufficiently continued; it is not
about Crick's Central Dogma but about the logic of pathways, circuits,
modules, etc. Probably both Torday and Ji have their own ideas about
that-- I would be curious to hear from them."
(1) Enzymes, like all molecular and sub-molecular species (generally called microscopic entities, quantum objects, quons [1], or wavicles) exhibit the wave-particle duality (as evidenced by the fact that they obey the Planckian Distribution Equation (PDE) [2-4]). And yet most of the descriptions of enzyme mechanisms given in the current literature are based on the particle aspect of enzymes including all the efforts directed to understanding enzyme activities in terns of the causal role of the static 1-dimensional sequences of amino acids or their 3-dimensional folds as revealed by the X-ray crystallography. Alternatively, we can describe enzyme structure and function based on their wave attributes, in which case enzymes are viewed as systems of oscillators and their functions are determined by the collective vibrational motions of amino acid residues called "standing waves" (see Figure 8 in [3]).
(2) Like electrons (see (4) below)), enzymes (and biopolymers in general, including DNA; see Table 1 below) may possesses two complementary attributes -- static and dynamic. Just as the position and momentum of the electron cannot be accounted for by their static attributes alone, so perhaps the static attributes of enzymes (e.g., amino acid sequences) alone may not be sufficient to account for their dynamic attributes, i.e., their catalytic activities. The missing link may be sought in their wave attributes which have collective organizing power. Traveling waves generated within a volume can interact to form "standing waves", also called "resonant waves", as exemplified by the Chladini plate shown below:
https://www.youtube.com/watch?v=wvJAgrUBF4w<https://www.youtube.com/watch?v=wvJAgrUBF4w>
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(3) There is accumulating evidence (references available upon request) to support the following mechanism of enzyme action:
E <-----------> E' (1)
E' + S <-----------> [E.S <===> E.P] (2)
[E.S <===> E.P] <-----------> E + P (3)
________________________________________
E + S <-----------> E + P (4)
Figure 1. The pre-fit mechanism (in contrast to the better-known "induced-fit mechanism of Koshland) of enzyme catalysis [1]. Symbols are defined as follows: E = ground-state enzyme; E' = conformationally excited enzyme through thermal fluctuations; S = substrate; E.S = Enzyme-substrate complex in the transition state; E.P = the enzyme-product complex in the transition state; <-----> = thermally equilibrium; <===> = the resonance hybrid between the enzyme-substrate and enzyme-product complexes.
Step (1) indicates that an enzyme molecule is a collection of oscillators that interact with one another to form higher-order structures, either local or global, known as resonances or standing waves. In the Chladni plate, what causes the 'visible' standing waves of particles on it is the 'invisible' vibrational motions of the plate itself and the particles are forced to form standing waves through resonance energy transfer from the plate to individual particles. In enzymes, what causes the formation of the standing waves or resonant waves of the enzyme molecule are the component amino acid residues acting as elementary oscillators whose periodic motions can combine, obeying the Fourier theorem, to form almost infinite number of standing waves, some of which are 'selected' by the substrate via complementary binding.
I am not a quantum mechanician, but I think (please correct me if I am in error) the enzyme catalytic mechanism depicted in Figure 1 can be represented in terms of the matrix algebra used in quantum mechanics thus:
A*S =λ*S (5)
where A is the matrix consisting of all the possible conformational states of an enzyme, S is the substrate, and λ is the conformational state of the enzyme that is selected by S binding because it transforms S to P. In physics, A is called the operator, S is the eigenvector, and λ is the eigenvalue.
From the infomation-theoretic point of view, an enzyme molecule can be viewed as the information source containing all the conformaitonal states accessible through thermal fluctuations or Brownian motions, and substrate binding selects a subset of those conformational states that are conducive to catalytic actions. If the number of all possible conformational state of an enzyme is N and substrate S selects n of these to be transformed into P, then the the amount of information generated by the catalytic reaction would be
log_2(N/n) bits, (6)
assuming for simplicity that all the conformations accessible to the enzyme have equal probabilities of being exposed to the substrate.
(4) Physicists recognize two complementary attributes of quantum entities, also called quons or wavicles -- (i) static and (ii) dynamic attributes. For example, the electron has the static attributes of mass, charge and spin magnitude and the dynamic attributes of position, momentum, and spin direction. Herbert [6. p. 99] writes:
"Each quon possesses two kinds of attributes static and dynamic. A static attribute always has the same size each time it is measured, and thus serves to distinguish one type of quon from another. . . . " .
Similarly, I think it is reasonable to assume that DNA (and other biopolymers, including enzymes, see (3) above) has two kinds of attributes -- (i) static (e.g., nucleotide sequences of genes) and (ii) dynamic (e.g., vibrational patterns of DNA as a whole which are predictable in principle, based on the Fourier theorem, from the elementary vibrational motions of the molecules constituting the genetic alphabet, A, C, G and T).
(5) The dynamic attributes of DNA may be compared to the audio music and its static attributes with sheet music (see Rows 4 and 5 in Table 1). Table 1 contains other interesting comparisons between a piano and the DNA molecule viewed as a self-organizing or self-playing molecular piano, in agreement with the recent conclusions drawn by S. Petohukhov who developed the novel system-resonance approach to studying the genetic codes [7, 8]. According to my crude estimation, the maximum information capacity of DNA is about 200 bits (see the 2nd Row, Table 1).
Table 1. The Postulate that DNA is a self-organizing molecular piano keyboard (SOMPK)
DNA
Piano
1. Units of oscillations
~ 1010 nucleotides
88 keys
2. Number of possible resonant oscillations
410^10 ~ almost infinite
Maximum Shannon information content of DNA =
log_2(4)^(10^10) =200 bits, if each oscillation can act as a potential message
almost infinite (?)
3. Agent
Living cell
Pianist
4. Dynamic structures
(including standing waves)
Time-dependent folding patterns of DNA, chromatins and chromosomes
which are thought to determine its biological functions (see Figure 8 in [3])
Musical melodies
(also called Audio music)
5. Static structures
Nucleotide sequences of individual cells, not of species
Sheet music
6. Scale
Microscopic
Macroscopic
7. Thermal Fluctuations
Essential for Function
Detrimental to Function
8. Obeys
Matter-Energy Conservation Law
Wave-Particle Duality Principle
[2-4]
Fourier Theorem
Minimum Energy Requirement for Information Transmission
Matter-Energy Conservation Law
Wave-Particle Duality Principle
[2-4]
Fourier Theorem
Minimum Energy Requirement for Information Transmission
Any questions, corrections, or suggestions are welcome.
All the best.
Sung
References:
[1] Ji, S. (2012). The Kinetics of Ligand-Protein Interactions: The“Pre-fit” Mechanism <http://www.conformon.net/?attachment_id=983> Based on the Generalized Franck-Condon Principle. In: Molecular Theory of the Living Cell: Concepts, Molecular Mechanisms, and Biomeduical Applicaitons. Springer, New Y0ork. Pp. 209-214. http://www.conformon.net/wp-content/uploads/2014/01/Pre_fit_hypothesis_p209_p213.pdf<http://www.conformon.net/wp-content/uploads/2014/01/Pre_fit_hypothesis_p209_p213.pdf><http://www.conformon.net/wp-content/uploads/2014/01/Pre_fit_hypothesis_p209_p213.pdf>
[2] Ji, S. (2016). WAVE-PARTICLE DUALITY IN PHYSICS AND BIOMEDICAL SCIENCES.<http://www.conformon.net/wp-content/uploads/2016/09/PDE_SymmetryFestival_2016.pdf> Symmetry: Science and Culture 27 (2): 99-127 (2016). http://www.conformon.net/wp-content/uploads/2016/09/PDE_SymmetryFestival_2016.pdf
[3] Ji, S. (2015). Planckian distributions in molecular machines, living cells, and brains: The wave-particle duality in biomedical sciences.<http://www.conformon.net/wp-content/uploads/2016/09/PDE_Vienna_2015.pdf> In: Proceedings of the International Conference on Biology and Biomedical Engineering, Vienna, March 15-17, 2015. Pp. 115-137. http://www.conformon.net/wp-content/uploads/2016/09/PDE_Vienna_2015.pdf
[4] Ji, S. (2015). PLANCKIAN INFORMATION (IP): A NEW MEASURE OF ORDER IN ATOMS, ENZYMES, CELLS, BRAINS, HUMAN SOCIETIES, AND THE COSMOS. <http://www.conformon.net/wp-content/uploads/2016/09/PDE_Vigier9.pdf> In: Unified Field Mechanics: Natural Science beyond the Veil of Spacetime (Amoroso, R., Rowlands, P., and Kauffman, L. eds.), World Scientific, New Jersey, 2015, pp. 579-589). http://www.conformon.net/wp-content/uploads/2016/09/PDE_Vigier9.pdf
<http://www.conformon.net/wp-content/uploads/2016/09/PDE_Vigier9.pdf><http://www.conformon.net/wp-content/uploads/2016/09/PDE_Vigier9.pdf> [5] Ji, S. (2017). The Cell Language Theory: Connecting Mind and Matter. World Scientific Publications, New Jersey. Section 4.12.
[6] Herbert, N. (1987). Quantum Reality: Beyond the New Physics, an Excursion into Metaphysics . . . Anchor Books, New York.
[7] Petoukhov, S. V. (2016). The system-resonance approach in modeling genetic structures. BioSystems 139:1-11. http://www.sciencedirect.com/science/article/pii/S0303264715001732
[8] Petoukihov, S. V. (2017). The rules of long DNA-sequences and tetra-groups of oligonucleotides. https://arxiv.org/ftp/arxiv/papers/1709/1709.04943.pdf
________________________________
From: Fis <fis-bounces at listas.unizar.es> on behalf of Christophe Menant <Christophe.Menant at hotmail.fr>
Sent: Monday, November 13, 2017 11:27 AM
To: pcmarijuan.iacs at aragon.es
Cc: fis at listas.unizar.es >> fis at listas.unizar.es
Subject: [Fis] TR: some notes
Thanks for that Pedro,
Just a few comments.
All the best,
Christophe
________________________________
De : Fis <fis-bounces at listas.unizar.es> de la part de Pedro C. Marijuan <pcmarijuan.iacs at aragon.es>
Envoyé : lundi 13 novembre 2017 14:30
À : 'fis'
Objet : [Fis] some notes
Dear All,
Herewith some notes on the exchanges of past weeks (sorry, I was away in
bureaucratic tasks).
1. Agents & Information. There were very good insights exchanged;
probably both terms make a fertile marriage. Actually I have been
writing about "informational entities" or "subjects" as
receivers/builders of information but taking into account the other
disciplines around, "agents" look as the most natural companion of
information. The only thing I don't quite like is that they usually
appear as abstract, disembodied communicative entities that do not need
self-producing. Their communication is free from whatever life
maintenance...
Yes, agents naturally go with information as they are the source of meaning
generation, of sense making. Agents can be organic, human and artificial.
(I look at agents as identifyable entities submitted to internal
constraints and capable of actions for the satisfaction of the constraints).
Artificial agents can be looked at as disembodied but their being is
derived from our human ones. So their self (if any) is part of the
human designer's self.
2. Eigenvectors of communication. Taking the motif from Loet, and
continuing with the above, could we say that the life cycle itself
establishes the eigenvectors of communication? It is intriguing that
maintenance, persistence, self-propagation are the essential motives of
communication for whatever life entities (from bacteria to ourselves).
With the complexity increase there appear new, more sophisticated
directions, but the basic ones probably remain intact. What could be
these essential directions of communication?
Perhaps it could be interesting here to highlight that physics/chemistry
and biology/psychology cannot address information the same way.
Physics and chemistry use tools with precise definitions allowing to
model our environment in a deterministic and predictable way
(QM and Chaos deserving more investigations).
Biology/psychology do not benefit of such rigorous mathematical
support. We do not even know how to define life or consciousness,
and our models are incomplete.
So what about separating the two domains and looking at their relations
as a third domain?
1) Thermodynamics, entropy, quantity of information, channel capacity,
data transmission.
2) Meaning generation, biology and self-consciousness
3) Emergence and locality of constraints, emergence of meanings
This puts again the focus on meaning generation, a key evolutionary
step without which we would not be here.
Also, let's not forget that data transmission and quantification of
information are about meaningful information.
So why not consider internal constraint satisfaction, the source of
meaning generation, as an essential direction of communication?
3. About logics in the pre-science, Joseph is quite right demanding that
discussion to accompany principles or basic problems. Actually
principles, rules, theories, etc. are interconnected or should be by a
logic (or several logics?) in order to give validity and coherence to
the different combinations of elements. For instance, in the
biomolecular realm there is a fascinating interplay of activation and
inhibition among the participating molecular partners (enzymes and
proteins) as active elements. I am not aware that classical ideas from
Jacob (La Logique du vivant) have been sufficiently continued; it is not
about Crick's Central Dogma but about the logic of pathways, circuits,
modules, etc. Probably both Torday and Ji have their own ideas about
that-- I would be curious to hear from them.
4. I loved Michel's response to Arturo's challenge. I think that the two
"zeros" I mentioned days ago (the unsolved themes around the cycle and
around the observer) imply both multidisciplinary thinking and
philosophical speculation...
Best wishes--Pedro
-------------------------------------------------
Pedro C. Marijuán
Grupo de Bioinformación / Bioinformation Group
Instituto Aragonés de Ciencias de la Salud
Centro de Investigación Biomédica de Aragón (CIBA)
Avda. San Juan Bosco, 13, planta 0
50009 Zaragoza, Spain
Tfno. +34 976 71 3526 (& 6818)
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