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Molecular Nanotechnology: Golden Mean as a Driving Force of Self-Assembly


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In this paper we are considering self-assembly approach from nanobiology to molecular nanotechnology. Because the genetic code, as a most complex biomolecular system, is determined by Golden mean, we used it knowledge to study approaches to nanotechnology. Understanding protein self-assembly driving force and structure of clathrin and microtubules based on Golden mean we have found that fullerene C60 and nanotubes could be very useful materials for molecular nanotechnology. One possible solution as a sample is given.
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Molecular Nanotechnology:
Golden Mean as a Driving Force of Self-Assembly
Molecular Machines Research Center, Faculty of Mechanical Engineering, University of
Belgrade, 27.Marta br.80, 11120 Belgrade, SERBIA
Institute for Chemical Power Sources, Batajnicki put 27,11080 Belgrade, SERBIA
Mechanical Textile College, Starine Novaka 23,11000 Belgrade, SERBIA
Abstract: In this paper we are considering self-assembly approach from nanobiology to molecular
nanotechnology. Because the genetic code, as a most complex biomolecular system, is
determined by Golden mean, we used it knowledge to study approaches to nanotechnology.
Understanding protein self-assembly driving force and structure of clathrin and microtubules
based on Golden mean we have found that fullerene C
and nanotubes could be very useful
materials for molecular nanotechnology. One possible solution as a sample is given.
Key-words: Golden mean, nanobiology, clathrin, microtubules, molecule C
, nanotubes,
molecular nanotechnology
1 Introduction
Beauty is a conspicuous element in
the abstract completeness aimed at in the
higher mathematics. Also, trough the
symmetry law it is the goal of physics as it
seeks to construe the order both elementary
particules and the Universe. However, it
ought to be the inspiration of genetic and
molecular study of life.
Beauty is a word which has defied
the efforts of philosophers to define in a way
that commands general agreement. In
mathematics it is mean ratio, golden triangle
or Fibonacci golden series. In material
science it is crystal state based on number of
transformations of point symmetry groups.
In molecular machines technology it could
be driving force of self-assembly based on
structure, energy and environmental
2 Problem Formulation
Human organism is the most
complex local Universe technology. In spite
of that, structural information code (DNA) is
based on only four elements, in form as an
aperiodic crystal. [1] However, it has been
shown that the genetic code is a Golden
mean determined system. [2] On the other
hand, the Golden mean is driving force of
protein biomolecular machinery [3] For
nannotechnology it is important to find
biomolecules (proteins) as a systems which
structure and energy properties are based on
Golden mean. Based on nanobiology
knowledge we can develop new materials
with self-assembles properties for molecular
nanotechnology. [4]
2.1 Golden Mean in Nanobiology:
Clathrin and microtubules are two
main proteins which structure and energy
properties are based on Golden mean.
Clathrin was discovered in 1969 by two
Japanise scientists, Kanaseki and Kadota [5],
while microtubules at the first time was
predicted and published by a 24-year-old
Austrian cell biologist Sigmund Freud (well
known psychologist) [6].
2.1.1 Clathrin
Clathrin- coated vesicles are cell
structures found in all nucleated cells, from
yeast to human. It is a protein with a
molecular weight of 180,000 daltons
(dalton: “D” is the equivalent of the weight
of one hydrogen atom). Clathrins are the
major components of coated vesicles,
important organelles for intracellular
material transfer including synaptic
neurotransmitter release. Based on
molecular weights, isoelectric points and
antigenic determinants, two proteins,
- and
-tubulin subunits, have been found to be
associated with coated vesicles in both
bovine brain and chicken liver.
The basic form of clathrin is a
trimer (three subunits), but the basic form of
assembly protein, which associates with
clathrin, is a dimer. Clathrin is highly
conserved in evolution and is composed of
three large polypeptide chains and three
smaller polypeptide chains that together
form a triskelion. A different number of
triskelions assemble into a basket-like
network with Golden mean properties based
on 12 pentagons and various numbers of
Clathrin as a truncated icosahedron
is dominant in neurons, while clathrin with
30 hexagons is found in other types of cells
(e.g. liver, etc.). Large clathrin of 60
hexagons with a diameter of about 120 [nm]
have been found in fibroblasts. The number
of amino acids with negative charges
(aspartic acid and glutamic acid) is 378 per
clathrin, while the number of amino acids
with positive charges (histidine, lysine and
arginine) is 201. This means that there are
Figure 1: Clathrin self-assembly: Clathrin triskelions are the assembly units of the sphere lattice
on the surface of coated pits and coated vesicles [4]
77 more electrons than positive charge per
molecule, or per “cage” there are about
8.316 more electrons than positive charges.
Figure 2: Neural cells (neurons) contain CV and clathrin with 12 pentagons and 20 hexagons with
diameters of 70-80 nm [4]
2.1.2 Microtubules
Microtubules are biopolymers
present in all eucariotic cells. They are
involved in several specialized functions,
including cell shape regulation, mitosis,
intracellular translocation, cell motility, and
secretion. Structurally, microtubules are
hollow cylinders 25 nm in diameter which
are composed of 13 linear chains
(protofilaments) which consist of proten
subunits called tubulin. Microtubules are
composed of equimolar amount of the two
globular 50 kD subunits, alfa and beta
tubulin, each having a similar amino acid
sequence and a similar overall shape.
Tubulin is a globular (spherical)
protein composed of amino acids. α -tubulin
subunits usually contain 450 amino acids,
while β -subunits contain about 445 amino
acids. There are about two times more
negative charges (Asp and G1u) than
positive charges (Lys, Arg and His). The
diameter of tubulin subunits is about 4 nm.
This heterodimer is the main building
element of microtubules. Microtubules may
exist from 7-17protofilaments, but usually
(85%) a microtubule contains 13
Figure 3: Most neuronal CV and clathrin are
concentrated in synapses (where
consciousness arise), some associated with
microtubules (usually there are five CV per
one microtubule). [4]
The subunits of tubulin molecules
are assembled into long tubular structures
with an average exterior diameter of 25-30
nm, capable of changes of length by
assembly or disassembly of their subunits.
Assembly/disassembly is sensitive to cold,
high hydrostatic pressure, several specific
chemicals such as colchicine and
vinblastine, and other factors.
Since some experimental results link
tubulin and microtubules to bioinformation
processes such as memory, learning and
consciousness microtubules have become
the subject of intensive research.
2.3 Golden Mean in Nanomaterials
2.3.1 Molecule C
The C
molecule is the third known
pure crystal form of carbon, in addition to
graphite and diamond. It is predicted in 1970
by Japanise scientist Osawa, and synthesis in
1985 by Kroto/Smalley research team. The
electronic structure is a complex, “many
body” problem, because there are 360
electrons. Conversely, the C
molecule has
attributes of a “big atom”, because it has a
close spherical electronic shell and possesses
unique icosahedral symmetry properties. In
Figure 5: Nanotubes as a double-helix
(proposed by Osawa [10]) could be very
important basic element for molecular
nanotechnology based on self-assembly.
the truncated icosahedral structure there are
two characteristic C-C bond lengths: C
in pentagons, C
double bonds in
hexagons (or link between two pentagons).
There are sixty carbon p
each pointed along radial axes. If
interactions among p
orbitals belonging to
carbon atoms on a certain pentagon are
considered and interactions among orbitals
located on different pentagons (there are 12
such pentagons) are neglected, then the five
eigenstates based on K
symmetry (spherical
Figure 4: Golden mean surface energy state
of molecule C
There are three sets of orbitals
which occur grouped together: ψ
, ψ
and ψ
. Interaction among 12 pentagons
will split the twelve ψ
orbitals to A
+ H
+ T
, while the 24 ψ
orbitals, two
per pentagon, will split into T
+ G
+ H
+ G
+ H
, irreducible representations (or
symmetries). The final 24 ψ
with the highest energy, will be split into
, G
, G
, H
, T
and H
. Irreducible
representations T
, T
and T
symmetry elements C
and S
Golden mean properties.[4]
2.3.2 Nanotubes
Nanotubes are similar to
microtubules like C
molecule is similar to
clathrin. Nanotubes are quasi-1D structure,
while C
is quasi-0D entity; first crystallize
around axis (1-dimension) and second
crystallize around point (0-dimension).
There are single-wall and multi-wall
nanotubes with different physical properties.
All types of nanotubes are intersting for
nanotechnology, but helical one could be
very intersting for molecular
nanotechnology based on self-assembly.
3 Problem solution
We are proposing one possible approach to
problem solution of molecular
nanotechnology based on Golden mean.
Nanomaterials will be fullerene molecule
with intelligent solvent and magnetic
field with density of magnetic flux by
Golden mean (Figure 6).
We plan to use knowledge from
nanobiology (self assembly of clathrins and
microtubules) to molecular nanotechnology
and nanotubes) in sense like
relationship between the flight of a bird and
the flight of an aircraft: both use wings but
in different manners. [11] However,
molecular coding chain of spiral nanotubes,
with C
and endohedral M@C60 as basic
elements, should exist.
Figure 6: One possible approach of molecular nanotechnology based on Golden mean and
symmetry reduction (from
trough 48 to 9 and from
trough 120, 60, 24 to 12 - adapt from
reference [4]).
4 Conclusion
Golden mean is very powerful force
of self-assembly in molecular biology (DNA
and proteins). It is possible to take this
knowledge from nanobiology and
implement into molecular nanotechnology.
Very promising nanomaterials for self-
assembly approach based on Golden mean
in molecular nanotechnology are fullerenes
and carbon nanotunbes. Environment for
self –assembly process should be intelligent
solvent and internal pulsing magnetic field
by Golden mean.
[1] Schrodinger, E, What is Life? & Mind
and Metter, Cambridge University
Press, 1967
[2] Rakocevic, M., The genetic code as a
Golden mean determined system,
BioSystems, 46: pp283-291,1998
[3] Koruga, D. et. al. A new classification
of amino acids by module 3/2, Archive
of Oncology, Vol.5, No.3, pp.137-139,
[4] Koruga, D., et al, Fullerene C
History, Physics, Nanobiology,
Nanotechnology, North-Holland,
Amsterdam, 1993
[5] Kaneski, T. Kadota,K., Structure of
Clathrins, J. Cell Biology, 20:pp.202-
[6] Freud, S. Sitzungsber. d. Wiener
Acad., Math-nat. Cl. 85:pp. 9, 1882
[7] Hameroff, S., Ultimate Computing:
Biomolecular Consciesness and
NanoTechnology, North-Holland,
Amsterdam, 1987
[8] Hameroff, S. Penrose,R., Orchestrated
Reduction of Quantum Choherance in
Brain Microtubules: A model for
Consciousness, pp.508-540, in book:
Toward of a Science of
Consciousness, MIT Press 1996
[9] Penrose, R., Shadows of the Mind: A
Search for the Missing Science of
Consciousness, Oxford University
Press, Oxford 1994
[10] Osawa, E, Shape and Fantasy of
Fullerenes, MRS Bulletin, Vol.XIX,
No.11, pp.33-36, 1994
[11] Koruga, D., at al. Self-Assembled
Molecular Computer Based on
Fullerene C
: From Nanobiology to
Nanotechnology, The 4
Int.Symposium on Bioelectronic and
Molecular Electronic Devices,
BMED’92 pp.1-4, Miyazaki, Japan,
... Due to that specific packing the surface of C 60 is three times smaller than expected for biological molecules with the same molecular weight of 720.7 Da. The presence of 120 symmetry operations, like rotations around an axis or reflections in a plane, which map the molecule onto itself, has made C 60 the most symmetrical molecule that follows the Golden Mean rule (Koruga et al., 2002;Yadav & Kumar, 2008). The unusual structure of C 60 determines its unique physico-chemical properties and biological activity (Nielsen et al., 2008;Scharff et al., 2008;Montellano et al., 2011) (Fig. 2). ...
Full-text available
Recent progress in nanotechnology has attracted interest to a biomedical application of the carbon nanoparticle C60 fullerene (C60) due to its unique structure and versatile biological activity. In the current study the dual functionality of C60 as a photosensitizer and a drug nanocarrier was exploited to improve the efficiency of chemotherapeutic drugs towards human leukemic cells. Pristine C60 demonstrated time-dependent accumulation with predominant mitochondrial localization in leukemic cells. C60’s effects on leukemic cells irradiated with high power single chip LEDs of different wavelengths were assessed to find out the most effective photoexcitation conditions. A C60-based noncovalent nanosized system as a carrier for an optimized drug delivery to the cells was evaluated in accordance to its physicochemical properties and toxic effects. Finally, nanomolar amounts of C60-drug nanocomplexes in 1:1 and 2:1 molar ratios were explored to improve the efficiency of cell treatment, complementing it with photodynamic approach. A proposed treatment strategy was developed for C60 nanocomplexes with the common chemotherapeutic drug Doxorubicin, whose intracellular accumulation and localization, cytotoxicity and mechanism of action were investigated. The developed strategy was revealed to be transferable to an alternative potent anticancer drug – the herbal alkaloid Berberine. Hereafter, a strong synergy of treatments arising from the combination of C60-mediated drug delivery and C60 photoexcitation was revealed. Presented data indicate that a combination of chemo- and photodynamic treatments with C60-drug nanoformulations could provide a promising synergetic approach for cancer treatment.
... 13. Clathrins, closely associated with microtubules, are truncated isocahedra with 3 :1  geometric resonance, and are involved in synaptic neurotransmitter release [75]. 14. ...
Full-text available
In this condensed paper, by combining the insights from E-Infinity theory, along with Plato's initiatory insights into the golden section imbedded in his Principles of the One and Indefinite Dyad, David Bohm's ontological framework of the superimplicate, implicate and explicate orders, andthe pervasive presence throughout physics, chemistry, biology and cosmology of the golden ratio (often veiled in Fibonacci and Lucas numbers), a profound golden mean number system emerges underlying the cosmos, nature and consciousness. This ubiquitous presence is evident in quantum mechanics, including quark masses, the chaos border, fine structure constant and entanglement, entropy and thermodynamic equilibrium, the periodic table of elements, nanotechnology, crystallography, computing, digital information, cryptography, genetics, nucleotide arrangement, Homo sapiens and Neanderthal genomes, DNA structure, cardiac anatomy and physiology, biometric measurements of the human and mammalian skulls, weather turbulence, plant phyllotaxis, planetary orbits and sizes, black holes, dark energy, dark matter, and even cosmogenesis-the very origin and structure of the universe. This has been pragmatically extended through the most ingenious biomimicry, from robotics, artificial intelligence, engineering and urban design, to extensions throughout history in architecture, music and the arts. We propose herein a grand unification of the sciences, arts and consciousness, rooted in an ontological superstructure known to the ancients as the One and Indefinite Dyad, that gives rise to a golden mean number system which is the substructure of all existence.
... As all of the biomolecules are dissolvable in water (aqueous systems), the solution to the problem may lie in controlling and forcing a dysfunctional biomolecule to oscillate in its natural state by using hydrogen bonds of water around the molecule [17]. The presence of a water based nano-harmonized substance (wNHS) in biological tissues imparts the Golden Mean driving force of a natural self-assembly process, which is capable of the restoration of damaged functions of biomolecules [18]. An energetically stabilized nano-harmonized substance could be considered a biomimetic nanomaterial that, through its symmetric and energetic properties, resembles clathrin – a protein that plays a critical role in intracellular information trafficking. ...
Full-text available
Since their discovery in 1985, fullerenes have attracted considerable attention. Their unique carbon cage structure provides numerous opportunities for functionalization, giving this nanomaterial great potential for applications in the field of medicine. Analysis of the chemical, physical, and biological properties of fullerenes and their derivatives showed promising results. In this study, functionalized fullerene based nanomaterials were characterized using near infrared spectroscopy, and a novel method -Aquaphotomics. These nanomaterials were then used for engineering a new skin cream formula for their application in cosmetics and medicine. In this paper, results of nano cream effects on the skin (using near infrared spectroscopy and aquaphotomics), and existing results of biocompatibility and cytotoxicity of fullerene base nanomaterials, are presented.
A completely new doublet-triplet system of amino acids in module 3/2 is given, determined with stereochemical specificity and polarity of amino acids presented either separately, or within four stereochemical types (alanine, valine, proline, and glycine types).
One of the many wonders that fullerenes have brought to us during the past few years is the variety of their shapes. When the elusive C 60 finally showed up in 1990, the perfect symmetry and astounding beauty of its molecular structure touched the hearts of scientists before they could consider the molecule's vast technical possibilities. Already much has been said about the unique shape of C 60 and its potentialities. C 70 and higher fullerenes have simultaneously been found in the same soot that produced C 60 and were quickly revealed to be shaped like rugby balls or oblong eggs. Hence we were aware that there had to be an extensive series of roundish polyhedral clusters of carbon atoms. Then, in the following year, multilayered tubular fullerenes (Figures 1a and 1b) were discovered by Iijima and were named buckytubes (see the article by Iijima in this issue). Iijima also observed similarly huge and multilayered carbon balls, before C 60 was discovered. Soon after, buckyonions were recognized as an important class of fullerene (Figure 1c, see article by Ugarte in this issue). So, in the early days of fullerene research, we already knew three forms of fullerene: sphere, tube, and particle. At that time, however, nobody anticipated that this was only the beginning of a big show of stunning variations in the shapes of fullerenes. This article introduces current developments in the study of these fullerene styles.
Features of consciousness difficult to understand in terms of conventional neuroscience have evoked application of quantum theory, which describes the fundamental behavior of matter and energy. In this paper we propose that aspects of quantum theory (e.g. quantum coherence) and of a newly proposed physical phenomenon of quantum wave function “self-collapse” (objective reduction: OR - Penrose, 1994) are essential for consciousness, and occur in cytoskeletal microtubules and other structures within each of the brain's neurons. The particular characteristics of microtubules suitable for quantum effects include their crystal-like lattice structure, hollow inner core, organization of cell function and capacity for information processing. We envisage that conformational states of microtubule subunits (tubulins) are coupled to internal quantum events, and cooperatively interact (compute) with other tubulins. We further assume that macroscopic coherent superposition of quantum-coupled tubulin conformational states occurs throughout significant brain volumes and provides the global binding essential to consciousness. We equate the emergence of the microtubule quantum coherence with pre-conscious processing which grows (for up to 500 ms) until the mass-energy difference among the separated states of tubulins reaches a threshold related to quantum gravity. According to the arguments for OR put forth in Penrose (1994), superpositioned states each have their own space-time geometries. When the degree of coherent mass-energy difference leads to sufficient separation of space-time geometry, the system must choose and decay (reduce, collapse) to a single universe state. In this way, a transient superposition of slightly differing space-time geometries persists until an abrupt quantum → classical reduction occurs. Unlike the random, “subjective reduction” (SR, or R) of standard quantum theory caused by observation or environmental entanglement, the OR we propose in microtubules is a self-collapse and it results in particular patterns of microtubule-tubulin conformational states that regulate neuronal activities including synaptic functions. Possibilities and probabilities for post-reduction tubulin states are influenced by factors including attachments of microtubule-associated proteins (MAPs) acting as “nodes” which tune and “orchestrate” the quantum oscillations. We thus term the self-tuning OR process in microtubules “orchestrated objective reduction” (“Orch OR”), and calculate an estimate for the number of tubulins (and neurons) whose coherence for relevant time periods (e.g. 500 ms) will elicit Orch OR. In providing a connection among (1) pre-conscious to conscious transition, (2) fundamental space-time notions, (3) non-computability, and (4) binding of various (time scale and spatial) reductions into an instantaneous event (“conscious now”), we believe Orch OR in brain microtubules is the most specific and plausible model for consciousness yet proposed.
A New York Times bestseller when it appeared in 1989, Roger Penrose's The Emperor's New Mind was universally hailed as a marvelous survey of modern physics as well as a brilliant reflection on the human mind, offering a new perspective on the scientific landscape and a visionary glimpse of the possible future of science. Now, in Shadows of the Mind , Penrose offers another exhilarating look at modern science as he mounts an even more powerful attack on artificial intelligence. But perhaps more important, in this volume he points the way to a new science, one that may eventually explain the physical basis of the human mind. Penrose contends that some aspects of the human mind lie beyond computation. This is not a religious argument (that the mind is something other than physical) nor is it based on the brain's vast complexity (the weather is immensely complex, says Penrose, but it is still a computable thing, at least in theory). Instead, he provides powerful arguments to support his conclusion that there is something in the conscious activity of the brain that transcends computation--and will find no explanation in terms of present-day science. To illuminate what he believes this "something" might be, and to suggest where a new physics must proceed so that we may understand it, Penrose cuts a wide swathe through modern science, providing penetrating looks at everything from Turing machines (computers programmed for artificial intelligence) to the implications of Godel's theorem maintaining that conscious thinking must indeed involve ingredients that cannot adequately be simulated by mere computation. Of particular interest is Penrose's extensive examination of quantum mechanics, which introduces some new ideas that differ markedly from those advanced in The Emperor's New Mind , especially concerning the mysterious interface where classical and quantum physics meet. But perhaps the most interesting wrinkle in Shadows of the Mind is Penrose's excursion into microbiology, where he examines cytoskeletons and microtubules, minute substructures lying deep within the brain's neurons. (He argues that microtubules--not neurons--may indeed be the basic units of the brain, which, if nothing else, would dramatically increase the brain's computational power.) For physics to accommodate something that is as foreign to our current physical picture as the phenomenon of consciousness, we must expect a profound change--one that alters the very underpinnings of our philosophical viewpoint as to the nature of reality. Shadows of the Mind provides an illuminating look at where these changes may take place and what our future understanding of the world may be.
The book advances the premise that the cytoskeleton is the cell's nervous system, the biological controller/computer. If indeed cytoskeletal dynamics in the nanoscale (billionth meter, billionth second) are the texture of intracellular information processing, emerging ''NanoTechnologies'' (scanning tunneling microscopy, Feynman machines, von Neumann replicators, etc.) should enable direct monitoring, decoding and interfacing between biological and technological information devices. This in turn could result in important biomedical applications and perhaps a merger of mind and machine: Ultimate Computing.
For the first time it is shown that the genetic code, as a binary code, is determined by Golden mean through the unity of the binary-code tree and the Farey tree, corresponding to the Watson-Crick table and Gray code model of the genetic code at the same time. On the other hand, the Golden mean relations also correspond with the essentiality-nonessentiality of protein amino acids, as well as with their splitting into two classes handled by two classes of aminoacyl-tRNA synthetases.
Structure of Clathrins
  • T Kaneski
  • K Kadota
Kaneski, T. Kadota,K., Structure of Clathrins, J. Cell Biology, 20:pp.202-220,1969
Self-Assembled Molecular Computer Based on Fullerene C 60 : From Nanobiology to Nanotechnology
  • D Koruga
Koruga, D., at al. Self-Assembled Molecular Computer Based on Fullerene C 60 : From Nanobiology to Nanotechnology, The 4 th Int.Symposium on Bioelectronic and Molecular Electronic Devices, BMED'92 pp.1-4, Miyazaki, Japan, 1992