HIERARCHIC MODEL OF CONSCIOUSNESS:

FROM MOLECULAR BOSE CONDENSATION

TO SYNAPTIC REORGANIZATION

A basically new hierarchic quantitative theory, general for solids and liquids (Kaivarainen,
2000a), has been used as a background of quantum features of our Hierarchic model of
consciousness. It is assumed in theory, that anharmonic oscillations of particles of condensed
matter lead to emergence of three-dimensional (3D) superposition of standing de Broglie waves
of molecules, electromagnetic and acoustic waves. Consequently, any condensed matter could 
be considered as a gas of 3D standing waves of corresponding nature. Our approach unifies and
develops the Einstein’s and Debye’s models.

Four strongly interrelated new types of quasiparticles (excitations) were introduced in our
hierarchic theory: 1. Effectons (tr and lb), existing in "acoustic" (a) and "optic" (b) states
represent the coherent clusters in general case; 2. Convertons, corresponding to interconversions
between tr and lb types of the effectons (flickering clusters); 3. Transitons are the intermediate
[a<--> b] transition states of the tr and lb effectons; 4. Deformons are the 3D superposition of IR
electromagnetic or acoustic waves, activated by transitons and [lb<--> tr] convertons.

Hameroff and Penrose (1996; 1998) proposed the "orchestrated objective reduction (Orch
OR)" model of quantum computation in microtubules (MT) of brain. They suppose, that quantum
nonlocal interaction between huge number of MT may provide coherency of their thermal
dynamics. Based on principle of uncertainty in coherent form it was calculated, that if the
difference in volume of alternative states of very big dynamically coherent number (10^9 of
tubulin dimers (alpha, beta) is about 10% during 0.5 s (arbitrary assumption), the quantum gravity
induced self-collapse to one of such state may occur. However, even accepting these calculations
as valid, their model do not explain the following crucial moments:

There are six main forms of actin existing. Most general F-actin is a polymer, constructed
from globular protein G-actin with molecular mass 41.800. Each G-actin subunit is stabilized by
one ion Ca2+ and is in noncovalent complex with one ATP molecule. Polymerization of G-actin
is accompanied by splitting of phosphate group. The velocity of F-actin polymerization is
enhanced strongly by hydrolysis of ATP. However, polymerization itself do not needs energy.
Simple increasing of salt concentration (decreasing of water activity), approximately till to
physiological one - induce polymerization and strong increasing of viscosity.

The actin filaments are composed from two chains of G-actin with diameter of 40 Å and
forming double helix. The actin filaments are the polar structure with different properties of two
ends. Disassembly of actin and (gel<-->sol) transition is dependent strongly on water activity and
energy of thermal fluctuation.

Let us consider the properties of microtubules (MT) as one of the most important
component of cytoskeleton, responsible for spatial organization and dynamic behavior of
the cells. The stability and dynamics of microtubules composed of alpha and beta tubulins is also
dependent on water activity aH2O see Section 13.7 of book: Kaivarainen 1995 and Kaivarainen,
2000c), concentration of Ca2+ and on the electric field gradient change due to MTs piezoelectric
properties. The alpha and beta tubulins are globular proteins with equal molecular mass
MM 55. 000 , usually forming alpha-beta dimers with linear dimension 8nm. Polymerization of
microtubules can be stimulated by NaCl, Mg2+ and GTP (1:1 tubulin monomer) (Alberts et al.,
1983). The presence of heavy water (deuterium oxide) also stimulates polymerization of MT. In
contrast to that the presence of ions of Ca2+ even in micromolar concentrations, action of
colhicine and lowering the temperature till 4°C induce disassembly of MT.

Microtubules are hollow cylinders, filled with water. Their internal diameter about
din 140Å and external diameter dext 280Å. These data, including the dimensions of  alpha-beta
dimers were obtained from x-ray crystallography (Amos and Klug, 1974). The length of 
microtubules (MT) can vary in the interval:

Microtubules sometimes can be as long as axons of nerve cells, i.e. tenth of centimeters long.
Microtubules (MT) in axons are usually parallel and are arranged in bundles. Microtubules
associated proteins (MAP) form a "bridges", linking MT and are responsible for their interaction
and cooperative system formation. Brain contains a big amount of microtubules. Their most
probable length is about 10^5Å.

The biggest cavitational fluctuations of internal water - (superdeformons) in the volume of
3D standing IR photons can induce total cooperative disassembly of MT. Superdeformons
excitation in MT internal water could be an explanation of experimentally revealed dynamic
instability (catastrophes) as a stochastic switching of MT growth to shrinkage (Mitchison and
Kirschner, 1984; Horio and Hotani, 1986; Odde at al., 1994). The frequency of superdeformons
excitation in bulk water is about 10^4s¯¹, however, in cytoplasm of high viscosity this value may
strongly decrease till 10^2s¯¹. Consequently, the coherent excitation of superdeformons in
cytoplasm of neurons ensemble in a course of their firing may be interrelated with disassembly of
actin and partially MTs, leading to [gel--> sol] transition.

Intra-microtubular clusterphilic interactions (see Kaivarainen, 2000d) stimulate the growth
of tubules from tubulin dimers. The structural physical-chemical asymmetry of dimers in
composition of microtubules determines their different rates of growth from the opposite ends 
([+] and [- ]).

The linear dimensions of the edge llb ef  of coherent water clusters - primary librational
effectons in pure water at physiological temperature 36ºC - is about 11 Å and 45 Å in the ice at
0°C. We assume that in the rigid internal core of MT, the linear dimension (edge length) of
librational effecton, approximated by cube is between 11Å and 45 Å i.e. about  llb ef ~23Å.

It will be shown below, that this assumption fits the spatial and symmetry properties of MT
very well. The most probable group velocity of water molecules in composition of primary lb
effectons is: 

The librational mobility of internal water molecules in MT, which determines vlb gr should be
about 2 times less than in bulk water at 37°C, if we assume  llb ef ~23Å (see Kaivarainen, 2000a).

The length of a orchestrated group of primary lb effectons in the direction of microtubule
main axis can be determined by the length of edge of primary librational IR deformons, i.e. about
10 microns.

Results of our computer simulations for pure bulk water shows, that the distance between
centers of primary [lb] effectons, approximated by cube exceed their linear dimension to about
3.5 times (Fig 1b). For our case it means that the average distance between the effectons centers
is about:

It gives a possibility for equidistant (80 Å) localization of the primary lb effectons in clefts
between alpha and beta tubulins of each (alpha-beta) dimer in the internal core of MT. 
Such a regular spatial symmetry of the internal flickering clusters distribution in MT is an 
important factor for realization of the [optoacoustic-conformational] signal propagation of 
configurational waves along the MT, accompanied by their bending. It is related to alternating 
[closing <-->opening] clefts between alpha and beta tubulins. This large-scale protein 
dynamics is correlated with dissociation/association of water clusters in clefts between 
(alpha -beta) dimers of MT due to [lb/tr] convertons excitation with frequency ~10^7s¯¹.

The size of tr primary effectons in MT is significantly smaller, than that of lb ones and the
microviscosity of water in regions, occupied by translational effectons - lower. The average 
angle between alpha and beta tubulins change and the cavity’s [open <--> closed] states 
equilibrium shifts to the closed one as a result of conversion of lb effectons to tr ones 
(dissociation of coherent water cluster).

The dynamic equilibrium between tr and lb types of the intra MT water effectons can be very
sensitive to alpha-beta tubulins interactions, dependent on nerve excitation.

Fig. 1. Theoretical temperature dependencies of: (a) - the space between centers of primary
[lb] effectons; (b) - the ratio of space between primary [lb] effectons to their length; (c) - the
space between centers of primary [tr] effectons; (d) - the ratio of space between primary [tr]
effectons to their length.

Our hypothesis of IR superradiation, produced by water in MT’s - is an inherent property of
our primary effectons, resulted from mesoscopic molecular Bose condensation (Kaivarainen
1992, 1995). This idea is independent of similar, used in the model of MT’s as wave guide of
superradiation for longitudinal photons, proposed by Jibu et al., (1994). The difference in two
approaches is that we assume in MT the existence of "transverse" radiation of IR photons as well
as "longitudinal" ones. Such assumption means that the density of electromagnetic energy in
MTs is low enough and not destroying the protein’s of MT’s. Another advantage of our model -
is the possibility of electromagnetic interaction between MT’s by the exchange of coherent
transverse IR photons. We also do not need to use in our model the strong assumption of
self-induced transparency in hollow core of MT, because the half of wave length of IR librational
photons (about 5 microns) is much more than the distance between neighboring primary librational
effectons, radiating photons.

In the normal state of nerve cell the dynamic equilibrium the gradient of ionic concentration, 
produced by ionic pumps activity, is compensated by the electric tension gradient. The 
electrochemical gradient is equal to zero at this state. The equilibrium concentration of
Na+ and Cl-  in space out of cell is bigger than in cell, the gradient of K+ concentration has an
opposite sign. The external concentration of Ca2+ (about 10^- 3M) is few orders higher than in
cytosol (about 10^- 7M) . Such a big gradient provide fast and strong increasing of Ca2+
internal concentration after activation of corresponding membrane channels.

At the "rest" condition of equilibrium the resulting concentration of internal anions of
neurons is bigger than that of external ones, providing the difference of potentials equal to
50-100mV. As far the thickness of membrane is only about 5nm or 50Å it means that the
gradient of electric tension is about:

                                                                100. 000 V/sm

Depolarization of membrane usually is related to penetration of Na+  ions into the cell. This
process of depolarization could be inhibited by selected diffusion of Cl-  into the cell. Such
diffusion can produce even hyperpolarization of membrane.

[I]. Increasing the dimensions and life-time of coherent water clusters (primary lb effectons)
in the open nonpolar cavities between alpha and beta tubulins;
[II]. Destabilization of MT, increasing the probability of its partial disassembly and
disconnection with plasmatic membrane;

The LS-dynamics of tubulin dimers represent the change of "bending" angle between alpha and
beta tubulins of about 210 Melki et al., 1989), corresponding to fluctuation of the inter-tubulins
cavity between closed (A) and open (B) states. Such bending may be a result of macroconvertons
(flickering clusters) excitations with frequency: 10^6 -10^7 Hz (Kaivarainen, 2000a).

The [assembly<--> disassembly] dynamic equilibrium of the actin filaments in cells in terms
of colloid chemistry represents [coagulation<--> peptization] or [gel<--> sol] equilibrium. These
cycles are rapid and correlate with neurotransmitter release and nerve excitation (Miyamoto,
1995; Muallem et. al., 1995). The increasing of cell’s volume, accompanied the actin
orchestrated disassembly is a result of cell "swelling" due to osmotic diffusion of water from the
extracell medium. The decreasing of water activity in cell, inducing osmotic flow of water to cell
cytoplasm, is a consequence of increasing of "bound" or "hydration" water fraction after actin
microfilaments disassembly to huge number of subunits. The nerve cell body and dendrites
swelling can trigger the collective nonspecific opening of big number of ionic channels and
strong resulting postsynaptic potential (PSP) emergency. The bigger is resulting PSP the higher is
frequency of the nerve impulses, generated by this cell and penetrating via axon to other neurons
(Coombs, et al., 1957).

3.1 The entropy-driven information processing

This process induces redistribution of probabilities of different water excitations in huge
number of microtubules. It means corresponding change of informational entropy <I>, related to
microtubules in accordance with known relations (Kaivarainen 1995; 2000b):

where:Pi is a probability of the (i) state with energy Ei , defined as:

the total number of internal water molecules in macrosystem of interacting MT is:
                                                            N=N1+N2+...+Nq; 
[q is number of non degenerated states of 24 quasiparticles of intra MT water.
The reduced information of condensed matter (Kaivarainen, 2000d) to the number of
molecules (ni) in each kind of excitations:

- gives characteristic not only of quantity (I) but also about the quality of the information:

where N0 and V0 are the Avogadro number and molar volume; ni is a concentration of
excitation of (i)-type.

The distant energy exchange between MT, accompanied by the change of Pi for different
excitations can be considered as an informational exchange between nerve cells. It is related to
change of fractions of water excitations in system of interacting MTs.

The INTUITION from such point of view means the ability to choose one right solution
(rigorously inadequate) from huge number of wrong, but adequate to the available information. It
looks that associative memory, helping the right choose, is the most probable background for
INTUITION.

1. The change of the electric component of neuron’s body internal electromagnetic field as a
result of cells depolarization; 2. Opening the potential - dependent Ca2+ channels and increasing
the concentration of these ions in cytoplasm. Activation of Ca2+  - dependent protein gelsolin,
which stimulate fast disassembly of actin filaments; 3. Shift of A<--> B equilibrium between the
closed (A) and open to water (B) states of cleft, formed by alpha and beta tubulins in tubulin 
pairs of microtubules (MT) to the right as a consequence of piezoelectric effect, induced by
depolarization of membrane of nerve cell; 4. Increasing the life-time and dimensions of coherent
"flickering" water clusters in MT, representing the 3D superposition of de Broglie standing
waves of H20 molecules in hollow core of MT. It is a result of the water molecules
immobilization by ’open’ nonpolar clefts of (alpha-beta) dimers in MT; 5. Increasing the superradiance
of coherent IR photons induced by synchronization of quantum transitions of the effectons
between acoustic and optic like states. Corresponding increasing of probability of
superdeformons (cavitational fluctuations) excitation in water of cytoplasm; 6. The disassembly
of actin filaments system to huge number of subunits, [gel--> sol] transition and increasing of
water fraction in hydration shell of proteins in cytoplasm. This transition is a result of
cavitational fluctuations and destabilization of actin filaments by Ca2+ . Corresponding
decreasing the water activity in cytoplasm - increases strongly the passive osmotic diffusion of
water from the external volume to the cell; 7. As a consequence of previous stage, a jump-way
increasing of the nerve cell body volume (pulsation), accompanied by disrupting the ( ) ends of
MTs with cytoplasmic membranes occur. This stage makes it possible for MTs to change their
orientation inside neuron’s body; 8. Spatial "tuning" - collective reorientation of MTs of
simultaneously excited neurons to geometry, corresponding to minimum potential energy of
distant (but not nonlocal) electromagnetic and vibro-gravitational interaction between MTs and
centrioles twisting; 9. Decreasing the concentration of Ca2 to the critical one, when disassembly
of actin filaments is stopped and [gel<--> sol] equilibrium shifts to the left again, stabilizing the
new MTs system spatial configuration and corresponding nerve cell body volume and geometry.
This new geometry of nerve cells after fixation of (+) ends of MTs back to plasmatic membrane -
determine the new distribution of ionic channels activity and reorganization of synaptic contacts
in all excited ensemble of neurons after relaxation, i.e. short-term and long-term memory.

This cyclic consequence (hierarchy) of quantum mechanical, physico-chemical and classical
nonlinear events can be considered as elementary acts of memorizing and consciousness. The
total period of listed above stages can be as long as 500 ms, i.e. half of second. The elementary
act of consciousness described, includes a stage of coherent electric firing in brain (Singer, 1993)
of distant neurons groups with period of about 1/40 sec. Corresponding frequency may be related
to frequency of superdeformons (cavitational fluctuations) origination in of cytoplasm,
stimulating [gel-sol] transition of cytoplasm, following after depolarization of nerve membranes.
This frequency for pure water, calculated on the base of Hierarchic theory (Kaivarainen, 1995;
2000a), is about 10^4 s¯¹. However, in viscous medium of cytoplasm it may be much lower 
(~10^2s¯¹) .

The dimension of IR superdeformon (3D superposition of IR photon) edge is determined by
the length of librational IR standing photon - about 10 microns. It is important that this
dimension corresponds to the average microtubule length in cells confirming in such a way our
idea. Another evidence in proof is that is that the resonance wave number of excitation of
superdeformons, leading from our model is equal to 1200 (1/cm) .

The experiments of Albrecht-Buehler (1991) revealed that just around this frequency the
response of surface extensions of 3T3 cells to weak IR irradiation is maximum. Our model
predicts that IR irradiation of microtubules system in vitro with this frequency will dramatically
increase the probability of microtubules catastrophes. It’s one of the way to verify our model
experimentally.

Except superradiance, two other cooperative optic effects could be involved in
supercatastrophe realization: self-induced bistability and the pike regime of IR photons
radiation (Bates, 1978; Andreev et al.,1988). Self-induced bistability is light-induced phase
transition. It could be related to nonlinear shift of [a<-->b] equilibrium of primary librational
effectons of intra MT water to the right as a result of saturation of IR (lb)-photons absorption. As
far the molecular polarizability and dipole moments in (a) and (b) states of the primary effectons
- differs, such shifts of [a<-->b]equilibrium should be accompanied by periodic jumps of
dielectric permeability and stability of coherent water clusters. These shifts could be
responsible for the pike regime of librational IR photons absorption and radiation. As far
the stability of b-states of lb effectons is less than that of a-states, the characteristic frequency of
pike regime can be correlated with frequency of MTs-supercatastrophe activation. This effect
can orchestrate the [gel-sol] transitions of neuronal groups in head brain.

Fig.2. The schematic presentation of the local, acousto-conformational and distant -
electromagnetic interactions between microtubules (MT1 and MT2), connected by MAP.

MAP– microtubules associated proteins stabilize the overall structure of MTs. They prevent
the disassembly of MTs in bundles of axons and cilia in a course of their coherent bending. In
neuron’s body the concentration of MAP and their role in stabilization of MTs is much lower
than in cilia. The local acousto-conformational signals between MT are realized via MTs -
associated proteins (MAP), induced by transitions of the cleft, formed by alpha and beta tubulins,
between closed (A) and open (B) states. The orchestrated dynamics of individual MT as quantum
conductor is a result of phonons (hvph) exchange between (alpha-beta) clefts due to lb/tr conversions,
corresponding to water clusters, "flickering", in-phase to [B<-->A] pulsations of clefts.
The distant electromagnetic and vibro-gravitational interactions between different MT are
the consequence of IR photons and coherent gravitational waves exchange. The corresponding
two types of waves are excited as a result of orchestrated (a<--> b) transitions of water primary
librational effectons, localized in the open B- states of (alpha-beta) clefts. When the neighboring (alpha-beta) clefts has the alternative open and closed states like on Fig 2, the general spatial structure
remains straight. However, when [A<-->B] equilibrium of all the clefts from one side of MT are
shifted to the left and that from the opposite side are shifted to the right, it leads to bending of
MT. Coherent bending of MTs could be responsible for [volume/shape] vibrations of the nerve
cells and the cilia bending.

The Brownian effects, which influence reorientation of MTs system and probability of
cavitational fluctuations, stimulating [gel - sol] transition in a course of nerve cells tuning and
excitation-relaxation cycles - represent in our model the non-computational element of
consciousness. Other models (Wigner, 1955 and Penrose, 1994) relate this element to wave
function collapsing.

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