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From: you already know
Date: 4/5/01
Time: 5:06:53 PM
Remote Name: 142.245.193.43
Tony's Home
Quantum Consciousness
| Clifford Math of Consciousness at the Edge of Chaos |
| Superposition Separation | Structures | OrchOR | TimeScales - Table - Graph |
| Cycles: Biology and Quantum |
| Conscious Universe |
Zizzi Quantum Inflation and Self-Decoherence How to Maintain Brain-Wide Quantum Coherent Superpositions? Resonance PSI ( Clover | Magons | Bohm | Akira-Abyss-Matrix ) Big Bang Error-Correcting Quantum Codes Enzymes Quantum Tunnelling Entanglement/Coherence/Superposition Preservation in Solution Superradiant Water Channels Hamiltonian Circuit of Tubulins Cellular Automata DNA Immune System Heart Brain Size Neural Network Learning GRW Consciousness Anesthesia BioMagnetite BioTopology Memory History
The Human Brain has about 10^18 Tubulins and 10^11 Neurons:
(image from Scientific American, September 1992, article by Gerald D. Fischbach, Mind and Brain, page 52)
Neurons are on the scale of a micron (or 1,000 nanometers) in size. The micron size scale of a Neuron is about the range of GravitoEM Induction Region Virtual Gravity Waves. Submillimeter gravity, which is being studied by experiments under way in 1998 at Stanford and the University of Colorado in Boulder.
Neurons are connected to each other by three types of Communicating Junctions.
Electrons can cross the Gap Junctions by Quantum Tunnelling, thus allowing Quantum Superposition States to extend from Neuron to Neuron across Gap Junctions.
Three types of Communicating Junctions are:
Chemical Synapses, shown in detail above, have soccer-ball shaped clathrins (made up of protein trimers called clathrin triskelions) that control the release of neurotransmitter chemicals at synapses. According to Evan Harris Walker "... using values for the [Synaptic Junction] barrier ... (... the energy of 0.07 eV [or 70 milli-electron-volts] (corresponding to the bias potential across a neuron, or at the synaptic cleft) ...) ... taken from neurophysiological data for the synapses, one can compute the size of the synaptic cleft that would be necessary for electrons to be able to tunnel across the cleft with a probability corresponding to the probability for nominal central nervous system (CNS) synapses to fire ... (... 0.3 to 3 milliseconds involved in typical synaptic firing ...) ... when an action potential arrives. The result of 180 Angstroms [or 18 nanometers] corresponds exactly to what is found for CNS synapses. ... This does not mean that the calcium ions play no role in synaptic transmission, but it does say that that role is probably secondary, and that the calcium hypothesis, taken alone, has turned out to be less than satisfactory in explaining all experimental data ...". Electrical Synapses, or Ephases: According to Evan Harris Walker "... Further, there is a class of synapses, called ephapses or electrical synapses, that fire electrically rather than by chemical release. These ephapses are morphologically identical to the synapses in all respects except one: their clefts are about 150 Angstroms [or 15 nanometers] wide. Calculations show that reducing the thickness of the cleft from 180 Angstroms to 150 Angstroms changes the electrical behavior of the synapse in just the fashion found experimentally in data that has been collected for these kinds of neurophysiological structures. ...". Gap Junctions are direct connections between cells, including not only Neurons and their Dendrites, but also Glial Cells. Gap Junction structure is shown in this image (from Figure 14-15 from Molecular Biology of the Cell, 2nd ed, by Alberts, Bray, Lewis, Raff, Roberts, and Watson (Garland 1989)):
According to Stuart Hameroff, "... A given cortical neuron may have 10,000 chemical synapses, and relatively few gap junctions (15% of the number of chemical synapses [or 1,500 Gap Junctions for a Neuron with 10,000 Chemical Synapses] is sometimes estimated). ... There are special organelles (dendritic lamellar bodies - DLBs) found only on either side of gap junctions in dendrites in the brain. The DLBs are attached by filamentous proteins to the microtubules, and their structure suggests they may be suitable if not ideal for quantum electron tunneling devices. ... What [Hameroff and Penrose have] suggested is that electron tunneling occurs [across Gap Junctions] between micotubules in each of two adjacent neurons. The distance across the gap junction itself is only 3.5 nanometers, though its a bit further to the [microtubules]. ...".
The cytoskeleton of cells, including neurons of the brain, is made up of microtubules:
which are connected to each other by Microtubule Associated Proteins (MAPs). With these structures in mind
Roger Penrose and Stuart Hameroff propose that Consciousness involves a Planck scale Decoherence of Quantum Superpositions that they call Orch OR
in their paper entitled Orchestrated Objective Reduction of Quantum Coherence in Brain Microtubules: The "Orch OR" Model for Consciousness. Figure 1 (shown above) is a "Schematic of central region of neuron (distal axon and dendrites not shown) showing parallel arrayed microtubules interconnected by MAPs [Microtubule Associated Proteins]. Microtubules in axons are lengthy and continuous, whereas in dendrites they are interrupted and of mixed polarity. Linking proteins connect microtubules to membrane proteins including receptors on dendritic spines.".
The human brain contains about 10^18 tubulins.
Each microtubule is a hollow cylindrical tube with about 25 nm outside diameter and 14 nm inside diameter, made up of 13 columns of Tubulin Dimers.
Each Tubulin Dimer is about 8 nm x 4 nm x 4 nm, consists of two parts, alpha-tubulin and beta-tubulin (each made up of about 450 Amino Acids, each of which contains roughly 20 Atoms), and can exist in (at least) 2 different geometrical configurations, or conformations, involving the position of a single Electron. Call this Electron the Conformation Electron, because in a single Tubulin Dimer its the position at the junction of the alpha-tubulin and the beta-tubulin determines the 2 different conformations of the Tubulin, which correspond to 2 different states of the dimer's electric polarization.
The Tubulins in a Microtubule can represent Information, and act as Cellular Automata to process it.
The human brain contains about 10^11 neurons. There are 10^7 Tubulin Dimers per neuron, with 10% of them, or 10^6, estimated to be involved in the consciousness process, and the remainder doing other things needed to keep the cell alive.
The equivalence of Gravitation of the massless spin-2 Gravitons of MacroSpace and the Gravitation of our physical SpaceTime, justifies the Superposition Separation idea of Penrose and Hameroff:
Roger Penrose says, in Shadows of the Mind (Oxford 1994), page 344, "... We can now consider the gravitational self-energy of that mass distribution which is the difference between the mass distributions of the two states that are to be considered in quantum linear superposition. The reciprocal of this self-energy gives ... the reduction timescale ...".
This is the decoherence time T = h / E.
For a given Particle, Stuart Hameroff describes this as a particle being separated from itself, saying that the Superposition Separation a is "... the separation/displacement of a mass separated from its superposed self. ... The picture is spacetime geometry separating from itself, and re-anealing after time T. ...".
Jack Sarfatti proposes that a Quantum Fluctuation in a State of Superposition is not Reduced until the Gravitational Binding Energy of the Difference among the Superposed States exceeds the Bekenstein threshold of One Bit of Shannon Classical Information, that is, the product of Energy E and Time T equals Planck's Constant h, giving the decoherence time formula T = h / E.
If the Superposition consists of States involving one Particle of Mass m, but with Superposition Separation a, then the Superposition Separation Energy Difference is the gravitational energy
E = G m^2 / a
An essential ingredient in this model is the gravitational interaction between the two different position states of tubulin electrons. Although the position separation between the two states of any single given tubulin electron is about a = 1 nanometer = 10^(-7) cm, which is well within the micron range of strong gravity, what is relevant is the total gravitational interaction among all N tubulin electrons, and the vast majority of them within the 10-cm scale human brain are far more distant from each other than the micron range of strong gravity, so in calculating the superposition energy E_N of N tubulin electrons and the corresponding time T_N, you should use (as do Hameroff and Penrose) ordinary Far Field gravity with ordinary G.
Since the human brain is on the order of 10 cm, its volume is about 10^3 cm^3. Since a micron is 10^(-6) m = 10^(-4) cm, and since the human brain has about 10^18 tubulin electrons, it has about 10^18 / 10^3 = 10^15 tubulin electrons/cm^3, so that the typical linear distance between tubulin electrons is about 1 / (10^15)^(1/3) = 1 / 10^5 = 10^(-5) cm = 0.1 microns. Therefore the micron range of strong gravity is far enough to connect a tubulin electrons with its near neighbors (near including nearest neighbors plus up to order 10 near neighbors). These overlapping Near Field Induction/Static region gravitational neighborhoods help the human brainto maintain superposition of its 10^18 tubulin electrons.
In other words, ordinary weak gravity determines E_N and T_N for the human brain as a whole, while micron-range strong Induction/Static Region gravity with overlapping micron-range neighborhoods helps maintain the superpositions during the T_N time of a conscious thought.
Therefore (ignoring for simplicity some factors like 2 and pi, etc.):
T = h / ( G m^2 / a ) = ( h / m c ) ( c^2 / G m ) ( a / c ) = ( Compton / Schwarzschild ) ( a / c )
where
2 G m / c^2 = Schwarzschild Radius of a classical blackhole of mass m and
h / m c = Compton Radius of the Sidharth Kerr-Newman naked singularity model of an elementary particle of mass m.
Consider the case of one free Electron and Ordinary Gravity:
Here, ordinary gravity is used, not because it is realistic for a 1-naonometer distance, but because the calculation for a single Electron will be used as the basis for a superpositon of N Electrons over the 10-cm scale human brain, for which ordinary gravity is realistic and should be used. If the single Conformation Electron with mass m_e has a Superposition Displacement a that is of the order of 10^(-7) cm, or one nanometer, then, since Compton = 10^(-11) cm and Schwarzschild = 10^(-55) cm and the speed of light c = 3 x 10^10 cm/sec, and since E_electron = G ( m_e )^2 / a, we have
for a single Electron and ordinary gravity
T_electron = h / E_electron =
= ( Compton / Schwarzschild ) ( a / c ) = 10^26 sec = 10^19 years.
Now consider the case of N Tubulin Electrons in Coherent Superposition, in which ordinary gravity is realistic.
As Jack Sarfatti says, "Since all the [Conformation] Electrons are nonlocally connected into a coherent whole we do not want to treat them as fluctuating statistically independent of each other ... .", and Stuart Hameroff agrees, saying "True. That's why we consider them coherently linked or entangled.". As Jack Sarfatti explains, "... this is for a macro-mass M. So change m to M = Nm for a network of N connected pieces forming a coherent whole. Note the pair binding energy is small. But we need the gravity self-energy of this big whole of N entangled pieces since this is some kind of a quantum collective mode! Therefore, the size parameter ... is the whole not the part. We are not looking at the gravity self energy of the part, but the gravity self energy of the whole. Since it also has to be a metric fluctuation, I use Wheeler's "L" for the scale of the metric fluctuation.So, I get ...[ E = G M^2 / L = N^2 G m^2 / L .... where] L is the scale of the metric quantum gravity fluctuation in the sense of John Archibald Wheeler. Clearly L is over the entire region of cortex containing N switching units that coherently participates in the "orch OR" process whatever it may be. So how do we relate L to the microdisplacements of the pieces of the whole? The obvious thing to try is L^3 = N a^3 [where] "a" is the displacement of each piece. Now you can use Hameroff's pictures of what the individual pieces are doing to get a number for "a". Remember we are only doing orders of magnitude so we are not interested in 1% or even 10% corrections. If we get roughly the right power of 10 we are happy. ... the entire model is still very primitive. ...
Ansatz:
( c Gravity Self-Collapse Time )^2 ( Classical )^2 = ( Quantum )^2 ( Spatial Coherence Length )^2 = 4D Blister Volume
for quantum gravity self-collapse from [Hameroff-Penrose] space-time geometry separation.
( c T )^2 ( G M / c^2 )^2 = ( h / M c )^2 L^2
That is
( c Coherence Time )( Classical Wormhole Radius ) = ( Quantum Wormhole Radius ) ( Spatial Coherence Length )
c T G M / c^2 = ( h / M c ) L
G M^2 / L = h / T
L = a N^(1/3)
M = N m
a = spatial coherence length of a single q-bit
m = mass of a single q-bit
N q-bits form a single coherent network or collective mode. So
( c Collective Coherence Time ) / (Collective Mode Coherence Length ) = ( Quantum / Classical )
The effective squared space-time interval is ( c Coherence Time ) - ( Spatial Coherence Length ). When is this zero or lightlike? Clearly only when Quantum = Classical [at the Planck scale of] M = 10^(-5) gm. For elementary particles (Quantum/Classical) >> 1, so the effective interval is timelike. For classical black holes the reverse is true so the effective interval is spacelike. ... Note the squares of the lengths are all Bekenstein information measures! So timelike means that in some sense the Bekenstein temporal information is greater than the spatial information since each bit of Bekenstein information has area h G / c^2 [which is the square 10^(-66) cm^2 of the Planck length, which can be compared to the square 10^(-22) cm^2 of the Electron Compton Radius]. So we see that the square of the space-time interval in Einstein's classical theory of relativity has a deeper informational meaning. The hyperbolic signature of spacetime means subtracting two informational measures. In Hawking's imaginary time we add the measures. This also connects with the Christodoulo black hole fusion formula that obeys the Pythagorean theorem ... . Both relativity and quantum theory are really surface forms of an information theory according to Wheeler's "IT FROM BIT". ... In first order perturbation theory in the space-time picture (not the momentum-energy space) use Huyghen's principle for the quantum information waves of the coherent spatially separated q-bit sources
(Gm^2/L)^(1/2) ( e^(i PHI(j+)) + e^(i PHI(j-)) ) / 2
is the Wheeler-Feynman quantum gravity near field Huyghen's wavelet from the jth q-bit, where j = 1 to N, + is the advanced phase and - is the retarded phase from the two poles of the Feynman propagators. Note the coherent absorbers in the nano-boxes protecting the q-bits from environmental decoherence allow for the Libet-Radin-Bierman back-causation from non cancellation of the advanced against the retarded amplitudes! That is the interference between past and future is no longer completely constructive in sentient matter. The total coherent Feynman amplitude is
( G m^2 / L )^(1/2) Pribram Brain Hologram Phase Modulation Pattern
This Phase Modulation Pattern is the coherent sum of the both the advanced (from the future) and the retarded (from the past) phase factors. All alternative histories have equal amplitude hence the common (Gm^2/L)^1/2 factor. In the "ground state" all the phases are zero and we get for the squared coherent amplitude
N^2 G m^2 / L = N^(5/3) G m^2 / a
where T = h / ( N^(5/3) G m^2 / a ) for the objective decay of the Bohm information field in the implicate order. (... in ... ordinary matter where the individual phases are random ... you would get N G m^2 / a for incoherence of individual pieces instead of N^2 G m^2 / L for the coherent mesoscopic collective mode ...) In addition, there is the self-organization time from the self-reaction of the Bohm world line to the action of the Bohm information field on that world line t = Tgrw / N ...".
Jack Sarfatti defines the Superposition Energy E_N of N superposed Conformal Electrons in N Tubulins as
E_N = G M^2 / L
where L is the mesoscopic quantum phase coherence length for the collective mode of N Conformational Electrons of total mass M in the N Tubulins, so that
E_N = N^2 G m^2 / a N^(1/3) =
= N^(5/3) G m^2 / a=
= N^(5/3) E_electron
To get the decoherence time for the system of N Tubulin Electrons, recall that T_electron = h / E_electron = ( Compton / Schwarzschild ) ( a / c ) = 10^26 sec = 10^19 years, so that
T_N = h / E_N = h / N^(5/3) E_electron =
= N^(-5/3) T_electron =
= N^(-5/3) 10^26 sec
and (ignoring for simplicity some factors like 2 and pi, or 4 in this case)
N = (10^26 / (T_N) )^(3/5) =
= 10^15 / (T_N)^(3/5)
From the above formulas get the following rough approximate Table of Decoherence Times T_N for various phenomena and structures involving various Numbers of Tubulin Dimers or Neurons:
Time Number of Number of Scale L = T_N Tubulins Neurons = N^(1/3) s
10^(-43) sec (Planck) 10^41 10^35 500 km
10^(-14) sec (local protein) 2 x 10^23 2 x 10^17 50 cm
10^(-10) sec (global protein) 10^21 10^15 10 cm 10^(-10) sec (Frohlich) 10^21 10^15 10 cm
10^(-5) sec 10^18 10^12 1 cm
5 x 10^(-4) sec (2 kHz) 10^17 10^11 0.5 cm
25 x 10^(-3) sec (40 Hz) 10^16 10^10 0.2 cm 100 x 10^(-3) sec (EEG alpha) 4 x 10^15 4 x 10^9 0.16 cm 500 x 10^(-3) sec (Radin/Bierman) 1.5 x 10^15 1.5 x 10^9 0.11 cm
1 sec 10^15 10^9 0.1 cm
10^10 sec = 300 years 10^9 10^3 10^(-3) cm
10^15 sec = 3 x 10^7 years 10^6 1 10^(-4) cm
10^26 sec = 3 x 10^18 years 1 10^(-6) cm
The 10^11 Neuron line of the table corresponds to the size of the human brain. The 10^16 Tubulin line of the table coorresponds to 40 Hz brain activity with 7,500 km wavelength and high Schumann Resonances. The 4 x 10^15 Tubulin line of the table corresponds to the 0.1 second GRW time limit of conscious phenomena, in the sense that shorter-term phenomena operate on a sub-conscious level, with (as Ira Einhorn notes, citing the Penrose footnote on page 374 of Shadows of the Mind) the possibility that short-term high frequency sub-conscious phenomena might be connected to "... the more familiar brain wave activity (such as the 8-12 Hz alpha-rhythm). ... such lower frequencies might arise as beat frequencies ...". It also corresponds to the scale of 0.16 cm, or a volume of about 1/200 cm^3, with respect to which Jack Sarfatti says (here I have substituted some of my numerical values for his): "... Note the volume ... is the sum of the volumes of all [5 x 10^15 Tubulins] even though they are separated in physical space from each other over the whole cortex of volume 10^3 cc - they are like one super-particle entangled in configuration space of [about 3 x 5 x 10^15 dimensions]! That is, this sentient post-quantum computing "enchanted web" is [5 x 10^15 little Tubulin nanoboxes] ... . Each box has a little arrow in Hilbert space and all the arrows are phase-locked over a time of order 0.1 sec. The actual physical distance between the boxes is irrelevant to this Einstein-Podolsky-Rosen network that is one coherent conscious system. The mesoscopic quantum coherence length L is what you would get if you lined up all these nanoboxes in a row - about [ 1/6 ] cm. It is really not a metrical property in ordinary space. ..." The 1.5 x 10^15 Tubulin line of the table corresponds to 0.5 seconds, roughly cosistent with the Radin/Bierman presponse time. Consider a Hamiltonian Circuit of 1.5 x 10^15 Tubulins in a Quantum Consciousness superposition, with each Tubulin being about 100 nanometers from a near neighbor. If gravitons moving at the speed of light traverse such a Hamiltonian circui, then the time for a traverse of the Quantum Consciousness Hamiltonian Circuit is 1.5 x10^15 x 100 nm / c = 1.5 x (10^15 x 10^(-5)) cm / c = 1.5 x 10^10 cm / c = 0.5 sec, which is also the T_N time for 1.5 x 10^15 Tubulins.
If N (number of Tubulins) is more than 1.5 x 10^15 (at 100 nm distance), then the time of traverse of a Quantum Consciousness Hamiltonian Circuit is greater than T_N, so there is not enough time to form a complete Hamiltonian Circuit, and the Quantum Consciousness Superposition will contain more than one Circuit., and none of them will be a complete Hamiltonian Circuit. If N is less than 1.5 x 10^15 (at 100 nm distance) there is time for the Quantum Consciousness Hamiltonian Circuit to be orbited more than once. These ideas arose from e-mail discussions with Jack Sarfatti and Daniel Lapadatu.
The Hamiltonian Circuit problem is NP-complete, but the brain's Quantum Consciousness acts as a Quantum Computer and tries all Many-Worlds possibilities at once, thus finding an optimal Hamiltonian Circuit very quickly.
The 10^6 Tubulin line of the table corresponds to the micron size of the Electron GravitoEM Induction Region. Sidharth-Sarfatti Electron Gravito EM Induction Region Virtual Gravitons (range about a micron, and corresponding period (10^(-15) sec) of submillimeter gravity, which is being studied by experiments under way in 1998 at Stanford and the University of Colorado in Boulder.
Other possibly relevant phenomena are:
the van der Waals interaction; and
Sidharth-Sarfatti Proton GravitoEM Induction Region Virtual Gravitons that have nanometer-scale range, similar to the scale of Tubulins, of the Superposition Separation Distance of the Conformation Electron of a Tubulin, and of gap junctions.
To see that this picture is consistent with the electron picture, start with the case of one Tubulin whose Conformation Electron is in Coherent Superposition with the Atoms of the Tubulin. Since the Tubulin has 2 parts (alpha and beta), each with about 450 amino acids, and each amino acid has about 20 Atoms, the Tubulin consist of about 2x450x20 = 18,000 Atoms, or about 20,000 Atoms. I consider that the entire Tubulin is only displaced by a distance a_tubulin such that the total Superposition Separation Energy of the entire Tubulin is equal to the Superposition Separation Energy of its Conformation Electron by a nanometer. Hameroff and Penrose, in Section 5.1.1 (Protein Spheres) of their Orch OR paper, have calculated the Superposition Separation Energy, saying (changing some of their notation): "... Since the [Superposition Separation] displacement is less than the sphere radius, we need a detailed calculation to obtain the gravitational self-energy E of the difference between the displaced mass distributions for each tubulin monomer, considered as a uniform sphere. Taking the sphere to have a radius R and the distance of displacement to be a, we find, as the result of a double integration:
E = m^2 G (a^2 / 2 R^3 - 3 a^3 / 16 R^4 + a^5 / 160 R^6) ...".
If the radius R of the Tubulin is taken to be about 2 nanometers as a rough estimate, and the displacement will be much less than R, then, as Hameroff and Penrose say, "... We can ignore the higher-order terms, so we obtain ...
E = m^2 a^2 / 2 R^3 ...".
If there are about 5 nucleons per Atom, and about 20,000 Atoms per Tubulin, then there are about 100,000 nucleons per Tubulin. Since the mass of a nucleon is about 2,000 Electron masses, the total mass of the Tubulin is about 2 x 10^8 m_e, where m_e is the Electron mass. If E_e is the Superposition Separation Energy of one Electron by one nanometer and the Tubulin is to be displaced by a distance a so that the Superposition Separation Energy E_tubulin of the Tubulin is equal to E_e, we have (ignoring some factors of 2 for simplicity):
E_tubulin = E_e = G (m_e)^2 / (1 nanometer ) = (G (2 x 10^8 m_e)^2 a_tubulin^2 / 2 (2 nanometer)^3 )
so that the Superposition Separation for the entire single Tubulin is given by
a_tubulin^2 = 4 x 10^(-16) nanometer ^2 = 4 x 10^(-30) cm^2
a_tubulin = 2 x 10^(-15) cm
and
T_tubulin = h / E_tubulin = h / E_electron = T_electron =
= 10^26 sec = 10^19 years.
Since 10^(-13) cm = 5 GeV^(-1), a_tubulin = 2 x 10(-15) cm = (1/50) x 10^(-13) cm corresponds to an energy scale of about 250 GeV, which is roughly the Higgs Vaccum Expectation Value (possibly related to the Compressibility of the Aether), and is of the order of the masses of the Truth Quark and Weak Force interactions involving W and Z gauge bosons, and probably of the (not yet experimentally observed) Higgs Scalar, all of whose masses are of the order of 100 GeV, or about 200,000 m_e.
Jack Sarfatti has noted the relevance of the fundamental
GRW Dynamical Decoherence time Tgrw,
which sets aa threshold for consciousness phenomena at Tgrw_N = Tgrw / N, since GRW Dynamical Decoherence scales as 1 / N. I use the value Tgrw = 3 x 10^14 sec. You can find the intersection point of the Tgrw_N function with the T_N Tubulin Back-Reaction function by setting
T_N = (1 / 10 ) T_electron / N^(5/3) = 10^25 / N^(5/3) = Tgrw / N
so that the number of Tubulins N_BRgrw at the intersection point is
N_BRgrw = ( 10^25 )^(3/2) Tgrw ^(-3/2) = ( 10^25 )^(3/2) ( 3 x 10^14 )^(-3/2) =
= ( 3 x 10^10 )^(3/2) = 5 x 10^15 Tubulins.
From the above table, N_BRgrw Tubulins roughly corresponds to:
0.1 seconds, so that shorter-term phenomena must operate on a sub-conscious level; EEG alpha waves, about 4 x 10^9 Neurons (or about 4 percent of the 10^11 Neurons in a human brain); and a part of the brain about 1/6 of a centimeter in size.
How are GRW and Tubulin Back-Reaction related?
The GRW event at Tgrw_N means that Su