As an explanation for order and long range correlations in living systems, Fröhlich (1968; 1970; 1975) proposed certain biomolecules pumped by metabolic processes could exhibit coherent phonon dynamics, perhaps even macroscopic quantum coherence akin to Bose-Einstein condensation or lasers. The biomolecular requirements, according to Fröhlich, were: 1) a geometric array or lattice of dipoles constrained in a common voltage gradient, and 2) ample, non-coherent biochemical energy. Eligible proposed candidates included membrane proteins, nucleic acids and cytoskeletal microtubules.
Microtubules are polymers of peanut-shaped ‘tubulin’ protein heterodimers, each composed of alpha and beta monomers with a dipole oriented negative toward the alpha monomer (Figure 1a, top). Tubulins self-assemble into hollow cylinders composed of 13 longitudinal chains (protofilaments – e.g. Figure 1a, bottom) with side-to-side interactions resulting in slightly twisted hexagonal lattices (Figure 1 b-g). Particular helical windings occur along various tubulin lattice pathways which repeat on protofilament chains at intervals which follow Fibonacci numbers of tubulin dimers. (3,5,8,13,21 etc., Dustin, 1978, Figure 1b and e). In living cells, relatively rigid microtubules are compressed (~100 piconewtons) by contractile actin and other filaments to form cytoskeletal tensegrity networks providing cell structural support (Brangwynne et al, 2006). Microtubules also dynamically organize and manifest cell movement, intra-cellular transport, mitosis/cell division, and synaptic plasticity in brain neurons. The mechanisms by which microtubules organize intra-cellular dynamical processes are unknown.
Figure 1. Microtubule structural geometry. a. (Top) 8 nanometer (nm) long tubulin protein heterodimer composed of alpha and beta monomers, with dipole oriented negative toward alpha monomer. a (Bottom) linear chain of tubulin dimers (protofilament). b-g. Thirteen protofilaments form an ‘A lattice’microtubule shown as a plane (b-d), and as actual cylinder (e-g). b. and e. Possible linear pathways include a protofilament and 3, 5 and 8-Start winding pathways. c-g. Super-lattices: highlighted tubulins mark two (out of many) different super-lattice patterns predicted as Frohlich resonance nodes by Samsonovich et al. These same super-lattice patterns precisely match functional attachment sites for microtubule-associated proteins (MAPs).
In the 1980s Hameroff and colleagues theorized microtubules were molecular computers, with phonon-coupled tubulin dipole states functioning as ‘bits’ interacting/computing with neighboring tubulin bit states in microtubule (cellular) automata (Hameroff and Watt, 1982; Hameroff, 1987; Rasmussen et al, 1990). Using Fröhlich coherent dynamics as a clock to synchronize microtubule automata computational time-steps, simulations showed patterns of tubulin states which repeat, interact, compute and propagate along microtubule lattice surfaces. Simulated networks of microtubule automata connected to others by microtubule-associated-proteins (MAPs) exhibit learning. Critical parameters in microtubule automata learning are specific tubulin sites for MAP attachments on the microtubule lattice.
In the 1990s Penrose and Hameroff (1995; Hameroff and Penrose, 1996a; 1996b; Hameroff 1998; 2007) suggested microtubules in brain neurons functioned also as quantum computers supporting consciousness. The quantum computations were proposed to be synchronized by Fröhlich coherent dynamics, terminated by Penrose objective reduction, and orchestrated by synaptic inputs via MAPs. The Penrose-Hameroff model became known as orchestrated objective reduction (Orch OR). Since its formulation in the mid 1990s, Orch OR has endured (and survived) heavy criticism, for example on whether the proposed macroscopic quantum states can occur in warm and wet biology (Tegmark 2000, Hagan et al 2001). But evidence in recent years has demonstrated quantum coherence in warm biomolecular systems (Engel et al 2007; Collini and Scholes, 2009).
In a recent PNAS paper, Reimers et al (2009) describe three types of Fröhlich condensation: weak, strong and coherent. Applying the Wu-Austin Hamiltonian to a linear chain of tubulin-like oscillators, Reimers et al conclude that strong and coherent Fröhlich condensation are not feasible in microtubules, but that weak condensation IS feasible. They also confirm that Pokorny (2004) has experimentally demonstrated weak Fröhlich condensation in microtubules at 8 MHz. Asserting the Penrose-Hameroff Orch OR model depends on strong/coherent Fröhlich condensation, Reimers et al conclude that Orch OR is untenable.
In defense of Orch OR I raise two points. The first is that so-called weak Fröhlich condensation at 8 MHz (with entanglement) may well be sufficient for Orch OR. The second is that Reimers et al clearly did not show that strong or coherent Fröhlich condensation in microtubules is unfeasible (nor that Orch OR is untenable).
Reimers et al base their conclusion not on a microtubule structure, but a linear chain of tubulin-like oscillators (e.g. Figure 1a, bottom). This is a fundamental and profound error. Microtubules are neither 1-dimensional chains nor 2-dimensional lattice plane surfaces extending in all directions. Microtubules are cylindrical lattice plane surfaces whose Fibonacci geometry ensures propagating signals collide and interact. Under compression in living cells, microtubules are well-suited to vibrational resonances. The Reimers et al claim is like plucking a loose string expecting to hear a piano concerto.
On the other hand, Samsonovich et al (1992) described a Hamiltonian which considered Fröhlich coherence in a proper microtubule model. Their results showed resonance nodes of phonon energy maxima and minima distributed on the microtubule lattice surface in periodic patterns. The periodic node patterns described various super-lattices overlying the microtubule lattice, two of which are shown in Figure 1. Moreover, specific super-lattice patterns of resonance nodes precisely match experimentally observed patterns of MAP attachments on microtubules, patterns which control and regulate cellular architecture and function (Burns 1978, Kim et al 1986, Amos 1995).
Precise super-lattice regularity over great distances on microtubules is difficult to explain by local rules or self-assembly due to finite probability of error. Thus the precisely identical super-lattice patterns seen in observed MAP attachment sites and calculated Fröhlich resonance nodes are unlikely to be coincidental, and imply some non-local effect. Samsonovich et al concluded that microtubule structural geometry resulted in a spectrum of functional Fröhlich-like global phonon modes.
So, two Hamiltonians examine possible Fröhlich effects in microtubules. One (Reimers et al, 2009) is based on a crude approximation of a microtubules as a linear string of oscillators, and reveals no effects. The other (Samsonovich et al, 1992) is based on actual microtubule structural geometry, and demonstrates Fröhlich resonance and coherent super-lattice patterns which match experimentally observed locations of functional MAP attachments.
Basing their stern refutation of Orch OR on a flimsy model bearing no resemblance to a microtubule, and in light of the Samsonovich et al Hamiltonian results which do rely on microtubule structure, Reimers et al owe Orch OR, and the scientific community, a retraction in PNAS.
I do thank them for bringing to light the findings of Pokorny, demonstrating 8 MHz coherent excitations in microtubules. This is indeed good news for Orch OR, and for classical theories of microtubule computation.
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There are two types of microtubule lattices. In the A-lattice, shown here, side-by-side tubulin alignment is alpha to beta and beta to alpha. This results in continuous spiral helices, as shown in Figure 1. In the B-lattice (not shown), tubulin alignment is alpha to alpha and beta to beta, resulting in spiral windings with dislocations along a vertical seam between two protofilaments.