microtubules are long cylinders of α- and β-tubulin dimers,
31 each with a molecular
weight of about 50 kDa formed in parallel association of thirteen protofilaments. In
total we have a weight of around 1000 kDa, corresponding to about 10
6 protons. With
a nuclear average of approximately 10 Da, one might expect roughly 10
5 nuclear
degrees of freedom to be at work in each of the ca 10
9 microtubules. Using Eq. (4.6)
one finds cilia beating frequencies of the order τ rel ≈ 25 ms at human body temperatures, which appears to be in the right range for motile cilia mediated pathways. It has
also been noted that defects in the structure of the cellular primary cilium leads to
various disorders and impairments [45]. Hence looking at recurrent frequencies,
around 10–40 Hz, one will conclude that obstructing cell organelle movements might
severely disturb the channel for stochastic communication. Despite the view that
perhaps 10–20,000 neurons are involved in a perception instigated by specific spike
trains, the present CDS concept, nevertheless, implies a more complex understanding
in that a Gödelian network must have all neurons ‘on alert’ in case of need.
Another critical challenge, while retaining quantum chemistry applications to
biological systems, is the temperature dependence, the thermoregulation, and the
associated problem of the necessary prohibition of short-time
32 decoherences. The
development and appearances of Correlated Dissipative Structures, CDS, not only
suggests answers to this dilemma, it also incorporates realistic time scales and the
linked nested ‘code-encode bearing’ transformation B. In this connection it is also
interesting to observe that so-called poikilotherms, i.e. organisms whose internal
temperatures varies considerably, have several different enzyme systems operating
at different temperatures, hence representable by different CDE’s.
Finally, a reminder regarding our biophysical organisation, termed a complex
enough system, CES, subject to the CDE, viz. the interactions between the cells
commensurate with the dynamics inside the cell, derived from a CDS, is neither
deterministic nor probabilistic.
33 This incurs no contradiction, even if the biological
process may appear deterministic at the mesoscopic level of understanding.
The CDE is an irreducible ensemble defined in terms of the CDS, the latter
exhibiting an analogous irreducible structure. Within this framework one might
finally be reminded of the words of Ernst Mayr [10, 46] regarding the characteristics of biological processes: a teleonomic process or behaviour is one that owes
its goal-directedness to the influence of an evolved program. Our interpretation
suggests that the stochastic hypothesis depicted here, i.e. a “Communication
31
Since the microtubules have a distinct polarity one obtains a direct coupling between the
mechanical- and the electromagnetic oscillations generating the train of neuronal spikes.
32
The notion ‘short’ is here in relation to any other time scales discussed in this article.
33
It has been stated that the mathematical structure of cosmos, with the origin of the physical laws
being in pure numbers, may discard the theory of biological evolution as well as being incommensurate with the non-deterministic interpretation of quantum mechanics [47]. It is clear, however, from the present work that numerical structures, like the formula 1 + 1 = 2, reveals
important and necessary facts about our universe that are essential for the communication between
life forms and contingent on evolution, see e.g. a recent scientific analysis of ‘Science and Music’
[48] focusing on musical transcriptions in the living world.
402
E. J. Brändas
31 each with a molecular
weight of about 50 kDa formed in parallel association of thirteen protofilaments. In
total we have a weight of around 1000 kDa, corresponding to about 10
6 protons. With
a nuclear average of approximately 10 Da, one might expect roughly 10
5 nuclear
degrees of freedom to be at work in each of the ca 10
9 microtubules. Using Eq. (4.6)
one finds cilia beating frequencies of the order τ rel ≈ 25 ms at human body temperatures, which appears to be in the right range for motile cilia mediated pathways. It has
also been noted that defects in the structure of the cellular primary cilium leads to
various disorders and impairments [45]. Hence looking at recurrent frequencies,
around 10–40 Hz, one will conclude that obstructing cell organelle movements might
severely disturb the channel for stochastic communication. Despite the view that
perhaps 10–20,000 neurons are involved in a perception instigated by specific spike
trains, the present CDS concept, nevertheless, implies a more complex understanding
in that a Gödelian network must have all neurons ‘on alert’ in case of need.
Another critical challenge, while retaining quantum chemistry applications to
biological systems, is the temperature dependence, the thermoregulation, and the
associated problem of the necessary prohibition of short-time
32 decoherences. The
development and appearances of Correlated Dissipative Structures, CDS, not only
suggests answers to this dilemma, it also incorporates realistic time scales and the
linked nested ‘code-encode bearing’ transformation B. In this connection it is also
interesting to observe that so-called poikilotherms, i.e. organisms whose internal
temperatures varies considerably, have several different enzyme systems operating
at different temperatures, hence representable by different CDE’s.
Finally, a reminder regarding our biophysical organisation, termed a complex
enough system, CES, subject to the CDE, viz. the interactions between the cells
commensurate with the dynamics inside the cell, derived from a CDS, is neither
deterministic nor probabilistic.
33 This incurs no contradiction, even if the biological
process may appear deterministic at the mesoscopic level of understanding.
The CDE is an irreducible ensemble defined in terms of the CDS, the latter
exhibiting an analogous irreducible structure. Within this framework one might
finally be reminded of the words of Ernst Mayr [10, 46] regarding the characteristics of biological processes: a teleonomic process or behaviour is one that owes
its goal-directedness to the influence of an evolved program. Our interpretation
suggests that the stochastic hypothesis depicted here, i.e. a “Communication
31
Since the microtubules have a distinct polarity one obtains a direct coupling between the
mechanical- and the electromagnetic oscillations generating the train of neuronal spikes.
32
The notion ‘short’ is here in relation to any other time scales discussed in this article.
33
It has been stated that the mathematical structure of cosmos, with the origin of the physical laws
being in pure numbers, may discard the theory of biological evolution as well as being incommensurate with the non-deterministic interpretation of quantum mechanics [47]. It is clear, however, from the present work that numerical structures, like the formula 1 + 1 = 2, reveals
important and necessary facts about our universe that are essential for the communication between
life forms and contingent on evolution, see e.g. a recent scientific analysis of ‘Science and Music’
[48] focusing on musical transcriptions in the living world.
402
E. J. Brändas