4 Some Biochemical Reflections on Information and Communication
83
26 without a zero, which make compact strings of alphabetic labels (which finally
gives rise to languages as developed from mathematics). It is also required that the
decoding depends on the prior “knowledge” of each “receiver” and in this sense the
code may have different interpretations and versions.
In Appendix B the cell’s Q-value factor was obtained, the latter essentially being
equal to the dimensional number m. Rewriting Eq. (4.27) (here ω 0 is the thermal
frequency, τ the lifetime corresponding to the resonance half-width, and τ corr is the
short time scale defined in Eq. (4.18), see Appendices A, B for details)
P = (ω 0 τ − i)I + J = m
ω 0 τ corr −
i
m
I + J
(4.5)
it is easy to see that resonance between correlated cells and STN structures of the
cell nucleus occurs when the dimension of the STN matches (essentially) the Qvalue of the cell, noting that the first term in Eq. (4.1) is short-lived compared the
second one.
Metaphorically the cell can be imagined as a tuning fork coupled to a resonance
box, i.e. the cell confinement containing the cell nucleus. The Q-value depends on
the actual position of the cell in the hierarchy of the organism and the corresponding
assignment for the business of building material structures of a particular kind. As
an example one might consider nerve cells or neurons, which regulates the flow of
information from sensory input to motor output, via the production of appropriate
neurotransmitters. Obviously high Q-factors contribute to various types of memory
and learning, see e.g. Kandel [45] for an excellent summary of the state of the art in
memory research.
Continuing the metaphor one can envisage the phonon assisted communication
between the cells as a number of “phone calls” between the cells during a given
time, t, being multiples of the characteristic time τ = τ rel , see Eqs. (4.31)–(4.34)
in the appendices. The probability that k “calls” are exchanged during a specific
time interval, with each “telephone call” occurring with a known average (intensity)
parameter λ l = (l − 1)τ rel /τ rel = (l − 1); l = 2, 3..m i.e. with a specific distribution
for each value of l, is trivially given by
P λ l (k) =
(l − 1) k
k!
e
−(l−1)
(4.6)
with the mean and variance given by λ = l − 1. The mean maximum number of
events during T l = (l − 1)τ rel are clearly given by l = m, with λ m = (m − 1) or
counting l = 0 as an event, the community of cells encompasses during T m−1 ,
according (4.6), m communications between M cells distributed over m possible
“sites” in the organism. From the properties of the Poisson distribution one can recognize that the maximum length m, of a message set, is directly matched by the
variance and the mean λ.
To put it concisely, each cell is characterized as an STN system, i.e. an open dissipative system, containing nested encodings, programmed in the factorized canonical vectors of the transformation B, from the genetic to higher order codes, e.g. the
blueprint for the protein build up, stored in the genetic alphabet and converted via a
resonating mechanisms (depending on the Q-value) from cell to cell.
83
26 without a zero, which make compact strings of alphabetic labels (which finally
gives rise to languages as developed from mathematics). It is also required that the
decoding depends on the prior “knowledge” of each “receiver” and in this sense the
code may have different interpretations and versions.
In Appendix B the cell’s Q-value factor was obtained, the latter essentially being
equal to the dimensional number m. Rewriting Eq. (4.27) (here ω 0 is the thermal
frequency, τ the lifetime corresponding to the resonance half-width, and τ corr is the
short time scale defined in Eq. (4.18), see Appendices A, B for details)
P = (ω 0 τ − i)I + J = m
ω 0 τ corr −
i
m
I + J
(4.5)
it is easy to see that resonance between correlated cells and STN structures of the
cell nucleus occurs when the dimension of the STN matches (essentially) the Qvalue of the cell, noting that the first term in Eq. (4.1) is short-lived compared the
second one.
Metaphorically the cell can be imagined as a tuning fork coupled to a resonance
box, i.e. the cell confinement containing the cell nucleus. The Q-value depends on
the actual position of the cell in the hierarchy of the organism and the corresponding
assignment for the business of building material structures of a particular kind. As
an example one might consider nerve cells or neurons, which regulates the flow of
information from sensory input to motor output, via the production of appropriate
neurotransmitters. Obviously high Q-factors contribute to various types of memory
and learning, see e.g. Kandel [45] for an excellent summary of the state of the art in
memory research.
Continuing the metaphor one can envisage the phonon assisted communication
between the cells as a number of “phone calls” between the cells during a given
time, t, being multiples of the characteristic time τ = τ rel , see Eqs. (4.31)–(4.34)
in the appendices. The probability that k “calls” are exchanged during a specific
time interval, with each “telephone call” occurring with a known average (intensity)
parameter λ l = (l − 1)τ rel /τ rel = (l − 1); l = 2, 3..m i.e. with a specific distribution
for each value of l, is trivially given by
P λ l (k) =
(l − 1) k
k!
e
−(l−1)
(4.6)
with the mean and variance given by λ = l − 1. The mean maximum number of
events during T l = (l − 1)τ rel are clearly given by l = m, with λ m = (m − 1) or
counting l = 0 as an event, the community of cells encompasses during T m−1 ,
according (4.6), m communications between M cells distributed over m possible
“sites” in the organism. From the properties of the Poisson distribution one can recognize that the maximum length m, of a message set, is directly matched by the
variance and the mean λ.
To put it concisely, each cell is characterized as an STN system, i.e. an open dissipative system, containing nested encodings, programmed in the factorized canonical vectors of the transformation B, from the genetic to higher order codes, e.g. the
blueprint for the protein build up, stored in the genetic alphabet and converted via a
resonating mechanisms (depending on the Q-value) from cell to cell.