80
E.J. Brändas
account refers to four different nucleotides, alternatively one can also make the optimal choice m = 2M preferring the general tautomeric structures of the two basic
proton configurations, see Appendix B for more details on the origin of Eq. (4.1).
The STN structure Eq. (4.1) describes a dynamical situation, which mimics the helical structure of the nucleotides. Note that the transformation engenders two fundamental undertakings: (i) it diagonalises the apposite second order reduced density
matrix, which in ideal cases might develop ODLRO, see Appendix A and Eq. (4.13),
(ii) it transforms the thermalized density, fulfilling the far from equilibrium boundary conditions (4.18), to classical canonical form (4.21)–(4.23). Hence B emerges
to “store information” in the helical arrangement before the cell division, where the
structure represented by Eq. (4.1) mimics the step operator properties of e.g. angular
momentum. The former property is wide-ranging and has actually been respected in
the context of cosmological evolution, see Ref. [37] and in the conclusion.
The opening up of the double helix, the copying of the gene, leads to a very complex process (here much oversimplified) where the copy is made via the so-called
messenger ribonucleic acid mRNA. In the subsequent step transfer RNA (tRNA), is
bound to mRNA. The former carry an amino acid at one end of the chain. Hence the
anticodon of the tRNA is bound to the complementary codon of the mRNA. Note
that in RNA the nucleotide base is uracil instead of thymine and of course it forms
no double helix. Note also that the anticodon defines the group of the three complementary nucleotide bases coding for the amino acid carried by the tRNA. The
process describes the generation of a protein from the complete sequence coding
of one gene, where triples of nucleotide bases code for one of the twenty natural
amino acids building up the protein. In addition to the protein coding genes, the
so-called extrons, there are interruptions by long DNA sequences, introns (missing
in the mRNA synthesis), which do not code proteins and whose biological role for a
long time appeared uncertain. We will return to this exon-intron mechanism below.
Before examining the factorization properties of the transformation B it is important to realize that the molecular constituents of the cell as formulated in Eq. (4.1)
and in the appendices is a coarse grained simplification and require further details.
At the outset the reader is reminded of the Watson and Crick stereo-model utilizing the hydrogen bond complementarity between the nucleotide base pairs, see e.g.
Löwdin [38] and references therein for the state-of-the-art of that period. Thus it
is important to model the preferred basis as essentially developed from the double
proton tunnelling movements inside the DNA helical order even if the description
refers to an open dissipative system. This is clearly not the whole story since the dynamics is intrinsically defined by the highly complex correlated motions of the light
fermionic carriers e.g. the electrons that accompany nuclear position changes and
vice versa. In this procedure one usually invokes the purported Born-Oppenheimer
(BO) approximation, implying essentially that electrons, being much lighter and
quicker, moves in a more or less nuclear equilibrium configuration. Obviously this
is not adequate here, cf. Ref. [39] where the mirroring between the “light carrier”
and its “heavy partner” should be perceived beyond the BO picture via corresponding traces over all nuclear degrees of freedom in the electronic picture and vice
versa for the nuclear dynamics. Without going into more details it will be sufficient
E.J. Brändas
account refers to four different nucleotides, alternatively one can also make the optimal choice m = 2M preferring the general tautomeric structures of the two basic
proton configurations, see Appendix B for more details on the origin of Eq. (4.1).
The STN structure Eq. (4.1) describes a dynamical situation, which mimics the helical structure of the nucleotides. Note that the transformation engenders two fundamental undertakings: (i) it diagonalises the apposite second order reduced density
matrix, which in ideal cases might develop ODLRO, see Appendix A and Eq. (4.13),
(ii) it transforms the thermalized density, fulfilling the far from equilibrium boundary conditions (4.18), to classical canonical form (4.21)–(4.23). Hence B emerges
to “store information” in the helical arrangement before the cell division, where the
structure represented by Eq. (4.1) mimics the step operator properties of e.g. angular
momentum. The former property is wide-ranging and has actually been respected in
the context of cosmological evolution, see Ref. [37] and in the conclusion.
The opening up of the double helix, the copying of the gene, leads to a very complex process (here much oversimplified) where the copy is made via the so-called
messenger ribonucleic acid mRNA. In the subsequent step transfer RNA (tRNA), is
bound to mRNA. The former carry an amino acid at one end of the chain. Hence the
anticodon of the tRNA is bound to the complementary codon of the mRNA. Note
that in RNA the nucleotide base is uracil instead of thymine and of course it forms
no double helix. Note also that the anticodon defines the group of the three complementary nucleotide bases coding for the amino acid carried by the tRNA. The
process describes the generation of a protein from the complete sequence coding
of one gene, where triples of nucleotide bases code for one of the twenty natural
amino acids building up the protein. In addition to the protein coding genes, the
so-called extrons, there are interruptions by long DNA sequences, introns (missing
in the mRNA synthesis), which do not code proteins and whose biological role for a
long time appeared uncertain. We will return to this exon-intron mechanism below.
Before examining the factorization properties of the transformation B it is important to realize that the molecular constituents of the cell as formulated in Eq. (4.1)
and in the appendices is a coarse grained simplification and require further details.
At the outset the reader is reminded of the Watson and Crick stereo-model utilizing the hydrogen bond complementarity between the nucleotide base pairs, see e.g.
Löwdin [38] and references therein for the state-of-the-art of that period. Thus it
is important to model the preferred basis as essentially developed from the double
proton tunnelling movements inside the DNA helical order even if the description
refers to an open dissipative system. This is clearly not the whole story since the dynamics is intrinsically defined by the highly complex correlated motions of the light
fermionic carriers e.g. the electrons that accompany nuclear position changes and
vice versa. In this procedure one usually invokes the purported Born-Oppenheimer
(BO) approximation, implying essentially that electrons, being much lighter and
quicker, moves in a more or less nuclear equilibrium configuration. Obviously this
is not adequate here, cf. Ref. [39] where the mirroring between the “light carrier”
and its “heavy partner” should be perceived beyond the BO picture via corresponding traces over all nuclear degrees of freedom in the electronic picture and vice
versa for the nuclear dynamics. Without going into more details it will be sufficient