TGD based model for the evolution of genetic code: V

First some context. I have discussed the model for the evolution of genetic code and the ideas inspired by this model in previous postings (I, II, III, IV).

Biochemistry represents extremely complex and refined choreography. It is hard to believe that this reduces to a mere an unconscious and actually apparent fight for chemical survival. In TGD Universe consciousness would be involved even at the molecular level and magnetic body would be the choreographer whose dance would induce the molecular activities. This picture combined with the idea of standard plugs through and terminals at which flux tubes end, leads to a third trial to understand catalytic code.

The third trial differs from the second trial in that the letters X,Y,Z of the codon XYZ coding for the aminoacid do not correspond to COOH, residy R, and NH₂ group. Rather, free aminoacid behaves like XY as in the first trial and X and Y correspond to flux tubes ending at OH and =O in COOH group. For the new option all - not only alpha helical and beta sheeted - aminoacids in the interior of the aminoacid sequence behave like the conjugate of letter Y for the codon XYZ coding for the aminoacid. The new model predicts that DNA, mRNA, tRNA, and aminoacids are in general connected by braid strands and provides a detailed picture about the role of braidings in transcription and translation. The topological dynamics of the magnetic body, its motor activities, would induce catalytic dynamics. Also a far reaching generalization of DNA as tqc paradigm emerges (see the postings I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII,XIII).

1. Flux tubes as a correlate for directed attention

Molecular survival is the standard candidate for the fundamental variational principle motivating the molecular intentional actions. There is entire hierarchy of selves and the survival at the higher level of hierarchy would force co-operation and altruistic behavior at the lower levels. One might hope that this hypothesis reduces to Negentropy Maximization Principle, which states the information contents of conscious experience is maximized. If this picture is accepted, the evolution of molecular system is analogous to the evolution of a society.

Directed attention is the basic aspect of consciousness and the natural guess would be that directed attention corresponds to the formation of magnetic flux tubes between subject and target. The directedness property requires some manner to order the subject and target.

1. The ordering by the values of Planck constant is what first comes in mind. The larger space-time sheet characterized by a larger value of Planck constant and thus at a higher level of evolutionary hierarchy would direct its attention to the smaller one.
2. Also the ordering by the value of p-adic prime characterizing the size scale of the space-time sheet could be considered but in this case directedness could be questioned.
3. Attention can be directed also to thoughts. Could this mean that attention is directed from real space-time sheets to p-adic space-time sheets for various values of primes but not vice versa? Or could the the direction be just the opposite at least in the intentional action transforming p-adic space-time sheet to real space-time sheet. Perhaps directions are opposite for cognition and intention.

The generation of wormhole magnetic flux tubes could be the correlate for the directed attention, not only at molecular level, but quite generally. Metaphorically, the strands of braid would be the light rays from the eyes of the perceiver to the target and their braiding would code the motions of the target to a topological quantum computation like activity and form a memory representation at least. The additional aspect of directed attention would be the coloring of the braid strands, kind of coloring for the virtual light rays emerging from the eyes of the molecular observer. In the case of DNA this can induce a coloring of braid strands emerging from aminoacids and other molecules so that it would indeed become possible to assign to aminoacid the conjugate of the middle nucleotide of the codon XYZ coding for it.

Attention can be also redirected. For this process there is a very nice topological description as a reconnection of flux tubes. What happens is that flux tubes A→ B and C → D fuse for a moment and become flux tubes A→ D and C→ B. This process is possible only if the strands have same color so that the values of the quark charges associated with A and B are same.

This kind of process can modify tqc programs. For instance, in the case of the flux tubes coming from nucleotides X and X_c and ending to the lipid layer this process means that X and X_c and corresponding lipids become connected and genome builds memory representation about this process via similar link. If proteins are connected with mRNA connected to DNA in this manner, this process would allow the formation of flux tubes between aminoacids of two proteins in such a manner that protein would inherit from DNA codon the color of the middle nucleotide and its interactions effectively reduce to base pairing.

DNA would have memory representation about molecular processes via these changing braiding topologies, and one could say that these molecular processes reflect the bodily motions of the magnetic body. Entire molecular dynamics of the organism could represent an enormous tqc induced by the motor activities of the magnetic body. At the level of sensory experience similar idea has been discussed earlier: Out of Body Experiences and illusions such as train illusion could be understood in terms of motor action of magnetic body inducing virtual sensory percepts.

Attention can be also switched on and off. Here the structure of the lipid ends containing two nearby situated =O:s suggest the mechanism: the short flux tube connecting =O:s disappears. The minimization of Coulomb interaction energy at each end implies that re-appearance of the flux tubes creates a short flux tube with the original strand color.

2. Where do flux tubes begin from?

The view about magnetic body as a controller of biological body using genome as a control tool suggests that DNA is to a high degree responsible for directed attention and other molecules as targets so that flux tubes emanate from DNA nucleotides. The reason would be that the aromatic cycles of DNA correspond to larger value of Planck constant.

Some chemical or geometric property of DNA nucleotides or of DNA nucleotides of DNA strand could raise them to the role of subject. Aromatic cycle property correlates with the symmetries associated with large value of Planck constant and is the best candidate for this property. If this is accepted then also some aminoacid residues might act as subjects. Phe, His, Trp, Tyr contain aromatic cycle. The derivatives of Trp and Tyr act as neurotransmitters and His is extremely effective nucleophilic catalyst. This would make possible more specific catalytic mechanisms through the pairing of Phe, His, Trp, and Tyr with residues having flux tube terminals.

This raises the question about the physical interaction determining the color of the strand emerging from the aromatic cycle. The interaction energy of quark at the end of flux tube with the classical electromagnetic fields of nuclei and electrons of the ring should determine this. The wormhole contact containing quark/antiquark at the throat at space-time sheet containing nuclei and electrons could also delocalize inside the ring. One of the earliest hypothesis of TGD inspired model for living matter was that wormhole Bose-Einstein condensates could be crucial for understanding of the behavior of biomolecules. Wormhole throats with quark and antiquark at their throats appear also in the model of high T_c superconductivity. The only manner for the electronic space-time sheet to feed its electromagnetic gauge flux to larger space-time sheets using exactly two wormhole contacts is to use wormhole contacts with u_c and d at their "upper" throat (T,G). For proton one would have d_c and u at their "upper" throat (A,C). The presence of electron or proton at nucleotide space-time sheet near the end of flux tube might allow to understand the correlation. The transfer of electrons and protons between space-time sheets with different p-adic length scale is basic element of TGD based model of metabolism so that there might be some relation.

3. What aminoacids can act as plugs and terminals of flux tubes?

Standardization constraint suggests that flux tubes are attached to standard plugs and terminals. The explicit study of various biological molecules and the role of water in biology suggests that =O serves as a plug to which flux arrives and from which it continues. The intuitive reason for the proposal is that =O allows two hydrogen bonds. OH would in turn correspond to a terminal at which flux tube ends. One might be very naive and say that conscious biomolecules have learned the fundamental role of oxygen and water in the metabolism and become very attentive to the presence of =O and OH. =O appears in the residues of Asp, Glu, Asn, Gln. OH groups appear inside the residues of Asp,Glu and Ser, Thr.

It might not be very wise to restrict the molecular attention to only =O and OH and it is probably better to speak about probabilities for the flux tubes to attach to various kinds of terminals. Both SH and NH₂ are chemically like OH both these them could act as terminals of flux tubes: NH₂ (Asp,Gly,Glu,Arg) contain NH₂ and Cys contains SH.

4. Directed attention generates memory representations and tqc like processes

Directed attention induces braiding if the target is moving and changing its shape. This gives rise to a memory representation of the behavior of the object of attention and also to a tqc like process. A considerable generalization of tqc paradigm suggests itself. Tqc could be induced by the braiding between DNA and lipids, DNA and proteins via folding processes, DNA RNA braiding and braiding between DNA and its conjugate, DNA and protein braiding. The outcome of tqc would be represented as the temporal patterns of biochemical concentrations and rates and there would be hierarchy of p-adic time scales and those associated with the dark matter hierarchy.

For instance, the protein content of lipid membranes is about 50 per cent and varies between 25 and 75 per cent so that protein folding and lipid flow could define tqc programs as self-organization patterns. The folding of protein is dynamical process: alpha helices are created and disappear in time scale of 10^-7 seconds and the side chains of protein can rotate.

The details of the tqc like process depend on what one assumes. The minimal scenario is deduced from the transcription and translation processes and from the condition that magnetic body keeps control or at least keeps book about what happens using genome as a tool. The picture would be essentially what one might obtain by applying a rough model for web in terms of nodes and links.

1. mRNA and mRNA and DNA must remain connected by flux tubes after transcription. The Y_c of mRNA codon could be connected to =O plug in the aminoacid of tRNA molecule and this to Y in tRNA anticodon so that one would have DNA-aminoacid-tRNA link. Z_c in mRNA would be connected to Z in tRNA anticodon giving mRNA-tRNA link. OH in aminoacid would be connected to X in tRNA dicodon XY giving aminoacid-tRNA link.

2. When tRNA donates its aminoacid to the growing chain, the formation of the peptide bond separates one H₂O and the X connection to OH becomes a connection to water molecule so that one obtains tRNA-H₂O link. DNA-mRNA-aminoacid-tRNA link with color Y is preserved. Dn depolymerization of mRNA H₂O molecule is used and the reverse change for linkings takes place.

3. The recombination process for two conjugate DNA-mRNA-aminoacid-tRNA links can transform the flux tubes in such manner that one obtains aminoadic-aminoacid Y link between the =O:s of aminoacids A₁ and A₂ characterized by Y and Y_c. As proposed, this mechanism could be central in the enzyme substrate interaction. The process would pair tRNAs corresponding to Y and Y_c together to give DNA-mRNA-tRNA-tRNA-mRNA-DNA link providing a memory representation about aminoacid pairing A₁-A₂. One can say that magnetic body creates with the mediation of the genome dynamical tqc programs to which much of the biomolecular activity reduces. Not all however, since two aminoacid pairs A₁-A₂ and A₃-A₄ can recombine to A₁-A₄ and A₃-A₂ without DNA knowing anything about it. Magnetic body however knows.

4. The constant part of the aminoacid inside aminoacid would behave like Y_c if aminoacid is coded by XYZ whereas the ends and the protein would behave like dicodons XY (in second trial it would have behaved like YZ). If one assigns to the hydroxyl and amino groups of the residue the roles of object and subject also flux tubes connecting the residue groups become possible and protein does not behave like single nucleotide anymore although one can still say that everything reduces in a well-define sense to the genetic code.

4. Introns and DNA-protein attachment

An example is the situation in which protein acts as an enzyme attaching on DNA. Suppose that this process effectively reduces to a base pairing between aminoacid and DNA nucleotide. Protein can attach to any portion of DNA. Since nucleotide triplets and aminoacids in the first approximation correspond to same length in the respective chains, amino-acid is expected to correspond to nucleotide triplet. The simplest interaction is the attachment to the gene coding for the aminoacid itself but much more general enzymatic interactions are possible. This works if the gene does not contain introns or if the attachment is along single exon.

It is known that DNA can change its conformation from strand during enzyme-DNA action and the contraction of DNA strand might make possible to have enzyme-DNA interaction also in the case that attachment region corresponds to several exons. One can of course ask whether genes containing introns tend to code for proteins which are used for topological quantum computations. Introns, perhaps the repeating sequences with no obvious function, would have at least this useful function but very probably much more useful ones too (they are now known to be transcribed to RNA and TGD suggest that language corresponds to intronic gene expression). The emergence of introns might be somewhat like the emergence of information society.

The foldings of proteins tend to be conserved in the evolution whereas primary structure can change quite a lot apart from some aminoacids critical for enzymatic action. This confirms with the effective base pairing interaction between aminoacids and DNA and would mean that DNA-aminoacid tqc programs are rather robust against mutations.

5. Evolution and braidings

The evolution at the molecular level corresponds to the emergence of increasingly complex molecules using as basic building blocks aminoacid chains and non-translated residues attached to them in the post-translational processing of the aminoacid chains. Also increasingly complex reaction paths emerge. Molecular survival and the competition for the metabolic resources at molecular level could be seen as the basic driving force of this evolution.

Typically, in the original situation the enzymes would have received the substrate molecules from the environment but sooner or later this would have become difficult. The solution would have been a synthesis of the substrate from simpler ingredients by starting from some precursor.

If molecules (with magnetic bodies included) are conscious entities able to direct attention, one can imagine that magnetic body controlling them with the mediation of genome and able to actively modify it, could help through modifications of the genome to create to the catalyst a binding site able to bind the precursor. Immune system is doing this very intensively. If the enzyme binding the precursor already exists, a combination of genes coding for the enzyme and the enzyme having the metabolites as ligands could allow to achieve this. All this would reduce to the motor activities of magnetic body, in particular reconnection of flux tubes, kind of Shivas dance. Genome would not be anymore a sequence of DNA developing through random mutations under selection pressures.

Can one make any clear cut predictions about preferred mutations?

1. Mutations are not expected to be always random point mutations but could be a result of a purposeful action of the magnetic body. Chemical similarity is expected to be conserved in good mutations. This is known to be the case. Allowed point mutations should conserve Y. Also bi-local mutations might occur and could be crucial for the coherence of the organisms. As found, the formation of flux tube between aminoacids A₁ and A₂ induces a flux tube between nucleotides Y and Y_c at the corresponding genes. This flux tube could force the possibly intentional mutations to occur as simultaneous point mutations of the two genes conserving the conjugacy property and leaving thus braiding invariant.

2. Folding is known to be more conserved than aminoacid sequence. Since folding is a collective property of gene, local chemistry might not be enough and the proposed non-local conservation laws might be needed. Bilocal mutations would also correlate the mutations of the binding sites of protein and ligand so that the crucial geometric conjugacy proposed to reduce to conjugation for Y would not be lost. The prediction would be conserved Y-Y_c pairs in genes coding for protein and ligand and these pairs might allow to deduce the paired points. The paired nucleotides need not belong to the same strand since genes are evenly distributed between strand and its conjugate and characterized by A,G surplus. Strong form of conjugacy stating that paired genes belong to the strand and its conjugate sounds beautiful in the ears of mathematician at least and would be mirror image for the mutual avoidance of quark matter and antimatter at protein level. Some examples are in order. Ala/Ser, Ser/Thr, Ile/Val/Leu, Asp/Glu do not change Y. Lys/Arg (A/G)), Tyr/Phe (A/U), Gly/Ala (G/C),... are also prevalent and one might hope that they correspond to binary mutations in some important cases.

3. If the flux tubes can connect also side chains the situation becomes more complex. There is a temptation to think that these flux tubes would connect only the nearby aminoacids and do not affect the large scale dynamics of folding. This would be the case if the value of Planck constant associated with these flux tubes is smaller than for the flux tubes connecting aminoacids as basic units. This kind of pairing would be consistent with Y-Y_c rule since hydrophobic and hydrophilic residues would tend to be connected by a long flux tube. If flux tubes can begin from the aromatic side chains, the replacement of an aromatic side chain with an aromatic side chain is favored (also chemical similarity explains this). The most basic facts about folding do not provide obvious support the idea about flux tubes between residues.
   1. Hydrophobic residues tend to cluster in dense packing in protein interior (antimatter at quark level) and Val (T), Leu (T), Ile (T), Phe (T), Ala (C), and Gly (G) make 63 percent of the interior of protein: the special role of Gly (matter rather than antimatter) is due to the reduction of the side chain to hydrogen atom.
   2. Asp (A), Glu (A), Lys (A) and Arg (G) with ionized residues are mostly at the surface of protein and make 23 per cent of protein surface and 4 per cent of interior. As noticed earlier, matter and antimatter at quark level tend to be far from each other.
   3. Polar groups tend to be paired by hydrogen bonds and oppositely charged groups tend to be near each other. Acidic Cys residues tend to be in positions where they can form S-S bonds. This cannot be explained by Y-Y_c pairing nor by the presence of bonds connecting residues in the proposed scenario. Aromatic residues tend to have favorable electrostatic interactions with each other and with S, O and amino groups.

In this framework aminoacids would have appeared before their precursors and possessed some function in RNA world, say the catalysis of join of RNA₂ dinucleotides to the increasing chain as I have proposed. Competition might have led to the situation in which RNA₂ learned to catalyze selectively generation of aminoacids from much simpler precursors (three of the proposed precursors contain only C,=O, and O^-). The reduced genetic code would have been present at two levels: reader can decide whether this is a shortcoming of the model or a fundamental biochemical duality implying an exponential amplification of RNA and aminoacid populations.

For details see the chapter Prebiotic Evolution in Many-Sheeted Space-time of "Genes and Memes".

TGD based model for the evolution of genetic code: IV

I have discussed the model for the evolution of genetic code in previous postings (I,II,III). Thanks to the Ulla Mattfolk I learned about the idea of protein folding code - something which is expected to exist but is not understood. This led to a trial for the folding code discussed in posting III and based on the assumption that aminoacid behaves like dinucleotide. This trial did not work but the learning of some basic facts about proteins and their interactions inspired second trial according to which aminoacid in the interior of aminoacid sequences behave like the conjugate of the nucleotide Y of the codon XYZ coding for it. This trial seems to work.

There exists a wonderful book "Proteins: Structures and Molecular Properties" by Thomas E. Creighton and published 1993 by W. H Freeman Company. In the following I freely refer to the general facts discussed in this book rather than referring separately to every detail. While reading this book I learned that the first guess for the code of catalysis was wrong but is also became clear what was wrong. It became clear that free aminoacid should behave like the conjugate of the DNA codon XYZ -rather than only XY- but that an aminoacid inside aminoacid sequence effectively reduces to Y since the formation of the peptide bonds by the elimination of water molecule and formation of NH---O= hydrogen bonds effectively eliminates X and Z. The ends of aminoacid behave like dicodons which conforms with their special role in biocatalysis. Only aminoacids for which Y corresponds to quarks (not antiquarks) can form hydrogen bonds so that hydrophilic-hydrophobic dichotomy corresponds to a strong matter antimatter asymmetry at quark level.

1. Matter antimatter asymmetry at the level of interactions of aminoacids

The first thing that I learned was that second nucleotide Y in the codon XYZ coding for aminoacid is what matters. Only Y=A,G aminoacid residue can form hydrogen bonds and is hydrophilic and thus interacts strongly with water and DNA and RNA. In T,C case the formation of hydrogen bonds is impossible or rare (ser,thr). In their interactions with water these aminoacids are passive, or rather-avoid water- and tend to interact with each other. This division is fundamental for the understanding of the interactions of aminoacids. The division of aminoacids to hydrophobic resp. non-hydrophobic ones corresponds to the assignment of quarks to A and G and antiquarks to T and C so that strong matter antimatter asymmetry is in question. Similar asymmetry appears in cosmology: in TGD Universe antimatter resides inside cosmic strings in the interior of big voids containing matter as galaxies at their boundaries so that one can understand why antimatter is not visible.

2. Flux tubes can connect with all electronegative atoms

Also a plausible answer to the question which atoms can be connected by flux tubes emerges.

1. The model for dinucleotide precursor code involves precursors for which 3 precursors contain only oxygen ions or double bonded oxygens. The only possible conclusion is that oxygen can connect to any DNA letter (quark or antiquark) and that first letter-precursor correlation is a selection of the most probable alternative. Also in water oxygen atoms should form flux tube contacts with each other and aminoacids and DNA. Also nitrogen atoms could form similar flux tube connections. Same would apply to sulphur appearing in met and tyr and to electronegative atoms in general.

2. The guess that the presence of the flux tube would be a necessary prerequisite for the hydrogen bond formation is wrong. Hydrogen bonds are formed between polar groups of hydrophilic aminoacids so that this rule does not seem to hold true. Quite generally, biologically important ions are assumed to reside as dark variants at magnetic flux tubes in the model for EEG and nerve pulse. The di-sulphur associated with cys-cys pairs play a fundamental role in protein folding. This bond is not allowed by the generalized base pairing rule which suggest that only the hydrogen bond formation which can be assigned with flux tube contacts.

3. Hydrophobic aminoacids could connect with the oxygen in water by flux tubes but they could not form hydrogen bonds. The phase transition increasing hbar would allow them to increase their distance from water molecules in a controlled manner. This would be essential for folding and make possible the formation of pockets connected by flux tubes of large hbar to water. In quantum models for evolution of consciousness these pockets are believed to play a prominent role.

3. What can one learn from the formation of alpha helices and beta sheets?

The formation of peptide bonds by the elimination of H₂O= molecules and generation of hydrogen bonds between NH and O= is an essential step in the formation of alpha helices and beta sheets. Second observation is that aminoacids decompose naturally into three parts corresponding to O=COH, R, and NH₂. This suggests that aminoacid actually corresponds to the entire DNA codon XYZ coding for it. OH could correspond to Z , R to Y, and NH₂ to Z. In the formation of peptide bond the flux tube connecting to COH and thus to Z would be taken by the water molecule created in the formation of peptide bond leaving only XY. The first flux tube would connect HN and O= so that X would pair with X_c assignable to O. There are no problems with the formation of bond if O= can correspond to any code letter as in the case of water. Water would correspond to matter antimatter symmetric phase and an interesting question is what counterpart this phase could have in cosmology (bosonic matter?).

The aminoacid inside protein would effectively behave like Y_c in the effective base pairing. Depending on whether it corresponds to quark or antiquark, aminoacid would be hydrophilic or hydrophobic- or rather - able to form hydrogen bonds or not. Since hydrophobic aminoacids cannot form hydrogen bonds, the formation of these residue pairs would be inhibited. The hydrophilic and hydrophobic residues could tend to avoid each other and the phase transitions increasing Planck constant would make this possible. It must be emphasized that this brings in strong long range correlation between the dynamics of the aminoacid residues belonging to the first and third (second and fourth) column of the code table.

Hydrophilic aminoacids would form hydrogen bonds which each other and with DNA and RNA. In catalytic biding sites this kind of hydrogen bonds are formed between polar groups: also hydrogen bonds with water are formed and they tend to neutralize possible static charges. Ser (UCZ) and thr (ACZ) are the only effectively hydrophobic aminoacids containing OH group (and thus strictly speaking amphiphilic). Perhaps it is not an accident thr the codon ACC coding for thr appears in the stem of tRNA containing aminoacid. Ser and thr are indeed able to form hydrogen bonds with hydrophilic aminoacids and the prediction is that these aminoacids have form XGZ belonging to the last column of the code table. There are however very few biochemical reactions of this kind useful for proteins. Ser is exceptional in that it is predicted to be able to form flux tubes connecting ser_1 coded by TCZ with ser₂ coded by AGZ, Z=T,C. The OH group of ser can be seen as a correlate for this property.

The aminoacids at the ends of the polymer behave effectively like dinucleotides. The aminoacid coded by XYZ would base pair like X_cY_c if in the beginning of polymer and to Y_cZ_c if at the end of polymer. These nucleotides should have very special selective role in DNA-aminoacid and RNA-aminoacid interactions. Remarkably, it is known that the cutting of COOH and NH₂ away from the end of polymer in general makes protein folding impossible (also mutations can affect dramatically folding). The first nucleotide of protein is usually met containing sulphur and the conjugation associates met with stop and tyr codons. The association of met with stop is indeed natural for the free NH₂ of met having no hydrogen bond in the beginning of the sequence.

According to Creighton, the binding sites of catalyst and ligand in the reaction complex are conjugates both geometrically and physically. It would be nice to have a concrete representation of this conjugacy in terms of the genetic code. Geometric conjugacy is easy to understand in terms of the lock and key picture but I am not quite sure what physical conjugacy could mean. Standard physics intuition would suggests that hydrophilic aminoacids that behave as acids resp. bases attract each other. This option does not possess any obvious formulation in the proposed picture. Matter antimatter conjugation for the second nucleotide Y of XYZ looks however very natural so that the aminoacids in the first and third (second and fourth) row of the code table would tend to pair with each other. This mechanism might be flexible enough to allow to find a conjugate of a given binding site by trial and error. The interpretation would be that hydrophobia tends to create concave and hydrophily convex structures. The attraction between Y and Y_c in the braided conjugate regions would due to the Coulomb interaction between quark and antiquark at the ends of the wormhole flux tube.

The strong correlation between RNA dinucleotide and aminoacid in the case of tRNA conforms with this picture. The third flux tube associated with the aminoacid could connect with the third codon after the transition to RNA-aminoacid era. During RNA era tRNA₂ would have connected the O=C-OH part of the aminoacid to water molecule.

4. Interactions with DNA

Also in the interactions with DNA and RNA the aminoacid in the interior of the sequence would base-pair" like Y_c. The original idea about molecular sex would transform in the sense that the companion of the hydrophilic aminoacid would DNA nucleotide in general. Hydrophobic aminoacids would behave like hermits. The generic contacts with DNA would be contacts with single nucleotide and there would be 4 different basic contacts. Aminoacids are indeed known to form contacts with single nucleotide. Hydrophilic contacts would be favored and hydrophobic contacts avoided so that again Y=A,G aminoacids would play at the outer boundary of DNA would play the active role. The aminoacids inside a given column of the code table would interact in very much the same manner with DNA nucleotides as far as formation of hydrogen bonds is considered. The terminals of the protein polymer are predicted to behave like X_cY_c resp. Y_cZ_c if the corresponding codon is XYZ. Again only hydrophilic codons are expected to be able to form hydrogen bonds. N-terminal is usually met and met and should avoid DNA.

5. Interactions of proteins with ions and electrons

Proteins interact also with electrons and ions. Typical process are the addition or removal of proton, electron, ion such Ca⁺⁺, or molecule such as O₂. These interactions are not well understood. For instance, the interactions involve the transfer of electrons between ligand protein and protein inducing oxidation (electron is given), reduction (electron is received) or redox reaction (both reduction and oxidation take place). In metabolism redox process is central. These reactions are reversible and it is difficult to understand how electrons are able make their long journey from the interior of the ligand so fast and avoiding dissipative effects. The formation of cyclotron Bose-Einstein condensates and electronic Cooper pair condensates at the magnetic flux tubes connecting ligand and protein could be the solution of the mystery.

6. How DNA nucleotides are connected with the hydrophilic ends of lipids?

The starting point of all these developments was the model for DNA as topological quantum computer (tqc) described in the earlier postings I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII, XIII.

It was assumed that braid strands defined by "wormhole magnetic" flux tubes join nucleotides to lipids and can continue through the nuclear or cell membrane but are split during tqc. The hydrophilic ends of lipids attach to water molecules and self-organization patterns for the water flow in gel phase induce a 2-D flow in the lipid layer which is liquid crystal defining tqc programs at the classical level as braidings. The flow indeed induces braiding if one assumes that during topological computation the connection through the cell membrane is split and reconnected after the halting of tqc.

The challenge is to understand microscopically how the flux tube joins DNA nucleotide to the phospholipid. What is clear that the points at which the flux tubes attach should be completely standard plugs and the mechanism giving rise to polypeptids is an excellent guide line here. Recall that phospholipid, the dancer, has two hydrophobic legs and head. Each leg has at the hydrophilic end O=C-O-C part joining it to glyceride connected to monophosphate group in turn connected to the hydrophilic residue R. The most often appearing residues are serine, inositol, ethanolamine, and choline. Only three of these appear in large quantities and there is asymmetry between cell exterior and interior.

Let us denote by =O₁ and =O₂ the two oxygens in question (analogs of right and left hemispheres!). The proposal is that DNA nucleotide and =O₁ are connected by a flux tube: the asymmetry between right and left lipid legs should determine which of the legs is "left leg" and which O= is the "left brain hemisphere". =O₂, the holistic "right brain hemisphere", connects in turn to the flux tube coming from the other symmetrically situated =O₂ at the outer surface of the second lipid layer. During tqc this flux tube is split or disappears. The lipid residue R couples with the flow of the liquid in gel phase. Since =O is in question the quark or antiquark at the end can correspond to the DNA nucleotide in question. Also the necessary complete correlation between quarks and antiquark charges at the ends of flux tubes associated with =O₁ and =O₂ can be understood as being due to the minimization of Coulomb interaction energy.

The phosphate groups associated with nucleotides of DNA strand contain also =O, which could act as a plug to which the flux tube from the nucleotide is attached. =O appears in biomolecules involved with varying functions such as signalling, control, and metabolism. =O might act as a universal plug to which flux tubes from electronegative atoms of information molecules can attach their flux tubes. This would also provide a concrete realization of the idea that information molecules (neurotransmitters, hormones) are analogous to links in Internet (see this): they would not represent the information but establish a communication channel. The magnetic flux tube associated with the information molecule would connect it to another cell and by the join to =O plug having flux tube to another cell, say to its nucleus, would create a communication or control channel.

To repeat the earlier statement, this proposal for the folding code - or rather, the code of entire biocatalysis - is so beautiful that it deserves to be killed: this should be easy for a professional biochemist. If the hypothesis survives, it would provide a royal road to the understanding of the catalytic bio-chemistry.

For details see the chapter Prebiotic Evolution in Many-Sheeted Space-time of "Genes and Memes".

TGD based model for the evolution of genetic code: III

Ulla Mattfolk sent me again an interesting link, which happened to relate directly to what I have been doing during the last week, that is application of DNA as topological quantum computer hypothesis to the understanding of the evolution of the genetic code. The link was to an article about the idea of protein folding code - something which is expected to exist but is not understood. See also this. I realized that the prebiotic 2-code assigning to RNA dinucleotides aminoacids might define the folding code. This code would specify also what kind of catalytic reactions can occur between proteins and would dictate the catalytic stereo chemistry - or rather its changes - to a high degree.

1. The cautious working hypothesis is that living aminoacids are braided in the sense that from a given aminoacid there emanates two braid strands represented by "wormhole" magnetic flux tubes - let as call them simply threads. The threads are colored in the sense that they carry four different colors so that one has 16 color pairs: the color is specified in terms of quarks and antiquarks in a manner that I have explained earlier. The colors are in one-one correspondence with DNA nucleotides A,T,G,C: this hypothesis has led to a quite variety of predictions already shown to be correct. The colors of aminoacid threads are determined completely by the dinucleotide XY of DNA codon XYZ coding for the aminoacid.

2. In accordance with the explanation of the finding discussed in previous posting, X codes for the precursor of given aminoacid and would begin from the part of aminoacid common to all four aminoacids associated with the same dicodon XY. The thread corresponding to Y would begin from the variable part of these 4 aminoacids.

3. If the aminoacid is coded by more than 4 codons, it can have two different colored thread pairs. Ser, arg, and leu are this kind of aminoacids in case of the nuclear genetic code. One can say that aminoacid "remembers" which was the pair XY for the DNA codon coding it. The two variants of ser will be denoted by ser₁ and ser₂, same for leu and arg.

4. The thread pair can connect aminoacid to another aminoacid, DNA triplet or RNA dinucleotide or perhaps even more general braided biomolecule (say precursor of aminoacid). Given aminoacid is effectively equivalent to the dicodon XY appearing in the codons coding for it and the basic step of the biocatalytic reactions would be analogous to base pairing. Genes would not code only for the aminoacids but also for their stereochemistry. In a well-defined sense aminoacids and DNA and RNA dinucleotides would form a social network in which two members are friends if they correspond to dicodon XY and its conjugate X_c Y_c. One might also speak about molecular sex. The potential companions of the aminoacid associated with dicodon XY would be aminoacids associated with dicodon X_c Y_c. Also these DNA and RNA dicodons would be potential companions of the aminoacid. An open question is whether aminoacid can attach to any dicodon in DNA and RNA sequence or only to the dicodon part XY of codon XYZ: if so also DNA rather than only mRNA and tRNA could contain information about 3-codon decomposition of gene.

5. The phase transitions reducing Planck constant for the magnetic flux tubes defining the threads could bring aminoacid and its conjugate to the vicinity of each other. If the folding involves phase transitions reducing Planck constant, this makes possible to make a list about possible self contacts of protein once one knows the amino-acid sequence. In the case of catalytic reactions involving aminoacids, RNA, and DNA similar list about possible contact points between reactants can be given. That biocatalysis would reduce to symbolic dynamics based on gluing together of pieces of text and cotext would have extremely far reaching implications. For instance, aminoacid sequences attaching to DNA and catalyzing various kinds of processes should obey these rules and aminoacid sequence and its various conjugates could form analogs of DNA double strands.

6. In terms of the code table the rule would be that the companions of a given aminoacid are found by going in the code table two units up or down and two units right or left so that one remains inside the code table (the table representing the proposed folding code is here). A couple of examples about this bio-molecular social network are in order.
   1. The conjugates (companions) of Phe and Leu₁ are Asn and Lys and the conjugates of Leu₂ are Asp and Glu. Arg₁ and Ala conjugates as also Gly and Glu. The conjugates of Thr are Sys and Trp.
   2. The conjugates of Ser₁ are Ser₂ and Arg₂. Ser is its own conjugate and thus a completely exceptional aminoacid.
   3. Ile, met (which serves as starting aminoacid) and thr have the formal aminoacid associated with stop codons as a conjugate. Whether this has some physical meaning remains open.

Consider now objections against the proposal.

1. If the magnetic flux tubes connecting nucleotide and conjugate correlates strongly with base pairing, then also aminoacid sequence and its various conjugates could form analogs of DNA double strands such that the residues of the paired aminoacids are hydrogen bonded. In the case of α helix and β sheet this kind of mechanism is not involved since the hydrogen bonds are associated with the non-varying H₂N-(CH)-COOH part of the paired aminoacids and there are no selection rules telling which residues can be paired. One must carefully distinguish between ordinary chemistry and the dynamical selection rules coming from the proposal. It would be the possible changes of tertiary and quaternary structures of proteins about which the hypothesis can possibly say something.

2. Gly is an aminoacid for which one has R=H. The naive expectation that the magnetic flux tube pair should end up to hydrogen atom looks somewhat strange. The naive expectation that the magnetic flux tube pair should end up to hydrogen atom looks somewhat strange. One cannot avoid the question whether also water could be living in the sense that the hydrogen atoms of water molecules can be connected to biomolecules so that the phase transitions changing Planck constant could be an essential part of hydrophobic and hydrophilic quantum dynamics.

3. The presence of water is a key determinant in protein folding so that if the code is important for the folding, it must relate to the possibility that hydrophobic and hydrophilic interactions induce changes of the Planck constant for magnetic flux tubes. From the table of the side chain properties of aminoacids one finds that aminoacids with Y=A,G are hydrophilic and polar so that hydrophily would correspond to quark matter and hydrophobia for quark antimatter. Quark antimatter would tend to be at protein interior surface and quark matter at protein exterior surface. The same would hold true for protein and its conjugate and the formation of nearby contacts would not be frequent. Lengthening of the magnetic flux tubes and thus an increase rather than reduction of Planck constant would be favored.

There is a proposal that protein folding corresponds to a motion in a fractal spin glass energy landscape in presence of external perturbations due to the presence of water and leading to the bottom of some deep valley (see this). In TGD framework 3-D spin glass landscape is replaced by 4-D one (see this). The vacuum degeneracy of Kähler action implies 4-D spin glass energy landscape in the sense that quantum jump sequences lead to space-time sheets representing asymptotic self organization patterns depending only weakly on the initial conditions (with respect to subjective time measured as quantum jumps). Proteins would be like skilled musicians possessing a repertoire of motor activities represented by deep valleys in 4-D spin glass landscape. This picture generalizes to the functioning of living matter in various scales and the quantum dynamics of brain is a natural application giving also a connection with p-adicity since ultametric topology is naturally associated with the space of valley bottoms. In the case of catalytic reactions a quantum jump changing Planck constant for some magnetic flux tubes connecting some living biomolecules (DNA, RNA, aminoacids, water(?), ...) and changing the lengths of these flux tubes could be the basic mechanism leading from a given valley to a new one and dinucleotide genetic code would code this quantum jumps.

To sum up, this proposal for the folding code - or rather, the code of entire biocatalysis - is so beautiful that it deserves to be killed: this should be easy for a professional biochemist. If the hypothesis survives, it would provide a royal road to the understanding of the catalytic bio-chemistry.

For details see previous posting and the chapter Prebiotic Evolution in Many-Sheeted Space-time of "Genes and Memes".

TGD based model for the evolution of genetic code: II

The net is wonderful. Yesterday evening I decided to search for articles about the possible role of dinucleotides in prebiotic evolution. "Dinucleotide" as a search word gave something about NADH and the only thing I understood that this is not relevant. Then I decided to be very optimistic and use as search words "dinucleotide" "prebiotic" simultaneously. To my surprise I found two gems which guaranteed that I did not sleep too much during the last night!

The first gem did not relate to dinucleotides in a direct manner but I learned that the attempts to synthesize RNA sequences from nucleotides lead to 2',5' form of RNA: recall that the production of 3',5' RNA sequences has not been successful, only single nucleotides have been produced (see the article Experimental Testing of Theories of an Early RNA World by A. D. Ellington). This fits completely with the cautious hypothesis that RNA₁ indeed corresponds to 2',5' form of RNA consisting of A,G,U,I and that ordinary 3',5' RNA, which I call RNA₂, emerged as dinucleotides, which can polymerize to longer sequences and that this process was catalyzed by aminoacids.

Second gem was directly related to dinucleotides, prebiotics, and genetic code. Somewhat disappointingly, I am not the only person who has considered the idea of 2-code. The title of the paper by S.D. Copley. E. Smith and H. J. Morowitz was A mechanism for the association of aminoacids with their codons and the origin of the genetic code. To very briefly summarize the content of the paper (I am of course not chemist and I see the paper from by "biomolecules connected by magnetic flux tubes" perspective so that it is easy to ridicule me).

1. The paper suggests that there was prebiotic code in which 2-codons formed by dinucleotides of RNA define the prebiotic code. The paper starts from facts well-known to biochemists (I wish I were a biochemist, really). The first nucleotide X of the dinucleotide XY assigns to XY one of the four simple precursors of aminoacids. The correspondence is

   C,A,U,G → α-keto glutarate (α-KG), oxaloacetate (OAA), pyruvate, α-keto acid.

   Ketone means a compound with a generic formula R₁-(CO)-R₂, where CO has double valence bond. For α-keto acid R₁ is replaced with O-(CO) group.

   These letter sequences tell to the typical reader probably as little as they tell to me (I am doing the ridicule myself!). If prebiotic code would be like the usual code the code would map 16 dinucleotides to 4 precursors.

2. It is the reaction pathway leading to the aminoacid rather than molecule, which is coded. This is new! We have move to a higher level of abstraction! The empirical observation is that second nucleotide Y of XY correlates very strongly with how hydrophobic the aminoacid is. Y= U corresponds to maximal hydrophobia and its conjugate Y=A to maximal hydrophily. Y= G and C are in between. At deeper level Y together with X determines which reaction pathway way leading from the precursor to the aminoacid is selected.

3. Authors propose that this correspondence means that dinucleotides XY form covalent bonds with precursors and this bonding catalysis the reaction leading to the aminoacid. For obvious reasons I do not have strong opinions about this.

Consider now the interpretation of the results in TGD framework.

The coding of the reaction pathway would be in terms of braid strands. The two ("wormhole") magnetic flux tubes beginning from the X and Y would end up to the precursor. The quark u,d or antiquark u_c, d_c labeling X would tell which precursor the magnetic flux tube ends at. What is the rule involved? What property of nucleotide X and precursor fixes the correspondence characterizing reaction pathway? It certainly seems that the flux tube connects X to a catalytic "hot spot" since X and this hot spot must end up near to each other in the phase transition reducing Planck constant and thus length of the magnetic flux tube. The charges possibly assignable with the hot spots - what ever they are - is a good guess but there is more involved.

It seems that the nucleotides of codon are like 4-digits with first digits having the highest significance. The division of dinucleotide XY to two nucleotides should correspond to a similar division UV of the precursor to two parts. U would change in the reaction in the same manner for all aminoacids resulting from a given precursor but the change should depend on X. One can identify at U as a portion at the right end of the precursor (see the article). The left end of precursor would in turn connect with Y.

1. To get some idea one an start from the formation of flux tubes between DNA nucleotides and their conjugates and hope that something very similar happens as flux tubes are formed between RNA dinucleotides and precursor structures. The electromagnetic charge Q_em(X) of the quark associated with nucleotide X should correlate with some property of the nucleotide, or rather the reaction pathway associated with the formation of the pair formed by nucleotide and its conjugate. Hydrogen bonds obviously characterize this pathway. Quark charge indeed correlates with the number of hydrogen bonds of the base pair: 3Q_em+1= n(bonds). The sign of the quark charge in turn correlates with the direction of the hydrogen bonds.

2. One might hope that also in the recent case the catalysis involves the formation of hydrogen bonds between dinucleotide and precursor structure. Authors suggest covalent bond and the appearance of double bonded oxygens in precursors does not leave much doubts. The reactions could however involve a co-catalyst forming hydrogen bonds with XY and covalent bonds with the precursor. Obviously also the co-catalyst should have UV type structure.

3. One can ask whether the co-catalyst could behave effectively like the conjugate of the RNA dinucleotide for the reaction considered. If so, one could understand the selection of the reaction pathway, and the strategy would be to find simple bio-molecules which behave like RNA dinucleotides in this sense. The strongest and probably unrealistic assumption would be that NH₂-N-O and O-NH-NH₂ portions corresponding to A-T type hydrogen bonds and O-NH and NH₂-N portions correspond to G-C type hydrogen bonds. Needless to say, neither the precursors nor aminoacids have this kind of portions: actually the precursors assigned to U,A,C contain only carbon and double-bonded O.

4. There could be a close connection with hydrogen bonds and magnetic flux tubes defining braid strands. I have already earlier proposed that hydrogen bonds might involve new physics, in particular the fractionization of electron and proton charge. This led to the notion of N-atom with the idea being that the fractionization of em charge leads to the emergence of symbolic dynamics in the sense that molecules forming hydrogen bonds between each other correspond to fractional charges for electron or proton summing up to the standard charge. These conjugate charges would define name and "co-name" and these names would be more important for the dynamics than the details of the ordinary chemistry just as names are for the development (or non-development - as you wish) of theoretical physics;-). Half-hydrogen bond and its conjugate would also bring in "sex" at the molecular level. It remains a future challenge to see whether the notion of N-atom and braid concept can be fused together.

An ideal experimentalist with infinite brilliance and funding resources and enjoying endless trust of decision makers might be interested in carrying out the following experiments.

1. Test whether RNA dinucleotides catalyze the transformation of the precursors (or something more complex behaving like RNA dinucleotide as far hydrogen bonding is involved) to aminoacids. In particular, test whether it is RNA₁ or RNA₂, which catalyzes the transformation of precursors to aminoacids.

2. Suppose that one has a prebiotic soup containing 4 precursors of aminoacids and some concentration of dinucleotides of RNA₁ or RNA₂. Suppose that this indeed leads to the formation of aminoacids. If these aminoacids still possess the braid connections with nucleotides, the aminoacids in turn could catalyze the formation of further dinucleotides as suggested in the previous posting and RNA era could begin. It might be worth of checking also this.

3. If this works then one has only the problem would be the generation of the seed dinucleotides. 2',5' RNA sequences are produced in the primordial situation but the sequences of 3',5' RNA are not in absence of catalyst or template. Primordial evolution should have resolved this problem in some very elegant manner.
   1. It is known that Na-montmorillonate, which is a clay mineral appearing in volcanic ash, catalyses a mixture of both 2'5' and 3'5' RNA dinucleotides, which are also dominantly L-L or D-D (see this). This solution looks fairly reasonable.
   2. The generation of aminoacids from precursors would be most naturally catalyzed by RNA₁ dinucleotides. Is it too much to hope that this process is not catalysis in the precise sense of the word but transforms RNA₁ dinucleotides to RNA₂ dinucleotides?! If so, primordial evolution could be initiated in laboratory! Check also this!
   3. Speaking more seriously, a process transforming RNA₁ to RNA₂ would be enough. 2',5' RNA appears in peach latent mosaic viroid DNA (see this), and there should exist a process transforming 3',5' RNA to 2',5' RNA and vice versa. One might hope that the mechanism is simple enough to be realized primordially.

For details see previous posting and the chapter Prebiotic Evolution in Many-Sheeted Space-time of "Genes and Memes".

TGD based model for the evolution of genetic code: I

The notion of many-sheeted space-time could allow to understand many puzzles related to the pre-biotic evolution (the popular article The Origin of Life on Earth, by Leslie Orgel gives a good overall view about the situation). There are many constraints on the models for pre-biotic evolution. The models have also many difficulties.

In TGD framework the situation looks much better.

1. TGD replaces materialistic view about universe with a continual re-creation in which classical universe in 4-dimensional sense is replaced by a new one in each quantum jump.
2. p-Adic length scale hypothesis allows to formulate the notion of evolution precisely as a generation of increasingly larger space-time sheets characterized by preferred p-adic primes. A second aspect is the emergence of new levels in dark matter hierarchy making possible macroscopic quantum coherence and inducing great leaps in evolution.
3. Also a hierarchy of dark weak bosons and gluons becomes an essential part of the physics of living matter.
4. The notion of field/magnetic body carrying dark matter is a further key element in the model and has become increasingly important during years, and the vision about DNA-cell membrane system as a topological quantum computer utilizing braids defined by magnetic flux tubes connecting nucleotides to lipids meant a breakthrough in the understanding of the real function of DNA in information processing. The magnetic flux tubes connecting biomolecuiles and the phase transitions changing the value of Planck constant associated with them and thus inducing shortening or lengthening of braid strands provide a completely new view about the miracles of bio-catalysis and this hypothesis has begun to show its power.

A good manner to introduce the essentials of the TGD inspired model for the prebiotic evolution is by a sequence of questions and answers.

Q: Is life as we know it result of an accident?

.

A: Quantum TGD predicts a genuine cosmic evolution occurring by quantum jumps for which dynamics is characterized by Negentropy Maximization Principle. The generalization of the notion of space-time implies dark matter hierarchy with levels characterized by arbitrarily large values of Planck constant so that macroscopic quantum coherence is possible even in astrophysical length scales. Even astrophysical systems are analogous to atomic systems which implies a strong standardization of planetary system so that Earth like planets are abundant. There are also other good reasons for why the evolution of life would not have been accident in TGD Universe and life should appear everywhere in TGD Universe.

Q: What were the most primitive living systems?

A: The notion of magnetic body brings to biology several completely new elements. Magnetic flux quanta containing dark charged matter and quantum controlling ordinary matter in plasma phase is perhaps the simplest system which can develop characteristics of a living system. The braiding of magnetic flux tubes makes possible topological quantum computation and a fundamental representation of memories and its presence could be even taken as a definition for what it is to be living. Tqc programs correspond to asymptotic self organization patterns for liquid flows inducing braidings and are non-trivial in presence of external energy feed.

Q: How metabolic machinery emerged?

A: Many-sheeted space-time concept predicts a hierarchy of universal metabolic energy quanta as differences of zero point kinetic energies for space-time sheets characterized by different p-adic length scales. What remains is to understand how chemical energy storage and utilization mechanisms developed.

Q: What is behind biocatalytic machinery?

A: The magnetic flux tubes connecting bio-molecules imply long range correlations between molecules. The reduction of Planck constant for magnetic flux tubes implying their shortening provides a mechanism making possible for bio-molecules to "find" each other in a very selective manner, and explains also why molecules end up to precisely defined conformations necessary for a selective bio-catalysis. This picture leads to amazingly detailed understanding of existing results about emergence of biomolecules in experimental arrangements modelling "primordial soup".

Q: How symbolic dynamics emerged?

A: The notion of N-atom suggested by the fractionization of electron quantum numbers for dark matter hierarchy brings in a candidate for a symbolic dynamics assigning to molecules "names" which need not correlate very strongly with the chemical properties of the molecule but would dictate to a high degree its biochemical behavior. Molecular "sex" emerges in the sense that molecules labeled with "names" and "co-names" tend to pair. The model of DNA as tqc assumes a 4-coloring of braid strands realized by an assignment of DNA nucleotides to quarks and anti-quarks. Also this means symbolic dynamics since only molecules connected by colored braids have high probability to participate in same biochemical reaction and do it in a very specific manner. Since the quarks involved with braid strands can have fractional charges, molecular sex can be realized also in this manner.

Q: What selected the bio-molecules during chemical evolution?

A: The proposed symbolic dynamics based on the notions of colored braids and N-atom poses very strong constraints on the subsets of bio-molecules that can react with considerable rates. The assignment of quark to nucleotides via the correspondence A,T,G,C→ u,u_c,d,d_c allows to basic rules about distribution of nucleotides in DNA and genes (differing from each other) and in mRNA in terms of approximate matter antimatter symmetry, isospin symmetry and the breaking of these symmetries. Matter antimatter asymmetry is visible also in the experiments trying to mimic primordial life.

Q: How biochemical pathways emerged?

A: It is now possible to realize in practice sequences of arbitrarily complex self-catalyzing biochemical reactions utilizing DNA hairpins. The mechanism generalizes to more complex molecules. At a given step of the reaction sequence the structure formed during the previous steps acts as a key fitting to a lock represented by some hairpin in the solution, and opens it to a linear molecule and in this manner makes it a key. The braids between reactants make it possible for the key and lock to find each other.

Q: How genetic code evolved?

A: The following gives a summary about what might have happened.

1. The symmetries of the third codon of the genetic code allow in DNA as tqc model an interpretation as isospin and matter antimatter symmetries for quarks and antiquarks assigned with DNA nucleotides and representing 4-color of braid strands. These symmetries together with the study of the detailed structure of tRNA lead to a model for the evolution of the genetic code as a fusion of a non-deterministic 1-code and one-to-one 2-code corresponding to the conjugation of mRNA molecules.
2. During RNA era two kinds of RNAs, call them RNA₁ and RNA₂, were present and played the roles of mRNA and aminoacid sequences. 2-code resp. 1-code mediated the analog of replication resp. translation using hairpin like molecules tRNA₁ and tRNA₂ to bring in RNA nucleotides and RNA doublets to the growing RNA_i sequence. Amino-acids attached to the stem of tRNA₂ acted as catalysts.
3. The transition to RNA-aminoacid(-sequence) era took place via a fusion of the tRNA₁ and tRNA₂ to the ordinary tRNA and instead of sequences of two kinds of RNAs were replaced by aminoacid sequences were formed. Without primordial RNA variant of ribosomes binding aminoacids together by peptide bonds the transition to RNA-protein dominated era would not have been possible. The active part of recent ribosomes is indeed RNA molecule.
4. After a period of symbiosis involving all these three tRNAs a transition to DNA-RNA-aminoacid world took place as an aminoacid sequence acting like reverse transcriptase emerged.

Q: Did RNA world precede the life as we know it?

A: The model for the evolution of the genetic code forces to conclude that RNA world preceded the recent biology and allows also to deduce that the nucleotides involved with second form of RNA where A,T,U,I(nositol). The exotic RNA in question could have been 2',5' form of RNA rather than 3',5' RNA but this is not the only possibility.

Genetic code was implicitly present already during RNA era in the sense that aminoacids and RNA di-nucleotides were paired by braid strands (given aminoacid was connected to a dinucleotide defining the first two nucleotides of codons coding aminoacid). Hence the strong form of RNA world hypothesis would be wrong: aminoacids would have played a key role although their sequences would have been absent. Some examples are in order.

1. For instance, the aminoacids found from meteorites correspond to four dinucleotides GX, X= A,U,G,C. Second example: it has been possible to synthesize only A and G but not T and C in absence of enzymes. The interpretation is in terms of strong matter antimatter asymmetry at quark level. The proposal is that in the presence of aminoacids braided to dinucleotides it should be possible to produce dinucleotides XY for which some codons XYZ code for the aminoacid.
2. One can also understand the strange finding that it possible to synthesize conjugate polymer from RNA template but the production of conjugate of conjugate is not possible. The braid strands connecting template and its conjugate explain the mysterious finding and the presence of aminoacids could provide a mechanism to overcome the difficulty.
3. Polymers are formed only if the solution contains right handed nucleotides. Also primordial chirality selection could be understood in terms of braids: right handed nucleotides would be connected to left handed aminoacids and vice versa and these phases separate from each other. The difference in energy of these states is large as compared to that predicted by standard model since TGD predicts scaled up variants of weak interactions for which weak bosons are effectively massless in biologically relevant length scales.

Q: Does the notion of protocell make sense?

A: The model of DNA as tqc involves essentially the magnetic flux tubes connecting DNA nucleotides and cell membrane. Since topological quantum computation should have taken place also during the RNA era, some kind of cell membrane consisting of exotic RNA should have been present. It has been found that DNA indeed forms membrane like structures which are liquid crystals consisting of sequences of DNA nucleotides with length up to 20 nucleotides (See this) and same might be true in the case of exotic RNA.

Q: How life could evolve in the harsh primordial environment? Does the notion of primordial ocean make sense?

A: It seems plausible that primordial life came from interstellar space. Evolving life had however to cope with the grave difficulties due to the irradiation by UV light and meteoric bombardment. A simple solution of these problems is to evolve in the interior of Earth, say in underground lakes. This idea conforms nicely with the observation that continents would have formed a single super continent at time of Cambrian explosion provided the radius of Earth at that time was by a factor 1/2 smaller than now. TGD predicts that cosmic evolution does not occur continuously but by quantum jumps in which the Planck constant of appropriate space-time sheet increases. A phase transition of this kind increasing the radius of Earth during a relatively short time interval would have led to a burst of life from underground lakes to the surface of Earth. This would also explain the sudden emergence of a huge variety of highly developed life forms during Cambrian explosion.

The answers to these questions give only a rough view about TGD based model of prebiotic evolution. A detailed picture (still developing) can be found from the completely rewritten chapter Prebiotic Evolution in Many-Sheeted Space-time of the book "Genes and Memes", which I have re-organized completely to better reflect the progress due to the model of DNA as topological quantum computer.

Microwave anomaly observed by WMAP and TGD

Almost every day brings in a new anomaly providing additional support for the TGD based view about Universe. I shouldn't say this but this is getting boring. At this time the anomaly was the microwave interstellar medium emission observed by WMAP used to map the anistropy of cosmic microwave spectrum (see D. P. Finkbeiner (2004), Microwave Interstellar Medium Emission Observed by the Wilkinson Microwave Anisotropy Probe). The anomaly was observed already 2003 but had escaped my attention.

Anomalous lines at frequencies f =23; 33, 41, 61, 94 GHz have been observed. In good approximation they correspond to harmonics of single frequency of f= 10 GHz. For the cyclotron transitions of electron the required magnetic field would be about 0.36 Tesla. The identification would be in terms of cyclotron transitions of dark electrons or of their Cooper pairs residing at magnetic flux tubes of galactic magnetic fields and characterized by so large value of Planck constant that cyclotron energy is above thermal energy. The emitted cyclotron radiation would decay into bunches of ordinary photons with same frequency but much smaller energy.

DNA as topological quantum computer: XIII

In previous postings I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII I have discussed various aspects of the idea that DNA could acts as a topological quantum computer using fundamental braiding operation as a universal 2-gate.

The model of DNA as topological quantum computer was originally motivated by the idea that quantum biology in TGD Universe might teach something about quantum computation like processes possibly taking place in living matter. It turned out that the model of DNA as topological quantum computer began to give lessons about quantum biology. In particular, one must assign 4-color to braid strands represented as flux tubes connecting DNA nucleotides A,T,C,G to lipids of nuclear or cellular membranes. In TGD Universe this color is naturally represented in terms 2 quarks u,d and their antiquarks (scaled up variants of ordinary quarks with large hbar and residing at flux tubes of "wormhole" magnetic fields defining the braid strands).

This sounds definitely something very weird for anyone still inhabiting the simple standard model universe and not gone through 28 year lasting process of discovery starting from the basic idea of TGD and ending up with the recent highly refined picture about how TGD Universe differs from that of standard model. Recall however that the discovery of Barbara Shipman that the patterns of honeybee dance can be understood in terms of the mathematics of color group SU(3) of strong interactions, led her to suggest that quarks are directly involved with cognition and memory. This makes sense since DNA as tqc using 4-colored braids is expected to be closely involved with cognition and memory.

The model led to the prediction that coding regions of DNA might be characterized by a breaking various symmetries at quark level, that is breaking of matter antimatter symmetry, isospin asymmetry, and asymmetry between uu_c and dd_c type matters (c refers to charge conjugation taking matter into antimatter) could take place at level of coding sequences. Three parameters should characterize this breaking.

I made some sample calculations and found support for the breaking of matter antimatter and symmetry and the generation of anomalous em charge implied by this. Yesterday I learned (thanks go to Dale Trenary for crucial references) that simple basic facts about DNA which can be found from Wikipedia support the proposed vision about symmetry breaking although details were not quite correct.

1. Chargaff's rules, which I already knew, imply an approximate but not complete matter antimatter symmetry at the level of the entire genome and one can find nice examples about the small breaking. Depending on the explicit corresponds of A,T,C,G with quarks. The breaking of matter antimatter symmetry is quite generally below per cent. The anomalous em charge per nucleon, which depends on scenario (2 options and their charge conjugates) is typically below .1 units per nucleotide. The following table gives representative examples about values of various parameters (anomalous em charge per nucleotide for two options, isospin per nucleotide, quark number per nucleotide, G+C/A+T ratio).

2. The deviation of C+G/A+T from unity used to classify genomes characterizes the asymmetry between uu_c and dd_c type matters. C+G/A+T increases as the length of coding sequence increases.

3. Szybalski's rules state that matter antimatter symmetry and isospin symmetry are broken for coding regions of DNA. The breaking pattern is however more intricate than I had expected. The coding part of the DNA decomposes in fifty-fifty manner into regions in which either matter or antimatter dominates and the directions of transcription and selection of template DNA are different for these regions so that mRNA breaks matter antimatter symmetry and always in the same manner. By the way, I had always thought that the template DNA is always the same. The structural matter antimatter asymmetry of mRNA is obviously translated to a functional asymmetry of DNA. A possible reason is that otherwise DNA would not be stable since it would generate too high anomalous em charge. One can wonder whether the matter antimatter asymmetry for mRNA is compensated by the opposite asymmetry for some other type of RNA inside cell nucleus.

It thus seems that DNA as tqc and the coding of braid color by quarks allows to understand the poorly understood empirical rules about the distribution of codons in DNA. Many fascinating questions and working hypothesis can be considered besides those proposed already earlier.

For details see the chapter DNA as Topological Quantum Computer of "Genes and Memes". See also the brief article here.

Superstrings: a collective cognitive and mood disorder or just one job among others?

Before starting I want to emphasize that I have nothing against strings nor string theorists. Superconformal symmetries are extremely profound discovery and super-conformal symmetries - albeit generalized ones - are symmetries of also TGD Universe. TGD Universe is also filled by string like objects but with a concrete connection to the existing physics unlike superstrings. The fact however is that superstring models have failed as a physical theory since something very very essential - about which I have tried to tell in this blog - has been lacking. Despite this the hegemony is in full power still today. Why this continues to be the case has baffled me often and stimulated my non-professional attempts to understand superstring hegemony as a social phenomenon with no intent to insult any individual who happens to be part of this community.

When super string models became the only game in the town, I painfully experienced what it is me who seems to be the only person in his right mind in the town. When collective madness prevails, it is healthy persons which are taken to the mental asylum as we know from history, and also I was thrown outside the academic community. Of course, not all people working with string models are possessed by a collective mania or suffer from the aggressive non-communicative mood often assigned to people that many of us call crackpots. For many people involved, super strings are just a job and they do their best to keep their jobs. Unfortunately, this pragmatic attitude has contributed to the continuation of the collective mood disorder so that super string models have become a deep professional tragedy for very many who have devoted their best years for them. For a physicist looking this collective cognitive disorder as an outsider, the situation has been a continual cause of frustration since it is clear that a collective belief in a claim like "Our theory cannot predict anything but because it is the only possible theory, we must just accept this" will destroy theoretical physics as science. There are indeed good reasons to cross the fingers and hope that the superstring era of physics will be over some day and transforms to a fascinating research topic for sociologists, psychologists and many others interested in collective cognitive and mood disorders.

What it is to be a crackpot?

Superstring hegemony has more than often labeled its critics as crackpots with inferior intelligence. I have personally tried to avoid the use of this term - perhaps for the simple reason that it has been applied systematically to me and I know how insulting this characterization is. With the experienced pains in good memory, I start by asking what are the reasons why person is experienced as a crackpot.

Probably every scientists has met someone whom he would call a crackpot, with good or not so good justifications. Consider first the manner how this kind of person tries to communicate his idea. In old days, when I had a job in university, I sometimes met a person in a kind of manic, almost aggressive mood, and telling about his great idea to everyone. I have also received year after year in mail the same pile of pages with nothing new added. I am also familiar with not so friendly emails: the person might start by stating "your theory is false" but without any justifications, and continue by telling that because you are incompetent in this and this manner, you should stop working with your theory about which you have written eight books. He could also continue with a long list of great scientists whom he has proven to be totally wrong. After all this he regards it as obvious that you will start to read the attached file and make comments about it.

Usually this kind of theory contains some horrible elementary blunder already at the first page. You can try communicate this state of affairs in a polite tone or at least tell that this point I fail to understand, perhaps you should try to make this point clearer. Typically this kind of theory also fails to explain or predict anything. You could also try to suggest that he should perhaps use some time to learn certain basic facts about physics and mathematics in order to get additional perspective. All this is useless, your friend is unable to listen, and approaches with his pile of material some other target.

When crackpot label is used for political purposes and it certainly is (quite routinely by some bloggers of super string Empire), it only means that person has "wrong" idea, he does not believe in string theory for instance. To be wrong is not of course to be a crackpot in any reasonable sense. Trial and error is the most important and effective method of science and perhaps the most important teaching of this method is the realization how easy it is to be wrong: bold "is" transforms to a cautious "might be" and the list of pros becomes accompanied by a list of cons.

If there is something special in the brain circuits of a scientists able to make discoveries, it is the ability to invent objections against their own ideas, and give up the dead idea and rapidly re-organize to create a new one. I cannot avoid the temptation to draw a parallel with a creative jazz musician or with classical composers who were able to produce new highly original compositions one after another and sometimes even transcend the style of their own time. There is nothing wrong in being wrong but the situation changes if person repeats fanatically decade after decade same claims without any progress and without taking any notice of objections.

Can community behave like a crackpot?

One could probably add more items to the list above but it already makes possible the attempt to define what the notion of crackpot like state of mind could mean at collective level. Here super string hegemony comes unavoidably in mind as a school example (with no personal insults intended: the neurons of a person suffering mania are just ordinary friendly neurons trying to receive rewarding and avoid punishing transmitters). The 20 first years of superstring model was very much like a period of collective mania accompanied by euphoria, hallucinations mixed with the perceived reality, and reckless and megalomanic behaviors. Mania reached its peak when the archive was filled with e-prints about dualities and we were told that even mathematics itself reduces to M-theory.

Then came the response of string model skeptics and suddenly the euphoria was over. No new fantastic discoveries anymore. A painful journey towars Monday morning had begun. Physics ceased to be just trivial low energy phenomenology and not so rewarding attempts to build what is called super string phenomenology have begun. It is easy to sense that the mood has been rather depressive for several years. Even string bloggers can only rarely drive themselves to praise or even discuss the string e-prints of hep-th. There are of course still talk about the inability to predict anything as the greatest breakthrough in natural sciences since Newton but even these prophets seem to have difficulties in reaching the trance. Also the extremely aggressive tone of the hegemony against critics became familiar during the first years and the bloggers defending M-theory were ready to make even the rudest personal insults. Perhaps it is needless to mention that most of these behaviors are assigned also to those whom many of us call maniacs or crackpots.

The inability and unwillingness of the superstring hegemony to accept critics and communicate with people thinking differently brings also in mind the behaviors described above. When I was young, dissidents were allowed to speak during the last day of physics conferences. They could tell about their pet theories and most importantly, inform about the anomalies of existing theory. Dissidents have indeed very keen eye for anomalies and this is why science community needs them. Even people working in loop quantum gravity have failed to receive invitations to superstring conferences despite that there are quite many of them. I am afraid that the situation is same in all physics conferences nowadays which very effectively supports the often expressed belief that the only problem of standard model is that it has no problems. I am not the only one who has tried to patiently communicate to colleagues about the rich spectrum of anomalies in various branches of physics but found this useless. A further problem is that the people who might have been able to understand my own theory are just superstring theorists. Unfortunately, people like me simply have not simply existed for super string hegemony just like the person politely suggesting that the theory of crackpot might be wrong ceases to exist for a crackpot.

From the crackpot who has chosen you to receive his message, you get year after year the same thick pile of pages with nothing new added. As far as physics is considered, the same pattern repeats itself in the case of superstring models. The tragic blunder in this case case was the completely ad hoc introduction of the notion of spontaneous compactification inspired by the need to build a contact with physics and get also general relativity from the theory. This led to the landscape problem. As Peter Woit observed, also this blunder appeared already at the first page so to say: the problem was pointed out already 1986 by Ströminger, only two years after the first superstring revolution. Nothing new from the point of physics has emerged after that but the hegemony continues to tell that things are better than ever. Obvious failures of internal coherence are also a characteristic for the crackpot theories. In superstring models the division into believers on single unique vacuum emerging magically from nowhere and to those who see the inability of the theory to predict nothing as its greatest victory since Newton represents similar deep internal incoherence.

Madness and genius

It is often said that madness and genius are very near to each other. I believe that this is true. To be creative is to be maximally sensitive and able to change and thus near quantum critical point. I do not claim of being genius but I know that when I am working hardly and ideas flow, I am near the critical point of the cusp catastrophe having mania and depression at its two stable sheets. The ability to develop strong enough reflective level of consciousness telling when things are going too fast is what saves from the catastrophe. In the case of super string community this reflective level would be the dissidents which are not invited to super string conferences and are not allowed to publish in arXiv.org or in journals.

String model as a job among jobs

It would very naive to believe that all people working with string models are in the same mood as the crusaders. Even in crusades there must have been many people who did just business since also crusaders had to eat something and sleep somewhere. I cannot believe that people suggesting that LHC might produce time machines are really serious: more probably they have realized that they get their name and ideas into publicity since this can be marketed as a prediction of super string theory so that New Scientist catches it immediately. For these practical people superstrings are not the final truth, but a job with high status which they are paid for. As long as funding continues all is well. As pragmatic individuals they also know that they must do their best that the funding indeed continues since decade or two as super string theorist means that they are not able to jump to the next fashion. If super string theory is to retain its status as the only known theory of quantum gravity, someone must take care that no-one indeed knows about the competitors. This is achieved by preventing the publication of both alternative ideas and more mature works, both in electronic archives and in so called respected journals. Personally I gave up attempts to publish for more than decade ago.

The second important aspect of being a pragmatic string theorist relates to anomalies. Scientific dissidents do not allow us the luxury of forgetting that our theories are full of anomalies. This is good. Every theoretician having a working theory and with some bits of imagination starts to work like a mad if he learns about an anomaly about which he might be able to say something interesting. Provided that he has the working theory! If not, then it is only human to adopt the attitude of an older statesman, perhaps of an earlier young rebel who has matured during years to realize that the existing theory is probably correct and anomaly a fake. In a fatherly mood this older statesman allows to understand that those trying to and perhaps even able to explain anomalies are lighthearted, ignorant, and - you said it - crackpots.

In the case of super string models the role of an older statesman requires among other things that you become a defender of general theory of relativity as the final description of gravitation in planetary length scales since this is what the arguments about long length scale limit of super string theory predict. For instance, a non-relativistic anomaly in planetary gravitation would be something very non-welcome since it could mean the end of "superstrings as the only known theory of quantum gravity" mantra if the competing theory manages to explain this kind of anomaly. Even worse, it might mean end of also superstring theory itself.

This kind of anomalies have indeed been discovered by NASA and known as Pioneer anomaly and Flyby anomaly. Super string hegemony has not expressed much enthusiasm in the possibility that super string theory could be finally demonstrated to be wrong. I have proposed TGD based explanation for both of these anomalies and discussed a detailed model reproducing the empirical formula for Flyby anomaly in the previous posting. This is a definite victory of TGD but I am afraid that it is not possible to publish this. On basis of the past experience I can guess the justifications of the referees for rejection: "too speculative", "no other researcher refers to TGD", and so on.

I hope that this analysis has made it clear why I feel so important that the superstring era in physics would come to an end. Unfortunately, the entire community cannot go to a therapist and take its medications every morning so that the situation probably will prevail for many years to come.

Dark matter based model of Flyby anomaly

The so called flyby anomaly provides a test for any theory of gravitation, quantal or not. I have already earlier discussed a model of this anomaly based on dark matter located either at spherical shell or tube around Earth's orbit. The recent data (see this and this ) allowed to fix the model to a tube around the orbit of Earth deformed by gravimagnetic force of Earth to the direction of equatorial plane of Earth.

1. Flyby anomaly

Fly-by mechanism used to accelerate space-crafts is a genuine three body effect involving Sun, planet, and the space-craft. Planets are rotating around sun in an anticlockwise manner and when the space-craft arrives from the right hand side, it is attracted by a planet and is deflected in an anticlockwise manner and planet gains energy as measured with respect to solar center of mass system. The energy originates from the rotational motion of the planet. If the space-craft arrives from the left, it loses energy. What happens is analyzed the above linked article using an approximately conserved quantity known as Jacobi's integral

J= e- ω e_z · r× v.

Here e is total energy per mass for the space-craft, ω is the angular velocity of the planet, e_z is a unit vector normal to the planet's rotational plane, and various quantities are with respect to solar cm system.

This as such is not anomalous and flyby effect is used to accelerate space-crafts. For instance, Pioneer 11 was accelerated in the gravitational field of Jupiter to a more energetic elliptic orbit directed to Saturn ad the encounter with Saturn led to a hyperbolic orbit leading out from solar system.

Consider now the anomaly. The energy of the space-craft in planet-space-craft cm system is predicted to be conserved in the encounter. Intuitively this seems obvious since the time and length scales of the collision are so short as compared to those associated with the interaction with Sun that the gravitational field of Sun does not vary appreciably in the collision region. Surprisingly, it turned out that this conservation law does not hold true in Earth flybys. Furthermore, irrespective of whether the total energy with respect to solar cm system increases or decreases, the energy in cm system increases during flyby in the cases considered.

Five Earth flybys have been studied: Galileo-I, NEAR, Rosetta, Cassina, and Messenger and the article of Anderson and collaborators gives a nice quantitative summary of the findings and of the basic theoretical notions. Among other things the tables of the article give the deviation δe_g,S of the energy gain per mass in the solar cm system from the predicted gain. The anomalous energy gain in rest Earth cm system is δe_E≈ v·δv and allows to deduce the change in velocity. The general order of magnitude is δv/v≈ 10^-6 for Galileo-I, NEAR and Rosetta but consistent with zero for Cassini and Messenger. For instance, for Galileo I one has v_inf,S= 8.949 km/s and δv _inf,S= 3.92+/- .08 mm/s in solar cm system.

Many explanations for the effect can be imagined but dark matter is the most obvious candidate in TGD framework. The model for the Bohr quantization of planetary orbits assumes that planets are concentrations of the visible matter around dark matter structures. These structures could be tubular structures around the orbit or a nearly spherical shell containing the orbit. The contribution of the dark matter to the gravitational potential increases the effective solar mass M_eff,S. This of course cannot explain the acceleration anomaly which has constant value. One can also consider dark matter rings associated with planets and perhaps even Moon's orbit is an obvious candidate now. It turns out that the tube associated with Earth's orbit and deformed by Earth's presence to equatorial plane of Earth explains qualitatively the known facts.

2. Dark matter at the orbit of Earth?

The almost working model is based on dark matter on the orbit of Earth. One can estimate the change of the kinetic energy in the following manner.

1. Assume that the the orbit is not modified at all in the lowest order approximation and estimate the kinetic energy gained as the work done by the force caused by the dark matter on the space-craft.

   ΔE/m= -Gdρ_dark/dl × ∫_γEdl _E∫_γS dr_S• r_SE /r_SE³ ,

   r_SE== r_S-r_E .

   Here γ_S denotes the portion of the orbit of space-craft during which the effect is noticeable and γ_E denotes the orbit of Earth.

   This expression can be simplified by performing the integration with respect to r_S so that one obtains the difference of gravitational potential created by the dark matter tube at the initial and final points of the portion of γ_S: ΔE/m= V(r_S,f)-V(r_S,i),

   V(r_S)=-G×(dρ_dark/dl)×∫_γEdl _E /r_SE

2. Use the standard approximation (briefly described in (see this)) in which the orbit of the spacecraft consists of three parts joined continuously together: the initial Kepler orbit around Sun, the piece of orbit which can be approximate with a hyperbolic orbit around Earth, and the final Kepler orbit around Sun. The piece of the hyperbolic orbit can be chosen to belong inside the so called sphere of influence, whose radius r is given in terms of the distance R of planet from Sun by the Roche limit r/R= (3m/M_Sun)^2/5. γ_S could be in the first approximation taken to correspond to this portion of the orbit of spacecraft.

3. The explicit expression for the hyperbolic orbit can be obtained by using the conservation of energy and angular momentum and reads as

   u=r_s/r= 2GM/r= (u₀²/2v₀²)×(1+X^1/2],

   X=1+4u ₀²×v_∞²v₀²/sin²(φ),

   u₀== r_s/a , |v×r|== vr ×sin(φ) .

   The unit c=1 is used to simplify the formulas. r_s denotes Schwartschild radius and v_∞ the asymptotic velocity. v₀ and a are the velocity and distance at closest approach and the conserved angular momentum is given by L/m= v₀ a. In the situation considered value of r_S is around 1 cm, the value of a around 10⁷ m and the value of v_∞ of order 10 km/s so that the approximation

   u ≈ u₀× (v_∞/v₀)×sin(φ)

   is good even at the distance of closest approach. Recall that the parameters characterizing the orbit are the distance a of the closest approach, impact parameter b, and the angle 2θ characterizing the angle between the two straight lines forming the asymptotes of the hyperbolic orbit in the orbital plane P_E.

Consider first some conclusions that one can make from this model.

1. Simple geometric considerations demonstrate that the acceleration in the region between Earth's orbit and the part of orbit of spacecraft for which the distance from Sun is larger than that of Earth is towards Sun. Hence the distance of the spacecraft from Earth tends to decrease and the kinetic energy increases. In fact, one could also choose the portion of γ_S to be this portion of the spacecraft's orbit.

2. ΔE depends on the relative orientation of the normal n_S of the the orbital plane P_E of spacecraft with respect to normal n_O the orbital plane P_O of Earth. The orientation can be characterized by two angles. The first angle could be the direction angle Θ of the position vector of the nearest point of spacecraft's orbit with respect to cm system. Second angle, call it Φ, could characterize the rotation of the orbital plane of space-craft from the standard orientation in which orbital plane and space-craft's plane are orthogonal. Besides this ΔE depends on the dynamical parameters of the hyperbolic orbit of space-craft given by the conserved energy E_tot =E_∞ and angular momentum or equivalently by the asymptotic velocity v _∞ and impact parameter b.

3. Since the potential associated with the closed loop defined by Earth's orbit is expected to resemble locally that of a straight string one expects that the potential varies slowly as a function of r_S and that ΔE depends weakly on the parameters of the orbit.

The most recent report (see this ) provides additional information about the situation.

1. ΔE is reported to be proportional to the total orbital energy E_∞ /m of the space-craft. Naively one would expect (E_∞/m)^1/2 behavior coming from the proportionality ΔE to 1/r. Actually a slower logarithmic behavior is expected since a potential of a linear structure is in question.

2. ΔE depends on the initial and final angles θ_i and θ _f between the velocity v of the space-craft with respect to the normal n_E of the equatorial plane P_E or Earth and the authors are able to give an empirical formula for the energy increment. The angle between P_E and P _O is 23.4 degrees. One might hope that the formula could be written also in terms of the angle between v and the normal n_O of the orbital plane. For θ_i ≈ θ_f the effect is known to be very small. A particular example corresponds to a situation in which one has θ_i=32 degrees and θ_f =31 degrees. Obviously the P_O≈ P_E approximation cannot hold true. Needless to say, also the model based on spherical shell of dark matter fails.

3. Is the tube containing the dark matter deformed locally into the equatorial plane?

The previous model works qualitatively if the interaction of Earth and flux tube around Earth's orbit containing the dark matter modifies the shape of the tube locally so that the portion of the tube contributing to the anomaly lies in a good approximation in P_E rather than P _O. In this case the minimum value of the distance r_ES between γ _E and γ_S is maximal for the symmetric situation with θ_i =θ_f and the effect is minimal. In an asymmetric situation the minimum value of r_ES decreases and the size of the effect increases. Hence the model works at least qualitatively of the motion of Earth induces a moving deformation of the dark matter tube to P_E. With this assumption one can write ΔE in a physically rather transparent form showing that it is consistent with the basic empirical findings.

1. By using linear superposition one can write the potential as sum of a potential associated with a tube associated with Earths orbit plus the potential associated with the deformed part minus the potential associated with corresponding non-deformed portion of Earth's orbit:

   ΔE/m= V(r_S,f)-V(r_S,i) ,

   V(r_S)=-G×(dρ_dark/dl)Z(r_S) ,

   Z(r_S)= X(γ_orb;r_S)+ X(γ_d;r_S) -X(γ_nd;r_S) ,

   X(γ_i;r_S) = ∫_γidl/r_Si.

   Here the subscripts "orb", "d" and "nd" refer to the entire orbit of Earth, to its deformed part, and corresponding non-deformed part. The entire orbit is analogous to a potential of straight string and is expected to give a slowly varying term which is however non-vanishing in the asymmetric situation. The difference of deformed and non-deformed parts gives at large distances dipole type potential behaving like 1/r² and thus being proportional to v _∞² by the above expression for the u=r_s/r. The fact that ΔE is proportional to v_∞² suggests that dipole approximation is good.

2. One can therefore parameterize ΔE as

   ΔE/m= V(r_S,f)-V(r_S,i) ,

   V(r_S)=-G×(dρ _dark/dl)×Z ,

   Z(r_S)= X(γ_orb;r_S)+ d×cos(Θ)/r_S ²,

   where Θ is the angle between r and the dipole d, which now has dimension of length. The direction of the dipole is in the first approximation in the equatorial plane and and directed orthogonal to the Earth's orbit.

Consider now the properties of ΔE.

1. In a situation symmetric with respect to the equator E_d vanishes but E_nd is non-vanishing which gives as a result potential difference associated with entire Earth's orbit minus the part of orbit contributing to the effect so that the result is by the definition of the approximation very small.

2. As already noticed, dipole field like behavior that the large contribution to the potential is proportional to the conserved total energy v₀²/2 at the limit of large kinetic energy.

3. From the fact that potential difference is in question it follows that the expression for the energy gain is the difference of parameters characterizing the initial and final situations. This conforms qualitatively with the observation that this kind of difference indeed appears in the empirical fit. 1/r²-factor is also proportional to sin²(φ) which by the symmetry of the situation is expected to be same for initial and final situation. Furthermore, ΔE is proportional to the difference of the parameter cos(Θ_f)-cos(Θ_i) and this should correspond to the reported behavior. Note that the result vanishes for the symmetric situation in accordance with the empirical findings.

To sum up, it seems that the qualitative properties of ΔE are indeed consistent with the empirical findings. The detailed fit of the formula of the recent paper should allow to fix the shape of the deformed part of the orbit.

4. What induces the deformation?

Authors suggest that the Earth's rotation is somehow involved with the effect. The first thing to notice is that the gravimagnetic field of Earth, call it B_E, predicted by General Relativity is quite too weak to explain the effect as a gravimagnetic force on spacecraft and fails also to explain the fact that energy increases always. Gravito-Lorentz force does not do any work so that the total energy is conserved and ΔE=-ΔV=-grad V.•Δ r holds true, where Δr is the deflection caused by the gravimagnetic field on the orbit during flyby. Since Δr is linear in v, ΔE changes sign as the velocity of space-craft changes sign so that this option fails in several manners.

Gravimagnetic force of Earth could be however involved but in a different manner.

1. The gravimagnetic force between Earth and flux tube containing the dark matter could explain this deformation as a kind of frame drag effect: dark matter would tend to follow the spinning of Earth. If the dark matter inside the tube is at rest in the rest frame of Sun (this is not a necessary assumption), it moves with respect to Earth with a velocity v=-v_E , where v_E is the orbital velocity of Earth. If the tube is thin, the gravito-Lorentz force experienced by dark matter equals in the first approximation to F=-v_E × B_E with B_E evaluated at the axis of the tube. TGD based model for B_E (see this) does not allow B_E to be a dipole field. B_E has only the component B^θ and the magnitude of this component relates by a factor 1/sin(θ) to the corresponding component of the dipole field and becomes therefore very strong as one approaches poles. The consistency with the existing experimental data requires that B_E at equator is very nearly equal to the strength of the dipole field. The magnitude of B_E and thus of F is minimal when the deformation of the tube is in P_E, and the deformation occurs very naturally into P _E since the non-gravitational forces associated with the dark matter tube must compensate a minimal gravitational force in dynamical equilibrium.

2. B^θ_E at equator is in the direction of the spin velocity ω of the Earth. The direction of v_E varies. It is convenient to consider the situation in the rest system of Sun using Cartesian coordinates for which the orbital plane of Earth corresponds to (x,y) plane with x- and y-axis in the direction of semi-minor and semi-major axes of the Earth's orbit. The corresponding spherical coordinates are defined in an obvious manner. v_E is parallel to the tangent vector e_φ(t)=-sin (Ωt) e_x+ cos(Ωt)e_y of the Earth's orbit. The direction of B _E at equator is parallel to ω and can be parameterized as e_ω= cos(θ) e_z+ sin(θ)(cos(α) e_x+sin(α)e_y). F is parallel to the vector -cos(θ) e_ρ(t) + sin(θ)cos(Ωt-α)e_z, where e_ρ(t) is the unit vector directed from Sun to Earth. The dominant component is directed to Sun.

Happy note added: The price of articles of PRL are really dirty, 25 dollars per article. Hence I decided to take the risk and put the prediction on blog without knowing whether it is quantitatively correct. Today I got the article in email. The prediction for the increment of kinetic energy was correct! Champagne for that! Flyby will be for the TGD based view about dark matter what the shift of perihelion of Mercury was for General Relativity! Let us now cross our fingers and hope that it would not take too many decades for this message to diffuse through the cognitive immune system of the super string hegemony.

For TGD based view about astrophysics see the chapter TGD and Astrophysics of "Physics in Many-Sheeted Space-Time".