About mRNA folding, quenching, blackhole-like objects and universal genetic code

mRNA is single stranded but can fold back to itself and involves secondary structure related to base pairing and also 3-dimensional tertiary structures. Folding depends on mRNA sequence. mRNA sequence is charged since there is negative charge per every nucleotide. This causes self-repulsion. Local charge neutralization by ions can affect and control the folding. Also the interactions of mRNA with water are involved. This brings in the dependence on temperature and pH.

1. The  folded RNA strand should minimize energy. In the more general case (temperature above T=0 K) free energy F is minimized  instead of energy. F=E-TS  includes energy E as well as  -TS term from entropy. Energy minimization and entropy maximization compete.
2. In the models considered it is assumed that, as a good approximation, free energy is quadratic in observables, which include the orientation angles of the segments formed by two nucleotides in the mRNA chain.    The total energy contains the sum of energies that depend on the orientation angles between the nucleotide and its successor and predecessor. A further simplification is  to limit the strand to a plane.
3. What makes the situation non-trivial is that there can be segments in the mRNA strand that are  conjugates of mirror images of each other. Conjugation means the replacement  A↔U, C↔G. These segments tend to undergo base-pairing just like in the DNA double helix. This reduces the total energy and has a stabilizing effect. The first task is to identify such segment pairs and to process all possible configurations involving them to find the energetically most promising configuration and minimize the energy of the remaining part of the strand.
4. The   model considered is as simple as possible and quadratic in the observables, which include the orientation angles between the two nucleotides. One can of course ask whether codons can be treated as linear units of three nucleotides, i.e. codons would not bend.
5. The first step is to consider only planar configurations. The natural assumption is that the mRNA chain has no self intersections. In a plane, this assumption is very strong. One can also consider configurations which define closed 2-surfaces such as Platonic solids. Maximal symmetry is highly suggestive and an interesting possibility is provided by Hamiltonian cycles or paths at the sphere, which go through every vertex without intersections. Also torus topology allowing lattice-like structure is interesting and one can consider even knotted tori for both DNA, RNA and proteins.
6. In the 3-D case, one can imagine that the paired segments can even have portions, which are double helices like DNA (and also RNA). Protein folding gives some  hint of what might happen. Protein involves 3-D helical structures (1-D aperiodic lattices deformed to a helical shape, two-dimensional planar lattice-like pieces in which the protein travels back and forth in a single direction, plus random sequences. The inactive state of protein is essentially 3-dimensional cluster-like configuration. Parameters like temperature and pH determine which kind of structures appear.

Although the model is in principle rather simple and computable, the actual calculation is difficult. Part of the reason is the large number of codons and the base-pairing. The situation is the same for proteins.

Quantum computing raises the hope that folding could be predicted even when the number of mRNA codons is large.

Quenching is the method used in the work that we discussed.

1. The basic observation is that the energy landscape of the system can be assumed to be fractal. There are potential wells inside potential wells. Spin glass is the standard term used for these kinds of systems.
2. The straightforward energy minimization by moving in the direction in which the energy decreases maximally leads to a lower well, which is hardly an absolute minimum. It is necessary to get out of it and therefore thermal energy must be fed into the system by using a suitable perturbation. After this one can try again. In this way, by gradually reducing the heating energy, it is hoped to end up to an absolute minimum.
3. The hardening of a scythe (I am a farmer's son) is a concrete example and is called quenching. First the scythe is forged and then cooled in a water tank. Then it is heated again and the same step is repeated. The amount of heating is reduced gradually. Finally, the energy minimum is obtained, which means the scythe is very hard.

The mRNA folding problem has a very general counterpart in TGD (see this and this).

1. Now the folding and tangling occurs for monopole flux tubes (see this, this and this), and the many-sheeted space-time makes cross-bonds between flux tubes portions as analogs of base pairing possible. Also now modelling as a spin glass is natural and in ZEO one can ask whether classical action rather than energy is a more natural quantity to be minimized.
2. The slight failure of determinism in holography= holomorphy vision (see this, this, this and this) implies that spin glass property is extended to time direction in a discrete way. If the classical action becomes Kähler action, the non-determinism is huge.
3. The scale of the flux tube tangles varies from the elementary particle level (see this and this), through nuclear physics (see this), molecular physics, and biology (see this, this, this, this) to astrophysics and cosmology (see this).

1. For the TGD equivalent of a black hole, the flux tube tangle fills the entire volume (see this). The quantized thickness of the flux tube is the basic parameter labelling an entire hierarchy of blackhole-like objects. Even the solar core could be a blackhole-like object in this generalized sense. For the TGD counterpart of the ordinary black hole, the thickness would correspond to the Compton wavelength of a nucleon.
2. What is important is that a 3-D lattice structure can be attached to the system, each point of which corresponds to one neutron in the flux tube. If the flux tube cannot intersect itself, then it corresponds to a Hamiltonian path and to a Hamiltonian cycle when the path is closed. This means a huge reduction in the number of degrees of freedom but could be favored by energy minimization.
3. The first task is to determine all Hamiltonian paths/cycles. This is a purely geometric, well-known mathematical problem. One can find the cycle which minimizes the energy or free energy. The separation of energetics/thermodynamics from the geometry simplifies the situation dramatically.

From black holes to mRNA and universal genetic code

Hamiltonian paths/cycles could also be considered in the case of mRNA.

1. The size of the codon/nucleotide is constant so it is natural to assign a lattice to the system. Also now can find Hamiltonian paths/cycles by purely geometric arguments and the calculation is dramatically simplified.
2. Quite concretely, the simplification means that the orientation angle for two nucleotides/codons takes only a few values corresponding to the nearest neighbors. For a cubic lattice there are only 6. This prediction should be testable. Even if not exact energy minima, these configurations could be excellent approximations to them. Note however, that minima favor symmetries and lattice symmetry is this kind of symmetry.

1. The essential thing is that icosa- and tetrahedral Hamilton cycles can be classified by using their symmetry group as a subgroup of the icosahedral or tetrahedral symmetries. Symmetry determines how many DNA codons code for a given amino acid and the model predicts correctly these numbers (see this and this). If the genetic code is universal, these symmetries might play an essential role even in systems with an astrophysical size.
2. TGD indeed predicts that genetic code is universal and based on the completely unique icosa tetrahedral tessellation of the hyperbolic 3-space (see this and this) playing a central role in TGD (mass shell, light-cone proper time constant surace). This tessellation would have tetrahedra, octahedra, and icosahedra, which are Platonic solids having triangles as faces, as basic building bricks. Does universality mean that both the notions of DNA, RNA and amino acids, or rather their dark variants realized in terms of flux tubes carrying dark nucleons, are universal?
3. TGD suggests a model for the Sun (see this) as a living system analogous to a cell or cell nucleus and perhaps realizing the universal genetic code. Could the Hamiltonian paths or cycles, defined by the monopole flux tube tangles and associated with the icosa tetrahedral tessellation, give rise to the analogs of DNA strands? If so, the Sun could be an extremely intelligent conscious entity, something totally different from a mere fusion reactor. In fact, the TGD view of the Sun proposes that the solar wind and solar radiation is produced at the surface layer of the Sun and that new physics predicted by TGD is involved.