Programming of bio-molecular self assembly pathways from TGD point of view

There is an interesting work about programming bio-molecular self assembly pathways [Y. Peng Yin et al (2007), Programming biomolecular self-assembly pathways, Nature 451, 318-322 (17 January 2008)]. The catalytic self assembly of complexes of nuclei acids is carried out automatically by a program represented implicitly as a mixture of linear DNA strand acting as catalyst and so called hairpin DNAs containing three nucleation sites a_t, b_t, c_t - so called toeholds.

A. Key ideas

The basic idea is that a set of bio-molecular reactions can be programmed to occur in a desired order by using a generalization of lock and key mechanism. The simplest self assembly pathway can be specified by a collection of keys and locks. In the beginning there is only one key and the this key fits to only one door, which leads into a room with several doors. The lock eats the key but gives one or more keys. If the room contains several doors to which the keys fits, the reaction corresponds to addition of several branches to the already existing reaction product. By continuing in this manner one eventually ends up to the last room and at the last step the lock gives back the original key so that it can act as a catalyst.

The translation of this idea to a program defining self assembly pathway is following.

1. DNA hairpin [stemloop] defines key structural element of the self-assembly program. Hairpin is a single-stranded DNA strand in meta-stable configuration having form A+B+C such that B forms a loop and C is a palindrome [palindrome]. The formal expression for palindromy is C= A_t^*: this means that C read backwards (C_t) is conjugate A^* of A implying that A and C running in opposite direction can form a double strand (duplex) by hydrogen bonding. As catalytic a^* acting as key forms a double strand with a, the hairpin molecule opens to a linear DNA molecule and energy is liberated. In this process original key is lost but the two other toe-holds b_t and c_t contained by the hairpin become available as keys. Each hairpin in the mixture of catalyst and hairpin molecules has its own lock and two keys.

2. The process of opening new doors continues until all hairpin molecules are used. The key given by the last lock must be catalyst strand a^*. The outcome is a molecule consisting of pieces of DNA strands and can possess a very complex topology. For instance, the formation trees and star like structures can be easily programmed.

3. To run this program one needs only an optimal mixture of catalyst molecule and hairpin DNA molecules. In the applications discussed in hairpins have length of order 10 nm which corresponds to p-adic length scale L(151) defining also cell membrane thickness. That L(151) corresponds also to the length of 30-nucleotide sequence defining the codon of the code associated with Mersenne prime M₆₁=2⁶¹-1 might not be an accident. The simplest applications are autocatalytic formation of DNA duplex molecules and of branched junctions, nucleated dendritic growth, and autonomous locomotion of a bipedal walker.

The basic idea in the realization of the autonomous motion of bipedal walker is to cheat the walker to follow a track marked by food. The walker literally eats the food and receives in this manner the metabolic energy needed to make the step to the next piece of food. The menu contains two kinds of hairpins as foods: hairpins A attached regularly along the desired path of the walker (second DNA strand) and hairpins B but not attached to the strand. The front leg l of the walker attaches to A and this catalyzes the formation of the duplex A*B as a waste and the liberated metabolic energy allows to make a step in which hind leg becomes the front leg.

B. TGD view about the situation

The possibility to program the self-assembly relies on the almost deterministic realization of the lock and key mechanism. The presence of braid strands could make this possible.

1. Consider first the hypothesis about the cancelation of anomalous DNA charge. The palindromic character of A means that the neck of the hairpin has vanishing anomalous em charge and also vanishing color charge is possible. Hence palindromes are favored in TGD Universe. The circular piece B is not in general color singlet. It could have braid strands connecting it to it to some other DNA or nuclear membrane but this is not necessary. Same applies to the toehold a_t at the end of the other strand of neck.

2. The attachment of the lock to key could be seen as a process in which a braid consisting of magnetic flux tubes connecting lock and key strands (DNA and its conjugate) is formed spontaneously and followed by a phase transition reducing hbar contracting the flux tubes and in this manner guiding the key to the lock.

For a more detailed exposition and background see the chapter DNA as Topological Quantum Computer of "TGD as a Generalized Number Theory".