Abstract
The base sequences of DNA contain the genetic code, and, to decode it, a double helical DNA has to be unzipped to reveal the bases. Recent studies have shown that a third strand can be used to identify the base sequences, not by opening the double helix but rather by forming a triple helix. It is predicted here that a three-strand DNA exhibits the unusual behaviour of the existence of a three-chain bound state in the absence of any two being bound. Such a state can occur at or above the duplex melting point. This phenomenon is analogous to the Efimov state in three-particle quantum mechanics. A scaling theory is used to justify the Efimov connection. Real space renormalization group (RG) and exact numerical calculations are used to validate the prediction of a biological Efimov effect.
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GENERAL SCIENTIFIC SUMMARY Introduction and background. The DNA double helix has room for a third strand to form a triple helix. This third chain's ability to recognize base sequences is of importance in biology but, beyond that, triplex DNA has very special traits for scaling in polymer physics. Thanks to sequential pairing, there is is a direct analogy between DNA and quantum mechanics, with the contour length analogous to time, and thermal jiggling to the randomness of the uncertainty principle. These fluctuations may unbind a pair that could have been bound by a short-range interaction, but the same may be used effectively by a third particle to form a loose trimer. This is the Efimov effect.
Main results. Close to duplex melting, large bubbles can form. If the bubbles are of any length (scale free), then two strands separated by a distance R would feel a 1/R2 attraction, purely mediated by the long-ranged excursion of a third strand. This attraction produces a three-chain bound state with a cross-section much larger than the hydrogen bond length. It can exist even above the duplex melting point. Such three-chain states where no two are bound are analogous to the quantum Efimov effect and have been seen in several model systems. This new state may be called Efimov-DNA.
Wider implications. Triplex DNA provides a unique, affordable biological testing ground for the Efimov effect. On the biological front, since enzymes are hypothesized to work on local bonds, one needs to assimilate enzyme activities to a large-sized bound state.
Figure. Two noninteracting chains, 1 and 3, separated at a distance R. Each of these can pair with a flexible chain, 2. The polymeric configurations are analogous to the trajectories of three quantum particles with the contour length s playing the role of time.