DNA AND MICROTUBULES AS VORTEX-STRINGS IN SUPERCONDUCTOR-LIKE DYNAMICS

Abstract

The non-stationary one-dimensional model for cell cycle control in my previous lecture entitled “Long range interaction between protein complexes in DNA controls replication and cell cycle progression: The double helix and microtubules behave like elastically braced strings”, also included in this book, is generalized here to three spatial dimensions with a complex scalar matter field and an electromagnetic field included. The leading order interaction obtained is superconductor-like and the DNA duplex and the MTs appear as string-like macromolecular configurations in the form of vortex solutions. Contrary to thermotropic and ad hoc type models, these vortex solutions emerge as a result of dependence on the initial reactant concentrations. A further, spherically symmetric generalization of that model with three scalar field components (three order parameters) yields a particular hedgehog solution which could be interpreted as a pre-replication conformation of the cytoskeleton. 1 Long range interaction between proteins in DNA controls the cell cycle In the previous lecture a nonstationary model that controls DNA replication and cell cycle progression was derived in terms of many-body physics [1]. That model, in which the DNA duplex and MTs behave like elastically braced strings, predicts a long range force between the protein complexes (ORCs), bound to DNA origins [2]. The molecular complexes of these string-like lattices are squeezed together by a long range force F, which is attractive in G1, such that mobile electrons in the same complexes can transfer, a prerequisite for oxidation-reduction processes encompassing replication to take place. Initiation of replication thus depends critically on the assembly of the pre-replication complexes (pre-RC), as well as their phosphorylation by cyclin-dependent kinases which could not function without electron transfer. All one-dimensional equations employed are given in my previous lecture presented in this book [1]. The long range force F(φ), which acts as a driving force for DNA replication and the cell cycle progression is attractive (+), hence condensating, in the (G1-phase) assembly state (0 < φ < N) as expected, φ being the number of ORCs, and N the threshold number for initiation. DNA replication is initiated by a switch of sign of the interaction at φ = N, from attraction (−) to repulsion (+). During DNA replication (N < φ < 2N), F is repulsive (+), thus explaining the disassembly with release of licensing factors (LFs) and hence also providing a mechanism for the prevention of re-replication during the S phase. This is one of the most essential prerequisites for the genome to be duplicated just one time. The termination of DNA replication at the S G2 interface is due to a vanishing of the driving force at φ = 2N, when all primed replicons are duplicated once. Thus the model makes sure that the DNA content of G2 cells is exactly twice that of G1