Charge transfer in DNA: effective Hamiltonian approaches

Abstract

Abstract. Aperiodic order plays a very significant role in biology, as it determines most informative content of genomes. Amongst the various physical, chemical or biological phenomena that might be inferred from sequence correlations, charge transfer properties deserve particular attention. Indeed, the nature of DNA-mediated charge migration has been related to the understanding of damage recognition process, protein binding, or with the task of engineering biological processes (e.g. designing nanoscale sensing of genomic mutations), opening new challenges for emerging nanobiotechnologies. Nevertheless, the solution of Schrö-dinger's equation with a potential that is given by a onedimensional array of the double-stranded DNA remains as a main open theme in solid state physics of biological macromolecules. In this contribution, I will shortly review several approaches introduced during the last few years in order to describe charge transfer migration in DNA in terms of tightbinding effective Hamiltonians. Conceptual and physical motivationsDuring the 1930s, DNA was considered to be merely a tetranucleotide composed of one unit each of deoxyadenylic, -guanilyc, -thymidylic, and -cytidilic acids (the particular order of appearance of each of these bases being considered as irrelevant). Even when it was subsequently realized that the molecular weight of DNA is actually much higher, it was still widely believed that the tetranucleotide unit was the basic repeating building block of the large DNA polymer, in which the four different kinds of nucleotides recur in periodic sequence i.e., (GACT) n [1]. Thus, DNA was originally viewed as a trivially periodic macromolecule, unable to store the amount of information required for the governance of cell function. The mystery of the nature of the genetic material attracted some physicists to genetics. Thus, Schrödinger suggested that a gene consists of a long sequence of a few repeating elements exhibiting a well defined order without the recourse of periodic repetition, and illustrated the vast combinatorial possibilities of such a structure. In this way, the notion of a one-dimensional aperiodic solid was introduced [2], and we can consider Schrödinger was the first person to put forward the notion of a linear genetic code [1]. Hence, Schrödinger's proposal of considering DNA as a one-dimensional aperiodic chain, with four different nucleotides arranged in a way able to store the required genetic information was progressively incorporated into dominant biophysical thinking. In fact, when macromolecules of biological interest are considered from the viewpoint of condensed matter physics, a fundamental question naturally arises regarding the potential role of certain physical properties on their biological functions. In particular, the role of charge migration in DNA mutation repair has been extensively discussed during the last decade, and the possible existence of correlation effects in electrical conductivity due to the presence of long-range spatial correlations in DNA ha...

Aperiodic crystals in biology

“…The chemical order of the base pairs sequence itself is beyond the reach of diffraction techniques, but it can be properly characterized via ab initio quantum chemistry calculations, which nicely highlight the emergence of molecular orbitals when going from the atomic to the molecular scale. Accordingly, one may think of DNA as a sort of hybrid order system exhibiting both aperiodic (nucleobase subsystem) and periodic (sugar-phosphate backbone double-helix subsystem) order features [76].…”

Synchronized Oscillations in Double-Helix B-DNA Molecules with Mirror-Symmetric Codons

“…The time scale of the bp twist Equation ( 5) is completely determined by the characteristic frequency ω ϕ , whereas the radial Equation ( 6) involves three different characteristic frequencies, namely, ω ϕ , ω ϕS,n,n±1 (related to twist-stacking coupling), and ω ϕSH (fully coupling twist, stacking, and stretching interactions). The set of coupled Equations ( 5) and ( 6) describes the dynamics of general dsDNA molecules, with two kinds of bps arranged either periodically or aperiodically [32][33][34][35][36], and their mathematical structure clearly shows the correlated nature of next-neighboring bps dynamics. Thus, it is most convenient to zoom our perspective and consider the dynamics of consecutive triplets of bps, known as codon units in genomics.…”

Base-Pairs’ Correlated Oscillation Effects on the Charge Transfer in Double-Helix B-DNA Molecules

“…In this case, the site label dependence involves all the terms. The set of coupled Equations ( 19 ) and ( 21 ) describes the dynamics of general dsDNA molecules, where two kinds of bps can be arranged either periodically or aperiodically [ 21 , 46 , 47 , 48 , 49 ].…”