Quasi-Periodic and Fractal Polymers: Energy Structure and Carrier Transfer.

Marilena Mantela,Konstantinos Lambropoulos,Marina Theodorakou,Constantinos Simserides

doi:10.3390/ma12132177

Abstract

We study the energy structure and the coherent transfer of an extra electron or hole along aperiodic polymers made of N monomers, with fixed boundaries, using B-DNA as our prototype system. We use a Tight-Binding wire model, where a site is a monomer (e.g., in DNA, a base pair). We consider quasi-periodic (Fibonacci, Thue–Morse, Double-Period, Rudin–Shapiro) and fractal (Cantor Set, Asymmetric Cantor Set) polymers made of the same monomer (I polymers) or made of different monomers (D polymers). For all types of such polymers, we calculate the highest occupied molecular orbital (HOMO) eigenspectrum and the lowest unoccupied molecular orbital (LUMO) eigenspectrum, the HOMO–LUMO gap and the density of states. We examine the mean over time probability to find the carrier at each monomer, the frequency content of carrier transfer (Fourier spectra, weighted mean frequency of each monomer, total weighted mean frequency of the polymer), and the pure mean transfer rate k. Our results reveal that there is a correspondence between the degree of structural complexity and the transfer properties. I polymers are more favorable for charge transfer than D polymers. We compare of quasi-periodic and fractal sequences with that of periodic sequences (including homopolymers) as well as with randomly shuffled sequences. Finally, we discuss aspects of experimental results on charge transfer rates in DNA with respect to our coherent pure mean transfer rates.

Highlights

Today, the electronic structure of biological molecules (e.g., proteins, enzymes, peptides and nucleic acids (DNA, RNA)) and their charge transfer and transport properties attract considerable interest among the physical, chemical, biological and medical communities, as well as a broad spectrum of interdisciplinary scientists and engineers [1,2,3,4,5,6]
It is not rare to see or hear the terms transport and transfer indiscriminately, if we want to be more precise, transport means that the system under investigation is held between electrodes and that a voltage is applied between these electrodes, while the term transfer means that a carrier, created or injected at a specific place, moves to a more favorable location, without the application of external voltage
The TB parameters for B-DNA are taken from Ref. [19]

Summary

Introduction

The electronic structure of biological molecules (e.g., proteins, enzymes, peptides and nucleic acids (DNA, RNA)) and their charge transfer and transport properties attract considerable interest among the physical, chemical, biological and medical communities, as well as a broad spectrum of interdisciplinary scientists and engineers [1,2,3,4,5,6]. DNA plays a fundamental role in genetics and molecular biology since its sequence of bases, adenine (A), guanine (G), cytosine (C), and thymine (T) contains the genetic code of living organisms. The base-pair stack of the DNA double helix creates a nearly one-dimensional π-pathway that favors charge transfer and transport. The rapid hole migration from other bases to guanine is connected to the fact that direct strand breaks occur preferentially at guanines [9]. It might be an indicator of discrimination between pathogenic and non-pathogenic mutations at an early stage [11]

Objectives

Results

Conclusion