FULL PAPER Bright solitary waves as charge transport in DNA: A variational approximation Didier Belobo Belobo | Adamou Dang Koko African Centre for Advanced Studies, Yaounde, Cameroon Correspondence Didier B. Belobo, African Centre for Advanced Studies, P.O. Box 4477, Yaounde, Cameroon. Email: belobodidier@acas-yde.org Abstract Modeling energy and charge transfer in DNA has been a challenging issue because of many conformations DNA can take. Due to its simplicity, we propose a discrete varia- tional approach to study the charge transfer mechanism in DNA based on the Holstein-Su-Schrieffer-Heeger model. It is shown that bright solitary waves may propagate through the DNA and the variational approximation provides explicit rela- tions between experimental parameters and important characteristics of the waves such as amplitude, width, chirp and homogenous phase, and energy. Our analytical predictions are confirmed by intensive numerical simulations with a good accuracy. 1 | INTRODUCTION The deoxyribonucleic acid commonly called DNA is a very important macromolecule constituent of cells in living organisms which carries genetic information. The DNA, as the molecule which encodes the infor- mation organisms need to ensure their living and reproduction, is at the heart of lots of processes and functions during the life of organisms. It has a plethora of remarkable properties which have been attracting a great deal of attention from physicists, chemists, and biologists. Among these properties, the charge transfer mechanism trough the DNA mole- cule remains important. A charge here is understood as an electron or a hole. It was clearly shown in a large number of experiments that a charge can travel or migrate through the DNA. [1–18] The charge movement in DNA is usually attributed to two different types of mechanisms [19,20] : (a) coherent hopping or tunneling or superexchange and (b) incoherent or thermal hopping. In the coherent case, sites have finite occupation probabilities, although those with adequate on-site energies, for each ini- tial carrier placement are more favored. [21–23] In the incoherent or ther- mal hopping case, the transfer rate depends on both the energetic and the spatial distance between sites. [24–26] However, our understanding of the mechanisms of charge transfer in the DNA remains a scientific chal- lenge. Many theoretical and experimental works have been dedicated to explain the process by which a charge moves through the DNA. [27] For example, considering the DNA as a one-dimensional disordered system where electrons are transported via variable range hopping between localized states, Yu and Song proposed a model which quantitatively explains the temperature dependence of the conductivity observed in the lambda phage. [28] Cuniberti et al. [29] introduced an Hamiltonian to describe charge transport through short homogeneous double stranded DNA molecules which explains the semiconducting behavior in short poly(G)-poly(C) DNA oligomers. Using a quantum mechanical description Lakhno and Fialko developed a general theory of excitation transfer dynamics in multi-site systems which applies to the calculation of charge transfer in DNA over many nucleotides base pairs. [30] Yamagami et al. reported the first direct observation of charge transport dynamics using time resolved microwave conductivity and transient absorption spec- troscopy on the photolysis of an anthraquinone-bound DNA complex. [31] In Thazhathveetil et al., [10] the authors observed that charge transport is coupled to solvent fluctuations and occurs via a thermally activated multi-step hopping mechanism. It is well known that the DNA molecule is highly deformable and its deformations affect important processes like charge transport. Comwell and Rakhmanova [32] and Ly et al. [12] explained that charge coupling with distortions in the DNA molecule may induce polarons which enhance efficient charge transfer. The Su-Schrieffer-Heeger (SSH) model [33,34] and the Peyrard-Bishop-Holstein (PBH) model [35–37] are two polaron based models which were used to unveil charge transfer properties in DNA. Using the PBH DNA model, the authors in Komineas et al. [35–37] showed that fluctuating intrinsic disorder can trap the charge and inhibit polaronic charge transport. In the SSH DNA model, the polaron is formed by the nonlinear interaction between the lattice and the electron, it was suggested that the charge transfer may be explained by a soliton [33,34] which moves along the molecule. Solitons are localized solutions of integrable nonlinear Received: 21 August 2019 Revised: 17 November 2019 Accepted: 29 November 2019 DOI: 10.1002/bip.23346 Biopolymers. 2019;e23346. wileyonlinelibrary.com/journal/bip © 2019 Wiley Periodicals, Inc. 1 of 5 https://doi.org/10.1002/bip.23346