Guanine-cytosine Base Pair Research Articles

Dynamics of proton tunneling in Hydrogen-Bonded systems through Green's function formalism

This study proposes a new theoretical model based on Green's function formalism for studying proton tunneling via hydrogen bonding. This approach allows calculating the tunneling probability and the tunneling energy that proton transfer occurs along a given path inferred a priori. The method is extended to multiple protons tunneling, characterizing the behaviour of some biological molecules. Specifically, the cases of the proton transfer in the Fujicurin A molecule and the double proton tunneling in the Guanine-Cytosine base-pair are investigated. The new approach is an alternative to those present in the literature. It allows straightforwardly predicting the mechanisms of intramolecular and intermolecular proton transfers involving the rearrangement of conjugated electrons.

Exploring the influence of metal cations on individual hydrogen bonds in Watson-Crick guanine-cytosine DNA base pair: An interacting quantum atoms analysis.

This study delves into the nature of individual hydrogen bonds and the relationship between metal cations and hydrogen bonding in the Watson-Crick guanine-cytosine (GC) base pair and its alkali and alkaline earth cation-containing complexes (Mn+-GC). The findings reveal how metal cations affect the nature and strength of individual hydrogen bonds. The study employs interacting quantum atoms (IQA) analysis to comprehensively understand three individual hydrogen bonds within the GC base pair and its cationic derivatives. These analyses unveil the nature and strength of hydrogen bonds and serve as a valuable reference for exploring the impact of cations (and other factors) on each hydrogen bond. All the H D interactions (H is hydrogen and D is oxygen or nitrogen) in the GC base pair are primarily electrostatic in nature, with the charge transfer component playing a substantial role. Introducing a metal cation perturbs all H D interatomic interactions in the system, weakening the nearest hydrogen bond to the cation (indicated by a) and reinforcing the other (b and c) interactions. Notably, the interaction a, the strongest H D interaction in the GC base pair, becomes the weakest in the Mn+-GC complexes. A broader perspective on the stability of GC and Mn+-GC complexes is provided through interacting quantum fragments (IQF) analysis. This approach considers all pairwise interactions between fragments and intra-fragment components, offering a complete view of the factors that stabilize and destabilize GC and Mn+-GC complexes. The IQF analysis underscores the importance of electron sharing, with the dominant contribution arising from the inter-fragment exchange-correlation term, in shaping and sustaining GC and Mn+-GC complexes. From this point of view, alkaline and alkaline earth cations have distinct effects, with alkaline cations generally weakening inter-fragment interactions and alkaline earth cations strengthening them. In addition, IQA and IQF calculations demonstrate that the hydration of cations led to small changes in the hydrogen bonding network. Finally, the IQA interatomic energies associated with the hydrogen bonds and also inter-fragment interaction energies provide robust indicators for characterizing hydrogen bonds and complex stability, showing a strong correlation with total interaction energies.

XMECP: Reaching State-of-the-Art MECP Optimization in Multiscale Complex Systems.

The Python-based program, XMECP, is developed for realizing robust, efficient, and state-of-the-art minimum energy crossing point (MECP) optimization in multiscale complex systems. This article introduces the basic capabilities of the XMECP program by theoretically investigating the MECP mechanism of several example systems including (1) the photosensitization mechanism of benzophenone, (2) photoinduced proton-coupled electron transfer in the cytosine-guanine base pair in DNA, (3) the spin-flip process in oxygen activation catalyzed by an iron-containing 2-oxoglutarate-dependent oxygenase (Fe/2OGX), and (4) the photochemical pathway of flavoprotein adjusted by the intensity of an external electric field. MECPs related to multistate reaction and multistate reactivity in large-scale complex biochemical systems can be well-treated by workflows suggested by the XMECP program. The branching plane updating the MECP optimization algorithm is strongly recommended as it provides derivative coupling vector (DCV) with explicit calculation and can equivalently evaluate contributions from non-QM residues to DCV, which can be nonadiabatic coupling or spin-orbit coupling in different cases. In the discussed QM/MM examples, we also found that the influence on the QM region by DCV can occur through noncovalent interactions and decay with distance. In the example of DNA base pairs, the nonadiabatic coupling occurs across the π-π stacking structure formed in the double-helix system. In contrast to general intuition, in the example of Fe/2OGX, the central ferrous and oxygen part contribute little to the spin-orbit coupling; however, a nearby arginine residue, which is treated by molecular mechanics in the QM/MM method, contributes significantly via two hydrogen bonds formed with α-ketoglutarate (α-KG). This indicates that the arginine residue plays a significant role in oxygen activation, driving the initial triplet state toward the productive quintet state, which is more than the previous knowledge that the arginine residue can bind α-KG at the reaction site by hydrogen bonds.

DNA Sequences Under Multiple Guanine-Cytosine (GC) Base Pairs Constraint.

DNA computing is a new computing method that has high efficiency in solving large-scale nonlinear and Non-deterministic Polynomial complete problems. The design of DNA sequences is an important step in DNA computing, and the quality of the DNA sequences directly affects the accuracy of DNA computing results. Efficiently designing high-quality DNA sequences is currently a significant challenge. In order to improve the efficiency of DNA sequence design, a sparrow evolutionary search algorithm (SESA) is proposed by us. It inherits the fast convergence of the sparrow search algorithm and avoids the situation that the sparrow search algorithm is prone to fall into a local optimum, which greatly improves the search performance of the algorithm on discrete numerical problems. In order to improve the quality of DNA sequence, a new constraint, multiple GC constraint, has been proposed in this paper. Simulated experiments in NUPACK show that this constraint can greatly improve the quality of the DNA sequences designed by us. Compared with previous results, our DNA sequences have better stability.

Multiple hydrogen-bonded dimers: are only the frontier atoms relevant?

Non-frontier atom exchanges in hydrogen-bonded aromatic dimers can induce significant interaction energy changes (up to 6.5 kcal mol-1). Our quantum-chemical analyses reveal that the relative hydrogen-bond strengths of N-edited guanine-cytosine base pair isosteres, which cannot be explained from the frontier atoms, follow from the charge accumulation in the monomers.

Multiscale simulations reveal the role of PcrA helicase in protecting against spontaneous point mutations in DNA

Proton transfer across hydrogen bonds in DNA can produce non-canonical nucleobase dimers and is a possible source of single-point mutations when these forms mismatch under replication. Previous computational studies have revealed this process to be energetically feasible for the guanine-cytosine (GC) base pair, but the tautomeric product (G∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^*$$\\end{document}C∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^*$$\\end{document}) is short-lived. In this work we reveal, for the first time, the direct effect of the replisome enzymes on proton transfer, rectifying the shortcomings of existing models. Multi-scale quantum mechanical/molecular dynamics (QM/MM) simulations reveal the effect of the bacterial PcrA Helicase on the double proton transfer in the GC base pair. It is shown that the local protein environment drastically increases the activation and reaction energies for the double proton transfer, modifying the tautomeric equilibrium. We propose a regime in which the proton transfer is dominated by tunnelling, taking place instantaneously and without atomic rearrangement of the local environment. In this paradigm, we can reconcile the metastable nature of the tautomer and show that ensemble averaging methods obscure detail in the reaction profile. Our results highlight the importance of explicit environmental models and suggest that asparagine N624 serves a secondary function of reducing spontaneous mutations in PcrA Helicase.

Electron density analysis of the ionized states of Watson-Crick GC base pair: A novel approach to investigate the cause of altered base pairing

Using electron density analysis, we present a model study to investigate the effect of ionization on the structure of the guanine-cytosine (GC) base pair. The structures of G, C, GC, GC–, and GC+ were optimized using DFT. NBO analysis were made to compare the interaction energies and the H-bond strengths in GC, GC–, and GC+. Electron difference density map (EDDM) of GC, GC–, and GC+ were plotted in the hydrogen bonding plane of GC. EDDM map shows the electronic density redistribution upon ionization which locate the important regions that controls the strength of hydrogen bonds in GC base pair. EDDM along with the optimized structures of G, C and GC confirms the localization of positive charge on G and negative charge on C in GC+ and GC–, respectively. Using this novel approach, it has been shown pictorially the cause of induced instability on hydrogen bonding interaction upon ionization. This deviates the linearity and planarity of the structure, providing an opportunity to alter the base pairing.

Environmental and Nuclear Quantum Effects on Double Proton Transfer in the Guanine-Cytosine Base Pair.

In the present letter, we investigate the double proton transfer (DPT) tautomerization process in guanine-cytosine (GC) DNA base pairs. In particular, we study the influence of the biological environment on the mechanism, the kinetics and thermodynamics of such DPT. To this end, we present a molecular dynamics (MD) study in the tight-binding density functional theory framework, and compare the reactivity of the isolated GC dimer with that of the same dimer embedded in a small DNA structure. The impact of nuclear quantum effects (NQEs) is also evaluated using Path Integral based MD. Results show that in the isolated dimer, the DPT occurs via a concerted mechanism, while in the model biological environment, it turns into a stepwise process going through an intermediate structure. One of the water molecules in the vicinity of the proton transfer sites plays an important role as it changes H-bond pattern during the DPT reaction. The inclusion of NQEs has the effect of speeding up the tautomeric-to-canonical reaction, reflecting the destabilization of both the tautomeric and intermediate forms.

Tunneling Effect in Proton Transfer: Transfer Matrix Approach

The transfer matrix (TM) method was applied to calculate the transmission probability (TP) for proton transfer reactions. The tunneling factors in the reaction rate constants were also evaluated using the TPs. To test this method, TPs for the Eckart potentials modeled as a guanine-cytosine base pair were calculated by the TM method and compared to TPs by the analytical solution. As a result, the errors in the TPs by the TM method were quite small. The tunneling factors for the guanine-thymine (G-T) and adenine-cytosine (A-C) mispair reactions were then evaluated by the TM method. A shoulder appears on each potential for these reactions [Odai, K.; Umesaki,K. J. Phys. Chem. A. 2021, 125, 8196-8204]. As a result, the shoulder for the G-T mispair reaction contributes significantly to the tunneling, while the shoulder for the A-C mispair reaction contributes little to the tunneling. These results are difficult to obtain with methods such as Wigner's tunneling factor.

Selective conformer detection of short-lived base pair tautomers: A computational study of the unusual guanine-cytosine pairs using ultrafast resonance Raman spectroscopy

Base pair mismatch has been regarded as the main source of DNA point mutations, where minor short-lived tautomers were usually involved. However, the detection and characterization of these unnatural species pose challenges to existing techniques. Here, by using systematic structural and ultrafast resonance Raman (RR) spectral analysis for the four possible conformers of guanine-cytosine base pairs, the prominent marker Raman bands were identified. We found that the hydrogen bonding vibrational region from 2300 cm−1 to 3700 cm−1 is ideal for the identification of these short live species. The marker bands provide direct evidence for the existence of the tautomer species, thus offering an effective strategy to detect the short-lived minor species. Ultrafast resonance Raman spectroscopy would be a powerful tool to provide direct evidence of critical dynamical details of complex systems involving protonation or tautomerization.

Electron Attachment to Wobble Base Pairs

We have analyzed the low-energy electron attachment to wobble base pairs using the equation of motion coupled cluster method and extended basis sets. A doorway mechanism exists for the attachment of the additional electron to the base pairs, where the initially formed dipole-bound anion captures the incoming electron. The doorway dipole-bound anionic state subsequently leads to the formation of a valence-bound state, and the transfer of extra electron occurs by mixing of electronic and nuclear degrees of freedom. The formation of the valence-bound anion is associated with proton transfer in hypoxanthine-cytosine and hypoxanthine-adenine base pairs, which happens through a concerted electron-proton transfer process. The calculated rate constant for the dipole-bound to valence-bound transition in wobble base pairs is slower than that observed in the Watson-Crick guanine-cytosine base pair.

Evaluation of the Reax Force-Field for Studying the Collision of an Energetic Proton with the DNA.

The early DNA damage induced by ionizing radiation depends on how ionizing particles transfer energy to this molecule and the surrounding medium, mostly water. In preliminary studies, we found that the energy transferred by a 4 keV proton to a cytosine-guanine base pair in a classical simulation collision using the ReaxFF potential is much smaller than that obtained by a quantum calculation using time-dependent density functional theory (TDDFT). We observed that there are two main reasons for that: no accurate force-field for this situation and problems while dealing with the proton charge during the collision. Here, we only focus on the interaction potential. We calibrated the van der Waals energy term of the ReaxFF potential using TDDFT calculations and a genetic algorithm, specifically for the interaction of a proton with the DNA constituent atoms (carbon, hydrogen, phosphorus, nitrogen, and oxygen). We obtained a significant improvement in the interaction potential and, consequently, in the scattering angle of the proton colliding with the target atoms in question. However, we conclude that despite the improvement for the force-field and scattering angle, the classical charge equilibration method should also be improved to properly describe the proton-DNA collision process.

Accelerating Hybrid Density Functional Theory Molecular Dynamics Simulations by Seminumerical Integration, Resolution-of-the-Identity Approximation, and Graphics Processing Units.

The computationally very demanding evaluation of the 4-center-2-electron (4c2e) integrals and their respective integral derivatives typically represents the major bottleneck within hybrid Kohn-Sham density functional theory molecular dynamics simulations. Building upon our previous works on seminumerical exact-exchange (sn-LinK) [Laqua, H., Thompsons, T. H., Kussmann, J., Ochsenfeld, C., J. Chem. Theory Comput. 2020, 16, 1465] and resolution-of-the-identity Coulomb (RI-J) [Kussmann, J., Laqua, H., Ochsenfeld, C., J. Chem. Theory Comput. 2021, 17, 1512], the expensive 4c2e integral evaluation can be avoided entirely, resulting in a highly efficient electronic structure theory method, allowing for fast ab initio molecular dynamics (AIMD) simulations even with large basis sets. Moreover, we propose to combine the final self-consistent field (SCF) step with the subsequent nuclear forces evaluation, providing the forces at virtually no additional cost after a converged SCF calculation, reducing the total runtime of an AIMD simulation by about another 25%. In addition, multiple independent MD trajectories can be computed concurrently on a single node, leading to a greatly increased utilization of the available hardware─especially when combined with graphics processing unit acceleration─improving the overall throughput by up to another 5 times in this way. With all of those optimizations combined, our proposed method provides nearly 3 orders of magnitude faster execution times than traditional 4c2e integral-based methods. To demonstrate the practical utility of the approach, quantum-mechanical/molecular-mechanical dynamics simulations on double-stranded DNA were performed, investigating the relative hydrogen bond strength between adenine-thymine and guanine-cytosine base pairs. In addition, this illustrative application also contains a general accuracy assessment of the introduced approximations (integration grids, resolution-of-the-identity) within AIMD simulations, serving as a protocol on how to apply these new methods to practical problems.

Influence of conventional hydrogen bonds in the intercalation of phenanthroline derivatives with DNA: The important role of the sugar and phosphate backbone.

The influence of hydrogen bonds in model intercalated systems between guanine‐cytosine and adenine‐thymine DNA base pairs (bps) was analyzed with the popular intercalator 1,10‐phenanthroline (phen) and derivatives obtained by substitution with —OH and —NH2 groups in positions 4 and 7. Semiempirical and Density Functional Theory (DFT) methods were used both including dispersion effects: PM6‐DH2, M06‐2X and B3LYP‐D3 along with the recently developed near linear‐scaling coupled cluster method DLPNO‐CCSD(T) for benchmark calculations. Our results given by QTAIM and non‐covalent interaction analysis confirmed the existence of hydrogen bonds created by —OH and —NH2. The trends in the energy decomposition analysis for the interaction energy, ΔE int, showed that the ΔE elstat contributions are equal or even a little bit higher than the values for ΔE disp. Such important ΔE elstat attractive contribution comes mainly from the conventional hydrogen bonds formed by —OH and —NH2 functional groups with DNA not only with bps but specially with the sugar and phosphate backbone. This behavior is very different from that of phen and other classical intercalators that cannot form conventional hydrogen bonds, where the ΔE disp is the most important attractive contribution to the ΔE int. The inclusion of explicit water molecules in molecular dynamics simulations showed, as a general trend, that the hydrogen bonds with the bps disappear during the simulations but those with the sugar and phosphate backbone remain in time, which highlights the important role of the sugar and phosphate backbone in the stabilization of these systems.

Collision-induced dissociation of homodimeric and heterodimeric radical cations of 9-methylguanine and 9-methyl-8-oxoguanine: correlation between intra-base pair proton transfer originating from the N1-H at a Watson-Crick edge and non-statistical dissociation.

It has been shown previously in protonated, deprotonated and ionized guanine-cytosine base pairs that intra-base pair proton transfer from the N1-H at the Watson-Crick edge of guanine to the complementary nucleobase prompts non-statistical dissociation of the base-pair system, and the dissociation of a proton-transferred base-pair structure is kinetically more favored than that of the starting, conventional base-pair structure. However, the fundamental chemistry underlying this anomalous and intriguing kinetics has not been completely revealed, which warrants the examination of more base-pair systems in different structural contexts in order to derive a generalized base-pair structure-kinetics correlation. The purpose of the present work is to expand the investigation to the non-canonical homodimeric and heterodimeric radical cations of 9-methylguanine (9MG) and 9-methyl-8-oxoguanine (9MOG), i.e., [9MG·9MG]˙+, [9MOG·9MG]˙+ and [9MOG·9MOG]˙+. Experimentally, collision-induced dissociation tandem mass spectrometry coupled with an electrospray ionization (ESI) source was used for the formation of base-pair radical cations, followed by detection of dissociation product ions and cross sections in the collisions with Xe gas under single ion-molecule collision conditions and as a function of the center-of-mass collision energy. Computationally, density functional theory and coupled cluster theory were used to calculate and identify probable base-pair structures and intra-base pair proton transfer and hydrogen transfer reactions, followed by kinetics modeling to explore the properties of dissociation transition states and kinetic factors. The significance of this work is twofold: it provides insight into base-pair opening kinetics in three biologically-important, non-canonical systems upon oxidative and ionization damage; and it links non-statistical dissociation to intra-base pair proton-transfer originating from the N1-H at the Watson-Crick edge of 8-oxoguanine, enhancing understanding towards the base-pair fragmentation assisted by proton transfer.

Statistical and bioinformatic analysis of hemimethylation patterns in non-small cell lung cancer

BackgroundDNA methylation is an epigenetic event involving the addition of a methyl-group to a cytosine-guanine base pair (i.e., CpG site). It is associated with different cancers. Our research focuses on studying non-small cell lung cancer hemimethylation, which refers to methylation occurring on only one of the two DNA strands. Many studies often assume that methylation occurs on both DNA strands at a CpG site. However, recent publications show the existence of hemimethylation and its significant impact. Therefore, it is important to identify cancer hemimethylation patterns.MethodsIn this paper, we use the Wilcoxon signed rank test to identify hemimethylated CpG sites based on publicly available non-small cell lung cancer methylation sequencing data. We then identify two types of hemimethylated CpG clusters, regular and polarity clusters, and genes with large numbers of hemimethylated sites. Highly hemimethylated genes are then studied for their biological interactions using available bioinformatics tools.ResultsIn this paper, we have conducted the first-ever investigation of hemimethylation in lung cancer. Our results show that hemimethylation does exist in lung cells either as singletons or clusters. Most clusters contain only two or three CpG sites. Polarity clusters are much shorter than regular clusters and appear less frequently. The majority of clusters found in tumor samples have no overlap with clusters found in normal samples, and vice versa. Several genes that are known to be associated with cancer are hemimethylated differently between the cancerous and normal samples. Furthermore, highly hemimethylated genes exhibit many different interactions with other genes that may be associated with cancer. Hemimethylation has diverse patterns and frequencies that are comparable between normal and tumorous cells. Therefore, hemimethylation may be related to both normal and tumor cell development.ConclusionsOur research has identified CpG clusters and genes that are hemimethylated in normal and lung tumor samples. Due to the potential impact of hemimethylation on gene expression and cell function, these clusters and genes may be important to advance our understanding of the development and progression of non-small cell lung cancer.

De Novo Profiling of Long Non-Coding RNAs Involved in MC-LR-Induced Liver Injury in Whitefish: Discovery and Perspectives.

Microcystin-LR (MC-LR) is a potent hepatotoxin for which a substantial gap in knowledge persists regarding the underlying molecular mechanisms of liver toxicity and injury. Although long non-coding RNAs (lncRNAs) have been extensively studied in model organisms, our knowledge concerning the role of lncRNAs in liver injury is limited. Given that lncRNAs show low levels of sequence conservation, their role becomes even more unclear in non-model organisms without an annotated genome, like whitefish (Coregonus lavaretus). The objective of this study was to discover and profile aberrantly expressed polyadenylated lncRNAs that are involved in MC-LR-induced liver injury in whitefish. Using RNA sequencing (RNA-Seq) data, we de novo assembled a high-quality whitefish liver transcriptome. This enabled us to find 94 differentially expressed (DE) putative evolutionary conserved lncRNAs, such as MALAT1, HOTTIP, HOTAIR or HULC, and 4429 DE putative novel whitefish lncRNAs, which differed from annotated protein-coding transcripts (PCTs) in terms of minimum free energy, guanine-cytosine (GC) base-pair content and length. Additionally, we identified DE non-coding transcripts that might be 3′ autonomous untranslated regions (3′UTRs) of mRNAs. We found both evolutionary conserved lncRNAs as well as novel whitefish lncRNAs that could serve as biomarkers of liver injury.

The influence of external electric fields on proton transfer tautomerism in the guanine-cytosine base pair.

The Watson–Crick base pair proton transfer tautomers would be widely considered as a source of spontaneous mutations in DNA replication if not for their short lifetimes and thermodynamic instability. This work investigates the effects external electric fields have on the stability of the guanine–cytosine proton transfer tautomers within a realistic strand of aqueous DNA using a combination of ensemble-based classical molecular dynamics (MD) coupled to quantum mechanics/molecular mechanics (QM/MM). Performing an ensemble of calculations accounts for the stochastic aspects of the simulations while allowing for easier identification of systematic errors. The methodology applied in this work has previously been shown to estimate base pair proton transfer rate coefficients that are in good agreement with recent experimental data. A range of electric fields in the order of 104 to 109 V m−1 is investigated based on their real-life medicinal applications which include gene therapy and cancer treatments. The MD trajectories confirm that electric fields up to 1.00 × 109 V m−1 have a negligible influence on the structure of the base pairs within DNA. The QM/MM results show that the application of large external electric fields (1.00 × 109 V m−1) parallel to the hydrogen bonds increases the thermodynamic population of the tautomers by up to one order of magnitude; moreover, the lifetimes of the tautomers remain insignificant when compared to the timescale of DNA replication.

Interactions of Solvated Electrons with Nucleobases: The Effect of Base Pairing.

We have investigated the effect of base pairing on the electron attachment to nucleobases in bulk water, taking the guanine-cytosine (GC) base pair as a test case. The presence of the complementary base reinforces the stabilization effect provided by water and preferentially stabilizes the anion by hydrogen bonding. The electron attachment in bulk-solvated GC happens through a doorway mechanism, where the initial electron attached state is water bound, and it subsequently gets converted to a GC bound state. The additional electron in the final GC bound state is localized on the cytosine, similar to that in the gas phase. The transfer of the electron from the initial water-bound state to the final GC bound state happens due to the mixing of electronic and nuclear degrees of freedom and takes place at a picosecond time scale.

Revisiting the Hole Size in Double Helical DNA with Localized Orbital Scaling Corrections.

The extent of electronic wave function delocalization for the charge carrier (electron or hole) in double helical DNA plays an important role in determining the DNA charge transfer mechanism and kinetics. The size of the charge carrier's wave function delocalization is regulated by the solvation induced localization and the quantum delocalization among the π stacked base pairs at any instant of time. Using a newly developed localized orbital scaling correction (LOSC) density functional theory method, we accurately characterized the quantum delocalization of the hole wave function in double helical B-DNA. This approach can be used to diagnose the extent of delocalization in fluctuating DNA structures. Our studies indicate that the hole state tends to delocalize among 4 guanine-cytosine (GC) base pairs and among 3 adenine-thymine (AT) base pairs when these adjacent bases fluctuate into degeneracy. The relatively small delocalization in AT base pairs is caused by the weaker π-π interaction. This extent of delocalization has significant implications for assessing the role of coherent, incoherent, or flickering coherent carrier transport in DNA.