Point-mutation effects on charge-transport properties of the tumor-suppressor gene p53

Emergence of Boltzmann Subspaces in Open Quantum Systems Far from Equilibrium

Single molecule junctions are important examples of complex out-of-equilibrium many-body quantum systems. We identify a nontrivial clustering of steady state populations into distinctive subspaces with Boltzmann-like statistics, which persist far from equilibrium. Such Boltzmann subspaces significantly reduce the information needed to describe the steady state, enabling modeling of high-dimensional systems that are otherwise beyond the reach of current computations. The emergence of Boltzmann subspaces is demonstrated analytically and numerically for fermionic transport systems of increasing complexity.

Electronic Structure and Hole Transfer of All B-DNA Dimers and Homopolymers, via the Fishbone-Wire Model

We employ the Tight Binding Fishbone-Wire Model to study the electronic structure and coherent transfer of a hole (the absence of an electron created by oxidation) in all possible ideal B-DNA dimers as well as in homopolymers (one base pair repeated along the whole sequence with purine on purine). The sites considered are the base pairs and the deoxyriboses, with no backbone disorder. For the time-independent problem, we calculate the eigenspectra and the density of states. For the time-dependent problem after oxidation (i.e., the creation of a hole either at a base pair or at a deoxyribose), we calculate the mean-over-time probabilities to find the hole at each site and establish the frequency content of coherent carrier transfer by computing the Weighted Mean Frequency at each site and the Total Weighted Mean Frequency of a dimer or polymer. We also evaluate the main oscillation frequencies of the dipole moment along the macromolecule axis and the relevant amplitudes. Finally, we focus on the mean transfer rates from an initial site to all others. We study the dependence of these quantities on the number of monomers that are used to construct the polymer. Since the value of the interaction integral between base pairs and deoxyriboses is not well-established, we treat it as a variable and examine its influence on the calculated quantities.

LCAO Electronic Structure of Nucleic Acid Bases and Other Heterocycles and Transfer Integrals in B-DNA, Including Structural Variability

To describe the molecular electronic structure of nucleic acid bases and other heterocycles, we employ the Linear Combination of Atomic Orbitals (LCAO) method, considering the molecular wave function as a linear combination of all valence orbitals, i.e., 2s, 2px, 2py, 2pz orbitals for C, N, and O atoms and 1s orbital for H atoms. Regarding the diagonal matrix elements (also known as on-site energies), we introduce a novel parameterization. For the non-diagonal matrix elements referring to neighboring atoms, we employ the Slater–Koster two-center interaction transfer integrals. We use Harrison-type expressions with factors slightly modified relative to the original. We compare our LCAO predictions for the ionization and excitation energies of heterocycles with those obtained from Ionization Potential Equation of Motion Coupled Cluster with Singles and Doubles (IP-EOMCCSD)/aug-cc-pVDZ level of theory and Completely Normalized Equation of Motion Coupled Cluster with Singles, Doubles, and non-iterative Triples (CR-EOMCCSD(T))/aug-cc-pVDZ level of theory, respectively, (vertical values), as well as with available experimental data. Similarly, we calculate the transfer integrals between subsequent base pairs, to be used for a Tight-Binding (TB) wire model description of charge transfer and transport along ideal or deformed B-DNA. Taking into account all valence orbitals, we are in the position to treat deflection from the planar geometry, e.g., DNA structural variability, a task impossible for the plane Hückel approach (i.e., using only 2pz orbitals). We show the effects of structural deformations utilizing a 20mer evolved by Molecular Dynamics.

Tight-Binding Modeling of Nucleic Acid Sequences: Interplay between Various Types of Order or Disorder and Charge Transport

This review is devoted to tight-binding (TB) modeling of nucleic acid sequences like DNA and RNA. It addresses how various types of order (periodic, quasiperiodic, fractal) or disorder (diagonal, non-diagonal, random, methylation et cetera) affect charge transport. We include an introduction to TB and a discussion of its various submodels [wire, ladder, extended ladder, fishbone (wire), fishbone ladder] and of the process of renormalization. We proceed to a discussion of aperiodicity, quasicrystals and the mathematics of aperiodic substitutional sequences: primitive substitutions, Perron–Frobenius eigenvalue, induced substitutions, and Pisot property. We discuss the energy structure of nucleic acid wires, the coupling to the leads, the transmission coefficients and the current–voltage curves. We also summarize efforts aiming to examine the potentiality to utilize the charge transport characteristics of nucleic acids as a tool to probe several diseases or disorders.

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

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 k ( N ) 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.

Periodic, quasiperiodic, fractal, Kolakoski, and random binary polymers: Energy structure and carrier transport

We study periodic, quasiperiodic (Thue-Morse, Fibonacci, period doubling, Rudin-Shapiro), fractal (Cantor, generalized Cantor), Kolakoski, and random binary sequences using a tight-binding wire model, where a site is a monomer (e.g., in DNA, a base pair). We use B-DNA as our prototype system. All sequences have purines, guanine (G) or adenine (A), on the same strand, i.e., our prototype binary alphabet is {G,A}. Our aim is to examine the influence of sequence intricacy and magnitude of parameters on energy structure, localization, and charge transport. We study quantities such as autocorrelation function, eigenspectra, density of states, Lyapunov exponents, transmission coefficients, and current-voltage curves. We show that the degree of sequence intricacy and the presence of correlations decisively affect the aforementioned physical properties. Periodic segments have enhanced transport properties. Specifically, in homogeneous sequences transport efficiency is maximum. There are several deterministic aperiodic sequences that can support significant currents, depending on the Fermi level of the leads. Random sequences is the less efficient category.

Influence of Electron-Holes on DNA Sequence-Specific Mutation Rates

Biases in mutation rate can influence molecular evolution, yielding rates of evolution that vary widely in different parts of the genome and even among neighboring nucleotides. Here, we explore one possible mechanism of influence on sequence-specific mutation rates, the electron–hole, which can localize and potentially trigger a replication mismatch. A hole is a mobile site of positive charge created during one-electron oxidation by, for example, radiation, contact with a mutagenic agent, or oxidative stress. Its quantum wavelike properties cause it to localize at various sites with probabilities that vary widely, by orders of magnitude, and depend strongly on the local sequence. We find significant correlations between hole probabilities and mutation rates within base triplets, observed in published mutation accumulation experiments on four species of bacteria. We have also computed hole probability spectra for hypervariable segment I of the human mtDNA control region, which contains several mutational hotspots, and for heptanucleotides in noncoding regions of the human genome, whose polymorphism levels have recently been reported. We observe significant correlations between hole probabilities, and context-specific mutation and substitution rates. The correlation with hole probability cannot be explained entirely by CpG methylation in the heptanucleotide data. Peaks in hole probability tend to coincide with mutational hotspots, even in mtDNA where CpG methylation is rare. Our results suggest that hole-enhanced mutational mechanisms, such as oxidation-stabilized tautomerization and base deamination, contribute to molecular evolution.

Formulation of Long-Range Transport Rates through Molecular Bridges: From Unfurling to Hopping

Weak fluctuations about the rigid equilibrium structure of ordered molecular bridges drive charge transfer in donor-bridge-acceptor systems via quantum unfurling, which differs from both hopping and ballistic transfer, yet static disorder (low frequency motions) in the bridge is shown to induce a change of mechanism from unfurling to hopping when local fluctuations along the molecular bridge are uncorrelated. Remarkably, these two different transport mechanisms manifest in similar charge-transfer rates, which are nearly independent of the molecular bridge length. We propose an experimental test for distinguishing unfurling from hopping in DNA models with different helix directionality. A unified formulation explains the apparent similarity in the length dependence of the transfer rate despite the difference in the underlying transport mechanisms.

Electronic structure and carrier transfer in B-DNA monomer polymers and dimer polymers: Stationary and time-dependent aspects of a wire model versus an extended ladder model

We employ two tight-binding (TB) approaches to systematically study the electronic structure and hole or electron transfer in B-DNA monomer polymers and dimer polymers made up of N monomers (base pairs): (I) at the base-pair level, using the onsite energies of base pairs and the hopping integrals between successive base pairs, i.e., a wire model and (II) at the single-base level, using the onsite energies of the bases and the hopping integrals between neighboring bases, i.e., an extended ladder model since we also include diagonal hoppings. We solve a system of M (matrix dimension) coupled equations [(I) M=N, (II) M=2N] for the time-independent problem, and a system of M coupled first order differential equations for the time-dependent problem. We perform a comparative study of stationary and time-dependent aspects of the two TB variants, using realistic sets of parameters. The studied properties include HOMO and LUMO eigenspectra, occupation probabilities, density of states and HOMO-LUMO gaps as well as mean over time probabilities to find the carrier at each site [(I) base pair or (II) base], Fourier spectra, which reflect the frequency content of charge transfer, and pure mean transfer rates from a certain site to another. The two TB approaches give coherent, complementary aspects of electronic properties and charge transfer in B-DNA monomer polymers and dimer polymers.

Length-independent transport rates in biomolecules by quantum mechanical unfurling

Experiments on hole transfer in DNA between donor and acceptor moieties revealed transfer rates which are independent of the molecular bridge length (within experimental error). However, the physical origin of this intriguing observation is still unclear. The hopping model implies that the hole propagates in multiple steps along the bridge from one localized state to another, and therefore the longer the bridge, the slower the transfer. This can explain weak length-dependence but not a length-independent transfer rate. We show that the rigid molecular structure of a poly-A bridge supports single step transitions from a localized hole state to delocalized states, spread over the entire bridge. Since propagation to the bridge end is a single step process (termed quantum unfurling) the transfer rate becomes independent of the bridge length. This explanation is consistent with experimental results, and emphasizes the importance of structural order in charge transfer through bio-molecular systems.

Computational DNA hole spectroscopy: A new tool to predict mutation hotspots, critical base pairs, and disease 'driver' mutations

We report on a new technique, computational DNA hole spectroscopy, which creates spectra of electron hole probabilities vs. nucleotide position. A hole is a site of positive charge created when an electron is removed. Peaks in the hole spectrum depict sites where holes tend to localize and potentially trigger a base pair mismatch during replication. Our studies of mitochondrial DNA reveal a correlation between L-strand hole spectrum peaks and spikes in the human mutation spectrum. Importantly, we also find that hole peak positions that do not coincide with large variant frequencies often coincide with disease-implicated mutations and/or (for coding DNA) encoded conserved amino acids. This enables combining hole spectra with variant data to identify critical base pairs and potential disease 'driver' mutations. Such integration of DNA hole and variance spectra could ultimately prove invaluable for pinpointing critical regions of the vast non-protein-coding genome. An observed asymmetry in correlations, between the spectrum of human mtDNA variations and the L- and H-strand hole spectra, is attributed to asymmetric DNA replication processes that occur for the leading and lagging strands.

DNA/RNA transverse current sequencing: intrinsic structural noise from neighboring bases

Nanopore DNA sequencing via transverse current has emerged as a promising candidate for third-generation sequencing technology. It produces long read lengths which could alleviate problems with assembly errors inherent in current technologies. However, the high error rates of nanopore sequencing have to be addressed. A very important source of the error is the intrinsic noise in the current arising from carrier dispersion along the chain of the molecule, i.e., from the influence of neighboring bases. In this work we perform calculations of the transverse current within an effective multi-orbital tight-binding model derived from first-principles calculations of the DNA/RNA molecules, to study the effect of this structural noise on the error rates in DNA/RNA sequencing via transverse current in nanopores. We demonstrate that a statistical technique, utilizing not only the currents through the nucleotides but also the correlations in the currents, can in principle reduce the error rate below any desired precision.

Tunable spin-selective transport through DNA with mismatched base pairs

In our theoretical analysis of spin-selective transport through a homogeneous poly(G)-poly(C) DNA we explore the influence of a mismatched base pair in the DNA chain. The spin polarization of the electrical current through DNA is strongly sensitive to the presence of the mispair in a DNA with less than 20 base pairs. Replacing a canonical G-C base pair by a G-A mispair in homogeneous DNA can strongly decrease, increase up to an order of magnitude, or even change the sign of spin polarization of the electrical current. The mispair induced spin-selective current through DNA also depends on the location of the mispair within the DNA.

The interplay of mutations and electronic properties in disease-related genes

Electronic properties of DNA are believed to play a crucial role in many phenomena in living organisms, for example the location of DNA lesions by base excision repair (BER) glycosylases and the regulation of tumor-suppressor genes such as p53 by detection of oxidative damage. However, the reproducible measurement and modelling of charge migration through DNA molecules at the nanometer scale remains a challenging and controversial subject even after more than a decade of intense efforts. Here we show, by analysing 162 disease-related genes from a variety of medical databases with a total of almost 20,000 observed pathogenic mutations, a significant difference in the electronic properties of the population of observed mutations compared to the set of all possible mutations. Our results have implications for the role of the electronic properties of DNA in cellular processes, and hint at the possibility of prediction, early diagnosis and detection of mutation hotspots.

Solvent effects on structural and thermochemical properties of p53 tumor-suppressor gene: a molecular modeling approach in drug design

The p53 tumor-suppressor protein is a cellular phosphoprotein and a negative regulator of cell growth. Most p53 mutations occur in exons 5-8 within the DNA-binding domain. Therefore, p53 can potentially be targeted with novel drugs designed to bind to a mutation and restore its stability or wild-type conformation. For the current study, Hartree-Fock calculations were used to investigate the solvent-induced effects of five different solvent media (acetone, ethanol, methanol, dimethyl sulfoxide, and water) on the thermochemical parameters and relative energies, and on the multinuclear nuclear magnetic resonance shielding tensors of oxygen, nitrogen, and phosphorus nuclei, of GAT. To understand how the solvent affects the mutation region (the "hot spot") of p53, the relative energies of GAT in selected solvent media were determined. Some biological evidence suggested the structural stabilities of hot spots of GAT have the optimum temperature and solvent type for mutation. All the authors' findings are in accordance with common biological phenomena. Another important objective of this study was to compare the hydration Gibbs free energies of CUA and GAT in water using two different approaches where the solvent was treated as a continuum of the constant at different levels of Hartree-Fock theory. The Gibbs hydration energy values obtained in water with the polarized continuum model directly applied on the isolated CUA and GAT sequences were compared with those determined from the hydrated models with four, six, and eight water molecule clusters around the hot spots uracil and adenine. The clustered structures of water molecules around the hot spots of GAT (in DNA level) and CUA (in transcriptional level) were found to be energetically favored. The results of this study provide a reliable insight into the nature of mutation processes, which is of utmost importance for the study of biochemical structures, and provide a basis for drug design.

Investigation of solvent effect and NMR shielding tensors of p53 tumor-suppressor gene in drug design

The p53 tumor-suppressor gene encodes a nuclear phosphoprotein with cancer- inhibiting properties. The most probable cancerous mutations occur as point mutations in exons 5 up to 8 of p53, as a base pair substitution that encompasses CUA and GAT sequences. As DNA drug design represents a direct genetic treatment of cancer, in the research reported computational drug design was carried out to explore, at the Hartree-Fock level, effects of solvents on the thermochemical properties and nuclear magnetic resonance (NMR) shielding tensors of some atoms of CUA involved in the hydrogen-bonding network. The observed NMR shielding variations of the solutes caused by solvent change seemed significant and were attributed to solvent polarity, and solute-solvent and solvent-solute hydrogen-bonding interactions. The results provide a reliable insight into the nature of mutation processes. However, to improve our knowledge of the hydration pattern more rigorous computations of the hydrated complexes are needed.

Quantum transport anomalies in DNA containing mispairs

The effect of mispairs on charge transport in DNA of sequence (GC)(TA)(N)(GC)(3) connected to platinum electrodes is studied using the tight-binding model. With parameters derived from an ab initio density functional result, we calculate the current versus bias voltage for DNA with and without a mispair and for different numbers of (TA) basepairs N between the single and triple (GC) basepairs. The current decays exponentially with N under low bias but reaches a minimum under high bias when a multichannel transport mechanism is established. A (GA) mispair substituting a (TA) basepair near the middle of the (TA)(N) sequence usually enhances the current by one order due to its low ionization energy but may decrease the current significantly when an established multichannel mechanism is broken.

Influence of backbone on the charge transport properties of G4-DNA molecules: a model-based calculation

We put forward a model Hamiltonian to describe the influence of backbone energetics on charge transport through guanine-quadruplex DNA (G4-DNA) molecules. Our analytical results show that an energy gap can be produced in the energy spectrum of G4-DNA by hybridization effects between the backbone and the base and by on-site energy difference of the backbone from the base. The environmental effects are investigated by introducing different types of disorder into the backbone sites. Our numerical results suggest that the localization length of G4-DNA can be significantly enhanced by increasing the backbone disorder degree when the environment-induced disorder is sufficiently large. There exists a backbone disorder-induced semiconducting-metallic transition in short G4-DNA molecules, where G4-DNA behaves as a semiconductor if the backbone disorder is weak and behaves as a conductor if the backbone disorder degree surpasses a critical value.

Violation of the single-parameter scaling hypothesis in human chromosome 22 with charge transfer models

We investigate transport properties of DNA sequences in human chromosome 22 and compare the results with those of a random artificial DNA sequence based on the single- and double-stranded charge transfer models. The statistical quantities, including the Hurst exponent, the distribution of Lyapunov exponent (LE), the central moments, and the scaling parameter, are numerically calculated by using the transfer-matrix approach. It is found that the existence of satellite DNA segments in human chromosome 22 could result in deviations from usual Gaussian distribution of LE. Our results suggest that the presence of the satellite DNA segments, together with the long-range correlations and the base-pairing correlations could lead to the violation of single-parameter scaling hypothesis which holds for the random artificial DNA sequence although the behaviors of the averaged LEs for both DNA sequences are similar. This provides a viewpoint to analyze differences between the genomic DNA sequences and the nonliving random ones on the basis of localization properties of wave functions in the sequences.

Enhancement of transport in DNA-like systems induced by backbone disorder

We report a theoretical study highlighting the fundamental effects of backbone disorder which simulates the environmental complications on charge transport properties of biological and synthetic DNA molecules. Based on effective tight-binding models of duplex DNA, the Lyapunov coefficient and current-voltage characteristics are numerically calculated by varying the backbone disorder degree. In contrast to the localization picture that the conduction of duplex DNA becomes poorer when the backbone disorder degree is increased, we find that the backbone disorder can enhance the charge transport ability of the DNA molecules when the environment-induced disorder surpasses a critical value, giving rise to a semiconducting-metallic transition. The physical origin for this is traced back to the antiresonant effects. These results provide a scenario to interpret a variety of transport behaviors observed in DNA molecules and suggest perspectives for future experiments intending to control the charge transport through DNA-based nanodevices.

Strong localization of positive charge in DNA induced by its interaction with environment

We investigate a quantum state of positive charge in DNA. A quantum state of electron hole is determined by the competition of the pi-stacking interaction b sharing a charge between different base pairs and the interaction lambda with the local environment which attempts to trap charge. To determine which interaction dominates, we investigate charge quantum states in various (GC)(n) sequences choosing DNA parameters that satisfy experimental data for the balance of charge transfer rates G(+) <--> G(n)(+), n = 2, 3. We show that experimental data can be consistent with theory only assuming b<<lambda, meaning that charge is typically localized within the single G site. Consequently, as follows from our modeling consideration, any DNA duplex including the one consisting of identical base pairs cannot be considered as a molecular conductor. Our theory can be verified experimentally, measuring balance of charge transfer reactions G(+) <--> G(n)(+), n > or = 4 and comparing the experimental results with our predictions.