Controlling the charge-transfer dynamics of two-level systems around avoided crossings.

Two-level quantum systems are fundamental physical models that continue to attract growing interest due to their crucial role as a building block of quantum technologies. The exact analytical solution of the dynamics of these systems is central to control theory and its applications, such as that to quantum computing. In this study, we reconsider the two-state charge transfer problem by extending and using a methodology developed to study (pseudo)spin systems in quantum electrodynamics contexts. This approach allows us to build a time evolution operator for the charge transfer system and to show new opportunities for the coherent control of the system dynamics, with a particular emphasis on the critical dynamic region around the transition state coordinate, where the avoided crossing of the energy levels occurs. We identify and propose possible experimental implementations of a class of rotations of the charge donor (or acceptor) that endow the electronic coupling matrix element with a time-dependent phase that can be employed to realize controllable coherent dynamics of the system across the avoided level crossing. The analogy of these rotations to reference frame rotations in generalized semiclassical Rabi models is discussed. We also show that the physical rotations in the charge-transfer systems can be performed so as to implement quantum gates relevant to quantum computing. From an exquisitely physical-mathematical viewpoint, our approach brings to light situations in which the time-dependent state of the system can be obtained without resorting to the special functions appearing in the Landau-Zener approach.

Unraveling the electronic origin of a special feature in the triplet-minus-singlet spectra of carotenoids in natural photosystems.

The influence of carotenoid triplet states on the Qy electronic transitions of chlorophylls has been observed in experiments on light-harvesting complexes over the past three decades, but the interpretation of the resulting spectral feature in the triplet minus singlet (T-S) absorption spectra of photosystems is still debated, as the physical-chemical explanation of this feature has been elusive. Here, we resolve this debate, by explaining the T-S spectra of pigment complexes over the Qy-band spectral region through a comparative study of chlorophyll-carotenoid model dyads and larger pigment complexes from the main light harvesting complex of higher plants (LHCII). This goal is achieved by combining state-of-the-art time-dependent density functional theory with analysis of the relationship between electronic properties and nuclear structure, and by comparison to the experiment. We find that the special signature in the T-S spectra of both model and natural photosystems is determined by singlet-like triplet excitations that can be described as effective singlet excitations on chlorophylls influenced by a stable electronic triplet on the carotenoid. The comparison with earlier experiments on different light-harvesting complexes confirms our theoretical interpretation of the T-S spectra in the Qy spectral region. Our results indicate an important role for the chlorophyll-carotenoid electronic coupling, which is also responsible for the fast triplet-triplet energy transfer, suggesting a fast trapping of the triplet into the relaxed carotenoid structure. The gained understanding of the interplay between the electronic and nuclear structures is potentially informative for future studies of the mechanism of photoprotection by carotenoids.

Quantum-Classical Hybrid Systems and Ehrenfest's Theorem.

The conceptual analysis of quantum mechanics brings to light that a theory inherently consistent with observations should be able to describe both quantum and classical systems, i.e., quantum-classical hybrids. For example, the orthodox interpretation of measurements requires the transient creation of quantum-classical hybrids. Despite its limitations in defining the classical limit, Ehrenfest's theorem makes the simplest contact between quantum and classical mechanics. Here, we generalized the Ehrenfest theorem to bipartite quantum systems. To study quantum-classical hybrids, we employed a formalism based on operator-valued Wigner functions and quantum-classical brackets. We used this approach to derive the form of the Ehrenfest theorem for quantum-classical hybrids. We found that the time variation of the average energy of each component of the bipartite system is equal to the average of the symmetrized quantum dissipated power in both the quantum and the quantum-classical case. We expect that these theoretical results will be useful both to analyze quantum-classical hybrids and to develop self-consistent numerical algorithms for Ehrenfest-type simulations.

Adenine Fine-Tunes DNA Photolyase's Repair Mechanism.

The comparative study of DNA repair by mesophilic and extremophilic photolyases helps us understand the evolution of these enzymes and their role in preserving life on our changing planet. The mechanism of repair of cyclobutane pyrimidine dimer lesions in DNA by electron transfer from the flavin adenine dinucleotide cofactor is the subject of intense interest. The role of adenine in mediating this process remains unresolved. Using microsecond molecular dynamics simulations, we find that adenine mediates the electron transfer in both mesophile and extremophile DNA photolyases through a similar mechanism. In fact, in all photolyases studied, the molecular conformations with the largest electronic couplings between the enzyme cofactor and DNA show the presence of adenine in 10-20% of the strongest-coupling tunneling pathways between the atoms of the electron donor and acceptor. Our theoretical analysis finds that adenine serves the critical role of fine-tuning rather than maximizing the donor-acceptor coupling within the range appropriate for the repair function.

Hermitian and Unitary Almost-Companion Matrices of Polynomials on Demand.

We introduce the concept of the almost-companion matrix (ACM) by relaxing the non-derogatory property of the standard companion matrix (CM). That is, we define an ACM as a matrix whose characteristic polynomial coincides with a given monic and generally complex polynomial. The greater flexibility inherent in the ACM concept, compared to CM, allows the construction of ACMs that have convenient matrix structures satisfying desired additional conditions, compatibly with specific properties of the polynomial coefficients. We demonstrate the construction of Hermitian and unitary ACMs starting from appropriate third-degree polynomials, with implications for their use in physical-mathematical problems, such as the parameterization of the Hamiltonian, density, or evolution matrix of a qutrit. We show that the ACM provides a means of identifying the properties of a given polynomial and finding its roots. For example, we describe the ACM-based solution of cubic complex algebraic equations without resorting to the use of the Cardano-Dal Ferro formulas. We also show the necessary and sufficient conditions on the coefficients of a polynomial for it to represent the characteristic polynomial of a unitary ACM. The presented approach can be generalized to complex polynomials of higher degrees.

Invariant-Parameterized Exact Evolution Operator for SU(2) Systems with Time-Dependent Hamiltonian.

We report the step-by-step construction of the exact, closed and explicit expression for the evolution operator U(t) of a localized and isolated qubit in an arbitrary time-dependent field, which for concreteness we assume to be a magnetic field. Our approach is based on the existence of two independent dynamical invariants that enter the expression of SU(2) by means of two strictly related time-dependent, real or complex, parameters. The usefulness of our approach is demonstrated by exactly solving the quantum dynamics of a qubit subject to a controllable time-dependent field that can be realized in the laboratory. We further discuss possible applications to any SU(2) model, as well as the applicability of our method to realistic physical scenarios with different symmetry properties.

Symmetry-Induced Emergence of a Pseudo-Qutrit in the Dipolar Coupling of Two Qubits.

We investigate a system of two identical and distinguishable spins 1/2, with a direct magnetic dipole-dipole interaction, in an external magnetic field. Constraining the hyperfine tensor to exhibit axial symmetry generates the notable symmetry properties of the corresponding Hamiltonian model. In fact, we show that the reduction of the anisotropy induces the invariance of the Hamiltonian in the 3×3 subspace of the Hilbert space of the two spins in which S^2 invariably assumes its highest eigenvalue of 2. By means of appropriate mapping, it is then possible to choose initial density matrices of the two-spin system that evolve in such a way as to exactly simulate the time evolution of a pseudo-qutrit, in the sense that the the actual two-spin system nests the subdynamics of a qutrit regardless of the strength of the magnetic field. The occurrence of this dynamic similitude is investigated using two types of representation for the initial density matrix of the two spins. We show that the qutrit state emerges when the initial polarizations and probability vectors of the two spins are equal to each other. Further restrictions on the components of the probability vectors are reported and discussed.

Mechanism of Side Chain-Controlled Proton Conductivity in Bioinspired Peptidic Nanostructures.

Bioinspired peptide assemblies are promising candidates for use as proton-conducting materials in electrochemical devices and other advanced technologies. Progress toward applications requires establishing foundational structure-function relationships for transport in these materials. This experimental-theoretical study sheds light on how the molecular structure and proton conduction are linked in three synthetic cyclic peptide nanotube assemblies that comprise the three canonical basic amino acids (lysine, arginine, and histidine). Experiments find an order of magnitude higher proton conductivity for lysine-containing peptide assemblies compared to histidine and arginine containing assemblies. The simulations indicate that, upon peptide assembly, the basic amino acid side chains are close enough to enable direct proton transfer. The proton transfer kinetics is determined in the simulations to be governed by the structure and flexibility of the side chains. Together, experiments and theory indicate that the proton mobility is the main determinant of proton conductivity, critical for the performance of peptide-based devices.

Temperature Dependence of Charge and Spin Transfer in Azurin.

The steady-state charge and spin transfer yields were measured for three different Ru-modified azurin derivatives in protein films on silver electrodes. While the charge-transfer yields exhibit weak temperature dependences, consistent with operation of a near activation-less mechanism, the spin selectivity of the electron transfer improves as temperature increases. This enhancement of spin selectivity with temperature is explained by a vibrationally induced spin exchange interaction between the Cu(II) and its chiral ligands. These results indicate that distinct mechanisms control charge and spin transfer within proteins. As with electron charge transfer, proteins deliver polarized electron spins with a yield that depends on the protein's structure. This finding suggests a new role for protein structure in biochemical redox processes.

Correlation between Charge Transport and Base Excision Repair in the MutY-DNA Glycosylase.

Experimental evidence suggests that DNA-mediated redox signaling between high-potential [Fe4S4] proteins is relevant to DNA replication and repair processes, and protein-mediated charge transfer (CT) between [Fe4S4] clusters and nucleic acids is a fundamental process of the signaling and repair mechanisms. We analyzed the dominant CT pathways in the base excision repair glycosylase MutY using molecular dynamics simulations and hole hopping pathway analysis. We find that the adenine nucleobase of the mismatched A·oxoG DNA base pair facilitates [Fe4S4]-DNA CT prior to adenine excision by MutY. We also find that the R153L mutation in MutY (linked to colorectal adenomatous polyposis) influences the dominant [Fe4S4]-DNA CT pathways and appreciably decreases their effective CT rates.

Mutation effects on charge transport through the p58c iron-sulfur protein.

Growing experimental evidence indicates that iron-sulfur proteins play key roles in DNA repair and replication. In particular, charge transport between [Fe4S4] clusters, mediated by proteins and DNA, may convey signals to coordinate enzyme action. Human primase is a well studied [Fe4S4] protein, and its p58c domain (which contains an [Fe4S4] cluster) plays a role in the initiation of DNA replication. The Y345C mutation in p58c is linked to gastric tumors and may influence the protein-mediated charge transport. The complexity of protein-DNA systems, and the intricate electronic structure of [Fe4S4] clusters, have impeded progress into understanding functional charge transport in these systems. In this study, we built force fields to describe the high potential [Fe4S4] cluster in both oxidation states. The parameterization is compatible with AMBER force fields and enabled well-balanced molecular dynamics simulations of the p58c-RNA/DNA complex relevant to the initiation of DNA replication. Using the molecular mechanics Poisson-Boltzmann and surface area solvation method on the molecular dynamics trajectories, we find that the p58c mutation induces a modest change in the p58c-duplex binding free energy in agreement with recent experiments. Through kinetic modeling and analysis, we identify key features of the main charge transport pathways in p58c. In particular, we find that the Y345C mutation partially changes the composition and frequency of the most efficient (and potentially relevant to the biological function) charge transport pathways between the [Fe4S4] cluster and the duplex. Moreover, our approach sets the stage for a deeper understanding of functional charge transfer in [Fe4S4] protein-DNA complexes.

Electrostatic Field-Induced Oscillator Strength Focusing in Molecules.

The development of light-harvesting devices based on molecular materials depends critically on the ability to focus the electronic oscillator strength of molecules into the UV-vis spectral window. Typical molecular chromophores have only about 1% of their total electronic oscillator strength in this spectral region and thus perform at a small fraction of their possible effectiveness. This theoretical study finds that the electronic oscillator strength of polyenes in the UV-vis region may be enhanced by 1 order of magnitude using electrostatic fields, motivating specific experimental studies of oscillator strength focusing. We find scaling relationships between the polyene length, the intensity of the applied field, and the field-induced increase in oscillator strength that are useful for the implementation of light-harvesting strategies based on polyenes.

2'-Deoxy-2'-fluoro-arabinonucleic acid: a valid alternative to DNA for biotechnological applications using charge transport.

The non-biological 2'-deoxy-2'-fluoro-arabinonucleic acid (2'F-ANA) may be used as a valid alternative to DNA in biomedical and electronic applications because of its higher resistance to hydrolysis and nuclease degradation. However, the advantage of using 2'F-ANA in such applications also depends on its charge-transfer properties compared to DNA. In this study, we compare the charge conduction properties of model 2'F-ANA and DNA double-strands, using structural snapshots from MD simulations to calculate the electronic couplings and reorganization energies associated with the hole transfer steps between adjacent nucleobase pairs. Inserting these charge-transfer parameters into a kinetic model for charge conduction, we find similar conductive properties for DNA and 2'F-ANA. Moreover, we find that 2'F-ANA's enhanced chemical stability does not correspond to a reduction in the nucleobase π-stack structural flexibility relevant to both electronic couplings and reorganization free energies. Our results promote the use of 2'F-ANA in applications that can be based on charge transport, such as biosensing and chip technology, where its chemical stability and conductivity can advantageously combine.

Correction: Charge Transfer between [4Fe4S] Proteins and DNA Is Unidirectional: Implications for Biomolecular Signaling.

[This corrects the article PMC6350243.].

How To Extract Quantitative Information on Electronic Transitions from the Density Functional Theory "Black Box".

Electronic couplings and vertical excitation energies are crucial determinants of charge and excitation energy transfer rates in a broad variety of processes ranging from biological charge transfer to charge transport through inorganic materials, from molecular sensing to intracellular signaling. Density Functional Theory (DFT) is generally used to calculate these critical parameters, but the quality of the results is unpredictable because of the semiempirical nature of the available DFT approaches. This study identifies a small set of fundamental rules that enables accurate DFT computation of electronic couplings and vertical excitation energies in molecular complexes and materials. These rules are applied to predict efficient DFT approaches to coupling calculations. The result is an easy-to-use guide for reliable DFT descriptions of electronic transitions.

Mapping hole hopping escape routes in proteins.

A recently proposed oxidative damage protection mechanism in proteins relies on hole hopping escape routes formed by redox-active amino acids. We present a computational tool to identify the dominant charge hopping pathways through these residues based on the mean residence times of the transferring charge along these hopping pathways. The residence times are estimated by combining a kinetic model with well-known rate expressions for the charge-transfer steps in the pathways. We identify the most rapid hole hopping escape routes in cytochrome P450 monooxygenase, cytochrome c peroxidase, and benzylsuccinate synthase (BSS). This theoretical analysis supports the existence of hole hopping chains as a mechanism capable of providing hole escape from protein catalytic sites on biologically relevant timescales. Furthermore, we find that pathways involving the [4Fe4S] cluster as the terminal hole acceptor in BSS are accessible on the millisecond timescale, suggesting a potential protective role of redox-active cofactors for preventing protein oxidative damage.

Charge Transfer between [4Fe4S] Proteins and DNA Is Unidirectional: Implications for Biomolecular Signaling.

Recent experiments suggest that DNA-mediated charge transport might enable signaling between the [4Fe4S] clusters in the C-terminal domains of human DNA primase and polymerase α, as well as the signaling between other replication and repair high-potential [4Fe4S] proteins. Our theoretical study demonstrates that the redox signaling cannot be accomplished exclusively by DNA-mediated charge transport because part of the charge transfer chain has an unfavorable free energy profile. We show that hole or excess electron transfer between a [4Fe4S] cluster and a nucleic acid duplex through a protein medium can occur within microseconds in one direction, while it is kinetically hindered in the opposite direction. We present a set of signaling mechanisms that may occur with the assistance of oxidants or reductants, using the allowed charge transfer processes. These mechanisms would enable the coordinated action of [4Fe4S] proteins on DNA, engaging the [4Fe4S] oxidation state dependence of the protein-DNA binding affinity.

A single AT-GC exchange can modulate charge transfer-induced p53-DNA dissociation.

Using molecular dynamics simulations and electronic structure theory, we shed light on the charge dynamics that causes the differential interaction of tumor suppressor protein p53 with the p21 and Gadd45 genes in response to oxidative stress. We show that the sequence dependence of this selectivity results from competing charge transfer to the protein and through the DNA, with implications on the use of genome editing tools to influence the p53 regulatory function.

Electron transfer characteristics of 2'-deoxy-2'-fluoro-arabinonucleic acid, a nucleic acid with enhanced chemical stability.

The non-biological nucleic acid 2'-deoxy-2'-fluoro-arabinonucleic acid (2'F-ANA) may be of use because of its higher chemical stability than DNA in terms of resistance to hydrolysis and nuclease degradation. In order to investigate the charge transfer characteristics of 2'F-ANA, of relevance to applications in nucleic acid-based biosensors and chip technologies, we compare the electronic couplings for hole transfer between stacked nucleobase pairs in DNA and 2'F-ANA by carrying out density functional theory (DFT) calculations on geometries taken from molecular dynamics simulations. We find similar averages and distribution widths of the base-pair couplings in the two systems. On the basis of this result, 2'F-ANA is expected to have charge transfer properties similar to those of DNA, while offering the advantage of enhanced chemical stability. As such, 2'F-ANA may serve as a possible alternative to DNA for use in a broad range of nanobiotechnological applications. Furthermore, we show that the (experimentally observed) enhanced chemical stability resulting from the backbone modifications does not cause reduced fluctuations of the base-pair electronic couplings around the values found for "ideal" B-DNA (with standard step parameter values). Our study also supports the use of a DFT implementation, with the M11 functional, of the wave function overlap method to compute effective electronic couplings in nucleic acid systems.

Determinants of Photolyase's DNA Repair Mechanism in Mesophiles and Extremophiles.

Light-driven DNA repair by extremophilic photolyases is of tremendous importance for understanding the early development of life on Earth. The mechanism for flavin adenine dinucleotide repair of DNA lesions is the subject of debate and has been studied mainly in mesophilic species. In particular, the role of adenine in the repair process is poorly understood. Using molecular docking, molecular dynamics simulations, electronic structure calculations, and electron tunneling pathways analysis, we examined adenine's role in DNA repair in four photolyases that thrive at different temperatures. Our results indicate that the contribution of adenine to the electronic coupling between the flavin and the cyclobutane pyrimidine dimer lesion to be repaired is significant in three (one mesophilic and two extremophilic) of the four enzymes studied. Our analysis suggests that thermophilic and hyperthermophilic photolyases have evolved structurally to preserve the functional position (and thus the catalytic function) of adenine at their high temperatures of operation. Water molecules can compete with adenine in establishing the strongest coupling pathway for the electron transfer repair process, but the adenine contribution remains substantial. The present study also reconciles prior seemingly contradictory conclusions on the role of adenine in mesophile electron transfer repair reactions, showing how adenine-mediated superexchange is conformationally gated.