The quantum-mechanical model proposed earlier by Skourtis and Nitzan (J. of Chem. Phys. 119, (2003) 6271) to describe a charge transfer in a fragment of artificial DNA molecule has been numerically investigated. The current rationale for the model is carried out and values of its parameters are indicated. Within this model, the description of the transport of a hole carrier in DNA is based on solutions to the time-dependent Schrödinger equation including damping effects. The non-unitary dynamics of the hole carrier is treated by us within the framework of a theory of continuous quantum measurements by the environment in an open quantum system. Results of numerical analysis of the model are in a good agreement with experimental observations and demonstrate two different types of the charged carrier motion, presumably tunneling and incoherent hopping. The main concepts of the theory of decoherence and superselection for open quantum systems and the prospects for their application for further study of various mechanisms of motion of a charged carrier in DNA are briefly discussed.
The quantum-mechanical model proposed earlier by Skourtis and Nitzan (J. of Chem. Phys. 119, (2003) 6271) to describe a charge transfer in a fragment of artificial DNA molecule has been numerically investigated. The current rationale for the model is carried out and values of its parameters are indicated. Within this model, the description of the transport of a hole carrier in DNA is based on solutions to the time-dependent Schrödinger equation including damping effects. The non-unitary dynamics of the hole carrier is treated by us within the framework of a theory of continuous quantum measurements by the environment in an open quantum system. Results of numerical analysis of the model are in a good agreement with experimental observations and demonstrate two different types of the charged carrier motion, presumably tunneling and incoherent hopping. The main concepts of the theory of decoherence and superselection for open quantum systems and the prospects for their application for further study of various mechanisms of motion of a charged carrier in DNA are briefly discussed.
The quantum-statistical model proposed earlier by Skourtis and Nitzan to describe a charge (hole) propagation in a fragment of artificial DNA molecule has been generalized and further investigated. A numerical simulation of a charge transport was carried out taking into account two different dissipative processes, including the capture of the charged carrier by the environment and the decoherence of its quantum wave properties due to the influence of stochastic fields of the environment. The interaction of the carrier with the environment is regulated by a small set of phenomenological parameters whose values vary in the process of simulation. Within this model, the propagation of a hole carrier in DNA is described by solving the quantum Franke-Kossakovski–Lindblad–Glauber–Sudarshan equation (hereinafter referred to as the Lindblad equation) for the carrier density matrix using the Lindblad MPO Solver program. Results of numerical analysis of the model are in a good agreement with experimental observations and demonstrate two different types of the charged carrier motion, presumably tunneling and incoherent hopping. The model is put in more general context and non-unitary dynamics of the hole carrier is treated within the framework of a theory of continuous quantum measurements by the environment in an open quantum system. The main concepts of the theory of decoherence and superselection for open quantum systems and the prospects for their application for further study of various mechanisms of motion of a charged carrier in DNA are briefly discussed.
The influence of quantum tunnelling on double hydrogen transfers within DNA base pairs is investigated by solving the time-dependent Schrodinger equation (TDSE) for a one-dimensional double well potential, whilst accounting for environment coupling. The energies of the canonical (standard, amino-keto) and tautomeric (non-standard, imino-enol) charge-neutral forms of the adenine-thymine base pair (A-T and A*-T*, respectively) are calculated using density functional theory. These compare favourably to results in existing literature. The reaction pathway is also calculated using a transition state search to provide the barrier height and shape, and these are combined to create the potential using a polynomial fit. It is found that tunnelling is very unlikely to be a significant mechanism for the creation of adenine-thymine tautomers within DNA, with the anti-Zeno effect from environment coupling only being able to boost the tunnelling probability at any given time to ~2 x 10-9. This is barely increased when varying several parameters, such as barrier height, potential asymmetry, and mass (kinetic isotope effect). In addition, the general effect on a quantum system by its surrounding environment is explored. A novel comparison between two distinct methods of environment coupling - dissipation (via the addition of a Lindblad term to the master equation) and von Neumann measurements - is performed. This is done using a simpler model of benzoic acid dimer, where it is shown that the two methods describe the same physical process of decoherence and can be thought of as equivalent until the link between them breaks down at high temperatures and measurement frequencies.
• Published in Nature's sister journal Communications Physics, proposing an 'open quantum systems approach to proton tunnelling in DNA'. • Analysis of G-C base pairs confirmed that the proton transfer rate by tunnelling is overwhelmingly higher than classical methods even at biological temperatures and in a dissipative environment. • Demonstrated a high tautomeric occupation probability... suggesting that DNA mutation is deeply governed by quantum mechanical processes. [Quantum Biology Society] Research revealing that the fundamental cause of mutations threatening the genetic stability of DNA—the core of life preservation—is based on quantum mechanical phenomena rather than classical biochemical reactions is drawing significant attention from the academic community. A paper published in Communications Physics, a sister journal of Nature, titled "An open quantum systems approach to proton tunnelling in DNA" verified this innovative hypothesis with a sophisticated physical model. A joint research team, including Louie Slocombe and Professor Jim Al-Khalili, thoroughly analyzed the quantum mechanical processes related to proton transfer. ■ Protons Piercing Through Hydrogen Bonds, Inducing 'Point Mutations' If a proton moves out of its orbit within the hydrogen bonds of the Guanine-Cytosine (G-C) base pair connecting the DNA double helix structure, tautomerisation occurs, altering the chemical structure of the base, which can lead to a point mutation, an error in genetic information. However, exactly how this process occurs in a warm and complex biological environment has long been a matter of debate. To solve this challenge, the research team applied an open quantum system that integrated an accurate structural model of the G-C base pair with the quantum dynamics of the hydrogen bond proton and the influence of the decoherent and dissipative cellular environment. ■ Quantum Effects Surviving Even in Biological Environments... "Tens of Thousands of Times Faster Than Over-the-Barrier Hopping" The analysis results completely overturned the conventional wisdom that quantum phenomena are confined only to the microscopic world or cryogenic temperatures. The research team found that, despite biological temperatures and environmental factors, the quantum tunnelling contribution to the proton transfer rate is several orders of magnitude (tens of thousands of times) larger than the classical 'over-the-barrier hopping' method, where particles gain energy to cross the barrier. Due to the strong quantum tunnelling effect, the canonical and tautomeric forms of the G-C base pair inter-convert over timescales far shorter than biological ones and very rapidly reach thermal equilibrium. ■ The Origins of Cancer and Evolution Lie in Quantum Probabilities What is even more surprising is that the tautomeric occupation probability through tunnelling reaches a significant level of 1.73 × 10⁻⁴. This suggests that such proton transfer may well play a far more dominant and important role in DNA mutation than the academic community has hitherto thought. This study, which proves that DNA mutations—the macroscopic consequences driving the onset of genetic diseases or cancer, and further, the evolution of life—are in fact thoroughly governed by microscopic quantum tunnelling phenomena, will serve as a powerful indicator of how Quantum Biology can innovate the paradigms of medicine and genetics in the future.
An open quantum system refers to a system that is further coupled to a bath system consisting of surrounding radiation fields, atoms, molecules, or proteins. The bath system is typically modeled by an infinite number of harmonic oscillators. This system-bath model can describe the time-irreversible dynamics through which the system evolves toward a thermal equilibrium state at finite temperature. In nuclear magnetic resonance and atomic spectroscopy, dynamics can be studied easily by using simple quantum master equations under the assumption that the system-bath interaction is weak (perturbative approximation) and the bath fluctuations are very fast (Markovian approximation). However, such approximations cannot be applied in chemical physics and biochemical physics problems, where environmental materials are complex and strongly coupled with environments. The hierarchical equations of motion (HEOM) can describe the numerically "exact" dynamics of a reduced system under nonperturbative and non-Markovian system-bath interactions, which has been verified on the basis of exact analytical solutions (non-Markovian tests) with any desired numerical accuracy. The HEOM theory has been used to treat systems of practical interest, in particular, to account for various linear and nonlinear spectra in molecular and solid state materials, to evaluate charge and exciton transfer rates in biological systems, to simulate resonant tunneling and quantum ratchet processes in nanodevices, and to explore quantum entanglement states in quantum information theories. This article presents an overview of the HEOM theory, focusing on its theoretical background and applications, to help further the development of the study of open quantum dynamics.
Abstract Simulating charge and energy transfer in extended molecular networks requires an effective model to include the environment because it significantly affects the quantum dynamics. A prototypical effect known as environment-assisted quantum transport (ENAQT) consists in the enhancement of the transfer efficiency by the interaction with an environment. A simple description of this phenomenon is obtained by a quantum master equation describing a quantum walk over the molecular network in the presence of inter-site decoherence. We consider the problem of simulating the dynamics underlying ENAQT in a digital quantum computer. Two different quantum algorithms are introduced, the first one based on stochastic Hamiltonians and the second one based on a collision scheme. We test both algorithms by simulating ENAQT in a small molecular network on a quantum computer emulator and provide a comparative analysis of the two approaches. Both algorithms can be implemented in a memory efficient encoding with the number of required qubits scaling logarithmically with the size of the simulated system while the number of gates increases quadratically. We discuss the algorithmic quantum trajectories generated by the two simulation strategies showing that they realize distinct unravellings of the site-dephasing master equation. In our approach, the non-unitary dynamics of the open system is obtained through effective representations of the environment, paving the way to digital quantum simulations of quantum transport influenced by structured environments.
Quantum biology, as introduced in the previous chapter, mainly studies the dynamical influence of quantum effects in biological systems. In processes such as exciton transport in photosynthetic complexes, radical pair spin dynamics in magnetoreception, and photo-induced retinal isomerization in the rhodopsin protein, a quantum description is a necessity rather than an option. The quantum modelling of biological processes is not limited to solving the Schrödinger equation for an isolated molecular structure. Natural systems are open to the exchange of particles, energy or information with their surrounding environments that often have complex structures. Therefore the theory of open quantum systems plays a key role in dynamical modelling of quantum-biological systems. Research in quantum biology and open quantum system theory have found a bilateral relationship. Quantum biology employs open quantum system methods to a great extent while serving as a new paradigm for development of advanced formalisms for non-equilibrium biological processes. In this chapter, we overview the basic concepts of quantum mechanics and approaches to open quantum system (or decoherence ) dynamics. Here, we do not intend to discuss all aspects of about a century-old theory of open quantum systems that dates back to the original work of Paul Dirac on atomic radiative emission and absorption (Dirac, 1927). Instead, we mainly focus on the integro-differential equations that are commonly used for modelling quantum-biological systems. Interested readers can learn more about open quantum systems in various books and review articles in both physics and chemistry literature, including the references (Kraus, 1983; Breuer and Petruccione, 2002; Kubo et al. , 2003; Weiss, 2008; May and Kühn, 2011).