This book presents a comprehensive survey of DNA physical properties. Over the last 60 years physical properties of DNA molecules have been studied in detail, and the author believes that it is the right time to review them. The book is intended for molecular biologists, biochemists and physicists who want to know more about DNA biophysics. In addition, the book briefly considers physical aspects of DNA interaction with proteins that bind DNA specifically and nonspecifically. The level of presentation assumes some knowledge of molecular biology and physical chemistry, mainly at the level of introductory courses.

In accordance with the author's own research experience, the book combines theoretical and experimental approaches to the properties. Wherever it is possible, the chapters start from the theoretical descriptions of the phenomena followed by the application of these descriptions to experimental studies of particular problems.

There are no descriptions of methods that are used in DNA studies, except short remarks on the application of the major biophysical methods in this field. These major methods have been described in detail in other books on molecular biophysics (van Holde et al. 1998, Bloomfield et al. 1999). Excellent descriptions of general principles of the physical chemistry, often used in this book, as well as descriptions of many methods can be found in the book by Tinoco et al. (1995). However, we analyze the methods that were developed specifically for DNA studies.

I am grateful to my colleagues, who made very valuable comments on the chapters of this book, Maxim Frank-Kamenetskii, Neville Kallenbach, Ioulia Rouzina, and to my wife, Maria Vologodskaia, for her help during the book preparation.

In 1963 Dulbecco and Vogt, and Weil and Vinograd, discovered that dsDNA of the polyoma virus exists in a closed circular form (Dulbecco & Vogt 1963, Weil & Vinograd 1963). It turned out that this form is typical of bacterial DNA and of cytoplasmic DNA in animals. The distinctive feature of closed circular molecules is that its topological state cannot be altered by any conformational rearrangement that does not involve breaking DNA strands. This topological constraint is the basis for the fascinating properties of circular DNA molecules. The physical properties of circular DNA molecules is a subject of the current chapter.

Linking number of complementary strands and DNA supercoiling

Two forms of circular DNA molecules are extracted from the cell; they were designated as form I and form II (Weil & Vinograd 1963). The more compact form I was found to turn into form II after a single-stranded break was introduced into one chain of the double helix. Subsequent studies performed by Vinograd and co-workers linked the compactness of form I, in which both DNA strands are intact, to supercoiling. Form I is called the closed circular form. In this form each of the two strands that make up the DNA molecule are closed in on themselves. A diagram of closed circular DNA is presented in Fig. 6.1. The two strands of the double helix in closed circular DNA are topologically linked. In topological terms, the links between two strands of the double helix belong to a particular class, called the torus class (see Section 6.7). The quantitative description of such links is called the linking number, Lk, which may be determined in the following way (Fig. 6.2). One of the strands defines the edge of an imaginary surface (any such surface gives the same result). Lk is the algebraic (i.e. sign-dependent) number of intersections of the surface by the other strand.

Introduction

Retinal is a biological chromophore ubiquitous in visual receptors of higher life forms, but serving also as an antenna in light energy transformation and phototaxis of bacteria. The chromophore arises in various retinal proteins, the best known two being the visual receptor rhodopsin and the light-driven proton pump bacteriorhodopsin. The ubiquitous nature of retinal in photobiology is most remarkable as the molecule shows an extremely wide adaptability of its spectral absorption characteristics and a precise selection of its photoproducts, both properties steered by retinal proteins.

Rhodopsin (Rh) is a membrane protein of the rod cells in the retina of animal eyes and contains a retinal molecule as a chromophore surrounded by the protein's seven transmembrane helices (Khorana, 1992), as shown in Figure 11.1. Rhodopsin serves as the receptor protein for monochromic vision, in particular, for vision in the dark. Analogous retinal proteins, called iodopsins, exist in the cone cells of the retina and serve as receptor proteins for colour vision in daylight (Nathans et al., 1986).

Retinal proteins also serve in certain bacteria as light-driven proton pumps that maintain the cell potential, as in case of bacteriorhodopsin (bR) (Schulten and Tavan, 1978), or as light sensors in bacterial phototaxis (Spudich and Jung, 2005).

All retinal proteins are structurally homologous, being composed of seven transmembrane helices with a retinal chromophore bound to a lysine side group. The photoactivation mechanisms of the proteins' retinal moieties are similar, but distinct from each other. The primary event of retinal photoactivation is a photoisomerization reaction (Birge, 1990).

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).

In this chapter, we explore the opportunities that the dynamical quantum effects recently revealed as components of key functions of plants and higher organisms and described in previous chapters, might offer for the design of new nano-scale materials possessing quantum-enhanced functionality. We discuss the potential applications of such biomimetic materials with engineered quantum properties, and present a review of progress thus far on two prototypical systems: biomimetic light-harvesting materials and biomimetic magnetic sensors.

Potential applications of bio-inspired quantum materials

It is well appreciated that quantum dynamics can lead to enhanced performance in tasks such asmetrology (Giovannetti et al., 2011), computing (Nielsen and Chuang, 2001) and communication (Gisin and Thew, 2007). However, such enhancements have yet to be realized for artificial systems in the biological domain. As discussed in earlier chapters of this book, it has been demonstrated or hypothesized that quantum processes are critical to the accurate description of the functional dynamics of several biological systems. What opportunities do these observations present for the motivation and development of biomimetic materials? The possibility of constructing artificial materials with the ability to mimic natural systems leads to a diverse range of potential applications. A key question is thus whether we can use nature's ingenuity as inspiration and incorporate quantum effects into synthetic systems to provide quantum-enhanced function? Such explorations also hold out the tandem promise of achieving greater understanding of the role of quantum mechanics in biological function, since in contrast with the traditional top-down approach to investigating natural systems, this perspective requires the development of a bottom-up approach to synthesis of unnatural systems possessing capability to mimic all or part of some biological role.

Detecting quantum coherence

Observing quantum coherence is a tricky business. Even before we fire up the femtosecond laser systems and start our search, we need to ask ourselves some basic questions: What is coherence? How does coherence manifest in measurements? What methods can we use to detect and measure coherence? Only then, can we begin to interpret data to search for coherence and to try to make sense of the observed signals. In this section, I will discuss detecting quantum coherence both in theory and in practice. The goal of this section is to present a unified view of experimental approaches in broad strokes and to provide useful references to guide further exploration.

What is ‘quantum coherence’?

Firstly, the precise meaning of ‘quantum coherence’ must be pinned down. I define quantum coherences to be off-diagonal elements of the density matrix representing the ensemble. (I am explicitly setting aside questions of ‘quantum’ versus ‘classical’ coherences; let us simply assume that the system in question is best described quantum mechanically and presume that the coherences in such a system are also quantum in nature. The simple fact is that we don't yet have the tools to answer this debate definitively.) This definition, however, is still insufficient. The density matrix and the magnitudes of its off-diagonal elements in particular depend on the basis set used to write down the matrix. For the purposes of this chapter, I will consider the density matrix only in the Hamiltonian eigenbasis.

Recent progress in science and technology has led to the revival of an old question concerning the relevance of quantum effects in biological systems. Indeed Pascual Jordan's 1943 book, Die Physik und das Geheimnis des Lebens had already posed the question “Sind die Gesetze der Atomphysik und Quantenphysik für die Lebensvorgänge von wesentlicher Bedeutung?” (Are the laws of atomic and quantum physics of essential importance for life?) and coined the term Quanten-Biologie (quantum biology). At the time this question was essentially of a theoretical nature as the technology did not yet exist to pursue it in experiment.

Indeed quantum biology has been benefiting considerably from the refinement in experimental tools which is beginning to provide direct access to the observation of quantum dynamics in biological systems. Indeed, we are increasingly gaining sensitivity towards quantum phenomena at short lengths and timescales. In recent years, these newly found technological capabilities have helped to elevate the study of quantum biology from a mainly theoretical endeavour to a field in which theoretical questions, concepts and hypotheses may be tested experimentally and thus verified or disproved. We should stress here that experiments are essential to verify theoretical models because biological systems already have a complexity and structural variety that prevents us from knowing and controlling all of the aspects. Results obtained using these refined experimental techniques lead to new theoretical challenges and thus stimulate the development of novel theoretical approaches. It is this mutually beneficial interplay between experiment and theory that promises accelerated developments within the field.

When the revolutionary conceptual structure for the description of the physical world which we know as quantum mechanics was first formulated nearly 90 years ago, and its predictions tested in the laboratory, most of the experiments in question were on systems which were both very well characterized and reasonably well isolated from their environments, such as single electrons and atoms, small molecules and near-perfect crystalline solids.

While from the very start most physicists have taken it for granted that the formalism of quantum mechanics, when combined with appropriate system-specific information, can “in principle” account for all phenomena occurring in the physical world, including those usually regarded as the subject-matter of biology, until quite recently the overwhelmingly majority opinion has been that in a biological context the role of quantum theory is confined to elucidating the equilibrium structures of the relevant molecules and their reaction processes, and that subtle phenomena such as superposition and entanglement, of which we can now routinely exhibit spectacular effects at the level of a few well-isolated photons or atoms, play at most a very indirect role in any phenomena of biological interest. A major reason conventionally given for this view has been that biological systems, at least working ones, are by their very nature “warm and wet” – a phrase which in the physicist's lexicon translates to “prone to massive decoherence”; it looks as though any interesting superposition, say of different energy eigenstates of one's system, would be rapidly decohered by the ever-present, and usually microscopically very complex, environment.

Transport phenomena at the nanoscale exhibit both quantum (coherent) and classical (noisy) behaviour. Coherent and incoherent transfer are normally viewed as limiting cases of a certain underlying dynamics. However, there exist parameter regimes where an intricate interplay between environmental noise and quantum coherence emerges, and whose net effect is an increase in the efficiency of the transport process. In this chapter we illustrate this phenomenon in the context of excitation transport across quantum networks. These are model systems for the description of energy transfer within molecular complexes and, in particular, photosynthetic pigment–protein molecules, a type of biologically relevant structures whose dynamics has been recently shown to exhibit quantum coherent features. We show that nearly perfect transport efficiency is achieved in a regime that utilizes both coherent and noisy features, and argue that Nature may have chosen this intermediate regime to operate optimally.

Introduction

The dynamical behaviour of a quantum system can be substantially affected by interaction with a fluctuating environment and one might initially be led to expect a negative effect on quantum transport involving coherent hopping of a (quasi-) particle between localized sites. In this section, however, we demonstrate that quantum transport efficiency can be enhanced by a dynamical interplay of the quantum dynamics imposed by the system Hamiltonian with the pure dephasing induced by a fluctuating environment.

Introduction

In this chapter, we will focus on the phenomenon of quantum entanglement. Entanglement is a special property that some states of two or more quantum particles may possess. When particles are in an entangled state they are correlated. But entanglement is far more than mere correlation. Entanglement is a type of correlation that macroscopic objects cannot have, even in principle; it is what we call a ‘non-local’ correlation.

Entanglement, and the non-locality that derives from it, is by now considered to be, arguably, the most important aspect of quantum mechanics. Philosophically it leads to many puzzles and to a complete change in our view of nature. At the same time, the practical implications of this type of correlation are very significant. In particular, they can lead to the dramatically enhanced information processing capabilities that quantum systems possess. The whole field of quantum information processing (Steane, 1998; Bennett and DiVincenzo, 2000; Zoller et al., 2005) has entanglement at its core.

Given the above, it is natural to ask whether biological systems make use and take advantage of the enhanced possibilities that entanglement offers. It seems natural to expect this, especially at biological molecular level, where the laws of quantum mechanics apply.

Entanglement between two isolated particles is easy to obtain: almost every time two particles interact they get entangled. But entanglement is very fragile. When two entangled quantum systems interact with a third, they easily become entangled in a tri-partite way; however, any entanglement between any two of them is reduced or disappears altogether.

Introduction

Migratory birds travel spectacular distances each year, navigating and orienting by a variety of means, most of which are poorly understood. Among these is a remarkable ability to perceive the intensity and direction of the Earth's magnetic field (Mouritsen and Ritz, 2005; Wiltschko and Wiltschko, 2006; Johnsen and Lohmann, 2008). Biologically credible mechanisms for the detection of such a weak field (25–65 μT) are scarce, and in recent years just two proposals have emerged as front-runners. One, essentially classical, centers on clusters of magnetic iron-containing particles in the upper beak, which appear to act as a magnetometer for determining geographical position (Kirschvink and Gould, 1981; Kirschvink et al., 2001; Fleissner et al., 2007; Solov'yov and Greiner, 2007; Walker, 2008; Solov'yov and Greiner, 2009a, b; Falkenberg et al., 2010). The other relies on the quantum spin dynamics of transient photoinduced radical pairs (Schulten et al., 1978; Schulten, 1982; Schulten and Windemuth, 1986; Ritz et al., 2000b; Cintolesi et al., 2003; Möller et al., 2004; Mouritsen et al., 2004; Heyers et al., 2007; Liedvogel et al., 2007b, a; Solov'yov et al., 2007; Feenders et al., 2008; Maeda et al., 2008; Solov'yov and Schulten, 2009; Ritz et al., 2009; Rodgers and Hore, 2009; Zapka et al., 2009). Originally suggested by Schulten in 1978 (Schulten et al., 1978) as the basis of the avian magnetic compass sensor, this mechanism gained support from the subsequent observation that the compass is light dependent (Wiltschko et al., 1993) (for a review see e.g. (Wiltschko et al., 2010)).