Photosynthesis is the biological process by which the energy of the Sun is collected, converted and stored in chemical bonds needed to power life. Therefore, photosynthesis serves as the vital link between the light energy of the Sun and almost all living organisms on Earth. In this chapter we will focus on the first steps of photosynthesis: energy collection and conversion, i.e. light-harvesting and charge separation, highlighting the role of quantum effects on the ultrafast dynamics and quantum efficiency of these two remarkable processes. Both experimental and theoretical approaches will be described and combined.

Photosynthesis

In photosynthesis solar energy is absorbed by the light-harvesting antenna and transferred to the photosynthetic reaction centre (RC) within several tens of picoseconds. In the RC, the absorbed excitation energy is converted into electrochemical energy by means of an ultra fast charge separation. Photosynthetic purple bacteria employ a single reaction centre, in contrast, in photosynthesis of plants, algae and cyanobacteria, two reaction centres, Photosystem II (PSII) and Photosystem I (PSI), operate in series. PSII uses light to extract electrons from water (to produce oxygen), while PSI uses light to reduce NADP+ to NADPH. The subsequent electron transfer from PSII to PSI is coupled to the build-up of a proton motive force (pmf) that is used to form ATP. NADPH and ATP are required in the Calvin–Benson cycle to produce a reduced sugar. In the following we will discuss photosynthetic charge separation and photosynthetic light-harvesting with an emphasis on the role of quantum effects.

Photo-induced dynamics of molecular systems

Life is intimately connected with the light from the sun, and many properties of living matter are tuned to its spectrum. Many biological functions, be it for harnessing the sun's power or for protection from its harmful rays, rely on interaction of specific molecules with ultraviolet (UV), visible or infrared (IR) light. In this chapter, we will develop a theoretical description of this interaction, which forms the basis both of our current understanding of photo-induced processes and the design of experimental methods used to investigate their details.

Among the biologically relevant photo-induced processes, photosynthesis probably occupies the most prominent place. Essentially all of the energy that is used by the biosphere is a result of photosynthesis, and the prospect of connecting humanity to the same energy source has recently motivated many interdisciplinary research lines. Insight about the design and function of natural photosynthetic systems is likely to play an important role in future research. Within the limited scope of this chapter it is therefore reasonable to limit ourselves to photosynthesis motivated molecular systems. Much of the theory presented in the following sections applies even beyond photosynthesis, e.g. in experiments on molecules related to vision, DNA photo-protection, or in IR spectroscopy of molecular vibrations. However, one has to keep in mind that approximations and models applicable in one field might not work well in another. In this chapter we will introduce and discuss concepts that, together with a good knowledge of a particular physical problem, should enable the reader to develop a theory in order to understand certain important classes of spectroscopic experiments on biomolecules.

Phonon assisted tunnelling in olfaction

Human vision is impressive, but the front-end mechanism – how the photons incident on the eye are detected – is quite well understood: they are absorbed by rhodopsin causing electronic transitions that lead, via a sequence of amplification steps, to a signal sent to the brain. Olfaction is somewhat more puzzling. Unlike photons, which differ only in wavelength, olfaction must detect and, harder still, discriminate between thousands of molecules (odourants) with their different physical and chemical properties. What is more, the repertoire of odourants is not fixed: newly synthesized odourants can be smelled immediately. It has been found empirically that to be detectable, the odourant molecules must of course be volatile, and typically contain fewer than 16 carbons: unless exotic heavy atoms are present, this means odourants have a maximum weight of 240 daltons (about 50 atoms). Empirically again, no two odourants (excluding enantiomer pairs) have ever been found to smell exactly identical.

How is odour character written into a molecule? A century of synthetic chemistry and hundreds of thousands of synthesized molecules have failed to provide an answer. There are some regularities in structure–odour relations, but none amount to a theory endowed with predictive power. Reviews of the field have for a long time consisted largely of lists of molecules grouped by odour character. More recent reviews suggest that a theory of structure–odour relations is not just around the corner and may, in fact, be impossible (Sell, 2006).

Introduction

Protein electron transfer (ET) reactions are central to biological function. They are important components of bioenergetic pathways (photosynthesis and respiration) and they are involved in biological signalling and in the generation and the control of disease (Marcus and Sutin, 1985; Bendall, 1996; Canters and Vijgenboom, 1997; Page et al., 1999; Blankenship, 2002; Gray and Winkler, 2003, 2005). For a fundamental understanding of these biological processes it is necessary to study protein ET mechanisms at the molecular level. Protein ET physics is very rich because it involves charge transport through dynamic and responsive (to the transferring charge) molecular media organized in cellular molecular assemblies. A common feature among protein ET assemblies is that they are designed to move electrons to specific locations along transport pathways that partially suppress backward ET (Figure 9.1). In many cases the structures and dynamics of the protein ET complexes are such that ET takes place with high efficiency (Blankenship, 2002). Needless to say, an understanding of structural and dynamical effects on protein ET processes is very important for the development of new biomimetic electronic and energy-conversion materials with controlled functionalities (Jortner and Ratner, 1997; Balzani et al., 2001; Adams et al., 2003; Blankenship et al., 2011). The field of biological ET (and in particular protein ET) is one of the oldest fields in molecular biophysics (Marcus and Sutin, 1985; Bendall, 1996; Page et al., 1999; Jortner and Bixon, 1999; Kuznetsov and Ulstrup, 1999; May and Kühn, 2011; Balzani et al., 2001; Blankenship, 2002; Gray and Winkler, 2003, 2005; Nitzan, 2006).

Introduction

Decades of effort in structural biology and ultrafast spectroscopy have elucidated many details of natural photosynthesis (Blankenship, 2002; Hu et al., 2002), and it is now a well-established fact that the initial light-harvesting process that leads up to the collection of energy at reaction centres, where charge transfer reaction occurs, is a process with almost perfect efficiency. The mechanism underlying the energy migration in a photosynthetic system is a fundamentally quantum-mechanical one, known as excitation energy transfer (EET) or resonance energy transfer (RET) (Silbey, 1976; Agranovich and Galanin, 1982; Scholes, 2003; May and Kühn, 2011; Olaya-Castro and Scholes, 2011).

Resonance energy transfer is ubiquitous, and had been observed as sensitized luminescence long before modern quantum-mechanical understanding of molecular systems was established (Agranovich and Galanin, 1982). Normally, when a molecule becomes excited electronically by absorbing a photon, it luminesces by emitting another photon, within about a nanosecond, if it is fluorescence, or much later for phosphorescence. However, when another molecule with similar excitation energy is present within a distance of tens of nanometres, it can swap its excitation with the molecule as follows:

D∗ + A → D + A∗,

where D∗ (D) is the excited (ground) state donor of the energy and A (A∗) is the ground (excited) state acceptor. Thus, the excitation of D sensitizes that of A.

Clear and sensible understanding of the RET process had been beyond the reach of classical mechanics as had any other molecular processes involving matter–radiation interaction.

Structure

Carbon nanotubes (CNT) and fullerenes are large molecules constructed entirely of carbons. Single-walled carbon nanotubes (SWNT) can be viewed as a strip cut from an infinite graphene sheet rolled up into a tube (see Figure 15.1). The diameter and helicity of a SWNTare uniquely defined by the roll-up vector Ck = na1 + ma2 that connects crystallographically equivalent sites on the graphene lattice, where a1 and a2 are the graphene lattice vectors and n and m are integers. Translation vector T is along the tube axis and, thus, orthogonal to Ck. In terms of such definitions, integers n and m characterize the rolling directions, chirality and diameter d = |Ck|/π of a particular carbon nanotube, therefore, SWNTs are usually defined by these two numbers as (n, m).

Electronic properties in 1D systems

Translation symmetry is the main feature of solid states, which permits classification of the wavefunctions of any electronic states. According to the so-called Bloch theorem, the wavefunctions of a periodic system ψ(r) are given as products of a periodic function unk(r) and the exponential phase function exp(ikr), ψnk(r) = exp(ikr)unk(r). The quantum number n is a property of the unit cell. The wavenumber, k, is the main quantum number of the periodic systems, which satisfies the translation symmetry (Peierls, 1995). Thus, the state corresponding to any k-number is the stationary state with the energy eigenvalue E(k).

Introduction

Photosynthesis is fundamental to life on Earth as it establishes access to the main energy source of the biosphere, sunlight (Blankenship, 2002). Photosynthesis is based on the interaction between living matter and the sun's radiation field, mainly visible light. This interaction involves the electrons of biological macromolecules and, accordingly, the process of light absorption is governed by quantum physics. During the course of biological evolution, photosynthetic lifeforms learned to exploit quantum physics in ingenious ways, in particular, under the circumstances of physiological temperature. A description of quantum phenomena under the influence of strong thermal effects as arise under these circumstances is challenging. Indeed, the quantum biology of photosynthesis is an active and fascinating research area.

Photosynthesis, in general, is understood to encompass the various processes in living cells by which lifeforms utilize sunlight to drive chemical synthesis. This involves primary processes of light-harvesting, transformation of electronic excitation energy into a membrane potential, as well as the splitting of water into oxygen, abstracting electrons that are added to molecules of nicotinamide adenine dinucleotide phosphate (NADPH+) at a high redox potential. The membrane potential drives the synthesis of adenosine triphosphate (ATP) which is used to fuel many processes in living cells. In plant photosynthesis NADPH+ and ATP are needed for the synthesis of sugar and starch, the most widely known products of photosynthesis. Because of its fundamental importance in cellular energetics, photosynthesis has been the subject of great evolutionary pressure such that, amidst a deep overall similarity, many variants have developed in the competition for habitats and efficiency.

Introduction

Key features of quantum mechanics are the uncertainty principle, wave–particle duality, quantization of energies and the modification of classical probability laws. Biology is concerned with how natural systems function – from understanding how genetically coded information is replicated, to attaining a mechanistic model for complex multistep reactions. Recently researchers have been asking whether quantum mechanics, normally the domain of physics, is also needed to understand some biological processes. This field includes fascinating developments in theory and experiment, as well as multidisciplinary discussion, and the state-of-the-art is documented in this book. Erwin Schrödinger, in his famous book What is Life? (Schrödinger, 1944), noted that quantum mechanics accounts for the stability of living things and their cellular processes because of our understanding, via quantum mechanics, of the stability and structure of molecules. The fact that quantum effects create, sometimes large, energy gaps between different states of a chemical system is also important. Such energy gaps, between electronic energy levels, enable living organisms to capture and store the energy carried from the sun by photons, and to visualize the world around them via optically induced chemical reactions. Davydov's view in Biology and Quantum Mechanics (Davydov, 1982) was that quantum mechanics is most relevant for isolated systems in pure states and therefore is of little importance for biological systems that are in statistical states at thermal equilibrium.

Introduction

For a system under thermal conditions in a heat bath with temperature T, the dynamics of each of the system particles is influenced by interactions with the heat-bath particles. If quantum effects are negligible (what we will assume in the following), the classical motion of any system particle looks erratic; the particle follows a stochastic path. The system can “gain” energy from the heat bath by these collisions (which are typically more generally called “thermal fluctuations”) or “lose” energy by friction effects (dissipation). The total energy of the coupled system of heat bath and particles is a conserved quantity, i.e., fluctuation and dissipation refer to the energetic exchange between heat bath and system particles only. Consequently, the coupled system is represented by a microcanonical ensemble, whereas the particle system is in this case represented by a canonical ensemble: The energy of the particle system is not a constant of motion. Provided heat bath and system are in thermal equilibrium, i.e., heat-bath and system temperature are identical, fluctuations and dissipation balance each other. This is the essence of the celebrated fluctuation-dissipation theorem [74]. In equilibrium, only the statistical mean of the particle system energy is constant in time.

This canonical behavior of the system particles is not accounted for by standard Newtonian dynamics (where the system energy is considered to be a constant of motion). In order to perform molecular dynamics (MD) simulations of the system under the influence of thermal fluctuations, the coupling of the system to the heat bath is required. This is provided by a thermostat, i.e., by extending the equations of motion by additional heatbath coupling degrees of freedom [75].

The intrinsic nature of secondary structures

Resolving structural properties of single molecules is a fundamental issue as molecular functionality strongly depends on the capability of the molecules to form stable conformations. Experimentally, the identification of substructures is typically performed, for example, by means of single-molecule microscopy, X-ray analyses of polymer crystals, or NMR for polymers in solution. With these methods, structural details of specific molecules are identified, but frequently these can not be generalized systematically with respect to characteristic features being equally relevant for different polymers. Therefore, the identification of generic conformational properties of polymer classes is highly desirable. To date the most promising approach to attack this problem is to analyze polymer conformations by means of comparative computer simulations of polymer models on mesoscopic scales, i.e., by introducing relevant cooperative degrees of freedom and additional constraints. In these modeling approaches – we have already made use of it in the previous chapters – the linear polymer is considered as a chain of beads and springs. Monomeric properties are accumulated in an effective, specifically parametrized single interaction point of dimension zero (“united atom approach”). Noncovalent van der Waals interactions between pairs of such interaction points are typically modeled by Lennard-Jones (LJ) potentials. In such models, only the repulsive short-range part of the LJ potentials keeps the monomers pairwisely apart. Although such models have proven to be quite useful in identifying universal aspects of global structure formation processes, these approaches are less useful in this form to describe local symmetric arrangements of segments of the chain.

Aggregation of semiflexible polymers

In the following, we will discuss the aggregation of interacting semiflexible polymers by analyzing the order and hierarchy of subphase transitions that accompany the aggregation transition.

Cluster formation and crystallization of polymers are processes that are interesting for technological applications, e.g., for the design of new materials with certain mechanical properties or nanoelectronic organic devices and polymeric solar cells. From a biophysical point of view, the understanding of oligomerization, but also the (de)fragmentation in semiflexible biopolymer systems like actin networks is of substantial relevance. This requires a systematic analysis of the basic properties of the polymeric cluster formation processes, in particular, for small polymer complexes on the nanoscale, where surface effects are competing noticeably with structure-formation processes in the interior of the aggregate.

A further motivation for investigating the aggregation transition of semiflexible homopolymer chains derives from the intriguing results of the similar aggregation process for peptides [254, 255] discussed in Chapter 11, which were modeled as heteropolymers with a sequence of two types of monomers, hydrophobic (A) and hydrophilic (B). By specializing the previously employed heteropolymer model to the apparently simpler homopolymer case, we now, by comparison, aim at isolating those properties that were driven mainly by the sequence properties of heteropolymers. In fact, while in both cases the aggregation transition is a first-order-like phase-coexistence process, it will turn out that for the homopolymer model considered in the following, aggregation and crystallization (if any) are separate conformational transitions, if the bending rigidity of the interacting homopolymers is sufficiently small. This was different in the example of heteropolymer aggregates that we discussed in the previous chapter, where these transitions were found to coincide [254, 255].

Structure formation at hybrid interfaces of soft and solid matter

The requirement of higher integration scales in electronic circuits, the design of nanosensory applications in biomedicine, and also the fascinating capabilities of modern experimental setup with its enormous potential in polymer and surface research, have produced an increased interest in macromolecular structural behavior at hybrid interfaces of organic and inorganic matter [273–278]. Relevant processes include, e.g., wetting [279–281], pattern recognition [282–284], protein–ligand binding and docking [285–287], effects specific to polyelectrolytes at charged substrates [288] as well as electrophoretic polymer deposition and growth at surfaces [289].

The recent developments of experimental single-molecule techniques at the nanometer scale, e.g., by means of atomic force microscopy (AFM) [290, 291] and optical tweezers [292, 293], allow for a more detailed exploration of structural properties of polymers in the vicinity of adsorbing substrates [278]. The possibility to perform such studies is of essential biological and technological significance. From the biological point of view, the understanding of the binding and docking mechanisms of proteins at cell membranes is important for the reconstruction of biological cell processes. Similarly, specificity of peptides and binding affinity to selected substrates are relevant features that need to be taken into account for potential applications in nanoelectronics and pattern recognition nanosensory devices on a molecular basis [282].

In this chapter, theoretical approaches to the modeling of hybrid systems of soft and solid matter will be discussed. A comprehensive analysis of conformational transitions experienced by polymers in the binding process, of the phase-diagram structure, and of dominant polymer conformations in these phases can only be performed efficiently by means of computer simulations of hybrid physisorption models on mesoscopic scales.