Physics of Life Reviews 4 (2007) 64–89

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Review

Low temperature spectroscopy of proteins.Part II: Experiments with single protein complexes ✩

Yuri Berlin a,1, Alexander Burin b, Josef Friedrich c, Jürgen Köhler d,∗

a Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3113, USAb Department of Chemistry, Tulane University, New Orleans, LA 70118, USA

c TUM Physik-Department E14, Lehrstuhl für Physik Weihenstephan, An der Saatzucht 5, 85350 Freising, Germanyd Universität Bayreuth, Lehrstuhl für Experimentalphysik IV und BIMF, Universitätstr. 30, 95447 Bayreuth, Germany

Received 10 January 2007; accepted 11 January 2007

Available online 19 January 2007

Communicated by M. Frank-Kamenetskii

Abstract

In this part of the review we describe aspects of the physics of proteins at low temperature as they are reflected in the spectraof individual pigment–protein complexes. The focus of this review is on the spectral diffusion of chromophores that are naturallyembedded in light-harvesting complexes from purple bacteria. From the spectral diffusion behaviour we can deduce details aboutthe organisation of the energy landscape of the protein and discuss the implications for the motions of the protein in conformationalphase space.© 2007 Elsevier B.V. All rights reserved.

PACS: 87.14.Ee; 87.15.-v; 87.15.He; 87.15.Kg; 82.37.Rs; 82.37.Vb

Keywords: Protein spectroscopy; Single-molecule spectroscopy; LH2; Spectral diffusion; Energy landscape; Excitons in biomolecules;Conformational substates

Contents

6. Basic aspects of spectral diffusion experiments with single molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657. Spectroscopy of single LH2 antenna complexes from purple bacteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

7.1. The light harvesting complex LH2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 667.2. Energy transfer, excitons, strong and weak coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 687.3. The B800-band . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

7.3.1. Intra- and intercomplex heterogeneity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 707.3.2. Protein dynamics probed by optically induced spectral fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . 77

✩ Research was supported by the DFG [SFB 533, B5], the Volkswagen Foundation, the DAAD and the Fonds der Chemischen Industrie.* Corresponding author.

E-mail addresses: berlin@chem.northwestern.edu (Y. Berlin), aburin@tulane.edu (A. Burin), j.friedrich@lrz.tu-muenchen.de (J. Friedrich),juergen.koehler@uni-bayreuth.de (J. Köhler).

1 This author is supported by the Louisiana Board of Regents [Contract No. LEQSF (2005-08)-RD-A-29].

1571-0645/$ – see front matter © 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.plrev.2007.01.001

Y. Berlin et al. / Physics of Life Reviews 4 (2007) 64–89 65

7.4. The B850 band . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 828. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

In part I of this review we focused on high resolution hole burning spectroscopy of protein ensembles at lowtemperature and the associated physics. In the following part (part II), the focus is on the spectroscopy of singlelight harvesting complexes, especially their dynamics at temperatures in the Kelvin-range as it is reflected in spectraldiffusion.

6. Basic aspects of spectral diffusion experiments with single molecules

As pointed out in part I above the exact energies of the electronically excited states of a chromophore are fine tunedby the interaction with its local surrounding. Accordingly, the spectral lineshape observed for an ensemble reflectsthe statistical distribution of local environments rather than dynamical properties of the chromophore (Section 2.3 ofpart I). However, if the local environment of the chromophore is not static but shows temporal fluctuations as well,the absorption frequency of a single-molecule undergoes also temporal fluctuations. In hole burning the ensembleaverage of these fluctuations show up as waiting time dependent line broadening phenomena. In experiments withsingle molecules they can be directly observed as a spectral diffusion trajectory in the time domain. Indeed, spectraldiffusion of a single molecule was one of the first effects observed by the Moerner group in the pioneering days ofthis technique [1].

In order to take advantage of a single molecule as a local probe to monitor fluctuations of its truly localenvironment—which is of particular interest if the “host” is a protein—we have to consider the mutual relation-ship between the timescales of the experiment and spectral fluctuations. In Fig. 1 we show a schematic plot of atwo-dimensional representation of sequentially “recorded” spectra stacked on top of each other. In each “scan” themolecule is supposed to absorb at a distinct wavelength that is given by a black dot and spectral fluctuations over timeshow up as “spectral trails” in the wavelength versus time pattern. Let us assume that our artificial molecule undergoes

Fig. 1. Sketch of the spectral diffusion of a molecule that features two timescales tfluc � Tfluc, together with the spectra that would have beenobtained in a hypothetical experiment (a)–(d). In the upper part the same sequence of consecutively recorded spectra is stacked on top of eachother. The spectral position of the molecular absorption is indicated by the black dot. The experimental timescales, tm (temporal resolution), andTm (duration of the experiment), are indicated by the solid lines in the panels. For details see text.

66 Y. Berlin et al. / Physics of Life Reviews 4 (2007) 64–89

spectral fluctuations between six different spectral positions on a fast, tfluc (small spectral jumps), and a slow, Tfluc(large spectral jumps), timescale. In addition, each experiment introduces two timescales, the temporal resolution ofthe detection process, tm, and the duration of the experiment, Tm, which we interpret here as the time over which thedata acquisition is averaged. We can distinguish four regimes [2]:

(a) Tfluc � tm; all spectral fluctuations occur fast with respect to the detection window. The spectral fluctuations ofthe probe molecule remain unresolved and appear as a broadening of the linewidth.

(b) tfluc � tm � Tfluc � Tm; fast spectral fluctuations of the probe molecule remain unresolved and contribute to thelinewidth whereas slower spectral fluctuations can be followed. The finding is that the single-molecule transitionfeatures an intermediate linewidth and appears at different spectral positions during the experiment.

(c) tm � tfluc � Tm � Tfluc; even the fastest spectral excursions of the molecule can be followed and a narrow linecan be observed for the absorption. Small fluctuations of the spectral position of the transition are resolved aswell, however, the total experimental observation time is too short to observe larger slow spectral excursions ofthe probe.

(d) Tm � tfluc; finally, within the experimental observation time all spectral fluctuations are sufficiently slow and canbe resolved. The experimental finding is a spectrally narrow absorption that appears static.

The schematic spectra that result for the four scenarios are shown in the lower part of Fig. 1, where the double-headed arrows on top of the absorptions indicate temporal fluctuations of the transitions. From this example it shouldbe clear that the information that can be obtained from a single-molecule experiment depends crucially on the interplayof the various timescales.

7. Spectroscopy of single LH2 antenna complexes from purple bacteria

7.1. The light harvesting complex LH2

Photosynthesis is the process by which plants, algae and photosynthetic bacteria convert solar energy into a formthat is used to sustain the life process. Basically, the photosynthetic light reactions occur in four primary steps, ab-sorption of light by a pigment, ultra-fast transfer of the excitation energy to a “photoactive” pigment, oxidation of thisexcited photoactive pigment, and stabilization of the charge-separated state by secondary electron-transfer reactions.The protein–pigment complexes involved in the first two processes are often called antenna or light-harvesting com-plexes. The last two processes are the primary electron transfer steps and usually occur in a special protein–pigmentcomplex which is referred to as the reaction center (RC). In most purple bacteria, the photosynthetic unit (PSU) presentin the membrane contains, besides the RC, two types of antenna complexes, the core complex which is usually termedlight-harvesting complex 1 (LH1) and the peripheral complex called light-harvesting complex 2 (LH2). It is knownthat LH1 is closely associated with the RC, whereas LH2 is not in direct contact with the RC, but transfers the energyto the RC via the LH1 complex [3]. The total conversion process, starting with the absorption of a photon and endingwith a stable charge separated state occurs in less than 100 ps and has an overall quantum yield of more than 90%.

During the last decade great progress has been made in high-resolution structural studies of antenna complexes ofpurple bacteria [4–6]. Remarkably, all peripheral light-harvesting complexes form circular oligomers of two hydropho-bic αβ-apoproteins that non-covalently bind three BChl a molecules and one carotenoid, featuring a highly symmetricnonameric (Rhodopseudomonas acidophila, Rhodobacter sphaeroides) or octameric (Rhodospirillum molischianum)quaternary protein structure. In contrast, the structures of LH1-RC complexes show a strong dependence on the speciesof the purple bacterium.

In the following we focus on the spectroscopy of the LH2 complex from which serves as a cornerstone for the gen-eral understanding of structure-function relationships in photosynthesis of purple bacteria. For Rhodopseudomonasacidophila the 3-dimensional structure of this pigment–protein complex is depicted in Fig. 2. It comprises 27 BChla molecules that are arranged in two concentric rings displaced with respect to each other along the common sym-metry axis perpendicular to the plane of the rings. The two pigment pools are labeled B800 and B850, according totheir room-temperature absorption maxima in the near infrared. The B800 ring consists of nine well-separated BChla molecules (B800) which have their bacteriochlorin plane aligned nearly perpendicularly to the symmetry axis. Theother ring consists of eighteen BChl a molecules (B850) oriented with the plane of the molecules parallel to the sym-

Y. Berlin et al. / Physics of Life Reviews 4 (2007) 64–89 67

Fig. 2. Structure of the LH2 complex from Rp. acidophila as determined by X-ray diffraction [4]. Parts (a) and (b) show the whole pigment–proteincomplex; parts (c) and (d) the BChl a chromophores only. Parts (a) and (c) display a top view; parts (b) and (d) a side view, respectively. (e) Thespatial arrangement of the BChl a pigments in LH2 of Rp. acdophila, in a tilted side-view. The numbers indicate the center-to-center distances ofthe pigments in Å. The arrows indicate the direction of the Qy transition moments. The phytol chains of the pigments are removed for clarity.

metry axis resembling the blades of a turbine. Both types of molecules are depicted on an enlarged scale in part (e)of Fig. 2 in light-grey (B800) and black (B850), respectively. From the crystal structure the magnitude of the dipolarcoupling strength between the pigments of the B800 ring can be estimated to be about 24 cm−1 [7]. The intermole-cular interactions between the B850 BChl a molecules are more difficult to calculate because the closest distancebetween the pigments is rather small compared to the size of the molecules. Several theoretical approaches have beenemployed [7–9] and resulted in values for the strength of the pigment–pigment interaction between 250 cm−1 and400 cm−1.

Upon excitation, energy is transferred from the B800 to B850 molecules in 1 to 2 ps, while among the B850molecules it is an order of magnitude faster. This has been observed as an ultrafast depolarization of the fluorescenceon a 100 fs timescale [10,11]. The transfer of energy from LH2 to LH1 and subsequently to the reaction center occursin vivo on a timescale of 5–10 ps, i.e. very fast compared to the decay of an isolated LH2 which has a fluorescencelifetime of 1.1 ns [12].

The great difficulty encountered when determining the various parameters that play a role in the descriptionof the electronic structure of light-harvesting complexes and the process of energy transfer, is the fact that theoptical absorption lines are inhomogeneously broadened. In order to avoid the difficulties arising from the hetero-geneity, single-molecule spectroscopic techniques have been applied to study light harvesting complexes [13–25]and energy-transfer processes in a single PSU [26]. The intriguing feature of this technique is that it enables oneto elucidate information that is commonly washed out by ensemble averaging. Besides the possibility to circum-vent spatial inhomogeneities, it allows also the observation of dynamical processes which are usually obscuredby the lack of synchronization within an ensemble. A single molecule that undergoes a temporal developmentbetween different states is at any time in a distinct, well defined state and the whole sequence of steps can be stud-ied.

The fluorescence–excitation spectra of several individual LH2 complexes are shown in Fig. 3 [16,17,19]. The uppertrace shows, for comparison, the fluorescence–excitation spectrum taken from a bulk sample (dashed line) together

68 Y. Berlin et al. / Physics of Life Reviews 4 (2007) 64–89

Fig. 3. Fluorescence–excitation spectra of individual of LH2 complexes of Rp. acidophila. The top traces show the comparison between an ensemblespectrum (dashed line) and the sum of spectra recorded from nineteen individual complexes (solid line). The lower five traces display spectra fromsingle LH2 complexes. Each individual spectrum has been averaged over all possible excitation polarizations. All spectra were measured at 1.2 Kat 20 W/cm2 with LH2 dissolved in a PVA-buffer solution. Taken from [16,17,19].

with the spectrum that results from the summation of the spectra of nineteen individual LH2 complexes (solid line).The two spectra are in excellent agreement and both feature two broad structureless bands around 800 and 860 nmcorresponding to the absorptions of the B800 and B850 pigments of the complex. By measuring the fluorescence–excitation spectra of the individual complexes, remarkable features become visible which are obscured in the ensembleaverage. In particular, a striking difference between the B800 and B850 bands becomes evident: the spectra around800 nm show a distribution of narrow absorption bands, whereas in the B850 spectral region 2–3 broad bands arepresent.

The differences between the two absorption bands can be understood by considering the ratio V/δn between theintermolecular interaction strength V and the spread in transition energies for the BChl a molecules in the two ringassemblies. A crude measure for the magnitude of the diagonal disorder δn can be obtained from the inhomogeneouslinewidth of the B800/B850 absorption bands. This suggests that V/δn differs by about an order of magnitude in thetwo ring assemblies. This puts forward the idea that for the electronically excited states of the B850 BChl a moleculescollective excitations (Frenkel excitons) play an important role whereas the excitations of the B800 BChl a moleculescan be described in first approximation as being localized on an individual BChl a molecule. Below, we will presenta more detailed discussion of this issue.

7.2. Energy transfer, excitons, strong and weak coupling

A good starting point for the description of the electronically excited states of a molecular aggregate is providedby the formalism of Frenkel-excitons [27]. For the description of N molecules we define a state |n〉 which representsmolecule “n” in the electronically excited state and all other molecules 1,2, . . . , n − 1, n + 1, . . . ,N in the groundstate. The states |1〉 to |N〉 feature the same excitation energy, E0, which is localized on an individual molecule. Theenergy transfer originates from the electronic interaction V between the pigments and the electronically excited states

Y. Berlin et al. / Physics of Life Reviews 4 (2007) 64–89 69

can be described by the Hamiltonian

(7.1)H =N∑

n=1

E0|n〉〈n| +N∑

n=1

∑m �=n

Vnm|n〉〈m|

where Vnm denotes the matrix element 〈n|V |m〉 of the interaction between molecules in excited states located onmolecule “n” and “m”. The eigenfunctions of this Hamiltonian are given by linear superpositions of the localizedwavefunctions, so-called Frenkel excitons and for a one-dimensional regular arrangement such as a linear chain or aring one finds

(7.2)|k〉 = 1√N

N∑n=1

ei2πk nN |n〉, k = 0, . . . ,N − 1.

For this ideal system where all molecules are equivalent, the exciton wavefunctions have equal amplitudes on eachpigment and the excitation is fully delocalized over all N pigments. For the energies of the exciton states one has tocalculate

(7.3)ε(k) = 〈k|H |k〉 = E0 + 1

2

∑n

∑m �=n

Vnmei2πk(n−m)

N

which yields in nearest-neighbor approximation

(7.4)ε(k) = E0 + 2V0 cosk2π

N

with the abbreviation Vn,n−1 = Vn,n+1 = V0. The initial degeneracy of the localized excited states is lifted by theinteraction and results in a manifold of energy levels—the exciton band.

However, various deviations from this situation tend to localize the excitation energy on a smaller part of the aggre-gate. For example, local variations in the transition energies of the individual molecules represented by a random shiftδn with respect to the average transition energy E0 reflect slight differences in their local environment. Alternatively,any structural deviation from perfect symmetry results in a variation of the mutual interactions, represented by �Vnm.

These factors can be combined into the following Hamiltonian [28]:

(7.5)H =N∑

n=1

(E0 + δn)|n〉〈n| +N∑

n=1

∑m �=n

(Vnm + �Vnm)|n〉〈m|.

Since the disorder in the energies δn affects the diagonal elements of the Hamiltonian this is commonly referred to asdiagonal disorder. For the same reason the variations in the interaction strength are referred to as off-diagonal disorder.The resulting energy levels of the total system are determined by the strength of the coupling and the site-energiesof the system. As far as the dynamics of the excitons is considered the effect from random off-diagonal disorder isindistinguishable from the effects of random diagonal disorder [28]. Many studies have focused on the latter type ofdisorder. Commonly, one distinguishes two limiting cases. In the regime of weak coupling, |V/δn| � 1, the interactionbetween the transition dipoles is much smaller than the difference in site energies of the pigments and the description ofthe excitations in terms of the localized states |n〉 is a good approximation. The “true” eigenstates are superpositions ofthe |n〉 states and the transfer of energy between the pigments is visualized as a diffusive hopping process (incoherentenergy transfer). Although the interaction mechanism does not have to be necessarily of the well-known dipole–dipoletype this is usually called the Förster-limit. In the other extreme, the strong coupling limit, |V/δn| � 1, the interactionis much larger than the difference in site energies of the pigments and the Frenkel-exciton states |k〉 provide a goodstarting point for the description of the excited states. The “true” eigenstates of the system are wave-packets whichare superpositions of the exciton states and the transfer of excitation energy occurs in a wavelike manner (coherentenergy transfer).

Another process that tends to localize the excitation energy is given by dynamic disorder or exciton–phonon inter-action [29]. The protein environment is not static but is subjected to temporal variations, for example low-frequencyoscillations of the protein backbone (phonons) which lead to time-dependent variations in the site energies andinteractions of the pigments. The concept introduced so far is valid only for temperatures close to absolute zero

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where the interactions of excitons with phonons are small. Raising the temperature and equivalently increasing theexciton–phonon interaction will lead to a growing scattering rate among the exciton states resulting in a change ofthe wavepacket in the course of time. Since the width of the wavepacket in k-space is inversely proportional to theextension of the excitation in real space, a change of the constitution of the wavepacket is associated with the degreeof localization of the excitation. As soon as the widths of the wavepacket in k-space is sufficiently large that the corre-sponding spatial extension of the excitation in real space approaches the average interpigment distance the excitationbecomes localized and the transition from coherent wavelike energy transfer to incoherent hopping occurs.

For molecular aggregates the degree of delocalization of their excitations has always been a matter of hot debate[16,17,30–34]. In one-dimensional aggregates the delocalization of the exciton can be described by the number ofmolecules that share the excitation and several expressions for the delocalization length have been introduced inRefs. [32,35]. A widely used measure for the delocalization is the inverse participation ratio given by [28]

(7.6)1

P= (

∑n |an|2)2∑n |an|4 ,

where an is the coefficient of the excited state wave function at site n. This ratio varies between 1 and N correspondingto the “correct” values for completely localized and delocalized states. A detailed comparison of the different measuresof the exciton delocalization in LH2 can be found in [36].

7.3. The B800-band

7.3.1. Intra- and intercomplex heterogeneityFig. 4 displays seven fluorescence–excitation spectra of the B800 band of an individual LH2 complex, each taken

with a different orientation of the polarization vector of the exciting laser light [17]. It is seen that the intensities ofthe absorption lines vary appreciably upon changing the polarization. This would be expected if the excitations are

Fig. 4. Dependence of the B800 fluorescence–excitation spectrum of a single LH2 complex from Rp. acidophila on the polarization of the incidentradiation. The polarization vector has been changed in steps of 30◦ from one spectrum to the next. The vertical scale is valid for the lowest trace,all other are displaced for clarity [17].

Y. Berlin et al. / Physics of Life Reviews 4 (2007) 64–89 71

Fig. 5. Dependence of the orientation of the transition-dipole moments μ+ (upper curve) and μ− (lower curve) on the ratio V/δ. The orientationsof the initial transition moments μ1 and μ2 were set to 0◦ and 45◦ and provide the reference frame. From [21].

largely localized on the individual BChl a pigments, because their transition-dipole moments are arranged in a circularmanner and, as a result of this, all have different orientations.

In order to address this issue in more detail, Hofmann et al. performed a study on the B800 excitation of individualLH2 complexes from Rhodospirillum molischianum [21]. The general idea of their approach was as follows: for thisbacterium the B800 ring features an octameric symmetry with an inter-chromophore distance of 22 Å. If the B800electronic excitation would be strictly localized on a single BChl a molecule the mutual angles between the transition-dipole moments of the individual BChl a chromophores would be equal to multiples of 45◦ (i.e. 360◦/8). However,coupling between two adjacent molecules will lead to eigenstates different from those of the uncoupled chromophoresand consequently to a change in the orientation of the transition-dipole moments. For the sake of brevity the followingdiscussion will be restricted to two adjacent BChl a molecules with excitation energies E1 and E2 (E1 > E2). For theresulting energies and eigenstates of the coupled system one finds

(7.7)E± = 1

2(E1 + E2) ± 1

2

√δ2 + 4V 2,

|Ψ+〉 = cosΘ

2|1〉 + sin

Θ

2|2〉,

(7.8)|Ψ−〉 = − sinΘ

2|1〉 + cos

Θ

2|2〉

where tanΘ = 2Vδ

, δ = E1 − E2, and |i〉 denotes the excited state localized on molecule i. The transition-dipolemoments of the eigenstates are

μ+ = μ1 cosΘ

2+ μ2 sin

Θ

2,

(7.9)μ− = −μ1 sinΘ

2+ μ2 cos

Θ

2where μi denotes the transition-dipole moment of an individual BChl a molecule in the B800 ring. From (7.9) theorientations of the transition-dipole moments of the B800 BChl a molecules have been calculated as a function ofV/δ, see Fig. 5. The orientations of the initial transition moments, μ1 and μ2, corresponding to V/δ = 0, were set to0◦ and 45◦.

For increasing V/δ the orientations of the transition moments μ+ and μ− change gradually with respect to theinitial orientations and level off at angles of 22.5◦ and 112.5◦ for values of V/δ larger than about 6. From the range ofvalues estimated for V/δ (0.3–2) a distribution of mutual orientations with preferences at 22.5◦ and (180◦ −112.5◦) =67.5◦ is expected. Taking into account BChl a molecules that are weakly coupled one expects, in addition, to observedifferences between the mutual angles of 45◦ modulo 45◦. In total this results for the mutual orientations of thetransition dipole moments in a distribution with preferential values around 0◦, 22.5◦, 45◦, 67.5◦, and 90◦.

In order to determine the orientations of the transition-dipole moments experimentally the laser has been sweptthrough the B800 spectral region and a sequence of spectra has been recorded in rapid succession, while the polar-ization of the incident radiation has been rotated by 1.8◦ between two successive scans. Fig. 6(a) shows a part ofthe B800 spectrum from an individual LH2 complex from Rhodospirillum molischianum. The horizontal axis gives

72 Y. Berlin et al. / Physics of Life Reviews 4 (2007) 64–89

Fig. 6. Two-dimensional representation of 513 fluorescence–excitation spectra from a part of the B800 band of an individual LH2 complex recordedconsecutively at a scan speed of 3 nm/s and an excitation intensity of 10 W/cm2. The grey scale gives the fluorescence intensity. Between twosuccessive scans the polarization of the incident radiation has been turned by 1.8◦ . The horizontal axis corresponds to wavelength and the verticalaxis to polarization (a). Average of all 513 spectra (b). Intensity of the fluorescence for the two absorptions indicated by the boxes in part (a) as afunction of the polarization of the excitation. The full and dashed line correspond to cos2(α(t) + α)-type functions fitted to the experimental datawith phase angles, α, of 148◦ and 57◦ , respectively (c). Histogram of mutual orientations of the transition-dipole moments from 88 absorptionlines from 24 individual complexes (d). From [21].

the wavenumber, the vertical axis the angle of the polarization of the incident light, and the intensity is coded by thegrey scale. In Fig. 6(b) the fluorescence–excitation spectrum is given that results from the summation of the traces inFig. 6(a). In Fig. 6(c) the fluorescence intensity is displayed as a function of the polarization of the incident radiationfor the two absorption lines indicated by the boxed regions in Fig. 6(a). The observed variation in intensity is fitted bya cos2-dependence (full and dashed line, respectively).

From the difference of the phases in the two traces the mutual angle between the transition-dipole moments relatedto these two absorption lines has been determined to be 91◦. This procedure has been applied to 88 absorption linesfrom 24 individual LH2 complexes in order to find the distribution of the mutual orientations of the transition-dipolemoments within each complex. The values have been obtained either directly from the phase difference |α1 − α2|

Y. Berlin et al. / Physics of Life Reviews 4 (2007) 64–89 73

Fig. 7. Two-dimensional representation of 614 fluorescence–excitation spectra from an individual B800 ring. Between two successive scans thepolarization has been turned by 1.8◦ . The arrows show the experimentally determined orientation of the transition-dipole moments of the individualabsorptions with respect to a laboratory frame. The phase difference between the transition-dipole moments of absorptions 2a and 2b amounts to67◦ . Experimental conditions as in Fig. 6(a). Average of the spectra in the boxed regions A and C, respectively (b). Taken partly from [21].

if the result was less than 90◦ and otherwise from |α1 − α2 − 180◦| to restrict the scale to the interval 0◦–90◦. Thehistogram in Fig. 6(d) shows the result of this study. The distribution covers nearly the whole range between 0◦ and90◦ with slight preferences for the values around 0◦, 20◦, 45◦, and 70◦.

From these experiments is was concluded that the observation of mutual orientations of transition-dipole momentsdifferent from 0◦, 45◦ and 90◦, provides direct evidence for an electronic coupling between the individual BChla molecules in the B800 assembly in the weak to intermediate range. Moreover, the actual strength of the electroniccoupling between adjacent molecules is distributed over a range of values as a result of the difference in site energies ofadjacent molecules. These findings agree quantitatively with the results of a theoretical study that has been publishedrecently [37].

For some complexes changes in the spectral position of the individual absorptions as well as in the orientation ofthe transition-dipole moments have been observed during the experiment. An example for such a behavior is shownin Fig. 7.

The figure is divided in a spectral pattern, Fig. 7(a), that can be grouped into three distinct regions A, B , and C

as indicated by the boxes and two spectra, Fig. 7(b), that result when the individual traces in the boxed regions A

and C are summed separately. The setup of the spectral pattern is similar to that of the previous figure. In intervalA four absorptions, labeled 1–4, with spectral positions 12525.2 cm−1 (1), 12489.1 cm−1 (2), 12417.9 cm−1 (3) and12367.7 cm−1 (4) were observed. The respective phase angles were determined to be 70◦ (1), 4◦ (2), 30◦ (3) and−5◦ (4) and are visualized in the pattern by the arrows. During interval A absorption 1 creeps continuously in spectralposition towards lower energy. None of the absorptions show changes of the phase angle. The creeping of absorption 1is continued at an increased rate in sequence B , again without any change of the phase angle. This absorption as well asabsorption 2 disappears at the end of interval B . No changes are observed for absorptions 3 and 4. With the beginningof interval C new absorptions, 2a and 2b appear at spectral positions (phase angles) of 12491.9 cm−1 (−26◦) and12481.4 cm−1 (41◦), respectively. As before absorptions 3 and 4 do not show any changes.

From the behavior of the absorptions 3 and 4 the option that the whole complex changes its orientation during theexperiment is excluded. The other absorptions are only visible either during the interval A (absorptions 1 and 2) orduring interval C (absorptions 2a and 2b). The two intervals are separated by a period B where absorption 1 shows adrastic change in spectral position and where absorption 2 vanishes. The conjecture was that the absorptions labeled

74 Y. Berlin et al. / Physics of Life Reviews 4 (2007) 64–89

Fig. 8. Schematic representation of the electronic states during intervals A and C. The encircled numbers refer to the absorptions shown in Fig. 7.For details see text.

2a and 2b result from two molecules that become electronically coupled during interval B , one of which has initiallyabsorption 2 for the uncoupled situation, Fig. 8.

This conclusion was based on the following arguments. Under the assumption that the transition-dipole momentsof the two uncoupled chromophores have initially a mutual orientation of 45◦, which is valid for nearest neighbors,from (7.9) the local ratio V/δ has been calculated from the difference of the polarization angles of absorptions 2a and2b. For the observed �α = 67◦ this yields V/δ = 1.07±0.15. Another way to calculate this ratio follows from (7.7) ifE+, E− and one of the unperturbed energies are known. Assigning E1 to absorption 2 and E+ and E− to absorptions2a and 2b yields V/δ = 0.95±0.1, in agreement with the value obtained from the polarizations. A further independentpiece of information was provided by the difference in angle of the transition-dipole moments μ1 and μ+ of theabsorptions corresponding to E1 and E+. From Fig. 5 a difference of 37◦ ± 5◦ is predicted, in reasonable agreementwith the observed value of 30◦ ± 5◦. So far, this interpretation yields a consistent description for the absorptions 2,2a and 2b. However, for the absorption strength of the transitions 2a and 2b one finds within this approach 1.6 and0.4 monomer units while the experiment yields about equal intensities for the two transitions. This discrepancy mayreflect differences in the energy transfer efficiency to the B850 pigment pool, which are not taken into account by thesimple dimer approximation.

For some LH2 complexes spectral patterns could be found that showed a reversible switching of the completeB800 spectra between two distinct realizations [22]. An example is shown in Fig. 9. As before, the spectra wererecorded sequentially. The horizontal axis corresponds to excitation energy, the vertical axis to time, and the greycode to the fluorescence intensity. The fluorescence–excitation spectrum that results when the whole sequence ofspectra is averaged is shown in Fig. 9(b). Visual inspection of the time-resolved representation of the spectra leads tothe conjecture that some of the absorptions show large spectral jumps between a limited number of spectral positions.This becomes even more evident if only parts of the total sequence of fluorescence–excitation spectra are displayed.Each spectrum shown in Fig. 9(c) results from the average of the individual traces over the time interval boxed inpart (a) of the figure. It is clearly revealed that for this particular complex the B800 spectrum corresponds to thetime average of two distinct spectra termed A and B hereafter. The conversion between the two spectra occurs as areversible sudden spectral jump which is recurrent on a timescale of minutes. Such a behavior has been observed fortwo complexes.

In order to characterize the spectral variations more quantitatively we use the spectral mean, ν̄, and standarddeviation, σν as defined in [18]. Accordingly, the distinct spectra A and B observed for the two complexes werecharacterized by the positions of the absorptions (νA, νB ), their spectral means (ν̄A, ν̄B ), their standard deviations(σA,σB ), and the rates, at which the spectral changes occur (kA→B, kB→A). For the complex shown in Fig. 9 thespectral mean changes by 61 cm−1 between the two spectral realizations whereas the standard deviation remainsnearly unchanged at about 90 cm−1. The mean observation times for the spectra are τA = 500 s (kA→B = 0.002 s−1)and τB = 83 s (kB→A = 0.012 s−1), respectively. For the other complex (data not shown) the spectral mean ν̄ changesbetween the A- and B-type spectra by 207 cm−1 and the standard deviation decreases from 163 to 63 cm−1. The

Y. Berlin et al. / Physics of Life Reviews 4 (2007) 64–89 75

Fig. 9. Two-dimensional representation of 70 fluorescence–excitation spectra from the B800 band of an individual LH2 complex. The spectra havebeen recorded consecutively at a scan speed of 50 cm−1/s at an excitation intensity of 10 W/cm2. The fluorescence intensity is indicated by thegrey scale. The horizontal axis corresponds to the laser-excitation energy and the vertical axis to time (a). Average of all 70 fluorescence–excitationspectra. (b) Fluorescence–excitation spectra that result when the individual traces are averaged over the time windows boxed in part (a). The verticalscale is valid for the lowest trace, all other traces were offset for clarity (c). From [22].

A-type spectrum can be observed on average for 110 s (kA→B = 0.009 s−1) before it switches to the B-type spectrumwhich remains on average for 250 s (kB→A = 0.004 s−1). A summary of these data is given in Table 1.

As has been mentioned above the ratio of the intermolecular interaction strength, V , and the energy mismatch insite energy between adjacent B800 BChl a molecules, δ, is estimated to be of the order of V/δ ≈ 0.3–2. Thereforeit is very likely that for some LH2 complexes the B800 excitations are slightly delocalized over 2–3 monomer units.However, both the differences in site energy, δ, and the intermolecular interaction strengths, V , depend critically onthe mutual orientation and the distance of the respective pigments. Any change in the protein backbone that induces avariation of the local V/δ ratio results in a change of the optical spectrum.

In order to illustrate this interpretation Fig. 10 shows a schematic sketch of a part of the B800 ring. The figurehas only illustrative character, the actual distribution of the excitation energy in the B800 assembly is unknown. Thecoupling strength between adjacent molecules “i” and “j” is denoted by Vij /δij and it is realistic to assume thatits actual value is different for each pair of molecules. In the top part of Fig. 10 an arbitrary situation, termed “A”,is shown where the excitation is localized on molecules 1 and 4 and delocalized between molecules 2 and 3. Thelower part of Fig. 10 shows an arbitrary situation, termed “B”, where the distribution of intermolecular couplings haschanged such that the excitation becomes delocalized between molecules 1 and 2 as well as between molecules 3and 4. Despite the arbitrarily chosen example for this illustration there is little doubt that such kind of variations in theelectronic couplings result in changes of the optical spectrum.

Possible explanations for the fluctuations in the electronic coupling are changes in the protein backbone or re-arrangements of the BChl a molecules in their binding pockets, for example a rotation of the acetyl group or thebreakage of hydrogen bonds. Such changes alter the electrostatic environment of the individual chromophores and re-sult in a shift of their absorption energies and consequently in changes of V/δ. The strength of the electronic couplingV/δ is of crucial interest to understand structure-function relationships of the B800 ring. Despite that photosynthesisis performed in nature under ambient conditions these data have been revealed by low-temperature single-molecule

76 Y. Berlin et al. / Physics of Life Reviews 4 (2007) 64–89

Table 1Spectral features for the A- and B-type spectra of two LH2 complexes

A B

νA

(cm−1)FWHMA

(cm−1)ν̄A

(cm−1)σA

(cm−1)kA→B

(s−1)νB

(cm−1)FWHMB

(cm−1)ν̄B

(cm−1)σB

(cm−1)kB→A

(s−1)

Complex 1, Fig. 9

12733 2812614 32

12609 3512639 91 0.002 12578 93 0.012

12541 2112522 3312477 10

Complex 2, data not shown

12850 3712654 12

12651 712748 163 0.009 12541 63 0.004

12557 2012477 11

12468 12

The spectral position ν of the absorption line is given together with the full spectral width (FWHM). The spectral mean is indicated by ν̄ andthe standard deviation σ is given for the overall B800 spectrum, and k gives the average rate for the spectral change from A → B or B → A,respectively.

Fig. 10. Schematic sketch to illustrate the interpretation of the experimental results in connection with Fig. 9. On the left hand side a part of theB800 assembly is shown. The local intermolecular coupling between the individual B800 molecules “i” and “j” is indicated by Vij /δij . The righthand side of the figure shows two (arbitrary) fluorescence–excitation spectra for two different sets of coupling parameters, denoted by the suffix A

and B . From [22].

spectroscopy. The intriguing feature of this technique is that it uncovers information that is commonly washed out byensemble averaging in bulk measurements, with direct observation of the dynamics of molecular processes withoutthe need for synchronization of events.

Y. Berlin et al. / Physics of Life Reviews 4 (2007) 64–89 77

Fig. 11. General idea of an experiment to use a molecular excitation to induce and to probe conformational changes in a protein. Left: in the initialconformational substate of the protein the chromophore experiences a distinct interaction with its local environment which determines the exactspectral position of its absorption energy. After excitation the molecule decays to the ground state and dissipates energy which induces nuclearmotions of the protein matrix. Right: upon relaxation back to thermal equilibrium there is a finite probability that the protein ends up in a differentconformational substate which will be reflected by a change in transition energy of the chromophore.

7.3.2. Protein dynamics probed by optically induced spectral fluctuationsConformational fluctuations of a protein are equivalent to rearrangements of its atoms. Consequently, chro-

mophores embedded in the protein experience those changes as fluctuations in the strongly distance-dependentinteractions and react to conformational changes of the protein with changes of their electronic energies (spectraldiffusion, see also Section 4 of part I). This feature makes such chromophores suited to monitor the dynamics ofa protein with optical spectroscopy. In the case of the pigment–protein complex LH2, the excitonic coupling betweenthe B800 BChl a molecules is relatively weak which makes these molecules suited to serve as local probes. Ide-ally, this allows to monitor the dynamics of the protein matrix without the requirement of any artificial labeling andconcomitant disturbance of the protein [22,38].

The general idea, sketched in Fig. 11, is that conformational changes of the protein can be induced by opticalexcitation of the pigments and subsequent relaxation of the excited state. Given the low fluorescence quantum yieldof LH2 of about 10%, a significant fraction of the average absorbed energy is dissipated by radiationless decay andexcites nuclear motions of the protein matrix (phonons). The photon-energy, about 1.5 eV in the case of the B800chromophores, that is dissipated this way exceeds by far the thermal energy kBT at the temperature of 1.4 K at whichthe measurements are performed. Consequently, the space of conformational substates that is probed by the inducedstructural fluctuations is not restricted to the part of the energy landscape that is accessible under thermal equilibrium.

Fig. 12(a) displays a sequence of B800 spectra from an individual LH2 complex (complex 1) from Rhodospirillummolischianum featuring two absorptions at 12921 cm−1 and 12642 cm−1, labeled a and a′. The time-dependenceof the emission intensity of the two transitions is shown in more detail in Fig. 12(c). For both resonances thesignal exhibits abrupt changes from up to 6000 counts per second (cps) to the background level. The auto- andcross-correlations of the two trajectories are presented in Fig. 12(d). Both auto-correlations drop within the temporalresolution of this experiment to an average value of zero, a signature that the observed intensity fluctuations are uncor-related on this timescale. In contrast the cross-correlation shows a clear dip around t = 0 which unambiguously showsthat the two absorption lines, separated by 278 cm−1, are closely associated. Similar changes in transition energyby several hundred wavenumbers have been observed also for the pair of absorptions labeled b and b′ in Fig. 12(a).Obviously, this information is masked in the time-averaged spectrum, Fig. 12(b).

Smaller spectral shifts on a faster timescale have been observed as well. This is illustrated in Fig. 13 which shows anexpanded view of the spectral region around the absorption labeled a′ in Fig. 12(a). On the left hand side the raw dataare shown in a similar representation as before and the width of the transition in the time-averaged spectrum amountsto 41.6 cm−1 (FWHM). From the data it is evident that the observed linewidth of the time-averaged spectrum resultspredominantly from the accumulation of smaller spectral changes. By fitting the spectrum in every single sweep witha Lorentzian, it was determined that, for this example, the peak position changed on average by 4.7 cm−1 per scanof 15 s duration. Similar values are observed for the other transitions, see Table 2. To obtain the spectrum on the

78 Y. Berlin et al. / Physics of Life Reviews 4 (2007) 64–89

Fig. 12. Large spectral changes of the B800 absorptions of an individual LH2 complex (complex 1). Time sequence of 256 consecutively recordedfluorescence–excitation spectra stacked on top of each other. The fluorescence intensity is indicated by the grey scale (a). Average of the stack ofspectra shown in A (b). Intensity of the fluorescence as a function of time for the spectral features labeled a and a′ displayed in a (c). Auto- (light-(a)) and dark grey (a′) lines) and cross-correlation (black line) of the absorptions a and a′ (d). From [38].

Fig. 13. Small spectral fluctuations of an absorption. (a) Stack of 256 fluorescence–excitation spectra, from a narrow spectral region of Fig. 12(a)at an expanded view around the position of line a′ . The fluorescence intensity is indicated by the grey scale. The average absorption line of allspectra is shown in the lower panel and has a linewidth of 41.6 cm−1 (FWHM). (b) Stack of 172 fluorescence–excitation spectra that were obtainedafter fitting each individual scan by a Lorentzian and subsequent shift that the peak positions of the fits coincided. The spectrum in the lower paneldisplays the average of all scans and features a width of 7.5 cm−1 (FWHM). From [38].

Y. Berlin et al. / Physics of Life Reviews 4 (2007) 64–89 79

Table 2Properties of the absorptions from complex 1 and 2 (Figs. 12–14)

Complex Label Spectralposition(cm−1)

Differencein spectralposition(cm−1)

Rate(s−1)

Observedlinewidth(cm−1)

Averagespectralchange/scan(cm−1)

Processedlinewidth(cm−1)

Scantimeacrosslinewidth(ms)

(1)

a 12921278

1.5 × 10−2 36.8 3.5 7.4 150a′ 12643 1.9 × 10−2 41.6 4.7 7.5 180

b 12753259

2 ×10−2 28.5 4.5 5.9 130b′ 12494 2.2 × 10−2 29.1 5.9 11.5 240

(2)

a 12928341

5 × 10−4 39.1 5.3 11.3 230a′ 12587 2 × 10−3 21.1 5.4 7 150

b 12754270

1 × 10−3 11.2 6.8 3.9 80b′ 12484 5.5 × 10−3 28.5 3.9 4.7 100

c 12698180

1.3 × 10−3 70.3 6 5 100c′ 12518 8.3 × 10−3 46.7 3.6 5 100

For each absorption line the following properties are listed: the spectral position, the mutual spectral distance between the two anti-correlatedline positions, the average rate at which the absorption fluctuates between the two anti-correlated spectral positions, the linewidth observed inthe averaged spectrum, the average spectral change of the peak position per scan, the linewidth of the averaged spectrum after data processing asdescribed in the text, and the time required to scan the laser through the processed linewidth.

right-hand side of Fig. 13 the individual scans have been shifted such that the fitted peak positions coincided, andsubsequent averaging uncovers a width of 7.5 cm−1 (FWHM) for this absorption. The same procedure yields in othercases linewidths between 4 and 12 cm−1 [38].

Another example (complex 2) is presented in Fig. 14 [38]. In the one but top-most panel in Fig. 14(c) the fluo-rescence intensities of the two absorptions at 12928 cm−1 and 12587 cm−1, labeled “a” and “a′” in Fig. 14(a), areplotted in black and grey, respectively, as a function of the polarization of the excitation light. It is obvious that theintensity fluctuations of the two spectral features are anticorrelated, which is testified by inspecting the sum of thetwo polarization traces, shown in the top-most panel of Fig. 14(c). It can be fitted by a cos2-function (dashed line)in agreement with the expectation for a linear absorber. The absorptions b–b′ and c–c′ show an anti-correlated timedependence as well (one but lowest and lowest panel in Fig. 14(c). The spectral changes between a ↔ a′, b ↔ b′, andc ↔ c′ occur mutually independent from each other and the width of the reversible spectral jumps lies between 180–341 cm−1. The rates at which these spectral fluctuations occur are in general very small and vary between 5 × 10−4

and 8 × 10−3 s−1 [22]. Interestingly, for none of the absorptions the change in resonance frequency is accompaniedby a significant change of the orientation of the transition-dipole moment.

Also for this complex smaller excursions in frequency space of about 5 cm−1 between two successive laser scanshave been observed and as before the observed linewidths between 10–70 cm−1 results mainly from the accumulationof small spectral shifts during the experiment. For both complexes a lower boundary for the rate of these spectralfluctuations has been estimated from the scan speed of the laser to be 3 × 10−2 s−1. Clearly, it cannot be excludedthat additional fast processes which remain unresolved while the laser scans through the resonance contribute to thelinewidth. However, the observed processed linewidths cover the same range as those reported for the homogeneouslinewidth of the B800 absorptions [18] which restricts additional contributions to the line broadening to about 1 cm−1

or less. Given the scan speed of the laser the underlying processes have to occur within less than 200 ms. The dataobtained for both complexes are summarized in Table 2.

The spectroscopic properties of the chromophores embedded in the photosynthetic complexes are determined to alarge extent by their mutual spatial arrangement and their interaction with the local environment. However, a proteinis not a rigid structure. Due to the relatively weak interactions that stabilize the three-dimensional protein structurethe lowest energy state of a protein is not unique (see Section 5 of part I). In order to describe protein dynamics andfunction a model has been put forward by Frauenfelder and others [39,40] which proposes an arrangement of theprotein energy landscape in hierarchical tiers. On each level of the hierarchy the conformational substates (CSs) arecharacterized by an average energy barrier between the CSs that decreases with descending hierarchy. A consequenceof this idea is that structural fluctuations of a protein become hierarchically organized as well, featuring characteristic

80 Y. Berlin et al. / Physics of Life Reviews 4 (2007) 64–89

Fig. 14. Two-dimensional representation of 425 fluorescence–excitation spectra from the B800 band of an individual LH2 complex (complex 2).The spectra have been recorded consecutively at a scan speed of 50 cm−1/s at an excitation intensity of 15 W/cm2. The fluorescence intensityis indicated by the grey scale. Between two successive scans the polarization of the excitation light has been rotated by 1.8◦ . The horizontal axiscorresponds to the laser-excitation energy and the vertical axis to polarization (a). Average of all 425 fluorescence–excitation spectra (b). The tracesin the lower three panels show the intensity of the three absorption pairs (a–a′ , b–b′ , and c–c′) indicated by the boxes in (a) as a function of thepolarization. The trace in the top-most panel shows the sum of the traces of line pair a–a′ and a fitted cos2-function (dashed line) (c) [22].

rate distributions in different tiers. Supporting evidence for this concept has been obtained from experimental workon myoglobin [41–43].

From pressure dependent spectral hole burning experiments on LH2 from Rhodopseudomonas acidophila it isknown that relative distance changes of �R/R ≈ 10−4–10−2 are already sufficient to result in spectral shifts of 1–100 cm−1 for the B800 absorptions [44]. Accordingly, the observed spectral fluctuations have been interpreted toreflect modulations of the pigment–protein interactions in the vicinity of the chromophore. Following the concept ofCSs, the three observed categories of spectral fluctuations have been assigned to the presence of at least three distinctenergy tiers in the energy landscape of the protein. To address this issue in more detail Hofmann et al. [38] introducedthe term “energetic span” of the chromophore absorption. This refers to the width of the spectral region that is coveredby the spectral fluctuations of the chromophore within a certain time window. In Fig. 15(a) a simplified protein-energy landscape along an arbitrary conformational coordinate is sketched, together with the information that hasbeen obtained for the relationship between the energetic spans of the chromophore absorptions and the correspondingtimescales. It has been assumed that the magnitudes of the observed spectral shifts represent a hierarchy of tiers wherethe average height of the energy barriers decreases from top to bottom. The observed huge spectral shifts are thoughtto result from conformational changes of the protein between two CSs that are separated by a significant barrier height,Fig. 15(a) top. As the chromophore absorption samples only few discrete spectral positions, the energetic span coveredby the pigment absorption at this level of the hierarchy was taken as the energy difference between two anti-correlatedlines. The underlying processes in this tier occur at rates of 10−2–10−3 s−1. The smaller spectral shifts are interpretedto result from conformational changes of the protein between several CSs at the next lower tier that are separated bya minor barrier height, Fig. 15(a) center.

Within this tier the average CS energy has been indicated by a bold bar and the distribution of states has been indi-cated by the smooth curve to the right. Accordingly, the spectral changes of about 5 cm−1 between two successivelyrecorded chromophore spectra have been attributed to reflect structural fluctuations of the protein between two CSsinside this tier of the energy landscape. During the experiment, the distribution of CSs on this tier is sampled andcauses the observed linewidth of several 10 cm−1 providing information about the distribution of the CSs energies

Y. Berlin et al. / Physics of Life Reviews 4 (2007) 64–89 81

Fig. 15. Schematic sketch of three subsequent tiers of the potential energy hypersurface of a protein as a function of an arbitrary conformationalcoordinate (a). Width of the spectral region that is covered by the spectral fluctuations of the chromophore within a certain time window—termedenergetic span—versus the rate of these fluctuations in the three tiers found (b). For details see text (from [38]).

within this level of the hierarchy. Boundaries for the rates of the protein dynamics which result in these spectral fluc-tuations can be estimated from the repetition rate of the individual laser sweeps (0.03–0.07 s−1) and the time requiredto scan the laser across the accumulated linewidth (1 s−1). The shaded box in the center of Fig. 15(b) indicates theseconstraints, the data points (crosses) are placed at the repetition rate of the experiments.

Descending further in hierarchy one finally reaches a situation that the protein transitions between the CS aregoing to cause only minor changes in the chromophore spectra. Certainly, the smallest detectable spectral changecorresponds to a broadening rather than a shift of the absorption line. At the bottom of Fig. 15(a) a situation issketched where the individual CSs are already quantized in energy (light bars) and can be characterized by a statisticaldistribution (smooth curve to the right) around a mean value (bold bar) which represents one of the average CSenergies of the next higher tier. Within the temporal resolution of the experiment all CSs of this tier are sampled.A lower boundary for the rate of the processes that are able to contribute to unresolved spectral dynamics hiddenin the residual linewidth of the B800 absorptions is provided by the time that is required to scan the laser acrossthis linewidth. Therefore the maximum possible energetic span for the chromophore absorptions and vice versa thesmallest possible rate for dynamical processes in the protein can be extracted from the broadest processed linewidth.This fixes the upper left corner of the shaded box at the lower right of Fig. 15(b). It should be mentioned that an upperboundary for the rate of these processes follows from the Fourier-transform of the linewidth itself which yields about1012 s−1. However, the described experimental approach is inappropriate to monitor the ultrafast dynamical processesand focuses on those that occur at very low rates. Accordingly, the possible parameter combinations in the lowestobservable hierarchical level are restricted to the shaded area at the bottom of Fig. 15(b). The data points (squares)correspond to the processed linewidth versus the reciprocal scan time of the laser. Certainly, Fig. 15(b) provides onlya crude picture. In addition, it should be noted that this approach does not permit to observe small spectral shifts thatoccur at slow rates or to resolve shifts significantly smaller than the homogeneous linewidth of the optical transitionat any rate. However, large spectral shifts at fast rates have not been observed and the data points in Fig. 15(b) shouldbe read as a boundary for the possible parameter combinations. Only combinations of rates and spectral shifts belowthe diagonal of the diagram are compatible with the observations.

The intriguing question that arises is whether the observed spectral shifts can be related to structural rearrangementsin the binding pocket of the chromophore, which is shown in Fig. 16 [38,45].

It is known from theoretical work that the Qy transition of BChl a is very sensitive to perturbation of the π -conjugation system of the bacteriochlorin macrocycle, and is also affected by the ligands to the central Mg-atom.For instance, an out-of-plane rotation of the C2 acetyl group with respect to the bacteriochlorin plane yields a blue

82 Y. Berlin et al. / Physics of Life Reviews 4 (2007) 64–89

Fig. 16. Part of the binding pocket for a B800 BChl a molecule in Rs. molischianum (very dark grey: N, middle grey: O, in center: Mg). Dashedlines refer to short distances (in Å) and indicate likely hydrogen bonds and metal ligands. From [38,45].

shift of the pigment transition of up to 500 cm−1 [46]. A deviation from planarity of BChl will have similar effects.Density-functional theory calculations that examined the ligand-binding of the BChl a central Mg-atom to the chargedα-Asp6 amino acid in the B800 binding pocket of Rhodospirillum molischianum estimated a red shift of 190 cm−1

[47] for the site energy of a BChl a molecule in the B800 ring. It has been inferred that the observed spectral vari-ations result from rather local conformational changes that affect the π -conjugation system of the bacteriochlorinmacrocycle, e.g., through affecting the planarity of the ring, through a reorientation of side-groups, or through somerearrangement involving the central-Mg atom and its ligands. In this regard several aspects have to be considered.First, the huge spectral changes might reflect fluctuations in the strength of a hydrogen bond between the β-Thr23amino acid and the C2 acetyl group of the BChl a molecule [45,48]. This is evidenced by site-directed mutagenesison LH2 from Rhodobacter sphaeroides [49,50]. For this species a β−10-Arg amino acid is hydrogen bonded to the C2acetyl carbonyl group of the BChl a molecule and spectral shifts of 100–200 cm−1 for the B800 absorption maximumare observed if this amino acid is substituted by a non-hydrogen bonding residue. Second, the polarity of the B800binding site might be of influence as follows from shifts of up to 300 cm−1 for the spectra from monomeric BChl a

upon solution in various organic solvents [51]. For Rhodospirillum molischianum the X-ray structure shows a watermolecule in close proximity to the α-Asp6 and the methyl ester carbonyl of the BChl a that might cause variations inthe electrostatic environment of the pigment [45]. In summary, it appears very reasonable that the observed spectralshifts result from structural fluctuations within the binding pocket of the chromophore.

Clearly, the observed rates for the conformational changes (at low temperatures) do not reflect the dynamics ofthe protein in its native environment. However, working at cryogenic temperatures shifts the timescale for thesefluctuations into a range that is experimentally accessible. This offers the opportunity to study the organization ofthe protein energy landscape directly, despite that the biological function of these pigment–protein complexes is toperform photosynthesis under ambient conditions. Such an experiment can be performed only on single molecules atlow temperature. Under ambient conditions, even for single molecules, the expected spectral changes are completelymasked because the homogeneous linewidth of the absorptions may exceed the spectral changes.

Finally, it might be an eye opener to realize that also the detailed knowledge about semiconductor physics thatis required to properly operate electronic devices like radios, computers, mobile phones etc. had to be elucidated bylow-temperature solid state physics, despite that such equipment is used at temperatures that appear more pleasant tous.

7.4. The B850 band

The closest distance between the B850 pigments is less than 1 nm, i.e. rather small with respect to the size ofthe molecules. Therefore a strong excitonic coupling between the molecules has to be considered to understand theoptical spectra. In order to calculate the intermolecular interaction strength, V , several theoretical approaches have

Y. Berlin et al. / Physics of Life Reviews 4 (2007) 64–89 83

been employed [7–9] and resulted in values of V ≈ 250–400 cm−1 which is about an order of magnitude larger thanthe interaction strength in the B800 ring. The magnitude of the energetic mismatch, δ, between adjacent B850 BChla molecules is not directly accessible due to the excitonic coupling. However, if we assume that the variations insite energy in the B850 ring are comparable to those in the B800 assembly these figures suggest that the electronicexcitations in the B850 are strongly delocalized among the pigments.

The details of the exciton manifold of the B850 assembly of LH2 has been subject of numerous studies [3,7–9,20,52–55]. For the purposes of this review we only want to provide an insight into the general features of the B850excited states and calculate the exciton states for an unperturbed B850 ring using Eq. (7.1), e.g. with no diagonaland off-diagonal disorder. The LH2 complex from Rps. acidophila consists of N = 9 dimers, each of two BChl a

molecules bound to the α- and β-polypeptides as the basic building block. In the following we label the dimers by n

and denote the two molecules within a dimer by the subscripts α and β , having site energies Eα and Eβ . If for theinteraction only contributions from adjacent dimers are considered, the Hamiltonian for the set of N dimers is

H =N∑

n=1

(Eα|nα〉〈nα| + Eβ |nβ〉〈nβ |)

+N∑n

(Vd

(|nα〉〈nβ | + |nβ〉〈nα|) + Vext(|nβ〉〈(n + 1)α| + |(n + 1)α〉〈nβ |))

(7.10)+N∑n

(Wα

(|nα〉〈(n + 1)α| + |(n + 1)α〉〈nα|) + Wβ

(|nβ〉〈(n + 1)β | + |(n + 1)β〉〈nβ |)).The contributions to the interaction are the nearest-neighbor intradimer interaction Vαβ,nn = 〈nα|V |nβ〉 = Vd ,the nearest-neighbor interdimer interaction Vext = 〈nβ |V |(n + 1)α〉, the α-next-nearest neighbor interaction Wα =〈nα|W |(n + 1)α〉, and the β-next-nearest neighbor interaction Wβ = 〈nβ |W |(n + 1)β〉. For the simplest case whereEα = Eβ = E0 and Wα = Wβ = W0 the eigenstates of this Hamiltonian are given by

(7.11)∣∣kj

⟩ = 1√N

N∑n=1

ei2πkj nN

∣∣njαβ

⟩, j = s, as

where

∣∣nsαβ

⟩ = 1√2

(|nα〉 + |nβ〉),(7.12)

∣∣nasαβ

⟩ = 1√2

(−|nα〉 + |nβ〉),are the symmetric (j = s) and antisymmetric (j = as) dimer states. The energies of the exciton states can be expressedas follows

(7.13)Ejk = E0 + 2W0 coskj 2π

N±

√V 2

d + V 2ext + 2VdVext coskj

2π

N

where j = s refers to the “+” and j = as to the “−” sign. The quantum number kj of each exciton state in themanifold extends from kj = 0,±1, . . . , to ±4. A full treatment of this exciton system including the conditions whereEα �= Eβ and Wα �= Wβ can be found in [20]. The resulting energy levels of the exciton manifold are depicted inFig. 17. This figure shows how the structure of the exciton manifold develops as one goes from a single dimer to asystem of N interacting dimers. The exciton states are separated in lower (as) and upper (s) branches. This reflects theinteractions within a dimer and is commonly known as Davydov splitting [27,56], see Fig. 17, manifold 1. In total oneobtains eight pairwise degenerate states, labeled by kj = ±1,±2,±3,±4, and one nondegenerate state kj = 0, seemanifold 2 of Fig. 17. As a result of the strong interaction within the B850 ring the initial degeneracy of the excitedstates of the 18 B850 BChl a molecules is lifted and the energy of the 18 exciton eigenstates is spread over a bandwith a width of about 1000 cm−1.

84 Y. Berlin et al. / Physics of Life Reviews 4 (2007) 64–89

Fig. 17. Schematic representation of the energy-level scheme of the excited state manifold of a dimer (manifold 1) and of the B850 ring of LH2(manifold 2). The mutual orthogonal orientation of the transition moments of the kas = ±1 degenerate pair is indicated by the small, black arrowsinside the ovals. The interaction within the dimer is Vd (intradimer), whereas the interaction between the dimers is Vext (interdimer). The energyscale is given in units of Vd . Adapted from [19,20].

For the optical transitions between the ground state and any given exciton state one has to calculate the resultanttransition-dipole moment according to

M(kj

) = 〈g| D∣∣kj⟩ = 〈g| D 1√

N

N∑n=1

ei2πkj nN

∣∣njαβ

⟩

(7.14)= 1√N

N∑n=1

ei2πkj nN 〈g| D∣∣nj

αβ

⟩︸ ︷︷ ︸

m(njαβ)

= 1√N

N∑n=1

ei2πkj nN μ(

njαβ

)

where D is the transition-dipole moment operator and μ(njαβ) refers to the transition-dipole moment of the respective

dimer wavefunction. Consequently, both the magnitude and the mutual arrangement of the individual transition-dipolemoments have a crucial influence on the resulting selection rules for the optical transitions. Due to the circular arrange-ment of the pigments in LH2 only the exciton states kj = 0,±1 have a non-vanishing transition-dipole moment. Thekj = 0 transitions can be excited with light polarized parallel to the C9-symmetry axis of the ring whereas transitionsto the kj = ±1 states can be excited with light of mutually orthogonal polarization within the plane of the ring. Sincethe individual transition-dipole moments of the B850 pigments are oriented mainly in the plane of the ring ratherlittle of the total oscillator strength is associated with the kj = 0 states. Due to the head-to-tail arrangement of thetransition-dipole moments within an individual dimer nearly all the oscillator strength is concentrated in the lowerexciton manifold (j = as) which results in a strong electronic transition from the kas = ±1 states, seen in vivo as thestrong near IR absorption band at approximately 860 nm. The upper exciton components ks = ±1 carry less than 3%of the total oscillator strength and give rise to very weak absorptions up to about 790 nm [7].

The fluorescence–excitation spectrum of the B850 spectral region from an individual LH2 complex are shown inFig. 18(a). They have been obtained for excitation with mutual orthogonal polarization. Apparently, the transition-dipole moments of these two transitions are perpendicular with respect to each other. Based on this observation andthe fact that these bands are by far the most intense ones in absorption, these transitions have been attributed to thekas = ±1 exciton states [16]. The observed line widths of the bands reflect the ultra-fast relaxation (∼100 fs) to thekas = 0 exciton state, consistent with time-resolved data.

Y. Berlin et al. / Physics of Life Reviews 4 (2007) 64–89 85

Fig. 18. Fluorescence–excitation spectrum of the long-wavelength region of an individual LH2 complex for mutually orthogonal polarized excita-tion. The inset shows a schematic representation of the energy-level scheme of the lowest states in the excited-state manifold of the B850 ring inLH2 of Rp. acidophila for nine-fold rotational symmetry of the pigment arrangement. The grey circles indicate the initial population of a givenexcited state and the arrows the relative orientation of the transition-dipole moments in the plane of the ring (a). Fluorescence–excitation spectraof the long wavelength part of the B850 band of three different complexes, featuring a very narrow transition at the red wing of the kas = ±1absorptions. The spectra are obtained by a summation of repetitively scanned spectra at a high scan rate, where the kas = 0 transitions are alignedbefore summation to correct for spectral diffusion (b). From [19].

A crucial check for this assignment was the observation of the kas = 0 exciton state. For this transition, which gainsoscillator strength when there is any deviation from a perfectly symmetric Bchl a arrangement, a relatively narrowabsorption line is expected because the lifetime of the kas = 0 state is about 1 ns. Such a narrow line on the low-energyside of the B850 band has indeed been detected [19], Fig. 18(b), which provides strong evidence that the descriptionof the lowest electronically excited states of the B850 assembly in terms of the exciton model is justified.

However, for the circular arrangement of the pigments, the exciton model predicts that the kas = ±1 states aredegenerate and have the same intensity. Random diagonal disorder, caused by stochastic variations in the protein envi-ronment, introduces the term δn into Eq. (7.5). The main effects on the exciton manifold are, a mixing of the differentexciton levels, a modification of the energy separation of the exciton levels and lifting their pair-wise degeneracy, anda redistribution of oscillator strength to nearby states, including the kas = 0 state. The random off-diagonal disorderdescribed by the term �Vnm in Eq. (7.5), is caused by the variations in the coupling between the BChl a pigmentsand originates from fluctuations in the orientations and positions of the individual transition-dipole moments. The in-fluence of these various types of disorder on the B850 exciton states have been analyzed intensively. Since the effectsof random off-diagonal disorder on the exciton dynamics are experimentally indistinguishable from those of randomdiagonal disorder [28] many studies have focused on the latter type of disorder [7,53]. More recently, studies havealso included combinations of random diagonal and correlated off-diagonal disorder [38] as well as combinations ofrandom on- and off-diagonal disorder and correlated on- and off-diagonal disorder on the B850 exciton states [53].Predictions based on these models differ with respect to subtle details in the spectra such as the extent and distributionof the energy separation between the kas = ±1 states and the intensity ratio of the respective transitions.

In order to discriminate between the different models widefield fluorescence excitation spectroscopy in combina-tion with a highly sensitive electron-multiplying charge-coupled device (EMCCD) camera has been used which leadto a massive parallelization of the experimental scheme [57]. From this experimental data the energetic splitting ofthe kas = ±1 states �Eblue,red, the ratio of the integrated intensities Iblue/Ired, and the relative orientation of the twotransition-dipole moments �αblue,red, where blue (red) refers to the energetically higher (lower) absorption band(s)

86 Y. Berlin et al. / Physics of Life Reviews 4 (2007) 64–89

Fig. 19. Comparison of the experimental distributions (histograms) for the energetic separation �Eblue,red (top), the intensity ratio Iblue/Ired(center), and the relative orientation of the transition-dipole moments �αblue,red (bottom) of the two broad transitions in the B850 spectra withnumerical simulations for (a) random diagonal disorder, (b) random diagonal and correlated off-diagonal disorder, and (c) random and correlateddiagonal disorder. The experimental data refer to the left vertical scale and the simulations refer to the right vertical scale. From [57].

were obtained. The distributions of these parameters are shown in the histograms in Fig. 19 together with numericalsimulations that will be discussed below [20,57]. As can be seen from Fig. 19 these parameters vary from complexto complex. The energetic separation �Eblue,red of the kas = ±1 states is centered at 126 cm−1 and has a widthof 101 cm−1 (FWHM). The center value (FWHM) of the integrated intensity ratio Iblue/Ired is 0.73 (0.54), and themutual orientation of the transition-dipole moments �αblue,red is 91◦ (19◦).

The experimental data have been compared with results from numerical simulations for three different models:(i) random diagonal disorder (energetic disorder), (ii) random diagonal disorder together with correlated off-diagonaldisorder (structural disorder), and (iii) random- and correlated diagonal disorder. It has been found that introduc-ing only random diagonal disorder, model (i), could not explain the observations even if higher exciton states wereincluded in the calculation, Fig. 19(a). Instead, a correlated off-diagonal disorder of C2 symmetry was introducedas a regular modulation of the interaction strength in the Hamiltonian to explain the observed large splitting of thekas = ±1 states, model (ii) [16,19,20]. The dominant effect of such a modulation is a coupling between exciton statesthat differ in their quantum number by �k = ±2. Since C2 is the lowest symmetry component of an ellipse the originof this modulation could be visualized as an elliptical deformation of the complexes with a deformation amplitudeδr/r0 = 7–8% where r0 is the radius of the unperturbed ring and the long and short axes of the ellipse deviate fromr0 by ±δr . Such a structural deformation will lead to a spatial displacements of the BChl a molecules and conse-quently to a modulation of the interaction strengths. Based on fluorescence–polarization experiments other groupscame to similar conclusions [15]. In combination with random diagonal disorder the model explained the splitting ofthe kas = ±1 states and the distribution of this parameter as well as the mutual orthogonal transition-dipole momentsof the two kas = ±1 transitions but it failed to explain the observed intensity ratio for these two transitions.

However, it is reasonable to assume that a possible structural deformation would also affect the conformation of theprotein residues in the binding pocket of the chromophores. Since it is known for the B800 absorptions that alreadytiny relative distance changes in the binding pocket are sufficient to result in large spectral shifts [44] it is obvious

Y. Berlin et al. / Physics of Life Reviews 4 (2007) 64–89 87

to ask whether a moderate modulation of the site energies would be compatible with the experimental data as well.If the modulation in site energies follows an imposed structural deformation of the LH2 complex a less pronounceddeviation from circular symmetry (which might not be resolved by X-ray crystallography) could be already sufficientto account for the observations. Indeed a model that takes into account random and correlated diagonal disorder, model(iii), is in good agreement with all measured experimental distributions, Fig. 19(c) [57].

8. Summary

We discussed in detail the physics of proteins in relation to our own research field which is high-resolution opticalspectroscopy at low temperatures. The questions addressed concern the chromophore protein interactions, their range,what kind of protein features are picked up by these interactions, how they change in an external field, and what kindof information, e.g. on symmetries, on field strength, on material parameters, etc., can be extracted. The major focusof the paper, however, was on spectral diffusion physics of proteins, a field with many open questions. We addressedthe behavior in ensemble experiments as well as in single-molecule experiments and tried to offer lines of reasoningwhich might serve as guidelines for an understanding of the phenomena. Apart from the aspect of functioning, thephysics of proteins at low temperature is interesting per se, for instance, the questions as to whether the energetics ofthe energy landscape reflect symmetry principles, or the question as to the driving forces in the dynamical transitionfrom a solid-like to a liquid-like behavior. Many of the important questions still wait to be answered despite thenumerous experiments on the behavior of proteins at low temperature. In a survey section we reviewed some of theseexperiments.

However, low-temperature spectroscopy on biomolecules often encounters great reluctance in the life science com-munity because it is a widespread opinion that information obtained from those experiments—far off from physiologicconditions—is at most of academic interest let alone of any relevance for the understanding of the biological function.Though, for most of the methods employed in the life sciences a situation close to physiological conditions does notapply either. Low temperatures are common practice in cryo (!) electron microscopy and X-ray crystallography to re-duce radiation damage and to improve resolution. There it is usually assumed that a protein structure in a single crystalat low temperatures resembles those at physiologic conditions. In other words, most of the three-dimensional proteinstructures which are at the basis of our current understanding of protein function are low temperature structures. Otherapproaches in biochemistry rely on the stabilization of intermediates, either as a modification of the protein, for ex-ample by substitution of amino residues, or as modification of the environment for example by a sudden drop in pHor concentration, and might be regarded as “chemical trapping” of the protein (far from physiologic conditions).

Concerning the physics of proteins, their biological functioning relies crucially on the interplay of structural disor-der and structural organization. Such aspects can be most clearly revealed when the thermal motion is suppressed andthe structure-changing rates become sufficiently slow to be measured conveniently over many orders of magnitudein time. From this point of view, lowering the temperature essentially means trapping the biomolecule in a physicalstate, i.e. “physical trapping”, where it can be investigated in much more detail as compared to experiments at ambienttemperatures. Compared to chemical trapping this appears as a rather mild perturbation [58].

Resuming we think to have demonstrated the significance of low temperature optical spectroscopy for understand-ing dynamics, structure and functioning of proteins. Low temperature optical techniques enable the direct investigationof the complex conformation space of proteins and the associated dynamics. We consider the low temperature prop-erties of proteins as important information which sheds light on their properties in the living cell environment.

Acknowledgements

We thank our friends who have collaborated with us on various aspects of low temperature physics of proteins:Thijs Aartsma, Judit Fidy, Fritz Parak, Vladimir Ponkratov, Mark Ratner, Jane Vanderkooi.

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