A Marshall Stoneham

Achterhold K

Alexander D M

Austin R H

Barker A S

D'Ovidio F

Davydov A S

Housely R M

Itoh N

Johnson D P

Landau L D

Per-Anker Lindg rd

Shluger A L

Steiner M J

Stoneham A M

Su W P

Wallace D S

Xie A

Zaccai G

English

Lindgard, PA

Stoneham, AM

UCL Discovery

INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTERJ. Phys.: Condens. Matter 15 (2003) V5–V9 PII: S0953-8984(03)61522-5VIEWPOINTSelftrapping, biomolecules and free electron lasersPer-Anker Lindgård1,2 and A Marshall Stoneham31 Materials Research Department, Risø National Laboratory, DK-4000 Roskilde, Denmark2 QUPC entre, Danish Technical University, DK-2800 Lyngby, Denmark3 Department of Physics and Astronomy, University College London, Gower Street,London, WC1E 6 BT, UKReceived 1 April 2003Published 28 April 2003Online  at  stacks.iop.org/JPhysCM/15/V5Forasolid-state physicist, the controlled movement of energy and charge are centralphenomena. Novel materials have often pointed to new mechanisms: self-trapping inhalides giving energy localization, the incoherent motion of small polarons in colossalmagnetoresistance oxides, solitons in conducting polymers, magnetic polarons in magneticsemiconductors, the quantum motion of electrons in mesoscopic metals, the regimes of bothcoherent and incoherent quantum propagation of muons in solids, and so on. The issues ofenergy and charge transport are equally crucial in living matter, but are understood less well.How can the energy from light or chemical processes be moved around and used efﬁciently?The important paper by Austin et al (2003) in this special issue shows that new experimentaltools,usingtheultrashort,tunablelaserpulsesfromfreeelectronlasers,openupthepossibilityof resolving outstanding problems in understanding the energy and charge processes whichunderpin life itself. In biological physics, one of the most intriguing ideas is that of thesoliton, whose coherent motion is believed to enable efﬁcient energy transport. Here we shalldiscuss the connectionbetween these ideas of solitons and similar concepts occurringin moreconventionalcondensed matter systems.Light is the most important source of energy for living matter, and the interaction withlight is of vital importance in many other circumstances. Yet, the optical properties of simplebio molecules—or even of simpler organic chemical analogues—are not fully understood. Isittruethat, inlivingmatter,energy(whetheritsoriginis fromlightorfromachemicalprocess)becomes localized, trapped in soliton modes, and subsequently transported deterministicallyin energy packets? This has been discussed widely in the 25 years since Davydov (1977)proposed that this might be what happens in the α-helices in proteins. However, the ideais unproven. There has been no ‘smoking gun’ proving the hypothesis for real proteins, asAustin phrased it in his talk presenting the subject to be highlighted here. It is probably fairto sayt hat there are two main reasons why interest in the Davydov model has been declining.First, itseemsuncertainthatsolitonswouldbestableinproteinsatphysiologicaltemperatures.Secondly, evidence for solitons has been at best circumstantial, based on the occurrence oftemperature-dependentside-bands to certain peaks in the vibrational response spectrum. Theproblem is that the temperature dependence reﬂects the mean square deviation  x2  of theatomsinvolved,andhence it is the same forstatic defectsas fordynamicand nonlinearsoliton‘defects’(AlexanderandKrumhansl1986);we remarkfurtherthat  x2  is notverysensitiveto0953-8984/03/180005+05$30.00 © 2003 IOP Publishing Ltd Printed in the UK V5V6 ViewpointFigure 1. Portion of an α-helical protein. The black, spiralling backbone is stabilized by hydrogenbonds,shownasgreendashedlines. AnumberofthekeyH–N–C=Opeptideunitscanbeidentiﬁed.The amide-I vibration gives a very characteristic resonance, and is dominated by a C=Os t r etchmotion. O atoms are red, H atoms silver, N atoms blue, and C atoms black, where the outwards-pointing ones indicate the beginning of usually different side-chains. These are attached to the Cαatoms, which are bound to the N and C in the peptide unit and form a ﬂat, strongly bound platelet.thed etails of the phonon spectrum (Stoneham 1975, p 316, Housely and Hess 1966, Johnsonand Kassman 1969). Notice that independent measurements of  x2  of speciﬁc atoms arepresented in this special issue using neutron scattering (Zaccai 2003) and using M¨ ossbauerspectroscopy (Achterhold and Parak 2003). The intensity of the response function (infraredabsorption,Ramanscattering, etc) shouldsimplyfollowan exp(−(T/θ)2) dependence,whereT is the temperature and θ ac onstant.The excitation of interest could be the C=Os t r e t ch frequency (typically near ν ∼1650 cm−1 = 205 meV = 6.06 µm = 49.5p s −1 in the various units used preferentially indifferent ﬁelds) of the hydrogen bonded peptide chain units ···H–N–C=O:H–N–C=O···along the α-helices (see ﬁgure 1). The frequency of that mode could be lowered if the localpotential is softened due to a local relaxationo ft he surroundingatom positions; this might bedue to a broken hydrogenbond giving a larger O–H distance. Hence a red-shifted sideband isexpected, corresponding to a non-linearly coupled mode pair. And the partner could be a lowfrequency, localized (soliton) excitation on the hydrogen bonded chains (the bonds indicatedby the dotted lines in ﬁgure 1) stabilizing the α-helices. However, the spectrum for a regularprotein containing a large number N of atoms (typically N ∼ thousands) is very complex.There will be at least 3N response peakscorrespondingto the 3N harmoniceigenfrequencies.Then there will be higher harmonics, and the various non-linear mode combinations. So thereliable assignment of a particular peak is very difﬁcult.What wouldbe the experimentalsignatures of such soliton modes or of the so-called self-trapping? The most distinct signature should be the frequencyresponse of the soliton itself—thatcouldbethe‘smokinggun’. Surprisingly,thatsignaturewasfoundin1Dmagneticsystemsas a peak centred on zero frequency,where no peak would be expected in a harmonic system.This has been much studied and discussed (Steiner et al 1976). For proteins there are manylow frequency excitations corresponding to large scale vibrations and a similar detection isextremelydifﬁcult. So what is new? Recent time-resolvedspectroscopicmeasurementsallowone to probe the lifetime of particular, chosen excitations. Long relaxation times suggestViewpoint V7soliton character and self-trapping. Using the possibilities of the free electron laser FELIX inthe Netherlands, Austin et al have studied a number of such sidebands, ﬁnding unexpectedlylong lifetimes ∼30 ps as opposed to only 5 ps for the neighbouring peaks. That is veryinteresting because it indicates that the energy isl ocalized and not easily dispersed in the fullprotein. The sideband excitation can hence act as an energyreservoir. Studies of real proteinsindicate long-lived states in sperm whale myoglobin (Xie et al 2000) as in bacteriorhodopsin(Austinetal 2003),bothmainlyconsistingoflongα-helices. A peakinthefarinfraredend(atν ∼ 115cm−1)inbacteriorhodopsinhasunexpectedlylongrelaxationtimes∼500ps(Xieetal2002). D’Ovidioetal(2003)demonstratethatthismodeisprobablyassociatedwithexcitationson the hydrogen bonds along the sides of the α-helices, and these have soliton character, aswell as minimal effect on the surrounding protein and solvent. Hence, the mode has all theproperties needed for being long-livedin comparison to other low frequencymodes involvinglarge-scaleﬂuctuations of the whole protein. Austin et al associate the temperaturedependentsideband observed in the static IR spectrum with the long lived mode, but are cautious indescribing it as a ‘self-trapped’excitation. In particular they demonstrate that the temperaturedependence is consistent with a simple two-state model—and do not use that expected forthe self-trapping model. A two state model was also used by Williams et al (1996), whoinvestigated a small artiﬁcial 21-residue α-helical peptide by time-resolved IR spectroscopy.They suggest the temperature dependence is due to broken hydrogen bonds (or a helix–coiltransition)athightemperatures,yetwithoutfullydestroyingtheα-helixarchitecture. Thisisasimplepicture,whichmayormaynotbethesame, physically,asprovidedbytheself-trappingtheory. Clearly, a great deal is to be learned from the new possibilities opened up by ultra fasttime-resolved experiments.At this point, it is appropriate to seek comparison with the longer-established ideasof conventional condensed matter systems with impurities or other imperfections. In suchsystems, light is absorbed and stored in excited states. These states are localized, and areseparated in frequency from other modes (phonons or electronic) in the crystal (Barker andSievers 1975, Stoneham 1975). There are various states (see below) in which electrons arestronglycoupledtohostlatticemotion(ShlugerandStoneham1993,Shlugeretal2000). Theseincludebehaviourassociatedwith ﬂuctuationsofpotentialsandforceconstantsdueto thermalvibrationalmotions. Thismayleadtoalocal‘dynamicdefect’. Thisisinterestingifithappensonthetimescalesimilartothatoftheself-trappingrelaxation. Inanharmonicsystemsdifferent(harmonic)excitationscouple,whensuchadynamicdefectmighttrapanotherexcitation. Thisis not necessarily a one-dimensional problem.Oneﬁ nds a number of related, thought provoking terms and concepts in both condensedmatter physics and in the biological physics problem discussed above. Since the terms andthec oncepts do not always correspond precisely, it may be useful in this viewpoint articleto mention concisely a few of the most important ideas in the form of a ‘dictionary withcomments’. Many more examples could be mentioned in a full-length review.Theﬁrstsetofideasrelatetothelocalizationandtransportofcharge. Oneimportantpointis thatthosecarrierswhichinteractwiththelattice(e.g.,polarons)areless mobilethancarrierswithout interaction. So the effects might be the opposite of what Davydov wanted his solitonto do.(1) Soliton: as oliton in biomolecules offers one possible way to understand how energyreleasedbyATPhydrolysiscanbe propagatedovera fairlylongdistance(maybe150nm)withoutsigniﬁcantdissipation. Sotheideaisthatthereisamotion(coherentinsomesense)enabledbyananharmonicinteractionbetweenconventionalvibrationsandtheC=Omode(Davydov1977). ThiscorrespondstothesolitonsofappliedmathematicsandsharestheirV8 Viewpointproperties in propagating roughly as desired (Scott 1992). In condensed matter physics,solitonsarecommonlydiscussedforconjugatedpolymers(semiconductingpolymersliketrans-polyacetylene,t-PA)andinthepropagationoflightdownopticalﬁbres. Thepolymersolitons are very like polarons(and indeed, the two words are used for similar excitationsdiffering mainly in topology). Models of t-PA (Su et al 1980, Wallace et al 1991) showsolitons propagating at just below the speed of sound. The idea is really rather similar tothe biomolecule case, but, instead of transporting a C=Ov i b r a tion, thec oupling is dueto the dimerization. On the borderline is the ‘biomolecular-like’ crystal of acetanilide,whichh as the same hydrogen bonded peptide chain units as found in α-helices. A recentpump–probeexperimentdiscusses the complex sidebandsof the N–H stretch vibration interms of the self-trapping mechanism (Edler et al 2002).(2) Polaron: intheconventionalcondensedmattercase,therearetwotypesofpolarons: largeand small (Stoneham1989). Both concerncarriers(electronsor holes) and the associatedstrain and polarization they cause in the host solid. Almost all the theory is harmonic:there is no need for anharmonicity. A large polaron means a carrier plus its associatedstrain/polarization ﬁeld, and perhaps the main effect of this ﬁeld is to alter the effectivemass of the carrier. So, for example, its mobility falls as temperature rises, because ofscatter by increasing vibrational amplitudes. A small polaron (using the conventionalview; there ares u b tleties) is self-trapped:t h edistortion or polarization is so large as toimmobilize the carrier (that was ﬁrst shown by Landau 1933).(3) Self-trapping charge localization: thes mall polaron moves by incoherent hopping, soits mobility increases as temperature rises (again, there are qualiﬁcations, and for muonsin solids there is another regime at low temperatures when the scattering vibrations arenot excited). Self-trapping localizes the carrier, so gives charge localization (Itoh andStoneham 2000). The localized carrier can be observed spectroscopically. The self-trappedhole(Vk centre)in halideshas beenstudiedextensivelybothopticallyandin spinresonance.(4) Self-trapping energy localization: excitons can also self-trap. Sometimes the result canbe considered as an electron trapped by a self-trapped hole (or vice versa); sometimesthe self-trappedexciton has quite a differentstructure. Excitonself-trappinggivesenergylocalizationandthelocalizedenergycancauselocalatomicchangesanddefectproduction.In principle, excitons can transport energy( c r eate an exciton at site 1, let it move to site2, recombine to release energy).(5) Localized vibrations: in solids have two main forms. Local modes have frequenciesdifferent from those of the host, whether at higher frequencies (the common case forlight impurities) or in a gap in the phonon density of states. Resonant modes concentratevibrational energy at speciﬁc sites, often at heavy impurities. However, some impurities(e.g., KCl:Li) show local modes, resonant modes, and even tunnelling states.How were the electronic and excitonic self-trapped states identiﬁed? Spectroscopy hasbeen especially powerful. For example, the self-trapped hole in KCl might be regarded as aCl−2 molecular ion replacing two Cl− ions, and it has characteristic spin resonance, Raman,optical and infrared transitions. The local distortion has observable effects. One might askwhether optical or spin resonance spectra, rather than vibrational spectroscopies, could yieldusefulinformationonpossibleDavydovsolitonsystems. Somestepsinthisdirectionarefoundin pump probe experiments,w hich test some of the key ideas by exploiting the possibilities oftunable lasers offering ultra fast pulses. Several examples of such experiments are presentedin the paper by Schoenlein et al (2000) in which the technique is described. The temperaturedependences and lifetimes of selected excitations can now be measured using modern pump–Viewpoint V9probe techniques. Such properties are also highly relevant in more conventional condensedmatter systems (Itoh and Stoneham 2000).The recent novel results for real proteins areb ringing new insight to the dynamical andoptical properties of living matter, and provide a substantial step towards understanding theirfunction. It is striking that the extremely high time resolution, typically femtoseconds, isan essential ingredient for insight into phenomena at much longer times scales, typicallynanosecondstomicrosecondsforproteins. Therearesigniﬁcantparallelsbetweentheconceptsfor proteins and those for inorganic solids, and there are signs that applying the full range ofexperimental tools would transform our understanding of both classes of system. This wouldprovide a powerfularray of ideas and approaches, and perhaps a route to understandingthosemany systems which involve the sophisticated dynamical behaviour of soft and hard matter.AcknowledgmentsWe thank Dr Geoffrey Wells and Dr Sarah Harris for the ﬁgure.ReferencesAchterhold K and Parak F G 2003 J. Phys.: Condens. Matter 15 1683Alexander D M and Krumhansl J A 1986 Phys. Rev. B 33 7172Austin R H, Xie A, van der Meer L, Shinn M and Neil G 2003 J. Phys.: Condens. Matter 15 1693Barker A S and Sievers A J 1975 Rev. Mod. Phys. 47 Suppl no 2Davydov A S 1977 J. Theor. Biol. 66 377Davydov A S 1979 Phys. Scr. 20 387D’Ovidio F, Lindgård P A and Bohr H G 2003 J. Phys.: Condens. Matter 15 1699Edler J, Hamm P and Scott A C 2002 Phys. Rev.L e tt. 88 067403-1Housely R M and Hess F 1966 Phys. Rev. 146 517Itoh N and Stoneham A M 2000 Materials Modiﬁcation by Electronic Excitation (Cambridge: Cambridge UniversityPress) p xv and 520Johnson D P and Kassman A J 1969 Phys. 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Selftrapping, biomolecules and free electron lasers

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