Fluorescence Studies of Complex Systems: Organisation of Biomolecules

Denys Marushchak

Department of Chemistry, Biophysical Chemistry Umeå University

SE-901 87 Umeå, Sweden 2007

ii

Organisation Document name UMEÅ UNIVERSITY DOCTORAL THESIS Department of Chemistry Biophysical Chemistry SE-901 87 Umeå, Sweden Date of issue Author 23-25 January 2007 Denys Marushchak Title Fluorescence Studies of Complex Systems: Organisation of Biomolecules Abstract The homo and hetero dimerisation of two spectroscopically different chromophores were studied, namely: 4,4-difluoro-4-bora-3a,4a-diazas-indacene (g-BODIPY) and its 5-styryl-derivative (r-BODIPY). Various spectroscopic properties of the r-BODIPY in different common solvents were determined. It was shown that g- and r-BODIPY in the ground state can form homo- as well as hetero dimers.

We demonstrate that the ganglioside GM1 in lipid bilayers of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) exhibits a non-uniform lateral distribution, which is an argument in favour of self-aggregation of GM1 being an intrinsic property of the GM1. This was concluded from energy transfer/migration studies of BODIPY-labelled gangliosides.

An algorithm is presented that quantitatively accounts for donor–donor energy migration (DDEM) among fluorophore-labelled proteins forming regular non-covalent polymers. The DDEM algorithm is based on Monte Carlo (MC) and Brownian dynamics (BD) simulations and applies to the calculation of fluorescence depolarisation data, such as the fluorescence anisotropy. Thereby local orientations, as well as reorienting motions of the fluorescent groups are considered in the absence and presence of DDEM among them.

A new method, in which a genetic algorithm (GA) was combined with BD and MC simulations, was developed to analyse fluorescence depolarisation data collected by the time-correlated single photon counting technique. It was applied to study g-BODIPY-labelled filamentous actin (F-actin). The technique registered the local order and reorienting motions of the fluorophores, which were covalently coupled to cysteine 374 (C374) in actin and interacted by means of electronic energy migration within the polymer. Analyses of F-actin samples composed of different fractions of labelled actin molecules revealed the known helical organiszation of F-actin, and demonstrated the usefulness of this technique for structure determination of complex protein polymers. The distance from the filament axis to the fluorophore was found to be considerably less than expected from the proposed position of C374 at a high filament radius. In addition, polymerisation experiments with BODIPY-actin suggest a 25-fold more efficient signal for filament formation than pyrene-actin.

Keywords: Fluorescence anisotropy, BODIPY, Ganglioside GM1, homo and hetero dimerisation, protein aggregates, protein polymer structures, actin polymerisation, FRET, donor–acceptor energy transfer DAET, donor-donor energy migration DDEM, homotransfer, Monte Carlo simulation, MC, Brownian dynamics, BD, Genetic Algorithm, GA.

Language: English Number of pages: 44 + 4 papers

Not for sale, Copyright © 2007 by Denys Marushchak ISBN 978-91-7264-260-7

Printed by Solfjädern Offset AB Umeå, Sweden 2007

iii

Akademisk avhandling

Beslut Dnr 542-4701-06, 2007-01-16 Nämnden beslutar enligt förslaget från slutexaminator, professor Göran Lindblom att utse docent Alexander Lyubartsev, Avdelningen för fysikalisk kemi, Arrhenius’ Laboratoriet, Stockholms universitet som fakultetsopponent att utse professor Anders Kastberg, Institutionen för fysik, Umeå universitet, professor Bernt Eric Uhlin, Institutionen för molekylärbiologi, Umeå universitet samt docent Eva Selstam, Institutionen för fysiologisk botanik, Umeå universitet som betygsnämnd att utse professor Lennart B-Å Johansson som ordförande vid disputationen. Disputation datum är 16 februari 2007 kl. 13.15 i sal KB3A9

iv

”Jag är inte me’, om jag inte får vara me’ ”, sa Karlsson. “Jag ska väl också ha nånting roligt!” ”I am not me, if I’m not allowed to be myself”, said Karlsson. ”I want something funny as well!”

Astrid Lindgren

Во всем мне хочется дойти In everything I want to reach До самой сути. For the very essence. В работе, в поисках пути, In work, in searching for the path, В сердечной смуте. And in the heart's distemper. До сущности протекших дней, For the essence of the passed days, До их причины, For their causes, До оснований, до корней, For foundations, for the roots, До сердцевины. And for the marrow. Всё время схватывая нить To grasp the meaning Судеб, событий, Of the fates and doings, Жить, думать, чувствовать, любить, To live, to think, to feel, to love, Свершать открытья. And to discover. … … Борис Пастернак Boris Pasternak

v

CONTENTS NOTATION vi

LIST OF PAPERS vii

1 INTRODUCTION 1

2 SYSTEMS AND MOLECULES 4

2.1 Green and red BODIPY 4

2.2 The lipid DOPC 6

2.3 The ganglioside GM1 8

2.4 Actin – a protein that forms filaments 9

3 INTRODUCTION TO FLUORESCENCE SPECTROSCOPY 11

3.1 Photophysical processes 11

3.2 Experimental part 12

3.3 Resonance Energy Transfer (RET) or Donor-Acceptor

Energy Transfer (DAET) 16

3.4 Homotransfer or Donor-Donor Energy Migration (DDEM) 18

4 PHYSICAL MODELS OF MOLECULAR SYSTEMS 21

4.1 DOPC vesicles with BODIPY-labelled GM1 mixtures 21

4.2 Linear aggregates/non-covalent polymers 23

5 DATA ANALYSIS 30

5.1 Genetic Algorithm PIKAIA 30

6 CONCLUSIONS 32

7 ACKNOWLEDGMENTS 34

vi

NOTATION

A acceptor of electronic energy D donor of electronic energy FRET fluorescence resonance energy transfer DAEM donor-acceptor energy migration DDEM donor-donor energy migration DOPC 1,2-dioleoyl-sn-glycero-3-phosphocholine PDDEM partial donor-donor energy migration EFT extended Förster theory F(t) time-dependent fluorescence intensity r(t) time-dependent anisotropy τ fluorescence lifetime, ns R distance between centres of mass of interacting molecules R0 Förster radius, Å λ wavelength, nm TCSPC time-correlated single photon counting g-BODIPY N-(4,4-difluoro-5,7-dimethyl-4-bora-3a,4a-diaza-s-indacene-3-

yl)methyl)iodoacetamide (BODIPY® FL C1-IA) r-BODIPY 4,4-difluoro-5-styryl-4-bora-3a,4a-diaza-s-indacene-3-pentanoic)

acid (BODIPY® 564/570 C5) MeOH methanol, CH3OH EtOH ethanol, C2H5OH GM1 ganglioside GM1 - sialic acid containing the glycosphingolipid BD Brownian Dynamic MC Monte Carlo simulations GA genetic algorithm AFM atomic force microscopy NMR nuclear magnetic resonance TCSPC time-correlated single photon counting

vii

LIST OF PAPERS

This thesis is based on the following papers, which are referred to in the text as Paper I-IV. Already published papers and figures reprinted with kind permission by the publishers. I Marushchak, D., Kalinin, S., Mikhalyov, I., Gretskaya N., Johansson, L.B.-Å. Pyrromethene Dyes (BODIPY) Can Form Ground State Homo and Hetero Dimers: Photophysics and Spectral Properties. Spectrochim. Acta A, 65(1) (2006) 113-122. Copyright© (2006), with permission from Elsevier II Marushchak, D., Gretskaya, N., Mikhalyov, I. & Johansson, L.B.-Å. Ganglioside GM1 is non-uniformly distributed in lipid bilayers as revealed by fluorescence studies. Accepted for publication in Molecular Membrane Biology, March-April 2007; 24(2). III Marushchak, D. & Johansson, L.B.-Å. On the quantitative treatment of donor-donor energy migration in regularly aggregated proteins. J. Fluorescence, 15 (2005): 797-803. Copyright© (2005), with permission from Elsevier IV Marushchak, D., Grenklo, S., Karlsson, R. & Johansson, L.B.-Å. Fluorescence Depolarisation Experiments on F-Actin Analysed by a Genetic Algorithm. Submitted to PNAS 2007.

1

1 INTRODUCTION The fluorescence itself is a special case of more general phenomenon called luminescence (Latin: lūmino - illuminate, light up). The luminescence is the emission of photons from electronically excited states(1-3). Emission is also referred to as fluorescence or phosphorescence, depending on whether it corresponds to a spin-allowed or a spin-forbidden transition, respectively (2,3). Transition from the first excited to the ground state (S1-S0) is much faster than the first triplet to the ground state (T1-S0). These transitions correspond to fluorescence (Latin: Fluores to flow) and phosphorescence (Latin: Phōsphorus - the morning star; Greek: φως – light, φέρω – to carry), respectively. The luminescence is quite common in the nature: e.g. glowing of a sea and sand on the beach, or that light-green bright spots in the darkness in the summer night – these are caused by chemoluminescence in glowworms, lighting beetles or fireflies. Other phenomena are the phosphorescence of the hands of a wristwatch and the ability of the white phosphorus to glow in the dark. A beautiful example of fluorescence in everyday’s life is a fluorescence of quinine. Actually, the first documented observation of the fluorescence phenomenon is an observation of Stokes’ shift, that was done by Sir G. G. Stokes in 1852 in Cambridge (4). These early experiments used relatively simple instrumentation. The source of UV excitation was provided by sunlight and a blue glass filter, which was part of a stained glass window. This filter selectively transmitted light below 400 nm, which was absorbed by quinine. The exciting light was prevented from reaching the detector (eye) by a yellow glass (of wine) filter. Quinine fluorescence occurs near 450 nm and is therefore easily visible. Quinine was extracted from the bark of the South American cinchona tree, isolated and named in 1817 by French researchers Pierre Joseph Pelletier and Joseph Caventou. The name was derived from the original Quechua (Native American) word for the cinchona tree bark, "Quina" or "Quina-Quina", which roughly means "bark of bark" or "holy bark". Prior to 1820, the bark was first dried, ground to a fine powder, and then mixed into a liquid (commonly wine) before being drunk. It is often that fluorescence spectroscopy is used as a molecular “ruler” for inter and intra-molecular distance measurements by means of time-correlated single photon counting (TCSPC) experiments(5-7). Such experiments are most often associated with the quantitative measurements of electronic energy

2

transfer rates between a donor and an acceptor group(7,8); energy migration rates between two identical donors in similar environments and with equal photophysics(5,9-11), as well as with different photophysics(6,12). Unlike X-ray and NMR techniques, fluorescence spectroscopic methods provide distance information in the range of ~ 10 – 100 Å, which is typically comparable with the size of proteins(13). In this work we have utilised BODIPY derivatives, which was first synthesised by Treibs and Kreuzer in 1968 (14). Several derivatives were available from Invitrogen Corporation with sulfhydril-specific linkers (15). We have used two BODIPY derivatives, denoted g-BODIPY and r-BODIPY to study their spectroscopic properties in different common solvents(16) (Paper I). It was shown that g- and r-BODIPY in the ground state can form homo- as well as hetero dimers. One of today’s “hot” topics in biomembrane research concerns the formation of so called “rafts” in cell membranes. It is believed that in the living cells, the lipids, gangliosides and proteins are not randomly distributed but organised into structures. Though nobody has proved their existence in cells, many groups report studies on model membranes (17-19). We decided to question this problem from aside. We studied a model system: GM1 gangliosides in the DOPC membranes(20) Paper II. Many proteins are known to form non-covalent polymers, which are related to various biological phenomena in e.g. muscle contraction, cell division, etc, as well as diseases like the Alzheimer(21), the Creutzfeldt-Jacob’s(22), and the Bovine Spongiform Encephalopathy (or the mad-cow disease)(23). We present a complementary method to the NMR and X-ray techniques to examine the spatial organisation of the monomers building up the non-covalent polymer(24,25) (Paper III and IV). Fluorescence spectroscopy is likely the most widely applied spectroscopic method in most various fields. In numerous applications the models used in the data analyses depend on several parameters, which are fitted to the data. The currently used methods for this exhibit severe short-comings, especially when three or more parameters are used. We present a new numerical approach for overcoming this by using simulations to mimic the data(24) and a Genetic Algorithm(26,27) for the data fitting. This method here is for the first time applied in the analysis of fluorescence data. As a trial system the structure of the filamentous actin was studied(25).

3

The results obtained about the filamentous actin should be of interest for the scientists in the field of actin research. Our results do agree with previous studies(28-30) as far as concern the geometric properties of the helical structure. However our data show that the orientation of the actin monomers is different from what was previously suggested(31-34). In addition, polymerisation experiments with BODIPY-actin suggest a 25-fold more efficient signal for filament formation than pyrene-actin.

4

2 SYSTEMS AND MOLECULES

2.1 Green and red BODIPY The choice of a fluorophore label in fluorescence experiments is not a trivial task. Such a molecule must fulfil several criteria in order to provide the experimentalist with reliable molecular information for the versatile research. The photostability should be high enough, to prevent samples from bleaching during the time of experiment. The quantum yield must be high in order to provide high sensitivity of the experiments. One needs to consider the solubility of the probe as well as the absorption and fluorescence spectra in order to design an experimental setup. In this work we have utilised BODIPY derivatives, which was first synthesised by Treibs and Kreuzer in 1968 (14). Several derivatives were available from Invitrogen Corporation with sulfhydril-specific linkers (15). We have used two BODIPY derivatives, denoted g-BODIPY and r-BODIPY, which chemical structures are shown in the Figure 1.

-NB

N+

F F

-NB

N+

F F

Figure 1 Chemical structure of BODIPY. On the left is a structure of a green BODIPY derivative (= g-BODIPY) (Invitrogen code D6003) N-(4,4-difluoro-5,7-dimethyl-4- bora-3a,4a-diaza-s-indacene-3-yl) methyl)iodoacetamide (BODIPY® FL C1-IA). Molecular Formula: C14H15BF2IN3O. Molecular Weight: 417.00. On the right is a structure of a red BODIPY (= r-BODIPY) (Invitrogen code D3838) 4,4-difluoro-5-styryl-4-bora-3a,4a-diaza-s-indacene-3-pentanoic acid (BODIPY® 564/570 C5). Molecular Formula: C22H21BF2N2O2. Molecular Weight: 394.23. The usual low solubility of BODIPY derivatives in water can be overcome by first dissolving g- or r-BODIPY in dimethylsulfoxide (DMSO), which can then be mixed with water at any ratio. Previously the fluorescent properties of r- and g-BODIPY were studied by Karolin et al (35) and by Marushchak et al (16)[Paper I]. The fact that g-BODIPY has the same spectral shape and

fluorescencsuitable for determiningof r-BODIPrespectivelyFörster radiThe spectraFrom the BODIPY wanisotropy vg-BODIPY(

Figure 2 No(4,4-difluoro

Figure 3 The3a,4a-diaza-s237 K. The a

e lifetime iDonor-Don

g intramolecuPY and pair oy (16,35). In us is R0 = 60

al properties time-resolv

when excitinvalues of r(0(35).

ormalised absoo-5,7-dimethyl

30

Arb

itrar

y un

its

0

20

40

60

80

100

120

140

160

e excitation ans-indacene-3-pabsorption and

irrespective nor Energy Mular distanceof g-BODIPYcase of FRE

0 Å(16). of the probeed fluorescng the S0 →0) = 0.38(16)

orption and fll-4-bora-3a,4a

W

00 400

nd emission apentanoic acidd the fluoresce

5

of its chemMigration (Des. For the caY the Förste

ET between a

es are illustraence depola

→ S1 transit). It was sho

uorescence ema-diaza-s-inda

Wavelength (nm)

500

anisotropies ofd forms of theence spectra a

mical envirDEM) experases of DDEer radiuses ara pair of r- a

ated in Figuarisation extion, we ob

own before th

mission spectracene-3-yl)met

600 70

f the 4,4-diflue r-BODIPY inare also display

onment makriments, aim

EM betweenre 68 Å and

and g-BODIP

re 2 and Figxperiments btained the hat r(0) = 0.

ra of g-BODIthyl)iodoaceta

00

Ani

sotr

opy

-0.1

0.0

0.1

0.2

0.3

0.4

uoro-5-styryl-4n 1,2-propaneyed.

kes it med for

a pair 57 Å

PY the

gure 3. on r-initial 37 for

IPY N-amide.

4-bora-ediol at

TanCDal

F DbwreogmÅDothisp

2.2 The The chemicand its chem

C44H84NO8P aDOPC is a phlone or in mi

Figure 4 Struc

DOPC is a nae dissolved

well as manyesemble biorganisms is

gangliosides membrane syÅ(36). In theDOPC bilaye

f fluorophorhan the bilays expected bolar head gro

Lipid DOPal name of mical structuand moleculahosphocholinixtures with

cture of 1,2-dio

aturally occuin most org

y other amphlipid membractually a mand protein

ystems. The e Paper II (

er thickness. re labels attacyer thicknessecause the goup region o

PC DOPC is 1

ure is shownar weight is 7ne lipid whiother lipids.

oleoyl-sn-glyc

urring biologanic solvent

hiphile substrane (cf. Fig

multicompons. Frequentlthickness of

(20) we havWe have fouched to GM1

s of 38 Å(36g-BODIPY aof the GM1 mo

6

,2-dioleoyl-sn on the Figu786.11 ich can form

cero-3-phosph

gical membrts. When solances can fogure 5). Th

nent bilayer y DOPC lipf the DOPCve performedund that the is about 41 Å). However,

and r-BODIPolecule.

sn-glycero-3-ure 4. Mole

m vesicles in

hocholine (DO

rane phospholubilised in worm bilayer she cell surfacomposed oposomes are

C bilayer is kd indirect mdistance bet

Å, which is sa somewhat

PY groups ar

-phosphochocular formul

aqueous me

OPC).

olipid whichwater, DOPCstructures w

ace of all livof phospholipe used as mknown to be

measurementtween the plasomewhat lont longer distare located in

oline la is

edia,

can C as hich ving pids,

model e 38 ts of anes nger ance n the

Figure 5 Thethe figure. Btopographic iline in sectio

e schematic velow are AFMimage of 3 × 3

on a; (c) statist

view of micellM images of D3 μm2, 200 potical estimate

7

, bilayer and lDOPC vesicleoints per line; of the vesicle

liposome are s deposited on(b) cross-sectdiameter (37)

shown on then a mica surfation line along).

e top of ace; (a) g white

LL(sG(cnstTceimcois

FC BGItfofocaco

2.3 The Lipids constiLipids are casuch as ether

Gangliosides ceramide and

n-acetylneuratructure of th

The GM1 is aell signal tramportant inonsidered tos also well kn

Figure 6 MoleC73H130N3O31N

By using a mGM1 in DOPCt is probablyormed on thormed. (40-4an support pontaining GM

Gangliosiitute a clas

ategorized byr and chlorofare a class od oligosacch

aminic acid) he particular a componentansduction e

n immunolo be potentialnown that GM

ecular structurNa. Molecular

model membrC bilayer is any because of he nerve cell 43). It is theprotein compM1, e.g. the ch

ide GM1 ss of hydroy the fact thform) and areof lipid compharide) with

which are lGM1 studied of the cell

events, and iogy. Naturall therapeuticsM1 is specific

re of sodium Weight: 1545

rane system,n intrinsic prthis propertysurface tend

en possible tplexes formeholera toxin

8

carbon-contaat they are se relatively inpounds compone or moreinked on thein this workplasma memit was recenl and semis for neurodec receptor for

salt of GM1 ga5.8

we have shroperty of GM

y, the GM1-amd to aggregato suggest thed with GM1

GM1 comple

aining organsoluble in nonsoluble in wposed of a gle sialic acidse sugar chaink is shown onmbrane whicntly found alisynthetic gegenerative dr cholera tox

anglioside. M

own that selM1 gangliosidmyloid β-pe

ate and β-amhat the GM1 to assemblex(44,45).

nic compouonpolar solvwater. lycosphingols (also known. The chemn Figure 6. ch modulateslso to be hig

gangliosides disorders (38

xin.(39)

Molecular Form

lf-aggregatiode (20), pape

eptide complemyloid fibrils

self-aggregae with lipid r

unds. vents

lipid wn as mical

s the ghly

are 8). It

mula:

on of er II. exes s are ation rafts

9

2.4 Actin – a protein that forms filaments Actin is 42 kDa ATPase which can covalently polymerise into a helical structure, i.e. the filament (cf. Figure 7). Actin was discovered as a binding partner to myosin in extracts of muscle tissues (46), and was first purified and characterised by Straub (47). As the main component of the filament system, actin is present in all eukaryotic cells. Prokaryotes possess proteins with actin homology. Actin is known to bind to more than one hundred different proteins, and new classes of actin binding proteins are discovered every year. A comprehensive review on actin is given by Sheterline et al(48). The crystal structures were solved for α-actin in complex with DNase I (49), the gelsolin segment I (50), the β-actin in complex with profiling (51-53), yeast and Dictyostelium actin in complex with gelsolin segment I (54,55). It has been concluded that actin is a two-lobed protein with a central cleft which harbours a nucleotide and a divalent cation. By virtue of its overall structure, actin is a member of a protein superfamily which is believed to have evolved from a common ancestor (56,57). The members of the superfamily have two important features in common: (1) a core of two approximately symmetric subdomains, each made up of a central five-stranded β-sheet flanked by three α-helixes; (2) the sequence DxGxG in the turns between the first and second β-sheet of these subdomains, which form the binding site for the nucleotide phosphates. These structure features are illustrated in Figure 7. The purification of actin from different sources using standard protocols (58-60) yields monomeric Ca-ATP-actin. Salts are then added to mimic physiological conditions whereby a non-covalent polymer is formed. A steady-state between a pool of filamentous actin and a low concentration of monomeric Mg-ATP-actin then occurs (61-64). The concentration of the unassembled actin at steady state is the critical concentration for non-covalent polymerisation, Acc. Formally, Acc might be called the steady-state dissociation constant of the system, since it is the ratio between all the dissociation rate constants and all the association rate constants. This involves G-actin and both ends of the filament, each with different states of the nucleotide bound (61,62). In the cell, the steady state is controlled by cations, nucleotides, as well as by several classes of actin binding proteins.

Fthsugrcofr TshhnsielthpFthspth

Figure 7. Overhe standard usuperfamily. Traphics is basomplex with rom RCSB pro

The actin filahaped actin p

helix, or as nucleation suimilar imporlectron micrhe protomeraper IV(25).

For decades the spatial strpectroscopiche fluoropho

rview of the βsed for actin

The N- and Csed on 2.65Å actin bindingotein data ban

ment is a helprotomers, a

a right-hanuggests that trtance as throscopy and s within the. the structureructure of th

c studies werore labelled p

β-actin molecuand, within th

C-termini in sresolution cr

g ATP phosphnk) using Acce

lical non-covand can be thnded doublethe protomerhose within

three-dimene actin filam

of F-actin hhe filament hre also perfoposition C374

10

ule. The subdohe parenthesesubdomain 1 ystal structurehates been acelrys Inc. Viw

valent polymhought of eithe helix. Thr interactionsthe same st

nsional reconment are clo

has been invhas been reprmed, and th4 was determ

omains are nus, as is used are subscribee of the bovinccessible to thwerLite 5.0.

mer of the rouher as a left-he kinetics os across the htrand. This nstructions, wsely packed

vestigated. Inported (28-30he residual d

mined (31-34

umbered followfor the actin

ed. The molecne β-actin-prohe solvent (1H

ughly matchbhanded one-of the filamhelix axis aris supportedwhich show

d (28,29,65)

nformation ab0). Fluorescedistance betw4).

wing fold

cular ofilin HLU

box-start

ment re of d by that and

bout ence

ween

3 INTSP

3.1 PhoElectronicallifetimes inresponsible to distingudeactivationvarious uniJablonski di

Figure 8. Thfluorescenceprocesses by= vibrational The Jablonsfirst and secand T2. For

TRODUCECTRO

otophysiclly excited sn the nanofor the dissi

uish between, although imolecular piagram (cf. F

he Jablonski , P = phosph

y wavy arrowsl relaxation) (1

ski diagram cond excitedr polyatomic

CTION OSCOPY

cal processtates of pol

osecond regiipation of theen photophy

such a distphotophysicaFigure 8).

diagram. Thehorescence) as (IC = intern1).

schematicalld singlet statec molecules t

11

TO FY

sses lyatomic moime. In gee energy of aysical and tinction is nal processes

e absorption (are indicated al conversion

ly displays tes S1 and S2,the spacing b

FLUORE

olecules haveneral, severan excited staphotochemi

not always s may be ov

(A) and emisby straight a, ISC = inters

the singlet gr, as well as tbetween the

ESCSEN

e typical radral processeate. It is impcal pathwayunequivocalverviewed b

sion processearrows, radiatisystem crossin

round state Sthe triplet sta vibrational

NCE

diative es are portant ys of l. The by the

es (F = ionless ng, VR

S0, the ates T1 levels

12

decreases rapidly with increasing energy, whereby the density of states very rapidly increases. The rotational levels are omitted since we are only considering molecules in the condensed phase where rotation is not quantified. The standard convention illustrates the absorption and emission processes as straight arrows and radiationless processes as wavy arrows. Bimolecular photophysical processes and photochemical processes are not illustrated in a Jablonski diagram, although they provide possible pathways for the deactivation of an excited state. The emission or luminescence is referred to as fluorescence or phosphorescence, depending on whether it corresponds to spin-allowed or spin-forbidden transitions, respectively. Similarly, radiationless transitions between states of the same multiplicity and of a different multiplicity are known as internal conversion (IC) and intersystem crossing (ISC), respectively. Figure 8 shows that a molecule can reach an excited vibrational level of the electronically excited state S1 either by the absorption of a photon of appropriate energy, or by internal conversion via the vibrational levels of a higher electronic state such as S2. In liquid solutions the vibrational relaxation (VR) to the vibrational ground state (or more accurately, to a Boltzmann distribution rate over the vibrational levels corresponding to thermal equilibrium) is very rapid (≈1012 s-1), and the excess of vibrational energy is converted into heat through collisions with the solvent molecules. From the zero-vibrational level of the S1 state, the molecule can return to the ground state S0 by fluorescence (F) or via the triplet state T1 by intersystem crossing (ISC). After the loss of excess vibrational energy in T1, the molecule can return to the ground state S0 by phosphorescence (P). The radiationless deactivation from S1 to S0 occurs via internal conversion (IC) and the subsequent vibrational relaxation (VR). The radiationless deactivation from T1 to S0 can occur by intersystem crossing (ISC) followed by vibrational relaxation.

3.2 Experimental part Time-Correlated Single-Photon Counting (TCSPC) Time-Correlated Single-Photon Counting (TCSPC) is a powerful experimental technique to study the photophysical properties and the orientational motions of fluorescent molecules (2,20). The principle of the TCSPC experiment is as follows:

13

One needs to perform a linearly polarised pulsed excitation of fluorescent molecules. The emitted light is collected perpendicularly to the excitation light through a polariser and a set of filters. The emission polariser is set to the magic angle (54.7°), or orthogonal and parallel to the excitation polariser to monitor the photophysics decay and the depolarisation, respectively. Because the excitation light is pulsed, one can determine the distribution of photon emission events as a function of time, i.e. time-resolved decay F(t). The excitation pulse serves as a start pulse for the Time to Amplitude Converter (TAC), and on the subsequent event of detecting the first emitted photon a stop pulse is given to to the TAC. The time difference between the start and stop pulses is then sent from TAC to the computer software and stored as a histogram (black dotes in the Figure 9).

Figure 9. The typical fluorescence decay F(t) (black dots), is shown together with the fitted curve (solid line) and the instrument response function IRF(t) (crosses). The top panel shows the weighted residuals of the fit wr(t)(20). In doing TCSPC experiments, there are some important precautions to consider. In this work light emitting diodes and diode laser from IBH Consultants Ltd (Glasgow, Scotland) were used as the excitation sources. As though these exhibit rather narrow spectral bandwidths, we have used interference filters and/or monochromators to select the excitation wavelength more accurately. The choice of excitation wavelength should be close to the peak maximum of the absorption spectrum. In order to reduce the influence of scattered light (Raman and/or Rayleigh), long-pass filters (Schott, Germany) are installed on the emission side. For the experiments performed at low temperature, water condensation was avoided by purging the cuvette surfaces

-2

0

2

wr(t)

0 10 20 30 40 50100

101

102

103

104

t, ns

F(t)

14

with nitrogen. To eliminate pile up of the fluorescence decay the rate of the photon detection should be less or equal to 1 % of the pulse repetition by means of e.g. grey filters(2). In order to avoid re-absorption, the absorbance of the samples was kept below 0.08 at its peak absorption. The experimental fluorescence decay (F(t)) is monitored as a convolution between the true decay of the photophysics f(t) and the instrument response function IRF(t), i. e.

( ) ( ) ( )0

- ´ ´ ´t

F t IRF t t f t dt= ⋅∫ (1)

One needs to incorporate a variable time-shift δ of the IRF to account for an eventual wavelength dependence of the detection system, which means that

( ) ( ) ( )F t IRF t f tδ= + ⊗ . The photophysics is usually modelled as a sum

of exponential functions:

i ii( ) exp(- / )f t a t τ= ∑ (2)

and deconvoluted by using a non-linear least-square analysis, based on the Levenberg-Marquardt algorithm(66). The average fluorescence lifetime ( ⟩⟨τ ) one calculates from:

2i ii

i ii

aaτ

ττ

= ∑∑

(3)

In Eqs. 2 and 3, τi stands for the i:th fluorescence lifetime component in a multi-exponential fluorescence decay. Fluorescence depolarisation Fluorescence depolarisation experiments can be used to determine either the steady-state anisotropy {r} or time-resolved one {r(t). Both contain information about the fluorophore itself as well as the orientational distribution of the fluorophore molecules. The fluorescence anisotropy is commonly determined in the biochemical studies. The anisotropy can provide information about the size and shape of proteins, or the rigidity of the molecular environment of a fluorescent molecule. Fluorescence depolarisation has been used to measure protein-protein associations and the mobility in lipid membranes. The depolarisation experiments are based on the principle of a photoselective excitation. The fluorophores absorb preferentially the photons whose electric vectors are parallel to the transition dipole moment of the

fluorophoremolecular fisotropicallyfluorophorevector of thpopulation in a partiallthe light pobetween the

0r =

The fluores

Ir =

where IVV anemission mexperimenta

Figure 10. SFluorophore monochromapolariser and For the timmeans of ahorizontal

e. The transiframe. In a y. Upon exces whose abhe excitationof excited flly polarised olarised alonese moments

22 3cos5 2

β⎛⎜⎝

cence steady

VHVV

VHVV

IIII2

-+

nd IVH are themeasured foral setup for a

Schematic of molecules in

ators and/or ad monochroma

e-resolved da polariser emission po

ition dipole solution, th

citation by pbsorption tran light. Thisluorophores fluorescence

ng a fixed axs determines -1⎞

⎟⎠

y-state anisot

e intensities r a stationaa depolarisati

a typical depthe sample a

a filter and a pators or filter a

depolarisationone collectsolariser sett

15

moment hashe fluorophopolarised lighansition dipos selection r(photoselect

e emission. Txis in the fluthe limiting

tropy r is def

of the verticary excitatioion experime

olarisation exare excited bypolariser. Theand is collecte

n experimens fluorescentings. The p

s a definiteores are orieht, one selecole is parallresults in a tion), and coThe emissionuorophore. Tmeasured an

fined by

cally and horin. The scheents is given

xperimental sey the light thate emitted lighted by detector

nts a TCSPC nce decays polarised flu

orientation ented randomctively excitlel to the epartially or

onsequently rn also occurThe relative nisotropy {r0

(4

(5

izontally poleme of a tin the Figur

etup is present passes throut passes throur.

setup is usewith verticauorescence

in the mly or tes the lectric

riented results s with angle

0}(2)

4)

5)

larised typical re 10.

nt here. ugh the ugh the

ed. By al and decay

16

curves ( )VVF t and ( )VHF t are linearly combined into a sum curve and a

difference curve ( )S t and ( )D t , respectively. These decay curves are

globally fitted to the decay laws by using a non-linear least squares procedure with an iterative re-convolution according to the following equations:

( ) ( )( )

( ) ( )( ) ( )

VV VHexp

VV VH2D t F t GF t

r tS t F t GF t

−= =

+ (6)

( ) ( ) ( ) ( ) ( )( ) ( )

VV VH

i ii

2

exp

S t F t GF t IRF t f t

IRF t a t

δ

δ τ

= + = + ⊗ =

= + ⊗ −∑ (7)

( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( )

VV VH

i ii

exp

D t F t GF t IRF t r t f t

IRF t r t f t

δ

δ φ

= − = + ⊗ =

⎧ ⎫= + ⊗ −⎨ ⎬

⎩ ⎭∑

(8)

The instrumental G-factor was calculated from the steady-state fluorescence anisotropy

( )( )

VVs

s VH

1-1 2

F trGr F t

=+

∫∫

(9)

The time-resolved fluorescence anisotropy reflects changes in the direction of transition dipole moment of the fluorophore

( ) ( ) ( )0 2 ˆ ˆ0r t r P tμ μ= ⋅⎡ ⎤⎣ ⎦ (10)

In Eq. 10 P2(x) = (3x2-1)/2 is the second-rank Legendre polynomial, μ̂ stands for the unit vector of the transition dipole moment of the fluorophore, and r0 is the steady-state anisotropy(2). The brackets <…> indicate an ensemble average over all excited molecules. The origin of the time-dependent anisotropy decay is Brownian rotational motion and in some cases the energy transfer or migration process between the fluorescent molecules.

3.3 Resonance Energy Transfer (RET) or Donor-Acceptor Energy Transfer (DAET)

Donor-acceptor energy transfer (DAET) has several names and often referred to as Förster resonance energy transfer – FRET, or just RET. However, DAET is the radiationless transfer of excitation energy from an excited donor (D) to an acceptor (A)(2). The nature of this phenomenon is described by electric dipole-dipole interaction. The theoretical description of RET was firstly done

17

by Theodor Förster in 1948 (67). The basic scheme of the process is as follows:

* *D A D A+ → + (11) Here the asterisk means that the molecule is electronically excited. Assuming a weak dipole-dipole coupling between an electronically excited donor and an acceptor, the rate of energy transfer ω is given by

2 60

D

32

RR

κω

τ⎛ ⎞= ⎜ ⎟⎝ ⎠

(12) Here Dτ , ⟨κ 2⟩, R and R0 denote the fluorescence lifetime of the donor, the averaged square of the angular part of the dipole-dipole interaction, the distance between the interacting molecules and the Förster radius, respectively. The latter is defined according to

6 D0 5 4

9000(ln10)(2 / 3)128 A

Q JRn Nπ

= (13)

where QD, n and NA stand for the fluorescence quantum yield of the donor, the refractive index of the medium and Avogadro's constant, respectively. The overlap integral J can be calculated from the normalised donor fluorescence spectra {FD(λ)} and the acceptor absorption of the acceptor {εΑ(λ)}

4D A( ) ( )J F dλ ε λ λ λ= ∫ (14)

The Förster radus R0 for different donor-acceptor pairs are in the range of 10 – 80 Å (3). At the distance equal to R0, on the average, half of the donor excitation events lead to irreversible energy transfer to acceptor. In general, the angular part of the dipole-dipole coupling (Eq. 12) is usually time dependent, i.e.

( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( )( )2221 2 1 2

ˆ ˆ ˆˆ ˆ ˆ ˆ- 3 /t t t t R t t R t R tκ μ μ μ μ= ⋅ ⋅ ⋅ (15)

Here ( )R̂ t is the unit vector connecting the centres of masses of interacting

fluorophores, ( )1ˆ tμ and ( )2ˆ tμ denote the unit vectors of the transition

dipole moments. In the limit when the local reorientation motion of fluorophores is isotropic and much faster than the RET, one can neglect the time-dependence. This gives an average value of ⟨κ 2⟩ = 2/3, which is a

dynamic average value. Due to the ⟨κ 2⟩1/6 dependence of ( )2

R̂ t , this

approximation is often reasonable. However, the ⟨κ 2(t)⟩ function cannot be calculated, unless additional knowledge of the system is available (e.g.

18

fluorescence depolarisation of the diluted fluorophores in the absence of RET is known). The time-resolved fluorescence experiments often provide good accuracy of

distance measurements in the range of distances ( ) 20 00.5 2R R t R≤ ≤ . The

fluorescence relaxation of the donor in the presence of FRET (2,7) is given by DA D( ) exp( / )F t t tτ ω= − − (16)

and the fluorescence decay of the acceptor (68,69) is AD D A( ) -exp(- / - ) exp(- / )F t t t tτ ω τ∝ + (17)

The analysis of F(t) curves provides information about the rate of energy transfer (ω) and distribution of donor-acceptor distances (70). As a historical starting point of RET applications in biosciences (7) the experimental work by Sttryer and Haugland (71) is worth citing. Nowadays, RET is widely used for distance measurements in biomacromolecules and supramolecular assemblies. Surveys of many related and relevant papers are found in books describing fluorescence spectroscopy (2,3), as well as in textbooks specialised on energy transfer (7). RET does not provide a complete 3D-structures and an atomic resolution comparable to that of X-ray and NMR methods. However, RET successfully complements these techniques when sensitivity and time-resolution are of importance. From the point of view of spatial resolution, in principle, RET has its place in-between X-ray and electron microscopy, while being much easier to experimentally implement.

3.4 Homotransfer or Donor-Donor Energy Migration (DDEM)

The process of an energy transfer between molecules of the same origin, i.e. between identical chromophores ( 1D , 2D ), is sometimes referred to as donor-

donor energy migration (DDEM) (5,9,11) or homotransfer (3,7). The scheme of such a process can be written as

* *1 2 1 2D D D D+ → + (18)

In principle, the energy transfer between identical fluorophores is reversible, which means that the electronic energy is exchanged back and forth within a pair. For this reason many scientists use the concept energy migration (EM) (72) in order to distinguish it from donor-acceptor energy transfer, which is irreversible.

19

If two interacting donors exhibit a single exponential photophysics, the fluorescence relaxation of the D1D2 pair is invariant to the rate of homotransfer. However, the energy migration causes fluorescence depolarisation, which was one of the earliest observations of energy transfer in solution (73). The depolarisation, as a result of homotransfer, indicates that the donors are separated at an average D1-D2 distance which is comparable to R0. This effect has been qualitatively used in many applications (74,75). On the other hand, very few studies deal with the quantitative analysis of fluorescence depolarisation in terms of energy migration rates and donor-donor distances. In fact, the idea of using homotransfer for distance measurements appears to be very attractive for the following reason. The conventional studies of proteins using FRET involve specific labelling of a protein molecule with one donor and one acceptor group. This is a crucial step and in practice, it is often extremely difficult to perform. The problem with donor-acceptor labelling is circumvented by introducing one kind of specific fluorophore. This is referred to as the DDEM method. However, it only perfectly works in such cases when the fluorophores photophysics is not affected by the fact that they are attached to different positions in the protein and situated in slightly different environments. A nice example when homotransfer has been successfully applied is given in Paper IV (25) and (5,11). In the case the fluorophore label is attached to different positions in the same protein, the local environment of the probe may affect the photophysics of the fluorophores. This case has also been extensively studied (6,12). Although the problem of specific labelling is solved, the use of DDEM introduces other practical problems and theoretical demands to be solved. Firstly, the process of EM is usually detected by performing fluorescence depolarisation experiments, which are more complicated and time-consuming than the fluorescence lifetime measurements. What is more important, the energy migration and the reorienting motions of the fluorescent molecules both contribute to the depolarisation measurements, and the separation of these processes is complex. As a result, an analytical expression for the time-resolved DDEM anisotropy can be obtained only for the case of immobile fluorophores (76-78), and in a few other simple cases (79). Several researchers have considered the problem of separating the energy migration and the reorienting motions and came up with different models. A complete theoretical description is referred to as the extended Förster's theory (EFT) (10). A difficulty with the EFT is the lack of an explicit analytical expression that can be used in the deconvolution procedure. Recent

20

studies show, however, that the EFT is applicable in studies of model systems (80,81), and even more recent results demonstrate how to apply EFT to the analyses of DDEM-data obtained with proteins (82). In addition to the EFT, several models of the fluorescence depolarisation in the presence of energy migration and reorienting motions have been suggested (9,83-86). One of these is the DDEM model, which was developed for analysing the fluorescence anisotropy obtained from experiments with singly and doubly fluorophore-labelled proteins (5,9,11). In these studies one considers the DDEM within a pair of chemically and photophysically identical fluorescent groups (denoted D1 and D2), which are covalently linked to a macromolecule, such as a protein. From the depolarisation measurements the time-resolved fluorescence anisotropy can be obtained for a coupled system (D1D2), as well as for the single donors: D1 and D2. These time-resolved anisotropies are denoted r(t), r1(t) and r2(t), respectively. The anisotropy contributions to r(t) from donors excited indirectly through the energy migration D1 → D2 and D2 → D1 are denoted by r12(t) and r21(t). The DDEM model reads

[ ] [ ][ ]1 2 12 211 1( ) ( ) ( ) ( ) ( ) ( ) 1- ( )2 2

r t r t r t p t r t r t p t= + + + (19)

2 2j 0 j j j( ) [(1- ) ( ) ] ( 1, 2)r t r S t S jγ= + = (20)

( )12 21 0 0 1 2 δ 1 2 1 2 δ1( ) ( ) ( - ) ( ) ( )2

r t r t r S S S t t S S Sρ γ γ⎡ ⎤= = × + +⎢ ⎥⎣ ⎦ (21)

In Eq. 19 p(t) is the excitation probability of the initially excited donor group in absence of fluorescence relaxation

[ ]1( ) 1 exp(-2 )2

p t tω= + (22)

In Eqs. 19-21, Sj is the second rank order parameter for each of the two donors. The order parameter describes the orienting distribution of the transition dipoles:

( )j 2 j jˆ ˆS P zμ⎡ ⎤= ⋅⎣ ⎦ (23)

The angle between the symmetry axes zj of the orientational distributions of the two donors is denoted by δ and δ 2 (cos )S P δ= - the second rank Legendre

polynomial. The maximum contribution to the anisotropy from the secondary excited fluorophores is given by 0ρ , and γj(t) describes the reorientation dynamics of the donor molecules. In the analyses of DDEM-data ω, 0ρ and δ are the fitting parameters. The DDEM model was extensively tested and used in practice (5,9,11,87-89).

21

4 PHYSICAL MODELS OF MOLECULAR SYSTEMS

In order to obtain molecular information from the experiments one needs to develop physical models, which describe the particular system of interest. By fitting the experimental data to the model equations or simulations, one can determine the physical parameters. Below are presented two physical models which were used for studying two complex biomolecular systems. The systems describe the spatial organisation of the ganglioside GM1 in the DOPC vesicles (20) and the ordered polymeric forms of F-actin (25) and (24).

4.1 DOPC vesicles with BODIPY-labelled GM1 mixtures One of today’s “hot” topics in biomembrane research concerns the formation of so called “rafts” in cell membranes. It is believed that in the living cells, the lipids, gangliosides and proteins are not randomly distributed but organised into structures. Though nobody has proved their existence in cells, many groups report studies on model membranes (17-19). We decided to question this problem from aside. We studied a model system: GM1 gangliosides in the DOPC membranes Paper II(20). The electronic energy transfer/migration among fluorophore-labelled gangliosides in lipid bilayers can take place within the same leaf of a bilayer, as well as between the two layers, hereafter referred to as intra and inter layer transfer, respectively. Because the fluorophore is covalently bonded to specific positions in the lipid molecule, we assume that the intra transfer process is effectively two-dimensional, while the inter layer transfer is between two parallel planes. The two different systems considered are schematically illustrated in Figure 11. In the first case the fluorescent groups are attached in the polar headgroup of GM1 (cf. Figure 11A) implying an intra layer energy transfer/migration, as well as an inter layer transfer/migration between planes that are separated at a fixed distance d. The second case refers to a mixture of gangliosides labelled with the same fluorophore in two different positions. These positions are in the polar headgroup and in the lipid-water interface, as illustrated in Figure 11B. The inter layer transfer then occurs between three parallel planes, while no intra layer transfer is present.

Fleinlais TfldrefldstT(7

ln

Inndca

(ρre

dthsud

Figure 11. Eneeaf of the lipidn different layayer as well ass intra layer as

The electronluorophores

different fluoespectively. luorescence r

donor, one netill in the exc

The probabili72);

intraln sG

( )sinternG μ =

n Eqs. 24-2number of eldetermined balculated fro

ρ). The paraespectively.

denotes the dihe thickness urface norm

dipole.

ergy transfer/md bilayer, i.e.yers of bilayers inter layers ss well as inter

nic energy and the e

orophores, wTo model threlaxation ofeeds to calcucited state atities of the in

( )a 2t C ⎛= − ⎜⎝

122 06

Cλν

⎧= − ⎨

⎩∫

5 C2 denotelectronically

by the Förstom 2C πρ=

ameter λ is In Eq. 2 =μistance betwof a lipid b

al and a line

migration occan INTRA lay

r, i.e. an INTEseparated by tlayers separa

migration energy transwhich are hehe corresponf the donor aulate the probt a time t latentra and inter

1/ 315 28 3λ

⎛ ⎞ ⎛Γ⎟ ⎜⎝ ⎠ ⎝

1 exp μ⎡− −⎢

⎣⎩es the reducy interacting ter radius, R

20Rρ with kno

a number e( ) 62/3= τνλ t

ween the monbilayer (cf. Fe connecting

22

curs either betyer process, o

ER layer procethe distance d.ted by the dist

is betweensfer is betwere referred nding experiand the fluorebability that er. This probr layer proce

1/ 323

tτ

⎞⎛ ⎞⎟⎜ ⎟⎠⎝ ⎠

4 / 35 34

s sμ ⎛ −⎜⎝

ced concentrmolecules

R0. The redowledge of

equal to 1 o1−τ , s cos=

nolayers, whiFigure 11). Tg the centres

tween fluoropor between fluess. (A): Energ. (B): Energy tances d1 and

n photophysween two s

to as DDEimental obseescence depothe initially

bability is desses were pr

3 5/ 394

s⎫⎤⎞+ ⎬⎟⎥⎠⎦⎭

ration, whichwithin the

duced concethe surface a

r 2 for DAE

rθ6s and =νich is approxThe angle θr

of mass of

phore labels inuorophores locgy transfer is migration/trand2.

sically idenspectroscopicEM and DAervables, i.e.olarisation ofexcited dononoted by G s

eviously der

(24)

4 / 3s ds−⎫⎬⎭

(25)

h stands forarea of a ci

entration canacceptor den

ET and DDE1

0−= dR . He

ximately equθr is between

each interac

n one cated intra nsfer

ntical cally

AET, the f the or is ( )ts .

rived

)

)

r the ircle n be nsity

EM, ere d

al to n the cting

23

For the energy transfer/migration within and between the two-dimensional planes the electronic transition dipoles are considered to be randomly oriented. The total excitation probability, ( )sG t , that accounts for both intra layer and

inter layer energy transfer/migration is given by the joint probability ( ) ( ) ( )s s s

intra j, interj

G t = G t G t∏ (26)

In Eq. 26, the multiplication accounts for the general case of energy transfer/migration between several planes of interacting donors/ acceptors. In the case when there is no intra layer energy transfer ( )s

intra 1G t = .

For a donor-acceptor system the fluorescence relaxation of the donor is given by

( ) ( ) ( )si i

j

α exp / τF t G t t= ∑ (27)

In Eq. 27 the sum of exponentials describes the donor fluorescence in the absence of acceptors. To monitor the rate of energy migration among donors one needs to measure the fluorescence depolarisation, which is conveniently expressed by the time-resolved anisotropy, r(t), according to(90):

( ) ( ) ( )2 s 20 0ρr t r t S G t r S⎡ ⎤= − +⎣ ⎦ (28)

Here r0 and S denote the limiting anisotropy and the order parameter of the transition dipole with respect to the bilayer normal, respectively. The reorientation of the excited donors is described by

j j( ) exp(- / )t a tρ φ= ∑ (29)

In Eq. 29 the rotational correlation time, φj, describes the donor’s local reorienting motions in the lipid bilayer. It is possible to perform experiments from which the surface acceptor density (ρ) can be calculated. However, it is also possible to calculate the surface average acceptor density (ρ) from the knowledge of concentration of gangliosides and lipids and the diameter of liposomes. The fact that experimentally obtained values of ρ are larger than estimated values, strongly suggests that the GM1 molecules are not uniformly distributed in the bilayers. It seems that GM1 forms more dense regions, which might be ascribed to “raft” formation. These strongly suggests that this is intrinsic property of GM1 in lipid model membranes.

4.2 Linear aggregates/non-covalent polymers The filamentous actin studied in the present work is just one of many complex systems that could be examined by using the GA to analyse fluorescence

24

depolarisation experiments. Depending on the role of the proteins these may form oligomers as well as large aggregates or non-covalent polymers, which are regular structures. In various topics of bioscience there is a progressive need to obtain structural information about monomeric proteins, as well as their non-covalent polymeric forms. For instance, transthyretin is known to form tetramers and mutants of transthyretin can form large non-covalent polymers, which are associated with the human amyloid disease, named the familial amyloidic polyneuropathy(91,92). The formation of protein complexes is also connected with conformational diseases, such as the Alzheimer’s and the Creutzfeldt-Jacob’s diseases(21,22). The prion is another type of non-covalent protein polymers. The prion is thought to infect and propagate by refolding abnormally into a structure, and thereby convert the normal protein molecules into abnormal structures. Well-known prion diseases are the Kuru(93), the Bovine Spongiform Encephalopathy (or the mad cow disease)(23) and the fatal familial insomnia. The latter is a rare autosomal dominant inherited disease of the brain(94). Cytolytic toxins associated with diseases in humans as well as animals(95,96) constitute other aggregating proteins which are thought to create pores in membranes(97). Tubulin is yet another well-known protein that forms the building unit of microtubules (98). Atomic force microscopy – AFM is a method which can be used to study the amyloid fibril formation. One can easily visualise amyloid structures under different conditions (cf. Figure 12) and therefore investigate different morphologies as a result of various conditions. By means of AFM, it was shown that the amyloid protofilaments from the calcium-binding protein equine lysozyme can form linear as well as cyclic structures (99,100). Even if different morphologies can be monitored, the resolution of AFM is not sufficient to tell about the spatial orientation of protomers in the assembly. Nevertheless, probably by applying a sophisticated data analysis, it is potentially possible to obtain more detailed picture of the morphologies, compare to ordinary AFM scans.

25

Figure 12. Amyloid structures of Equine Lysozyme observed by AFM. (Published with permission from Malisauskas M). A higher resolution can be achieved by means of transmission electron microscopy (TEM) and NMR experiments. For example, the hydrogen/deuterium exchange of Aβ-(1-42/43) fibrils under physiological conditions has been investigated using solution NMR spectroscopy, and it was shown that two protected core regions exist. Moreover, the residues accessible to the solution were identified(8). The amyloid fibrils commonly exhibit multiple distinct morphologies in the electron microscope and the atomic force microscope. By using electron microscopy and solid-state NMR measurements on fibrils formed by the 40-residue β-amyloid peptide that perhaps causes the Alzheimer’s disease (Aβ1-40), it was shown by the group of Robert Tycko that different fibril morphologies have different underlying molecular structures. The predominant structure can be controlled by a subtle variation in the fibril growth conditions, and both the morphology and the molecular structure are self-propagating when the fibrils grow from preformed seeds(101,102). Experimental methods like X-ray diffraction(103,104) and NMR(105,106) are of importance to the determination of macromolecular structures. Currently, intensive work is put into the development of complementary methods based on electronic energy transfer and fluorescence. Especially for structure determination of complex macromolecular assemblies these techniques may become very important. Most of them are based on irreversible energy transfer from an excited donor to an acceptor molecule(2,3,7,107), while electronic energy migration between fluorescent molecules of the same kind, so called donor-donor energy migration (DDEM) or homotransfer(75) is less commonly used.

Inthαcoprohstco2anflflM

FpZthtrflthtr

n the modellhe helical str

α1-antitrypsinovers the spearameters ofotation (θ) o

helical axis atructure of Foordinates o7.5 Å and θnd the Cys-3luorescence gluorescent g

Moens et al h

Figure 13. Sch

osition in regZA axis coincidhis axis to thransformationluorophore unhat is transforransition dipol

ling of reguructure, whicn(108,109). Tecial cases of a helix (cfof each neigand the positF-actin, the pof the precediθ = 166º, resp374 is of partgroup. The d

group wouldhave reported

hematic showgular structuredes with the Che position os between ne

ndergoes localrmed to the agle μ is transf

lar protein ach has been pThis prototyf linear and rf. Figure 13)ghbour protetion of the flposition of ting one by apectively(28ticular interedistance fromd then corresd Txy = 13.7 Å

wing the coores forming helC∞–axis of theof a fluoresceearest protein l reorienting mggregate fixedformed to the

26

aggregates wproposed for pe structure ring-shaped ) are the tra

ein, and the luorescent dothe next mo

an axial trans8). The distanest since this m the C∞-axisspond to thÅ(32).

rdinate systemlical, linear an aggregate anent group. Thneighbours a

motions aboutd frame by ΩD-frame by th

we have concF-actin(28) is also interestructures. T

anslational dradial distanonor (Txy). F

onomer is obslation and ance betweenposition cans to the centre Txy in Fig

ms used to dend ring-shape

nd Txy denotes he translationare θ and Tz, t an effective

ΩDA = (α DA , βhe angles ΩΜD

centrated(25and polymeresting becau

The characterdistance (Tz),nce betweenFor the propobtained froma rotation of n the helical n be labelled re of mass ofg. 1. Previo

escribe the proed aggregates.

the distance nal and rotati

respectively. symmetry axi

β DA ). The eleD = (αΜD, β ΜD

) on rs of

use it ristic , the

n the osed

m the Tz = axis by a f the

ously

otein The from ional The

is ZD ectric D).

27

In our work(25), one donor (D) group is covalently bonded to a protein molecule at a well-defined position in the structure. The local orientation of the D is assumed to be effectively uniaxial with respect to the ZD (cf. Fig. 14) and the donor may also undergo interaction under conditions of reorienting motions ranging from static to dynamic. The latter means that energy migration between the D-groups is treated for negligible local motions as well as for motions that occur on the time scale of interaction, respectively. A Maier-Saupe potential given by

MD 1 1 MD( ) (cos )U Pβ γ β= (30)

is used to describe restricted orientation and motion about the ZD axis. Here )(cos MD1 βP is the first Legendre polynomial. Brownian dynamic (BD)

simulations are applied to account for the local reorienting motions. Because the protein aggregates are rather large, their tumbling motions are negligible on the timescale of the BODIPY fluorescence. Monte Carlo simulations of energy migration in multi-donor systems Due to the extraordinary complexity in accounting for interactions among many donors, an analytical theoretical description does not exist for these systems. Additional difficulties are caused by the anisotropic orientation of the fluorophores and their internal motions. Here these questions are circumvented by using Monte Carlo (MC) simulations. The MC simulation of energy migration involves all donor molecules within some cut-off distance, which is usually ± 9 protein molecules counted from the protein (number 0) that carries an excited donor. The total migration rate is calculated from

0 jj

( ) ( )n

n

t tω=−

Ω = ∑ (31)

In Eq. 2 ω0j(t) stands for the rate of energy migration from the 0:th to the j:th donor. This rate is given by the well-known Förster equation:

620 j 0

0 j0 j

3 ( )( )

2t Rt

Rκ

ωτ

⎛ ⎞= ⎜ ⎟⎜ ⎟

⎝ ⎠ (32)

in which τ, R0, R0j and 2j0κ denote the donor fluorescence lifetime, the Förster

radius, the distance between the 0:th to the j:th donor, and the square of the angular part of the dipole-dipole coupling, respectively. The explicit expression for the latter reads:

( ) ( ) ( )( )220 j 0 j 0 0j j 0j

ˆ ˆˆ ˆ ˆ ˆ( ) ( ) ( ) 3 ( ) ( )t t t t R t Rκ μ μ μ μ= ⋅ − ⋅ ⋅ (33)

28

In Eq. 4 kμ̂ and j0R̂ are unit vectors of the electronic transition dipoles and a

distance vector between the centra of mass of the 0:th and j:th donor, respectively. The coordinates of jμ̂ with respect to the aggregate fixed frame are given by

),,,()()(ˆ zxyj jjTTOtAt θμ μ −= , where )(

jtAμ and ),,,( zxy jTTO θ denote

the vector pointing from the origin of XA, YA, ZA to the point described by jμ̂

and the position of the centre of mass of the j:th donor, respectively (cf. Fig. 1). The first question to solve in the MC simulation is when an energy migration event takes place, denoted τEM. We chose a time interval ∆t that is smaller than the characteristic time for the variation of )(tΩ caused by reorienting motions. It means that )(tΩ is approximated to be a constant within the time interval ∆t. Then we generate a random number from a uniform distribution

( ]1,0∈η , and calculate the time τEM according to

EM1 ln( )t

τ η= −Ω

(34)

The obtained value will only be accepted provided tΔ<η , which would ensure that )(tΩ can be considered constant. If tΔ>η one may step forward a time unit ∆t and calculate )( tt ΔΩ + . Using this Ω-value a new random number is generated. This procedure is repeated until one finds a value of

tΔ<η . The second decision concerns where the energy migrates, i.e. to which D group among the labelled proteins. From the above calculations one knows the time (T) of the energy migration event. By using BD simulations we can therefore account for the reorienting motions of all donors within the cut-off distance )(

jTAμ . This enables the calculation of )(2

j0 Tκ , ω0j(T) as well as

)(TΩ . The simulation of the orientational trajectories is for all particles performed in time window [ ]∞∈ TT ,0 within the cut-off distance, and it is only repeated when moving along the aggregate. To select the coming excited donor we normalize energy migration rates and sort it in decreasing order according to

0 j0 j

( )( )

( )T

TT

ωω =

Ω (35)

29

We then generate a random number from a uniform distribution ( ]1,0∈η , and select the i:th donor for which

j i 1 j i

0 j 0 jj 1 j 1

( ), ( )T Tη ω ω= − =

= =

⎛ ⎤∈⎜ ⎥

⎝ ⎦∑ ∑ (36)

The calculations above account for local anisotropic motions of the donors groups, i.e. energy migration under dynamic conditions. For energy migration in the static limit the scheme also holds, but the time-dependence of j0ω and

Ω is, of course no longer relevant. The time-dependent fluorescence anisotropy (r(t)) is calculated for times [ )TT ,τ− following the above scheme until one reaches the time ∞≥ TT . Moreover the procedure is repeated many times before the forming the following final ensemble average (= ....... ):

( )∑ ⋅=j

j02j0 )(ˆ)0(ˆ)()( tPtprtr μμ (37)

In eq. 8 the subfix j runs over all proteins, e. g. from -200 to +200 depending on the aggregate examined with the probability pj(t) = 1 if the j:th donor is excited and 0 otherwise. ( ))(ˆ)0(ˆ j02 tP μμ ⋅ is the second Legendre

polynomial.

GthnbGhalooufr

Fn RapdBoddso(ad adb“p

5 DAT

5.1 GeneGenetic Algohe principal i

numerical opehaved searc

GA, wrihttp://www.halgorithm origldest knownrganism was

using its bodrom the wate

Figure 14. Pikear Mount Pik

Recently GApproach is

depolarisationBriefly the GA

f N variabldimensional data and the olution is oanalogous to

dimensional v

. Evaluatdata by mean

. Select parents”, in p

TA ANAL

etic Algororithms (GA)ideas of bioltimisation tech spaces. Fitten inao.ucar.edu/Pginates from

n ancestor ofs about 50 m

dy and an exer as it swam

kaia is an extinka in the Burg

A were implehere employ

n data collectA can be desles. The obj“box” that mmodel pred

outlined by to “individuavectors (anal

te the models of the κ2-mpairs of “

proportion to

LYSIS

rithm PIKA) are compuogical evoluechniques whor the globa FortraPublic/mode

m Latin. Pikaif modern vermm in lengtxpanded tail

m along.

nct animal kngess Shale of B

emented in yed for theted by the TCscribed by co

bject is to fminimises thdiction. The the followinals”) from ogous to “ge

l for every “measure. “individuals”o their “fitne

30

AIA utational mettion (110), ahich are suit

al fitting, the an 77, els/pikaia/pikia gracilensrtebrates (cf.th. The Pikal fin. Pikaia

nown from theBritish Colum

fluorescence first time CSPC technionsidering a find a set ohe differenceprinciple of

ng: start by the N-metr

enomes”) and

“individual”

” from the ss”.

thods, whichand they are utable for thePIKAIA (2

was kaia.html). Tis the chorda

f. Figure 14).aia swam abo

may have f

e Middle Cammbia.

e spectroscopfor analysis

ique. model that d

of variablese between tf operation generating

ic “box” dd then perfor

and calculat

current po

h are inspiredused to conste analyses of6) variant of

used The name ofates, perhaps. In average ove the seaffiltered parti

mbrian fossil fo

py(27), and s of fluores

depends on a within the

the experimeto reach suca set of po

escribed byrm as follow

e its “fitness

opulation to

d by truct f ill-f the

(cf. f the s the this

floor icles

ound

this scent

a set e N-ental ch a oints y N-s:

s” to

o be

31

c. Breed the two N-vectors selected in b into two new “offsprings”. d. Repeat the steps b - c until the number of offspring produced equals the number of individuals e. Replace the old “population” with the new one, which becomes the next “generation”. f. Repeat the steps a - e until the “fitness” of one of the “individuals” becomes equal to some predefined value, or until a defined number of populations is reached. A good example of the problem suitable for GA is the surface plot of the function f(x,y) (cf. Figure 15), and the inset in the upper right is a color-coded version of the same function. The global maximum (indicated by the arrow and located at (x, y) = (0.5, 0.5), where f = 1) is surrounded by concentric rings of secondary maxima, where a simple hill-climbing method would most likely get stuck. This problem is easily solved with PIKAIA.

Figure 15. Three-dimensional landscape with almost vertical walls and concentric isolevels is a suitable task for Genetic Algorithm such as PIKAIA. We have successively applied PIKAIA for the TCSPC data analysis in our work related to non-covalent protein polymers (Paper IV (25)).

32

6 CONCLUSIONS The photophysical properties of g- and r-BODIPY make them suitable as fluorescence probes in studies that involve donor–donor energy migration and/or donor–acceptor energy transfer. In such studies it would be possible to measure distances ranging between 30 and 80 Å. Recently lipid derivatives of the r-BODIPY have been synthesised (Mikhalyov, I. & Gretskaya, N., Papers I(16),II(20)), which have proved to be valuable in studies of lipid–lipid(20) and lipid–protein interactions (Mikhalyov, I., Work in progress). We have studied BODIPY-labelled gangliosides (GM1) which were mixed with DOPC in unilamellar vesicles at lipid ratios varying between 1 : 325 and 1 : 4000. For all mixtures examined the analyses of the fluorescence lifetime decays and depolarisation data reveal that the labelled GM1 gangliosides exhibit a non-uniform distribution, which resembles the formation of a second phase or a “raft” formation. Separate experiments show a negligible influence by the BODIPY group in the GM1 aggregation Previously it was shown that cholesterol facilitates the formation of GM1 ‘clusters’ in model membranes(111-113). Our results, however, show that GM1 can aggregate into ‘clusters’ even in a model two-component lipid system (Paper II(20)). It therefore appears that self-aggregation is an intrinsic property of GM1. This property might explain that GM1-amyloid β-peptide complexes formed on the nerve cell surface, indeed helps the amyloid β-peptides to aggregate(42,113,114). This can now rationalise that this helps protein complexes formed with GM1 to assemble with lipid rafts containing GM1, e.g., the cholera toxin GM1 complex(44,45,115-117). A DDEM algorithm was developed, presented, tested and illustrated (Paper III(24)), which accounts for DDEM within regular polymer structures. Furthermore it accounts for the local anisotropic order and reorienting motions of the donor groups in a protein(25). Papers III-IV exemplify the application of the DDEM algorithm for analysing synthetic(24) and real(25) data. The Genetic Algorithm(25-27) was applied here in the analyses of the structural parameters of F-actin(25,28,30,31,33,65) which involves the search for the best fit with respect to five parameters(24). The results obtained are in agreement with the accepted view of the actin filament as a helical structure and refine the position of cysteine 374, which should encourage application of the GA in the analyses of TCSPC experiments. A versatile method was demonstrated with potential applicability to various non-covalent polymers (Papers III and IV(24,25)), e.g. in structural studies of diseases related to

33

amyloids(21,22,91,99-101,113,114,118) and prions(23,93,94). Other interesting examples are the cytolytic toxins(95,96), which are thought to create pores in membranes(97). A logical continuation of these studies on F-actin is to label other positions in the protein, possibly after site-directed mutagenesis as described previously(119), in order to reach new insights about the filament subunit orientation.

34

7 ACKNOWLEDGMENTS First of all I want to say thank you to my parents Oleksandr and Lyudmila Marushchak. Only because of you I am able to write these lines. Thank you so much. Lennart B-Å Johansson my supervisor for being kind and wise during these years, for the fact that you have had met me in Moscow and being given me the opportunity to become a real scientist. For helping to formulate difficult problems and giving real challenge, time, advises and resources in order to solve them. For your patience, when I was working during nights and slept during daytime. For allowing me to travel whenever I needed with only one question “Do you think you have time for this?” For giving me the freedom to be myself. Do you think that has been worth it? Thank you, Lennart! Anita Öystilä – the department’s secretary. Thank you for your help with all the administrative questions. For being the first one in the department who spoke Swedish with me, even if it was not fluent. Göran Lindblom – the head of the department of Biophysical Chemistry and my spare supervisor. Thank you for our fruitful economical and political discussions, for practical advises and a lesson about chocolate. Gerhard Gröbner – is probably the most optimistic person at the department. Thank you for your “More power”, “Don’t drink too much” and “Good, good”. It was you, who taught me that one needs to really love the job, the things one does and the friends. Otherwise it’s “useless” and one should find another job, hobby etc. Per-Olof Westlund - the Philosopher, who really thinks in philosophic terms, not only “purely scientific“. Thank you for the “Liouville” course. And for inspiration to perform research. I still remember when you told to Xiangzhi, that “You should think about your scientific problem day and night, day and night. Even, when you sleep, you must think about it. There is no other way to be a scientist.” With a great pleasure mention all the people I remember from Sweden and Umeå in particular. Thank you for all the time we share and for all the things You taught me. Marcus Bokvist, Xiangzhi, Tomas Gillbro, Mikael Isaksson, Matteus Lindgren, Fredrick Lindström, Nils Norlin, Greger Orädd, Leif Rilfors, Erik Rosenbaum, Britta Sethson, Vahid Shahedi, Tobias Sparrman, Staffan Tavelin, Andrey Filippov, Oleg Opanasyuk, Stanislav Kalinin, Ilya Mikhalev, Lijana Augulyte, Fredrick Gotby, Anton Lindström, Vladimir Zamotin,

35

Mykola Shykula, Arkadiy Petchenko, V’yacheslav Akkerman, Aleksey Chugreev, Aleksandr Talyzin, Damir Valiev, Oleg Pel, Olena Rzhepishevska, Patrik Brännberg, Mantas Malisauskas, Marija Pinne, Roger Karlsson, Staffan Grenklo, Anna Virel, Maribel Garcia, Lars Backman, Linus Ryderfors, Darius Saliunas, Rima Sulniute, Karolis Vaitkevicius, Ignas Bunikis, Oleg Seleznjev and Andrey Shchukarev, Leonid Gershuni …

36

REFERENCES (1)  M  Klessinger,  J Michl:  Excited  states  and  photochemistry  of  organic molecules, VCH Publishers, Inc., New York, 1995. (2)  JR  Lakowicz:  Principles  of  Fluorescence  Spectroscopy,  Kluwer Academic/Plenum Publishers, New York, 1999. (3)  B Valeur: Molecular Fluorescence. Principles and Applications., Wiley‐VCH, 2002. (4)  GG Stokes: On the change of refrangibility of  light. Phil. Trans. R. Soc. London 142 (1852) 463‐562. (5)  F Bergström, P Hägglöf, J Karolin, T Ny, LB‐Å Johansson: The use of site‐directed  fluorophore  labeling  and  donor‐donor  energy  migration  to investigate solution structure and dynamics in proteins. Proc.  Natl. Acad. Sci. 96 (1999) 12477‐81. (6)  SV  Kalinin,  JG  Molotkovsky,  LB‐Å  Johansson:  Partial  Donor‐Donor Energy  Migration  (PDDEM)  as  a  Fluorescence  Spectroscopic  Tool  of Measuring  Distances  in  Biomacromolecules.  Spectrochim.  Acta  Part  A  58 (2002) 1087‐97. (7)  BW Van der Meer, G Coker III , S‐YS Chen: Resonance Energy Transfer: Theory and Data, VCH Publishers, Inc., 1994. (8)  M  Olofsson,  S  Kalinin,  M  Oliveberg,  LB‐Å  Johansson:  Tryptophan  – BODIPY:  A  Versatile  Donor‐Acceptor  Pair  for  Probing  Generic  Changes  of Intraprotein Distances. Phys. Chem. Chem. Phys. 8 (2006) 3130 ‐ 40. (9)  LB‐Å  Johansson,  F  Bergström,  P  Edman,  IV  Grechishnikova,  JG Molotkovsky:  Electronic  Energy  Migration  and  Molecular  Rotation  within Bichromophoric  Macromolecules.  Part  1.  Test  of  a  Model  using  bis(9‐anthrylmethylphosphonate)  bisteroid.  J.  Chem.  Soc.,  Faraday  Trans.  92 (1996) 1563‐67. (10)  LB‐Å  Johansson,  P  Edman,  P‐O  Westlund:  Energy  migration  and rotational motion within  bichromophoric molecules.  II. A  derivation  of  the fluorescence anisotropy. J. Chem. Phys. 105 (1996) 10896‐904. (11)  J  Karolin, M  Fa, M Wilczynska,  T  Ny,  LB‐Å  Johansson:  Donor‐Donor Energy  Migration  (DDEM)  for  Determining  Intramolecular  Distances  in Proteins:  I.  Application  of  a  Model  to  the  Latent  Plasminogen  Activator Inhibitor‐1 (PAI‐1). Biophys. J. 74 (1998) 11‐21. (12)  S  Kalinin,  JG Molotkovsky,  LB‐Å  Johansson:  Distance Measurements Using  Partial  Donor‐Donor  Energy  Migration  (PDDEM)  within  Pairs  of Fluorescent Groups in Lipid Bilayers. J. Phys. Chem., B 107 (2003) 3318‐24. 

37

(13)  S  Kalinin:  Electronic  Energy  Transfer  within  Asymmetric  Pairs  of Fluorophores:  Partial  Donor‐Donor  Energy  Migration  (PDDM),  Umeå University, Umeå, 2004. (14)  AK Treibs, F.‐H.: Liebigs Annalen der Chemie 718 (1968) 203. (15)  RP  Haugland,  ed.:  Handbook  of  Fluorescent  Probes  and  Research Chemicals, Eugene, 1996. (16)  D Marushchak,  S  Kalinin,  I Mikhalyov, N Gretskaya,  LB‐Å  Johansson: Pyrromethene  dyes  (BODIPY)  can  form  ground  state  homo  and  hetero dimers: Photophysics and spectral properties. Spectrochim. Acta, A 65 (2006) 113–22. (17)  R de Almeida, L Loura, A Fedorov, M Prieto: Lipid rafts have different sizes  depending  on membrane  composition:  a  time‐resolved  fluorescence resonance energy transfer study. J. Mol. Biol. 346 (2005) 1109‐20. (18)  S Veatch,  S  Keller:  Seeing  spots:  Complexs  phase  behavior  in  simple membranes. Biochimica et Biophysica Acta 1746 (2005) 172‐85. (19)  J Silvius: Partitioning of membrane molecules between  raft and non‐raft  domains:  Insights  from  model‐membrane  studies.  Biochimica  et Biophysica Acta 1746 (2005) 193‐202. (20)  D Marushchak, N Gretskaya,  IJ Mikhalyov,  LBA.: Ganglioside GM1  is non‐uniformly  distributed  in  lipid  bilayers  as  revealed  by  fluorescence studies. Molecular Membrane Biology 24 (2007). (21)  CL Masters,  G  Simms,  NA Weinman,  G Multhaup,  BL McDonald,  K Beyreuther:  Amyloid  plaque  core  protein  in  Alzheimer  disease  and  Down Syndrome. Proc. Natl. Acad. Sci. 82 (1985) 4245‐49. (22)  PT  Lansbury,  Jr: Amyloid  fibrillogenesis:  themes  and  variations. Curr. Opin. Struct. Biol. 10 (2000) 60. (23)  F Houston, W Goldmann, A Chong, M  Jeffrey, L Gonzalez,  J Foster, D Parnham,  N  Hunter:  Prion  diseases:  BSE  in  sheep  bred  for  resistance  to infection. Nature 423 (2003) 498‐98. (24)  D  Marushchak,  LB‐Å  Johansson:  On  the  Quantitative  Treatment  of Donor‐Donor Energy Migration  in regularly Aggregated proteins. J. Fluoresc. 15 (2005). (25)  D Marushchak, S Grenklo, T Johansson, RJ Karlsson, LBA: Fluorescence Depolarisation Studies of Filamentous Actin Analysed by a Genetic Algorithm. PNAS (2007). (26)  P  Charbonneau:  Genetic  Algorithms  in  Astronomy  and  Astrophysics. Astrophys. J. Suppl. Ser. 101 (1995) 309‐34. (27)  JJ Fisz, M Buczkowski, MP Budzinski, P Kolenderski: Genetic algorithms optimization approach  supported by  the  first‐order derivative and Newton‐

38

Raphson methods:  Application  to  fluorescence  spectroscopy.  Chem.  Phys. Letters 407 (2005) 8‐12. (28)  E Egelman: The structure of F‐actin. J. Muscle Res. Cell Motil. 6 (1985) 129‐51. (29)  KC Holmes, D Popp, W Gebhard, W Kasch: Atomic model of the actin filament. Nature 347 (1990) 44‐49. (30)  M  Lorentz,  D  Popp,  KC  Holmes:  Refinement  of  the  F‐actin  model against  X‐ray  fiber  diffraction  data  by  the  use  of  a  directed  mutation algorithm. J. Mol. Biol. 234 (1993) 826‐36. (31)  AA Kasprzak, R Takashi, MF Morales: Orientation of actin monomer in the F‐actin filament: radial coordinate of glutamine‐41 and effect of myosin subfragment 1 binding on the monomer orientation. Biochemistry 27 (1988) 4512‐22. (32)  PDJ  Moens,  CG  dos  Remedios:  A  conformational  change  in  F‐actin when  myosin  binds:  fluorescence  resonance  energy  transfer  detects  and increase in the radial coordinate of Cys374. Biochemistry 36 (1997) 7353‐60. (33)  PDJ Moens,  CG  Dos  Remedios:  Analysis  of Models  of  F‐Actin  Using Fluorescence Resonance Energy Transfer Spectroscopy. Results and problems in Cell Differentiation 32 (2001) 59‐77. (34)  DL Taylor,  J Reidler,  JA Spudich, L Stryer: Detection of actin assembly by fluorescence energy transfer. J. Cell Biol. 89 (1981) 362‐67. (35)  J  Karolin,  LB‐Å  Johansson,  L  Strandberg,  T  Ny:  Fluorescence  and Absorption  Spectroscopic  Properties  of  Dipyrrometheneboron  Difluoride (BODIPY) Derivatives in Liquids, Lipid Membranes, and Proteins. J. Am. Chem. Soc. 116 (1994) 7801‐06. (36)  AB  Bergenståhl,  P  Stenius:  Phase‐Diagrams  of Dioleoylphosphatidylcholine  with  Formamide,  Methylformamide,  and Dimethylformamide. J. Phys. Chem. 81 (1987) 5944‐48. (37)  G Pompeo, M Girasole, A Cricenti, F Cattaruzza, A Flamini, T Prosperi, J Generosi,  C  A.C.:  AFM  characterization  of  solid‐supported  lipid multilayers prepared by spin‐coating. Biochimica et Biophysica Acta 1712 (2005) 29‐36. (38)  I Mocchetti:  Exogenous  gangliosides,  neuronal  plasticity  and  repair, and  the neurotrophins. Cellular and molecular  life sciences 62  (2005) 2283‐94. (39)  PH Fishman: Role of membrane gangliosides in the binding and action of bacterial toxins. Journal of Membrane Biology 69 (1982) 85. (40)  J McLaurin, T Franklin, PE Fraser, A Chakrabartty: Structural transitions associated  with  the  interaction  of  Alzheimer  beta‐amyloid  peptides  with gangliosides. J. Biol. Chem. 273 (1998) 4506‐15. 

39

(41)  SA  Waschuk,  EA  Elton,  AA  Darabie,  PE  Fraser,  J  McLaurin:  Cellular Membrane  Composition  Defines  A  ‐Lipid  Interactions.  J.  Biol.  Chem.  276 (2001) 33561‐68. (42)  A  Kakio,  S‐I  Nishimoto,  K  Yanagisawa,  Y  Kozutsumi,  K  Matsuzaki: Interactions  of  Amyloid  b‐Protein  with  Various  Gangliosides  in  Raft‐Like Membranes:Importance of GM1 Ganglioside‐Bound  Form  as  a  Endogenous Seed for Alzheimer Amyloid. Biochemistry 41 (2002) 7385‐90. (43)  PK Mandal,  Pettegrew:  Alzheimer´s  Disease:  NMR  Studies  of  Asialo (GM1) and Trisialo (GT1b) Ganglioside Interactions with Ab(1‐40) Peptide in a Membrane Minick Environment. Neurocehm. Res. 29 (2004) 447‐53. (44)  J Sattler, G Schwarzmann,  I Knack, K‐H Rohm, H Wiegandt: Studies of ligand binding  to  cholera  toxin  III,  cooperativity of oligosaccharide binding. Hoppe‐Seyler's Z. Physiol. Chem. 359 (1978) 719‐23. (45)  AT Aman,  S  Fraser, EA Merritt, C Rodigherio, M Kenny, M Ahn, WGJ Hol, NA Williams, WI Lencer, TR Hirst: A mutant cholera toxin B subunit that binds GM1‐ ganglioside but  lacks  immunomodulatory or toxic activity. Proc.  Natl. Acad. Sci. 98 (2001) 8536‐41. (46)  A  Szent‐Györgyi: Chemistry of muscular  contraction, Academic Press, New York, 1951. (47)  FB  Straub, G  Feuer: Adenosinetriphosphate.  The  functional  group  of actin. 1950 [classical article]. Biochim. Biophys. Acta, 1000 (1989) 180‐95. (48)  P  Sheterline,  JaS  Clayton,  J.:  Actin., Oxford University  Press, Oxford, 1998. (49)  W Kabsch, HG Mannherz, D Suck, EFaH Pai, K.C.: Atomoc structure of the actin: DNase I complex. Nature 347 (1990) 37‐44. (50)  PJ McLaughlin, JT Gooch, HGaW Mannherz, A.G.: Structure of gelsolin segment  1‐actin  complex  and  the mechanism  of  filament  severing. Nature 364 (1993) 685‐92. (51)  CE Schutt, JC Myslik, MD Rozycki, NCaL Goonesekere, U.: The structure of crystalline profilin‐b‐actin. Nature 365 (1993) 810‐16. (52)  JK Chik, U Lindberg, CE Schutt: The structure of an open state of beta‐actin at 2.65 Å resolution. J. Mol. Biol. 263 (1996) 607‐23. (53)  JK Chik, U Lindberg, CE Schutt, Structure of Bovine beta‐actin‐profilin complex with actin bound ATP phosphates  solvent accessible, Protein Data Bank, 1996, p. 1HLU. (54)  SaA Vorobiev, S., Structure of the yeast actin‐human gelsolin segment 1 complex. Brookhaven, 1998. (55)  SaA Vorobiev, S., Structure of  the Dictyostelium actin‐human gelsolin segment 1 complex. Brookhaven, 1999. 

40

(56)  P Bork, CaV Sander, A.: An ATPase domain common to prokaryotic cell cycle  proteins,  sugar  kinases,  actin,  and  hsp70  heat  shock  proteins.  Proc. Natl. Acad. Sci. 89 (1992) 7290‐94. (57)  KM  Flaherty, DB McKay, WaH  Kabsch,  K.  C.:  Similarity  of  the  three‐dimensional  structures  of  actin  and  the  ATPase  fragments  of  70lkDa  heat shock cognate protein. Proc.  Natl. Acad. Sci. 88 (1991) 5041‐45. (58)  U Lindberg, CE Schutt, E Hellsten, AC Tjader, T Hult: The use of poly(L‐proline)‐Sepharose  in  the  isolation  of  profilin  and    profilactin  complexes. Biochim. Biophys. Acta, 967 (1988) 391‐400. (59)  JD  Pardee,  JA  Spudich:  Purification  of  muscle  actin.  Methods  in Enzymology 85 (1982) 164‐81. (60)  JA  Spudich,  S  Watt:  The  regulation  of  rabbit  sceletal  muscle contraction.  I.  Biochemical  studies  of  the  interaction  of  the  tropomyosin‐troponin comples with actin and the proteolytic fragments of myosin. Journal of Biological Chemistry 246 (1971) 486648‐71. (61)  MF  Carlier:  Role  of  nucleotide  hydrolysis  in  the  dynamics  of  actin filamentsand microtubules. International Review of Cytology 115 (1989) 139‐70. (62)  F  Oosawa: Macromolecular  assembly  of  acint.  In  stracher,  A.  (ed.), Academic Press, New York, 1983. (63)  F Oosawa, M Kasai: Actin. , Dekker, New York, 1971. (64)  DL Purich, FS Southwick: Energetics of nucleotide hydrolysis in polymer assembly  /  disassembly:  the  cases  of  actin  and  tubulin.  Methods  in Enzymology 308 (1999) 93‐111. (65)  RA Mendelson,  EP Morris:  The  structure  of  f‐actin.  Results  of  global searches  using  data  from  electron  microscopy  and  X‐ray  crystallography. Journal of Molecular Biology 240 (1994) 138‐54. (66)  JN Demas: Excited state lifetime measurements, Academic Press, New York, 1983. (67)  T  Förster:  Zwischenmolekulare  Energiewanderung  und  Fluorescenz. Ann. Phys. 2 (1948) 55‐75. (68)  JB Birks: Photophysics of Aromatic Molecules,  John Wiley & Sons Ltd, London, 1970. (69)  T Kulinski, AJWG Visser, A O'Kane,  J Lee: Spectroscopic  Investigations of the Single Tryptophan Residue and of Riboflavin and 7‐Oxolumazine Bound to  Lumazine  Apoprotein  from  Photobacterium  leiognathi.  Biochemistry  26 (1987) 540‐49. 

41

(70)  E  Haas, M Wilchek,  E  Katchalski‐Katzir,  IZ  Steinberg:  Distribution  of End‐to‐End  Distances  of  Oligopeptides  in  Solution  as  Estimated  by  Energy Transfer. Proc. Nat. Acad. Sci. USA 72 (1975) 1807‐11. (71)  L  Stryer,  RP Haugland:  Energy  Transfer: A  Spectroscopic  Ruler.  Proc.  Natl. Acad. Sci. 58 (1967) 719‐26. (72)  J  Baumann,  MD  Fayer:  Excitation  transfer  in  disordered  two‐dimensional  and  anisotropic  three  dimensional  systems:  Effects  of  spatial geometry on the time‐resolved observables. J. Chem. Phys. 85 (1986) 4087‐108. (73)  E Gaviola, P Pringsheim: Z. Physik 24 (1924) 24. (74)  DM  Jameson,  JC  Croney,  PDJ Moens:  Fluorescence:  Basic  concepts, practical aspects, and some anecdotes. Methods Enzymol. 360 (2003) 1‐43. (75)  S Kalinin,  LB‐Å  Johansson: Utility and Considerations of Donor‐Donor Energy Migration as a Fluorescence Method for Exploring Protein Structure‐Function. J. Fluorescence 14 (2004) 681‐91. (76)  F  Tanaka,  N  Mataga:  Theory  of  time‐dependent  photoselection  in interacting  fixed media. Photochemistry  and Photobiology 29  (1979) 1091‐97. (77)  YR  Kim,  P  Share,  M  Pereira,  M  Sarisky,  RM  Hochstrasser:  Direct measurements  of  energy  transfer  between  identical  chromophores  in solution. J. Chem. Phys. 91 (1989) 7557‐62. (78)  PIH  Bastiaens,  A  Van  Hoek,  JAE  Benen,  JC  Brochon,  AJWG  Visser: Conformational dynamics and  intersubunit energy  transfer  in wild‐type and mutant  lipoamide  dehydrogenase  from  Azotobacter  vinelandii.  A multidimensional  time‐resolved polarized  fluorescence study. Biophys.  J. 63 (1992) 839‐53. (79)  P‐O Westlund, H Wennerström:  Electronic  energy  transfer  in  liquids. The effect of molecular dynamics. J. Chem. Phys. 99 (1993) 6583‐89. (80)  P  Edman,  P  Håkansson,  P‐O  Westlund,  LB‐Å  Johansson:  Extended Förster  Theory  of  Donor‐Donor  Energy  Migration  in  Bifluorophoric Macromolecules.  Part  I.  A  New  Approach  to  Quantitative  Analyses  of  the Time‐Resolved Fluorescence Anisotropy. Molec. Phys. 98 (2000) 1529‐37. (81)  P  Edman,  P‐O  Westlund,  LB‐Å  Johansson:  On  determining intramolecular distances from donor‐donor energy migration (DDEM) within bifluorophoric macromolecules. Phys. Chem. Chem. Phys. 2 (2000) 1789‐94. (82)  P  Håkansson, M  Isaksson,  P‐O Westlund,  LB‐Å  Johansson:  Extended Förster Theory for Determining Intraprotein Distances: The k2‐Dynamics and Fluorophore Reorientation. J. Phys. Chem. B 108 (2004) 17243‐50. 

42

(83)  LW  Runnels,  SF  Scarlata:  Theory  and  application  of  fluorescence homotransfer to melittin oligomerization. Biophys. J. 69 (1995) 1569‐83. (84)  ML Barcellona, E Gratton: Torsional dynamics and orientation of DNA‐DAPI complexes. Biochemistry 35 (1996) 321‐33. (85)  BD  Hamman,  AV  Oleinikov,  GG  Jokhadze,  RR  Traut,  DM  Jameson: Dimer/monomer  equilibrium  and  domain  separations  of  Escherichia  coli ribosomal protein L7/L12. Biochemistry 35 (1996) 16680‐86. (86)  MP Lillo, O Canadas, RE Dale, AU Acuna: Location and properties of the taxol  binding  center  in  microtubules:  A  picosecond  laser  study  with fluorescent taxoids. Biochemistry 41 (2002) 12436‐49. (87)  S‐T Bogen, J Karolin, JG Molotkovsky, LB‐Å Johansson: 1,32‐Dihydroxi‐dotriacontane‐bis(Rhodamine)  101‐ester  A  Lipid  MembraneSpanning Bichromophoric  Molecule  as  Revealed  by  Intramolecular  Donor‐Donor Energy Migration (DDEM). J. Chem. Soc., Faraday Trans. 94 (1998) 2435‐40. (88)  M Fa, F Bergström, P Hägglöf, M Wilczynska, LB‐Å Johansson, T Ny: The structure of a  serpin‐protease complex  revealed by  intramolecular distance measurements  using  donor‐donor  energy  migration  and  mapping  of interaction sites. Structure 8 (2000) 397‐405. (89)  I  Mikhalyov,  S‐T  Bogen,  LB‐Å  Johansson:  Donor‐Donor  Energy Migration  (DDEM)  as  a  Tool  for  Studying  Aggregation  in  Lipid  Phases. Spectrochim. Acta Part A 57 (2001) 1839‐45. (90)  B Medhage,  E Mukhtar, B  Kalman,  LB‐Å  Johansson,  JG Molotkovsky: Electronic  energy  transfer  in  anisotropic  systems.  5.  Rhodamine‐lipid derivatives  in model membranes.  J.  Chem.  Soc.,  Faraday  Trans.  88  (1992) 2845‐51. (91)  J‐C  Rochet,  PT  Lansbury,  Jr:  Amyloid  fibrillogenesis:  themes  and variations. Curr. Opin. Struct. Biol. 10 (2000) 60‐68. (92)  CM Dobson: Protein folding and misfolding. Nature 426 (2003) 884‐90. (93)  A Aguzzi, M Polymenidou: Mammalian prion biology: One  century of evolving concepts. Cell 116 (2004) 313‐27. (94)  C  Chakraborty,  S  Nandi,  S  Jana:  Prion  disease:  A  deadly  disease  for protein misfolding. Curr. Pharmaceut. Biotechn. 6 (2005) 167‐77. (95)  P  Stanley,  V  Koronakis,  C  Hughes:  Acylation  of  Escherichia    coli hemolysin:  a  unique  protein  lipidation  mechanism  underlaying  toxin function. Microbiol. Mol. Biol. Rev. 62 (1998) 309‐33. (96)  L  Abrami, M  Fivaz,  FG  van  der  Goot:  Adventures  of  a  pore‐forming toxin at the target cell surface. Trends Microbiol. 8 (2000) 168‐72. 

43

(97)  SN Wai, M Westermark, J Oscarsson, J Jass, E Maier, R Benz, BE Uhlin: Characterisation of Dominantly Negative Mutant ClyA Cytotoxin Proteins  in Echerichia coli. J, Bacteriol. 185 (2003) 5491‐99. (98)  J Howard, AA Hyman: Dynamics and mechanics of the microtubule plus end. Nature 422 (2003) 753‐58. (99)  M Malisauskas,  J  Ostman,  A  Darinskas,  V  Zamotin,  E  Liutkevicius,  E Lundgren, LA Morozova‐Roche: Does the cytotoxic effect of transient amyloid oligomers  from  common  equine  lysozyme  in  vitro  imply  innate  amyloid toxicity? Journal of Biological Chemistry 280 (2005) 6269‐75. (100) M Malisauskas, V Zamotin, J Jass, W Noppe, CM Dobson, LA Morozova‐Roche:  Amyloid  protofilaments  from  the  calcium‐binding  protein  equine lysozyme: Formation of ring and  linear structures depends on pH and metal ion concentration. Journal of Molecular Biology 330 (2003) 879‐90. (101)  A  Petkova,  R  Leapman,  Z  Guo,  W  Yau,  M  Mattson,  R  Tycko:  Self‐Propagating, Molecular‐Level Polymorphism in Alzheimer's b‐Amyloid Fibrils. Science 307 (2005) 262. (102)  A  Petkova, W  Yau,  R  Tycko:  Experimental  Constrains  on Quaternary Structure in Alzheimer's b‐Amyloid Fibrils. Biochemistry 45 (2006) 498‐512. (103)  RE  Dickerson:  X‐ray  analysis  and  protein  structure,  Academic  Press, New York, 1964. (104)  TL  Blundell,  LN  Johnson:  Protein  Crystallography,  Academic  Press, London, 1976. (105)  K Wütrich: NMR of Proteins and Nucleic Acids, Wiley, New York, 1986. (106)  GM  Clore,  AM  Gronenborn  (Ed.)^(Eds.),  NMR  of  Proteins.  The Macmillan Press Ltd, London, 1993. (107)  NL Vekshin: Energy Transfer in Macromolecules, Spie Press, 1997. (108)  DA Lomas, DL Evans, SR Stone, WS Chang, RW Carell: Effect of  the Z mutation  on  the  physical  and  inhibitory  properties  of  alpha1‐antitrypsin. Biochemistry 32 (1993) 605‐07. (109)  PR  Elliot,  JP Abrahams, DA  Lomas: Wild‐type  alpha1‐antitrypsin  is  in the canonical inhibitory conformation. J. Mol. Biol. 275 (1998) 419‐25. (110)  C Darwin: Origin of Species, Gramercy, 1995. (111)  C  Yuan,  J  Furlong,  P Burgos,  LJ  Johnston:  The  Size  of  Lipid Rafts: An Atomic  Force  Microscopy  Study  of  Ganglioside  GM1  Domains  in Sphingomyelin/DOPC/Cholesterol Membranes.  Biophys.  J.  82  (2002)  2526–35. (112)  B  Pei,  J‐W  Chen:  More  Ordered,  Convex  Ganglioside‐Enriched Membrane  Domains:  The  Effects  of  GM1  on  Sphingomyelin  Bilayers Containing a Low Level of Cholesterol. J. Biochem. 134 (2003) 575–81. 

44

(113)  A  Kakio,  S  Nishimoto,  K  Yanagisawa,  Y  Kozutsumi,  K  Matsuzaki: Cholesterol‐dependent  formation  of GM1  ganglioside‐bound  amyloid  beta‐protein, an endogenous seed for Alzheimer amyloid. J.Biol. Chem. 276 (2001) 24985‐90. (114)  K  Yanagisawa:  GM1  ganglioside  and  the  seeding  of  amyloid  in Alzheimer's disease: Endogenous seed for alzheimer amyloid. Neuroscientist 11 (2005) 250‐60. (115)  AM Surin, EI Astashkin, ON Smirnov,  II Mikhalev, YG Molotkovskii, LD Bergel'son:  Interaction of cholera toxin B‐subunit with  liposomes containing ganglioside GM1 and fluorescence‐labeled lipids. Biol. Membr. 9 (1992) 495‐508. (116)  A Kenworthy, N Petranova, M Edidin: High‐resolution FRET microscopy of  cholera  toxin  B‐subunit  and  GPI‐anchored  proteins  in  cell  plasma membranes. Molecular Biology of the Cell 11 (2000) 1645‐55. (117)  Y  Fujinaga,  AA Wolf,  C  Rodighiero,  H Wheeler,  B  Tsai,  L  Allen, MG Jobling, T Rapoport, RKL Holmes, W.I.: Gangliosides that associate with  lipid rafts  mediate  transport  of  cholera  and  related  toxins  from  the  plasma membrane to endoplasmic reticulm. Mol. Biol. Cell 14 (2003) 4783‐93. (118)  JD  Sipe,  AS  Cohen:  Review:  History  of  the  amyloid  fibril.  Journal  of Structural Biology 130 (2000) 88‐98. (119)  H Schuler, E Korenbaum, CE Schutt, U Lindberg, R Karlsson: Mutational analysis  of  Ser14  and  Asp157  in  the  nucleotide‐binding  site  of  b‐actin. Europian Journal of Biochemistry 265 (1999) 210‐20.