Inserm - Délégation Régionale Paca et Corse - BP 172 13276 Marseille Cedex 09 Contact : Marie-Laure OLIVE Tél. : 04 91 82 70 10 Fax : 04 91 82 70 54 [email protected]Didier MARGUET IM2V platform scientific manager Mathieu FALLET Sébastien MAILFERT Vincent ROUGER Arnauld SERGE Tomasz TROMBIK Molecular diffusion in living cells using Fluorescence Microscopy Comparison of FRAP, FCS and SPT October 19th - 22th 2010 Centre d’Immunologie de Marseille Luminy
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Molecular diffusion in living cells using Fluorescence ... · Fluorescence Recovery After Photobleaching - FRAP Principle of FRAP measurements Different FRAP modes (Spot FRAP, Confocal
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Inserm - Délégation RégionalePaca et Corse - BP 17213276 Marseille Cedex 09
The observations will be conducted on the optical setups available within the platform ’Molec-ular Interactions in Living Environment - IM2V’ at the CIML. Three methodological approacheswill be presented: Fluorescence Recovery After Photobleaching (FRAP), Fluorescence CorrelationSpectroscopy (FCS) & Single Particle Tracking (SPT).
� Fluorescence Recovery After Photobleaching - FRAPPrinciple of FRAP measurementsDifferent FRAP modes (Spot FRAP, Confocal FRAP / FLIP, Gaussian FRAP, Spot Vari-ation FRAP)Advantages and disadvantages of FRAP compared to other methods
� Fluorescence Correlation Spectroscopy - FCSPrinciple of FCS measurementsTheoretical modelsDescription of optical setupsComparison between with ’commercial’ and ’non-commercial’ FCS microscopesAdvantages and disadvantages of FCS compared to other methods
� Single Particle Tracking - SPTThe concept and interest of SPTDescription of experimental setupExperimental limitations during measurements (cell types, molecules types)Analysis 1: detection, estimation and reconnectionAnalysis 2: molecular interactions, Brownian motions and confinementAdvantages and disadvantages of SPT compared to other methods
� Labeling strategiesGeneral problems of molecular diffusion measurements linked to molecule detectionPhotophysical properties of fluorophoresIndirect labeling (monoclonal antibodies coupled with fluorophores)Direct labeling (fluorescent proteins or tags)Relationship between the labeling method and the microscopy technique
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Part II
Course Part
9
10
Chapter 1
General introduction of moleculardiffusion measurement aspects
11
12
1
IM2V platform
“Interactions Moléculaires en Milieu Vivant”
Biophotonics – interaction of light and matterThe conception, development and implementation of innovative optical and photonic technologies applied to the field of life sciences
Interdisciplinary research programs at IM2Va multidisciplinary approach for functional imaging at molecular levelmethodological innovation and technological development in the
specificity of the IM2V platform
methodological innovation and technological development in the biophysical approach
development of accurate analytical methodsproof of principle demonstrated for each new methodology
Relevance of IM2V platform for CIML teamsto provide experimental setups at the state of the art to provide expertise in quantitative microscopyto train collaborators at both the experimental and analytical levels
a need for quantification of new observables
2
location- at the Devenson level
5 optical benches one small lab for biological sample preparationone office & computer room
platform support and funding
IM2V organization
platform support and funding- since 2003, supported on specific grants from
platform staffSÉBASTIEN MAILFERT (CIML) supports users by setting up procedures for:- instrument quality control over the time sequence of a project- standardized analytical and statistical methods- standardized archival and access methods for data storage
The journey of a thousand miles begins with a single step.
Lao Tsufrom Tao Te Ching
m lysozyme = 2.3 10-20 g v2 ½ = 1.3 103 cm/sec
d t
1
probability of finding particles
d t
d = 2Dt4
16
6
m lysozyme = 2.3 10-20 g v2 ½ = 1.3 103 cm/sec
d
d t
d t
d = 2Dt
Brownian motion and diffusionD = 1μm2s-1
a Maxwell’s demon experiment
Brownianagitation
from Shinbrot & Muzzio (2001) Noise to order. Nature 410:251
order
"other than homogeneity can result from Brownian agitation"
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diffusion and domain formationspreading of a heterogeneity by diffusion
domain formation due to differential interaction
d lk i ll bi lrandom walk in cell biology
membrane [lipid] fluidity
8
GY S1
S2
T2
I C
Vibrational energy levelsRotational energy levelsElectronic energy levels
Singlet States Triplet States
fluorescence imaging
ENER
G
S0
T1
ABS FL I.C.
ABS - Absorbance S 0.1.2 - Singlet Electronic Energy LevelsFL - Fluorescence T 1,2 - Corresponding Triplet StatesI.C.- Nonradiative Internal Conversion IsC - Intersystem Crossing
PH - Phosphorescence
IsC
IsCPH
[Vibrational sublevels]
fast slow (phosphorescence)much longer wavelength
Triplet state
single moleculeimaging
ONGOING FLUORESCENCE TECHNIQUESMOLECULAR DYNAMICS IN LIVE CELLS
FCS, PCH, FCCS& FRAP
u
y
x
IXIYAPD
APD
EX
Y
Polarizationbeamsplitters
probing molecular organization in living cells
SPT at high density (MTT) nanoscopy polarimetric analysis
Raman & CARS microscopy
CONTRASTING METHODS
wave front technology
μ-stereolithography
ACCESSORY TOOLS
HOT & dual color imaging
FRAP (fluorescence recovery after photobleaching)- provides averaged information on motion of a population of molecule- high fluorescence signal, bleaching, separate weakly multiple components…
from Yechiel & Edidin (1987) J. Cell Biol. 105:755
increased focal spot size
spot variation FCS
spot area
longer diffusion time
effd D
t4
2
0
Lenne, Wawreziniek et al. EMBO J. (2006) 25:3245
meshwork
diffu
sion
tim
e
t0 > 0
dynamic partition(self-assembling)
accessible size
optical diffraction limit
free diffusion
spot area0
t0 < 02
0 41 wD
teff
d
Wawrezinieck et al. Biophys. J. (2005) 89:4029
16
FCS through nanoholes
Wenger et al. Biophys. J. (2007) 92:913
aluminium 100 to 500 nm
i l l l i isingle molecule imaging
Imaging a single molecule
-10 -5 0 5 10
inte
nsity
k a sin( )-10 -5 0 5 10
inte
nsity
k a sin( )
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Airy patterns & the limit of resolution
single molecule localization
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Dietrich et al., Biophys J 2002
19
the Multi Target Tracing algorithmallow to resolve the motion of thousands of molecule
to achieve an exhaustive detection of particlesby using deflation loop
to reconnect accurately trajectoriesby taking into account past information
to translate the data into a map of local molecular dynamicsby identifying confinement events
the source code of the MTT software is freely available online: http://www.ciml.univ-mrs.fr/labs/he-marguet.htm
dynamic map of the confinement areas
the source code of the MTT software is freely available online: http://www.ciml.univ-mrs.fr/labs/he-marguet.htm
32
Chapter 2
Fluorescence Recovery AfterPhotobleaching
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FRAPFluorescence Recovery After Photobleaching
Mathieu Fallet
Mathieu Fallet CIML septembre 2010
Plan :Plan :
1) Principe du FRAP 1) Principe du FRAP 2) La diffusion effective, la r2) La diffusion effective, la rééaction en 2Daction en 2D3) FRAP en mode spot (mod3) FRAP en mode spot (modèèle dle d’’AxelrodAxelrod))4) Le fit et le nombre de param4) Le fit et le nombre de paramèètrestres5) FRAP en mode 5) FRAP en mode confocalconfocal (mod(modèèle de le de SoumpasisSoumpasis))6) FRAP en mode LINE6) FRAP en mode LINE7) FLIP 7) FLIP 8) FRAP gaussien 8) FRAP gaussien 9) FRAP 9) FRAP àà deux deux waistswaists10) Strat10) Stratéégies dgies d’’acquisitionacquisition11) Conclusion11) Conclusion
1) Principe du FRAP 1) Principe du FRAP ::
R fraction mobile :
2) Les mod2) Les modèèles : Diffusion libre, les : Diffusion libre, ReactionReaction pure pure
Diffusion libre :Réaction:
Fraction libre non-bleachable
Les modLes modèèles : Diffusion effective les : Diffusion effective
3) Mod3) Modèèle dle d ’’AxelrodAxelrod : analyse d: analyse d’’un spot gaussien un spot gaussien
ω=1.1μm
90% de bleach
Intensité
Rayon
Le diamètre effectif = 2.2 μm
Kprofondeurde
bleach
La solution exacte :
Une approximation valide pour des faibles photo-blanchiment(<80%):
ModModèèle dle d ’’AxelrodAxelrod::
On détermine (intensité moyenne avant le bleach) :
Equation d’Axelrod (8 termes):
On tronque la série à 8 termes. On ajuste K, td, R et F(0).
F(0)/Fi=[1-e(-K)]/K
Equation de Kwon (2 termes):
On ajuste F(0), R et t1/2.
On calcule Beta à partir d’une table de conversion fonction du pourcentage de bleach.
4) Le Fit et le nombre de param4) Le Fit et le nombre de paramèètres :tres :
Avec 4 paramètres on peut fitter/ajuster un éléphant. Avec 5 paramètres, on peut lui faire bouger sa trompe !
Lorsque l’on a trop de paramètres, ceux-ci sont corrélées les uns aux autres, il est alors impossible de les déterminer (par exemple : a+b=2 !)
Exemple : Simulation dExemple : Simulation d’’une expune expéérience de FRAP avec un profil rience de FRAP avec un profil gaussiengaussien
Paramètres : Moyenné sur 30 valeurs, 500k molécules, Boite : 15um*15um, waist=0.5um, Intensité de frap=8000, D=1um²s-1, 16s (200 avant), toutes les 1msRésultat :D=1.03 um²s-1 ( stdev=0.35, moyenne sur 30 valeurs )
*Après moyennage temporel log à base de 2 : D=1.02 um²s-1 (stdev=0.18)
=>Le moyennage temporel (binning log) améliore l’erreur global du fit sans modifier la moyenne. Il donne autant de poids au début de la courbe qu’à la fin de la courbe.
*L’ajustement sur 2 secondes au lieu de 16s (sans binning) donne : D=1.06 (stdev=0.41)
Avec un td =0.065, 2s représente 30x le temps de demi-recouvrement ce qui est suffisant.
Comparaison Soumpasis : D=1.03 um²s-1 (stdev=0.07) sur 2s Meilleur car moins de paramètres de fit, les paramètres sont corrélées !
Temps de recouvrement =1s Temps de recouvrement=10std=0.25 s ! td=0.2sOn ne peut pas conclure sur 1 courbe =>faire de la stat
Sur un recouvrement de 2s et w=0.5um, on trouve : D=1.03 um²s-1 (stdev=0.07, moyenne sur 30 valeurs )
5) Mod5) Modèèle dele de SoumpasisSoumpasis : analyse d: analyse d’’un profil carrun profil carréé
6) FRAP en mode 6) FRAP en mode confocalconfocal ::
Facile à mettre en œuvre mais difficile à quantifier•FRAP puis mesure de la cellule entière
•FLIP pour la détermination connexion entre compartiments
•Line FRAP (« bleach » de bande, diffusion 1D)
Différences avec le mode spot:
(i)Temps de bleach plus long car la surface est plus grande
Possibilité de recouvrement pendant le « bleach »
(ii) Temps de recouvrement plus long
Possibilité de mouvement cellulaire pendant la mesure
(iii)Temps de mesure plus long
Processus d’échange membrane/cytoplasme
6) FRAP en mode 6) FRAP en mode confocalconfocal : Line FRAP: Line FRAP
FRAP avec GFP-L236P dans la membrane du R-E (d’après Lippincott-Schwartz)
7) FLIP en mode 7) FLIP en mode confocalconfocal ::
FRAP répétitifs sur deux molécules exprimées dans le R-E révèlent différents mécanisme de rétention (résidus de fluorescence).(d’après Lippincott-Schwartz)
8) FRAP pour 8) FRAP pour éétudiertudier les interactions entre les interactions entre protprotééinesines ::
--FRAPFRAP beambeam--size:size:Utilisation de deux « »waists » de laser (objectifs 40x et 63x)
« Pure lateral diffusion » : τ =τd proportionnel à w²/4D (rapport =2.56)
« Dynamic exchange » : τ ne dépend pas de la taille du faisceau (rapport=1)
--FRAPFRAP GaussienGaussien :: Analyse du profile dAnalyse du profile d’’intensitintensitéé ::
Bo = profondeur de bleachWo = largeur de la Gaussienne à t=0 Io= Intensité moyenne avant le bleach
Sigma²(t)=4.D.t+W0²
FRAPFRAP GaussienGaussien ::
Fit de D : analyse de la pente de sigma Fit de tau : analyse de la hauteur de la gaussienneaprès avoir injecté sigma trouvé précédemment :Fit en exp(-t/tau)
•Faire un « timelapse » pour déterminer la puissance laser qui ne provoque pas de « bleaching « conséquent (autours de 0.1% à 1% du laser).
•Optimiser la vitesse d’acquisition, l’ouverture du pinhole, la puissance laser et la taille du pixel pour obtenir un signal/bruit satisfaisant.
•Vérifier que le temps de « bleach » est très inférieur au temps de recouvrement de la moléculeTemps de bleach= 100ms pour une itération du laser sur un confocal ZeissD= 0.01 um²/s pour une protéine membranaire
•Vérifier que le temps d’enregistrement est égal à environ >20 fois le temps de demi-recouvrement de la molécule.
Conclusion : Conclusion :
FRAP/FLIP confocal:
Trafic intracellulaireMesure de la fraction mobile Diffusion macroscopique (moyenne entre diffusions microscopiques, réactions chimiques et échange entre compartiments)Forte concentration de marqueurs
Attention à l’interprétation du coefficient de diffusion D mesuré qui peut être de 10 à 100x supérieur sur un montage confocal commercial (temps d’acquisition, de bleach,..)
42
Chapter 3
Advances in Fluorescence CorrelationSpectroscopy
43
44
What is FCS ?Homemade or Commercial ?
FCS DerivatesImage Correlation techniques
Advances in Fluorescence Correlation Spectroscopy
Sébastien MAILFERT
October, 2010
Atelier INSERM, October 2010
What is FCS ?Homemade or Commercial ?
FCS DerivatesImage Correlation techniques
General PurposeConfocal based microscopyAuto-correlation analysisApplicationsLimitations
Summary
1 What is FCS ?General PurposeConfocal based microscopyAuto-correlation analysisApplicationsLimitations
2 Homemade or Commercial ?Optical SchemeHow to build your own FCS setup ?Market availability
3 FCS DerivatessvFCSFCCSScanning FCS
4 Image Correlation techniquesICSRICSSTICS
Atelier INSERM, October 2010
What is FCS ?Homemade or Commercial ?
FCS DerivatesImage Correlation techniques
General PurposeConfocal based microscopyAuto-correlation analysisApplicationsLimitations
General Purpose 3 / 24
• Single Molecule detection technique : recordind and computing fluorescence correlation withina small volume
• High spatio-temporal accuracy
Atelier INSERM, October 2010
Notes
Notes
Notes
What is FCS ?Homemade or Commercial ?
FCS DerivatesImage Correlation techniques
General PurposeConfocal based microscopyAuto-correlation analysisApplicationsLimitations
General Purpose 3 / 24
Click here
Atelier INSERM, October 2010
What is FCS ?Homemade or Commercial ?
FCS DerivatesImage Correlation techniques
General PurposeConfocal based microscopyAuto-correlation analysisApplicationsLimitations
General Purpose 4 / 24
Confocal measurement
� Fluorescence fluctuations analysis� Confocal spot : ωxy from 200 to
400 nm� Two main parameters :
1 Mean number of molecules :N
2 Mean diffusion time : τd
Advantages
� Low excitation power (few kW/s2)� Low numbers of molecules (from 1 to 100)� Physiological conditions @ 37◦C� Living cells� High spatio-temporal resolution (μs to s, 200 to 400 nm)� Photophysical aspects : triplet state, free diffusion (2D,
3D), active transport velocity, rotational motion, etc.
Atelier INSERM, October 2010
What is FCS ?Homemade or Commercial ?
FCS DerivatesImage Correlation techniques
General PurposeConfocal based microscopyAuto-correlation analysisApplicationsLimitations
Confocal based microscopy 5 / 24
� Excitation laser (green beamer here) focused with a high Numerical aperture (NA) microscopeobjective
� Excitation and fluorescence separated by a dichroïc mirror� Fluorescence at the focus plane selected by a pinhole (few μm typ.)� One point detector (Avalanche photodiode or photomultiplicator tube)
Excitation volume : 3D Gaussian, few femtoliter
V = π3/2ωxyωz
Click here !
Atelier INSERM, October 2010
Notes
Notes
Notes
What is FCS ?Homemade or Commercial ?
FCS DerivatesImage Correlation techniques
General PurposeConfocal based microscopyAuto-correlation analysisApplicationsLimitations
Auto-correlation analysis 6 / 24
Self-similarity analysis : signal is compared to itself after a lag time τ
The normalized autocorrelation function is defined as :
G(τ) =〈δF(t)δF(t + τ)〉
〈F(t)〉2
G(0) =1N
=1
Veff〈C〉Relative fluctuations become smaller with increasing numbers of fluorescent particles
≈ 10−10M to ≈ 10−6M
Atelier INSERM, October 2010
What is FCS ?Homemade or Commercial ?
FCS DerivatesImage Correlation techniques
General PurposeConfocal based microscopyAuto-correlation analysisApplicationsLimitations
Auto-correlation analysis 6 / 24
Different equations for different samples
Mobility (1 species, 3D diffusion) :
G(τ) = 1 +1N
1(1 +
τ
τd
) √1 + s2 τ
τd
Mobility (1 species, 3D diffusion) & Triplet blinking :
G(τ) = 1 +
⎛⎜⎜⎜⎜⎜⎜⎜⎜⎝1 − T + Te− ττT
⎞⎟⎟⎟⎟⎟⎟⎟⎟⎠1N
1(1 +
τ
τd
) √1 + s2 τ
τd
Mobility (2 species, 2D/3D diffusion) :
G(τ) = 1 +1N
⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝A(
1 +τ
τd1
) +1 − A(
1 +τ
τd2
) √1 + s2 τ
τd2
⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠
Atelier INSERM, October 2010
What is FCS ?Homemade or Commercial ?
FCS DerivatesImage Correlation techniques
General PurposeConfocal based microscopyAuto-correlation analysisApplicationsLimitations
Auto-correlation analysis 6 / 24
Example : 2 species, 3D (τd1 = 200μs) + 2D (τd2 = 200ms)
2.0
1.8
1.6
1.4
1.2
1.0
Aut
ocor
rela
tion
Func
tion:
G(
)
10-5 10-4 10-3 10-2 10-1 100 101
Lag Time (s)
Atelier INSERM, October 2010
Notes
Notes
Notes
What is FCS ?Homemade or Commercial ?
FCS DerivatesImage Correlation techniques
General PurposeConfocal based microscopyAuto-correlation analysisApplicationsLimitations
Applications 7 / 24
� Dyes : fluorescent proteins, inorganic dyes, etc.� Samples : on living cells, every cellular compartment could be analysed� Optical setup : easy to implement on a confocal microscope
� Size : hydrodynamic radius calculated from D =kT
6πηV Rhwith Rh = 3
√3m
NA 4πρ� Reaction kinetics� Membrane organization : see svFCS� Interactions : see FCCS
Atelier INSERM, October 2010
What is FCS ?Homemade or Commercial ?
FCS DerivatesImage Correlation techniques
General PurposeConfocal based microscopyAuto-correlation analysisApplicationsLimitations
Limitations 8 / 24
• Higher sensitivity to low probe concentration• Higher sensitivity to fast events (μs to ms)• Diffraction limit• Diffusion coefficients available : 0.1 to 10 μm2/s• Difficult to discriminate 2 populations with similar diffusion time
Atelier INSERM, October 2010
What is FCS ?Homemade or Commercial ?
FCS DerivatesImage Correlation techniques
Optical SchemeHow to build your own FCS setup ?Market availability
Summary
1 What is FCS ?General PurposeConfocal based microscopyAuto-correlation analysisApplicationsLimitations
2 Homemade or Commercial ?Optical SchemeHow to build your own FCS setup ?Market availability
3 FCS DerivatessvFCSFCCSScanning FCS
4 Image Correlation techniquesICSRICSSTICS
Atelier INSERM, October 2010
Notes
Notes
Notes
What is FCS ?Homemade or Commercial ?
FCS DerivatesImage Correlation techniques
Optical SchemeHow to build your own FCS setup ?Market availability
Optical setup 10 / 24
Atelier INSERM, October 2010
What is FCS ?Homemade or Commercial ?
FCS DerivatesImage Correlation techniques
Optical SchemeHow to build your own FCS setup ?Market availability
How to build your own FCS setup ? 11 / 24
Excitation : 1PE (i.e. argon or HeNe laser, fewmW are needed) or 2PE (i.e. IR pulsed laser)
Atelier INSERM, October 2010
What is FCS ?Homemade or Commercial ?
FCS DerivatesImage Correlation techniques
Optical SchemeHow to build your own FCS setup ?Market availability
How to build your own FCS setup ? 11 / 24
Objective : high NA (typ. 40X, C-Apochromat,NA=1.2, Water immersion, Zeiss), hightransmission, avoid achromatism & asphericalaberrations
Atelier INSERM, October 2010
Notes
Notes
Notes
What is FCS ?Homemade or Commercial ?
FCS DerivatesImage Correlation techniques
Optical SchemeHow to build your own FCS setup ?Market availability
How to build your own FCS setup ? 11 / 24
Optics : achromatic (i.e. Newport optics)
Atelier INSERM, October 2010
What is FCS ?Homemade or Commercial ?
FCS DerivatesImage Correlation techniques
Optical SchemeHow to build your own FCS setup ?Market availability
How to build your own FCS setup ? 11 / 24
Filters and dichroïc mirrors : highly selective,flat & thick mirrors to avoid beam distortions (i.e.Chroma filters)
Atelier INSERM, October 2010
What is FCS ?Homemade or Commercial ?
FCS DerivatesImage Correlation techniques
Optical SchemeHow to build your own FCS setup ?Market availability
How to build your own FCS setup ? 11 / 24
Pinhole : typ. 50μm, could be a simple multimodeoptical fiber
Atelier INSERM, October 2010
Notes
Notes
Notes
What is FCS ?Homemade or Commercial ?
FCS DerivatesImage Correlation techniques
Optical SchemeHow to build your own FCS setup ?Market availability
How to build your own FCS setup ? 11 / 24
Detectors : single photon sensitivity, low darknoise (i.e. APDs or PMT)
Atelier INSERM, October 2010
What is FCS ?Homemade or Commercial ?
FCS DerivatesImage Correlation techniques
Optical SchemeHow to build your own FCS setup ?Market availability
How to build your own FCS setup ? 11 / 24
Correlator : hardware (i.e. ALV or Correlator.com)or software (homemade with fast acquisitionboard)
Atelier INSERM, October 2010
What is FCS ?Homemade or Commercial ?
FCS DerivatesImage Correlation techniques
Optical SchemeHow to build your own FCS setup ?Market availability
How to build your own FCS setup ? 11 / 24
XYZ scanner : 2D imaging and spot positioning,nm accuracy (i.e. Physik Instrumente or Mad CityLabs)
Atelier INSERM, October 2010
Notes
Notes
Notes
What is FCS ?Homemade or Commercial ?
FCS DerivatesImage Correlation techniques
Optical SchemeHow to build your own FCS setup ?Market availability
How to build your own FCS setup ? 11 / 24
Microscope : motorized
Atelier INSERM, October 2010
What is FCS ?Homemade or Commercial ?
FCS DerivatesImage Correlation techniques
Optical SchemeHow to build your own FCS setup ?Market availability
Lippincott-Schwartz et al. Nat Rev Mol Cell Biol 2001
On which spatio-temporal scale these heterogeneities take place?
What are the major determinants dictating their organization?
What are the functional implications?
Lateral diffusion in the plasma membrane Lateral diffusion in the plasma membrane
mesoscopic assembly of aggregated molecules (~1012 molecules)
build up by weak interactions to produce a cooperative phenomena
non-random & non-uniform lateral organization
Why expecting local Why expecting local heterogeneities?heterogeneities?
IntersectionIntersection in Hanoi Vietnamin Hanoi Vietnam
Stochastic motions? Interactions?
Toward a cartography of Toward a cartography of membrane dynamicsmembrane dynamics
100 nm
confinementSPT -> global measure with local accuracy-> overall spatiotemporal dynamics-> cartography of heterogeneities
Jacobson et al. Science 1995
in the nanometer range, heterogeneities are weakly characterized
Small & dynamic structures
experimentally difficult to access
In 1827, the botanist Robert Brown observed the erratic motionof pollen particles on water. This was not strictly diffusion, sincethe particle is macroscopic, but this random walk, hence namedBrownian motion, will be used as a model system for diffusion.
In 1855, Adolph Fick propose empirical laws, in analogy with Fourier forheat and Ohm laws for electricity.
The flux of diffusion is proportional to the gradient of concentration, hence,in one dimension:
Albert Einstein demonstrates Fick’s laws and theirmolecular origin in 1905 with his work on stochasticity.
In 1908, Jean Perrin, funder of the CNRS and Nobel price in physics,achieved the first measure of trajectories of particles undergoingBrownian motion, hence confirming Einstein theory.
Louis Bachelier, in his thesis in 1900, demonstrated that it is not themean of the displacements <r> which characterizes the motion, butthemean square (in dimension n) :
<r²> = 2nDt
R: ideal gas constantT: temperatureNA: Avogadro number: viscosity
Major modifications brought to the fluid mosaic model.Size, composition, dynamics, physiological relevance of those structures ?
Dynamic map ?
SubSub--membranemembrane actinactin cortexcortex
Thomishige et al. 1998
50 - 700 nm ?
Lipid raftsLipid rafts
NanoNano--domains probed by FCSdomains probed by FCS
FCS has revealed the presence of dynamic confinement,related to • lipid nanodomains• actin meshworkWith confinement duration of a few tens of ms.
Wawrezinieck et al. Biophys J. 2005Lenne*, Wawrezinieck* et al. EMBO J. 2006 Wenger et al. Biophys J. 2006 Lasserre*, Guo*, Conchonaud* et al. Nature Chem .Biol. 2008
Single molecule on live cellsSingle molecule on live cellsDMPE-Cy5 and DOPE-Cy3in muscle cells
Detection of fluorescence peaks in each image, by test between hypotheses,then local adjustment with a Gaussian, leading to• peak intensity (-> stoichiometry)• position (-> trajectories & diffusion) with sub-pixel precision.
width intensity
offset+/- noise
Position x, y
mr
m
H0 hypothesis: no target
H1 hypothesis: presence of a centered Gaussian
?
?
Detection improvement by deflationDetection improvement by deflationRaw image
1st deflated image
Detected peaks
2nd deflated image
last deflated image
Deflated Gaussiansinitial datafirst fit
deflated datasecond fitsubtracted peak
Deflation allows to detect “hidden” peaks.
Detection becomes ~ exhaustive, reconnection is thus facilitated.
PIC
Evaluation of detectionEvaluation of detection
vs. fluo SNR vs. particles density
SNR density
Simulateddata
Evaluation of estimationEvaluation of estimation
MTT computation on MTT computation on experimental data experimental data
3rmax
3rmaxtblink1/2
P(x1,y1,I1,b1 | x2…)
Reconnecting peaksReconnecting peaks
Trajectory
Intensity
xn-1yn-1<r> = rlocal
x
y
Past information
<Ion>Ion
blink state
t
I fullon
fastblink
fulloff
<Ion>
Statistical laws
r
Pdiff
rmax
rlocal
2 Gaussians, for local & max. diffusion
t
Poff
off 3 off
Off: expo. decayBlink: equi-proba. On: Gaussian law
I
Pint
<Ion>
Reconnection test
xn-1
yn-1
3rlocal
3rmax
x
ySearch area
Use of past information for reconnectionUse of past information for reconnection
Connecting peaksConnecting peaks
ntrc > npk (blink @ t+1)
t
t+1
ntrc = npk (no blink)
t
t+1
ntrc = npk (multi-blink)
tblink
t
t+1
ntrc < npk (blink before t)
tblink
t
t+1
Diffusion Evaluation Tracing efficiency
Evaluation of connectionEvaluation of connection
Mean Square Displacement computationMean Square Displacement computation
MSD(3 t) = <MnMn+32>
MSD(2 t) = <MnMn+22>
MSD( t) = <MnMn+12>
1
2
3
4
5
67
MSD(4 t) = <MnMn+42>
...
…
MSD = <r2> Averaged over every possible step of the trajectory
t
MSD
1 2 3 4 …
MSD allows to discriminate between several MSD allows to discriminate between several characteristic movementscharacteristic movements
• Pure Brownian diffusionFick’s 2nd law gives<r2> = 4Dt
• Diffusive and linear movement
<r2> = v2t2+4Dt
• Confined movement
<r2> = Kusumi et al. Biophys. J. 1993
• Anomalous diffusion (with obstacles)
<r2> = 4Dt , < 1
• Rotative (or confined) and lateral diffusion
<r2> = 2R2{1-exp(-Drott)}+4DlattSergé et al. J. Neuro. 2002
R
R
t
MSD
odd,1n2
22
44
22
)R4Dtnexp(n
1R1283R4
Confinement Confinement detectiondetection
=> Succession of free& confined events
Detailed inspection of dynamics fluctuations in time, within each trace.
Confinement cartographyConfinement cartography
freeconfined
conf. level Lconf
10 μm 10 μm
MTT at increased acquisition rate MTT at increased acquisition rate