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Many molecular processes taking place in living cells can be visu-alized1,2 by using genetically encoded fluorescent probes (usuallyrelying on various fluorescent proteins) and techniques of f luores-cence microscopy, such as fluorescence resonance energy trans-fer (FRET), fluorescence lifetime imaging, fluorescence recoveryafter photobleaching or fluorescence anisotropy imaging3,4. While
developing a genetically encoded probe of cell membrane voltage,we decided to investigate whether anisotropic optical propertiesof fluorescent proteins could be used to observe molecular proc-esses involving membrane proteins.
Optical properties of most molecules are anisotropic. Forsingle-photon electronic absorption, the absorption propertiesof a molecule are characterized by a vector, called the transitiondipole moment (TDM). The rate of light absorption by a moleculeis proportional to the squared cosine of the angle between theelectric field vector (polarization) of the excitation beam andthe TDM vector of the molecule5. The TDM direction thereforerepresents, in the reference frame of the molecule, the directionof excitation light polarization with maximum absorption rate.
To our knowledge, the direction of only one fluorescent proteinsTDM has been determined6. Two-photon absorption is describedby an absorptivity tensor, and effects of molecular orientationare generally complex7. For some molecules (rod-like)8, how-ever, two-photon absorption rate is proportional to the cosineto the fourth power of the angle between the excitation light
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Josef Lazar14, Alexey Bondar1,2, Stepan Timr5 & Stuart J Firestein4
polarization and a vector (which we here term two-photonpseudo-TDM) describing the molecular orientation. Little isknown about fluorescent-protein absorptivity tensors, but GFPhas been shown6,9, in vitro, to exhibit anisotropic two-photonabsorption. Light emission is characterized by another TDM
(often similar in orientation to the excitation TDM), with fluores-cence preferentially emitted in directions perpendicular to theemission TDM and polarized in a TDM-containing plane.
Anisotropic optical properties of molecules can be observedin orientationally biased molecular assemblies. The cell mem-brane can provide sufficient orientational bias to dye molecules10,but fluorescent protein optical properties, linker flexibility andlimited photon counts might prevent observing anisotropicproperties in fluorescent proteinlabeled membrane proteins.Molecular rotation between excitation and emission, differencesbetween excitation and emission TDMs, and depolarization byan objective lens can hamper observations of fluorescence polari-zation. They should, however, have little effect on observing
dependence of fluorescence intensity on direction of excitationlight polarization or linear dichroism (LD).
Here we show that LD can indeed be observed in manyfluorescent proteintagged membrane proteins by two-photonpolarization microscopy (2PPM). The 2PPM technique pro-
vides information on molecular orientation and can be used forsensitive monitoring and quantification of protein-proteininteractions and conformational changes. We illustrate its usesby monitoring G-protein activation and changes in intracellularcalcium concentration.
results
maaa g
To investigate the possibility of using anisotropic proper-ties of fluorescent proteins to observe cellular processes, wedeveloped a mathematical model based on geometrical optics(Supplementary Fig. 1). We modeled absorption11 of a sphericalcell (approximating an oocyte, a yeast cell, a protoplast or, crudely,a mammalian cell) and a cylindrical cell (a generic elongated cell,
1Laboratory of Cell Biology, Institute of Nanobiology and Structural Biology, Global Change Research Centre, Academy of Sciences of the Czech Republic, Nove Hrady,Czech Republic. 2Department of Systems Biology, Institute of Physical Biology, University of South Bohemia, Nove Hrady, Czech Republic. 3Department of Biochemistryand Molecular Biology, Faculty of Sciences, University of South Bohemia, Ceske Budejovice, Czech Republic. 4Department of Biological Sciences, Columbia University,New York, New York, USA. 5Department of Physics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague, Czech Republic.Correspondence should be addressed to J.L. ([email protected]).
Received 13 ApRil 2010; Accepted 17 MAy 2011; published online 3 July 2011; doi:10.1038/nMeth.1643
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a neuronal projection or a small section of an irregularly shapedcell). We kept the TDMs of fluorophore moieties attached tothe cell membrane either at a fixed angle 0 with respect to thecell membrane or modeled them as a Gaussian distribution ofangles , with a mean of0 and an s.d. (), to consider proteindynamics, conformational flexibility and nanoscopic membraneroughness. Our models for single-photon (Fig. 1) and two-
photon (Supplementary Fig. 2) linearly polarized excitationshowed that 0 can have notable effects on both the appearanceof fluorescently labeled cells and on the amount of observed fluo-rescence (Fig. 1a,b). We visualized differences in absorption oflight with distinct polarizations, or linear dichroism, by coloringfluorescence generated with horizontal polarization (Fh) magentaand fluorescence generated with vertical polarization (Fv) green(Fig. 1c,d). Conveniently, the hue of a pixel then directlyexpressed the dichroic ratio, r(r= Fh/Fv). We used ras a measureof LD, owing to its simplicity, experimental accessibility with littleimage processing and closeness of the log(r) distribution to a normaldistribution (allowing facile statistical analysis). A deviation ofrfrom 1 (and log(r) from 0) signified presence of LD.
Our model showed (Fig. 1e) that LD should be observ-able under a variety of suboptimal circumstances (includingmembrane roughness and protein confor-mational flexibility). In fact, absence of LDshould be an exception, generally occur-ring only for 0 = 54.7 for single-photonand 52.0 for two-photon absorption(so-called magic angle of fluorescenceanisotropy) and for very disordered fluoro-phore orientations. Our model also showed(Fig. 1f) that even if the distribution ofTDM tilt angles is wide ( = 20), a 1change in 0 (the mean TDM tilt) should
cause a 24% change in r(12% changes in
both Fh and Fv, in opposite directions). Fluorescence of constructswith TDM close to perpendicular to the cell membrane shouldbe particularly sensitive to changes in 0. Results for two-photon excitation (Supplementary Fig. 2) were similar to thoseobtained for single-photon excitation, with more pronounced LDapparent (typically about two times higher rand r/r). However,reliability of our two-photon model is limited because of approxi-
mations that had to be made in virtually complete absence ofinformation on the nature of two-photon absorptivity tensors influorescent proteins.
In summary, our mathematical model predicts that LD shouldbe widespread among fluorescently tagged membrane proteins,and it should be observable by single-photon polarization micros-copy and 2PPM. Even small changes in orientation of the fluo-rescent moiety should lead to observable changes in LD. Owingto the monotonic relationship between rand 0, with knowledgeof fluorescent protein TDMs and other parameters, it shouldbe possible to use polarization microscopy to gain quantitativeinsights into membrane protein structure and function. Thus,polarization microscopy should allow observation of a range of
molecular processes taking place in living cells and rational designof sensitive optical probes of these processes.
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Fg | Mathematical models. (a,b) Simulatedimages o a luorescently labeled spherical cell(a) and cylindrical cell (b) shown as projectionso a single-photon conocalz-dimensionstack, or luorophore tilt angle 0 values 0,22.5, 45, 67.5 and 90 (let to right).(,) Simulated images or a sphericalcell () and cylindrical cell () showingluorescence excited by horizontally andvertically polarized light (Fh and Fv) coloredmagenta and green, respectively. Nongraycolor (excess o magenta or green) indicates
presence o LD. Direction o polarization andcoloring o corresponding luorescence isindicated by double-headed arrows. Orientationo the luorophore with respect to the cellmembrane (tilt angle 0) is indicated by theschematics in bottom right corners o individualimages. () LD, expressed as r= Fh/Fv andlog2(r), as a unction o mean luorophoretilt angle 0, or dierent widths (describedby ) o distribution o, or the cylindricalcell in . () Fractional changes in dichroicratio (r/r) o the cylindrical cell in and upon a change in mean tilt angle 0 by 1,or a range o starting tilt angles 0and tilt angle .
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F p a v
To test whether anisotropic effects predicted by our mathematicalmodel could be observed, we carried out measurements in livingcells (Fig. 2) on a construct termed doubly lipidated enhancedGFP (dleGFP)12 and constructs derived from it. DleGFP consistsof GFP and two lipophilic cell membrane targeting tags, thought toanchor the fluorescent protein to the cel l membrane in an almost
fixed orientation, with the fluorophore (and the single-photonTDM) close to perpendicular to the cell membrane (Fig. 2a).
When we observed cells expressing dleGFP using a wide-fieldfluorescence microscope with a polarizer placed in the excita-tion path, we discerned only subtle differences between imagesacquired with different polarizations (data not shown). Whenwe used a single-photon laser-scanning confocal microscope, weobserved anisotropic effects consistent with our mathematicalmodel (Fig. 2bf). These effects, however, were not particularlypronounced: the maximum observed dichroic ratio, rmax = (Fh/Fv)max, was 2.5 (15 cells). In contrast, when we used two-photonexcitation (Supplementary Fig. 3) to observe dleGFP-expressingcells, the observed LD was notable (rmax > 15, 200 cells, Fig. 2gk,
Supplementary Fig. 4 and Supplementary Video 1), consistentwith the pseudo-TDM orientation close to perpendicular to thecell membrane. In all cases, we also observed weak polarizationof the emitted fluorescence (data not shown). To confirm that itwas indeed the fixed orientation of the fluorophore that causedthe apparent LD, we created and examined, using 2PPM, twoconstructs based on dleGFP: internally lipidated eGFP (ileGFP)and C-terminally lipidated eGFP (cleGFP) (Fig. 2lo). Each ofthese contructs contained only one of the two original membrane-targeting tags, which presumably would not be sufficient to maintaina fixed orientation of the GFP moiety. Whereas cleGFP absorptionappeared isotropic (rmax < 1.1, 25 cells), ileGFP showed distinctLD (rmax = 6, 32 cells; two-photon pseudo-TDM close to perpen-
dicular to the cell membrane). Thus, the anisotropic phenomena
observed in dleGFP were indeed due to the orientation of thefluorophore. Furthermore, the LD observed in ileGFP, withfluorophore orientation likely only partly restricted because ofmembrane linkage through a loop region, was consistent withour mathematical model predicting that LD should be observ-able even in such cases. Membrane attachment through a flexibleC terminus (in cleGFP) did not give rise to LD.
Our results indicate that the sectioning ability of single-photonconfocal and two-photon imaging is beneficial for observationsof LD. The observed difference between single-photon and two-photon LD is likely due to nonlinearity of the two-photon exci-tation process (suppressing excitation by sides of the focal areacontaining unwanted polarizations), lower sensitivity of the two-photon polarization setup to minor alignment errors and stricterorientational requirements of two-photon excitation. Differentorientations of the single-photon TDM and two-photon pseudo-TDM in the eGFP molecule are also a possibility. Thus, likely fora combination of reasons, two-photon polarization fluorescencemicroscopy with non-descanned detection appears to reportfluorescent protein LD with markedly higher sensitivity than single-
photon microscopy. Our observations of LD in living mammaliancells using one-photon polarization microscopy and better using2PPM validate our mathematical model.
iagg p-p a: G-p px
To test whether 2PPM of fluorescently labeled membrane pro-teins can report on protein-protein interactions in living cells,we focused on processes involving heterotrimeric G proteins(composed of G, G and G subunits). Because there arefunctional, fluorescent proteinlabeled constructs available, weperformed most of our experiments on fluorescent proteintagged G subunits, particularly of the Gi-Go family. Weinvestigated 14 different Gi and Go constructs (Fig. 3 and
Supplementary Table 1).
DleGFP
CleGFPIleGFP
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Fg | Proo o principle. (a) Schematico the dleGFP construct. (b) Single-photonconocal images o a dleGFP-expressing cell.Direction o polarization and coloring ocorresponding luorescence is indicated as inFg . Shown are projections oz-dimensionstacks acquired with excitation light polarizedhorizontally (b) and vertically (); a compositeo images in b and colored magenta and green,respectively, without any color lookup table(LUT) adjustment (); a single conocal sliceo the same cell (); and the same image as
in , but ater application o an LUT suitableor displaying the range o dichroic ratio rinthe image (12.5; pixels exceeding this rangeappear pure magenta or pure green; only a smallnumber o such pixels are visible, indicating thatrmax = (Fh/Fv)max = ~2.5) (). (g) Images as inbbut acquired using two-photon excitation.() Schematic o the ileGFP construct. () Atwo-photon section o an ileGFP-expressing cell,processed as in but with a color scale coveringa narrower range o values as indicated.() Schematic o the cleGFP construct. () Atwo-photon section o a cleGFP-expressing cell,processed as in but with a dierent color scaleas indicated. All scale bars, 5 m.
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On the basis of LD, we could distinguish three distinctcategories of fluorescent proteinlabeled Gi-Go constructs.Constructs were named either as G subunit name followedby a fluorescent protein insertion site location and proteinname or as N-terminal tag name (GAP43) followed by a fluores-cent protein name and G subunit name. Two constructs (Gi2-Leu91-YFP13 and Go-Gly92-CFP
14) did not exhibit LD (rmax < 1.1)when overexpressed alone or when expressed together withG1 and G2. Another four constructs (Gi1-Leu91-CFP
15,Gi1-Leu91-YFP
16, Gi3-Leu91-YFP13 and Gi1-Ala114-YFP
17)showed pronounced LD (rmax = 26) both when expressed
alone and when expressed together with G1 and G2. A thirdgroup of constructs (GAP43-CFP-Gi1 (ref. 18), GAP43-CFP-Gi2 (ref. 18), GAP43-CFP-Gi3 (ref. 18) and Go-Leu91-YFP13) showed little or no LD when overexpressed alone butdistinct LD (rmax = 1.53) when expressed together with G1and G2.
These results illustrate structural differ-ences between the investigated constructs,even between constructs of similar overallamino acid sequences (Gi1-Leu91-YFP
16,Gi2-Leu91-YFP
13 and Go-Leu91-YFP13).
These structural differences are consist-ent with amino acid sequence diversity in
vicinity of the insertion site (the a-b loopregion) as well as with known19 functionaldifferences within this group of G subu-nits. Our results also support existenceof a physical interaction between at leastfour of the overexpressed fluorescent pro-teintagged G constructs and the overex-pressed G and Gsubunits (presumablyforming a Gcomplex), and suggest that2PPM can be used to monitor protein-protein interactions in live cells.
To ascertain whether the observedinteractions were physiological and not
an artifact owing to presence of multipleproteins overexpressed at high levels, we
carried out a series of G-protein activation experiments. Weexpressed four constructs together: a Gfluorescent protein,G1, G2 and a suitable G proteincoupled receptor (GPCR; typi-cally, the 2a adrenergic receptor tagged with YFP or CFP). Wethen activated the overexpressed receptor with an agonist (nore-pinephrine). Little or no changes in LD upon receptor activationcould be seen in G constructs lacking LD and in constructsshowing high LD both in absence and presence of G(data notshown). In contrast, all four Gfluorescent protein constructsthat showed differing amounts of LD in absence and in presenceof overexpressed G exhibited changes in LD upon receptor
activation (>10 cells examined for each construct, >80% cellsshowing responses; Fig. 4, Supplementary Videos 2 and 3and data not shown). Changes in LD in fluorescent proteintagged subunits could only be observed in cells in which expres-sion of a receptor (fluorescently labeled) was detectable. TheGo-Leu91-YFP
13 construct showed complete disappearance
r
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Fg | 2PPM imaging o G-protein complexes. (a) Images o cells expressing luorescentlytagged G subunits GAP43-CFP-Gi2 (a), Gi2-Leu91-YFP (b), Go-Leu91-YFP () and Gi1-Leu91-YFP (). () Images o the same G subunits as in a but expressed together with G1 and G2.Coloring is as in Fg . Scale bars, 5 m.
Fg | 2PPM imaging o G-proteinactivation. (a) Cyan luorescence o acell expressing GAP43-CFP-Gi2, G1,G2 and 2a-adrenergic receptor-YFPbeore addition o norepinephrine (let),ater addition o norepinephrine (center)
and ater removal o norepinephrine(right). Coloring is as in Fg a .(b) Plot o LD (expressed as rand log2(r)) othe GAP43-CFP-Gi2expressing cell in a, as aunction o time. Triangles and squares denotedata rom the indicated horizontally andvertically oriented sections o the membrane,respectively. Dashed traces indicate s.e.m.,n = 110160 pixels. The 10-s period opresence o norepinephrine is indicated bya bar (top let). () Yellow luorescence o acell expressing Go-Leu91-YFP, G1, G2 and2aadrenergic receptorCFP beore additiono norepinephrine (let), ater addition o norepinephrine (center) and ater removal o norepinephrine (right). () Plot as in b but or theGo-Leu91-YFPexpressing cell in (n = 90160 pixels). All scale bars, 5 m.
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of LD, consistent with dissociation of the G-G-Gcomplex.In contrast, the fluorescent proteintagged Gi subunits typicallyshowed only a decrease, not complete disappearance of LDupon activation, consistent either with incomplete (~80%)activation (Supplementary Note) or with rearrangement16(rather than dissociation17,20) of the G-protein complex uponactivation. Notably, a constitutively active mutant21 (Q204L) ofGi1-Leu91-YFP
16 showed significantly higher LD (P< 0.001)when expressed together with G and G(rmax = 2.8, 0 > 52,25 cells) than when expressed alone (rmax = 2.0, 0 > 52, 30 cells),providing strong evidence for existence of a G-protein trimer inactivated Gi subunits.
Our results show that it is possible to use 2PPM to visualizephysical interactions between subunits of heterotrimeric G proteins.The observed molecular interactions are physiological: that is,in presence of a suitable GPCR (and only in its presence) theyrespond to presence of a receptor agonist, in a fashion consistentwith current knowledge. The size of the responses observed duringG-protein activation is remarkable:F/Fof up to 50% in a particularchannel. In comparison, only ~2% changes in donor fluorescenceand 10% in acceptor fluorescence have been reported16 for FRETbetween Gfluorescent protein and Gfluorescent protein sub-units. Sensitivity of 2PPM is such that it should allow distinguish-ing between resting and activated states of the current Gi-Goconstructs within 200 s (Supplementary Discussion). Thus,
2PPM permits visualization of protein-protein interactions in liv-ing cells, yielding insights into molecular mechanisms of G-proteinactivation and allowing monitoring the process of activation ofGPCRs in live cells, in real time, with very high sensitivity.
iagg ag p a: a agg
To test the ability of 2PPM to report conformational changes inmembrane proteins, we used 2PPM to image changes in intracel-lular calcium concentration. Several lines of genetically encodedcalcium indicators have become commonly used22. Two of them(Cameleon-based23 and troponin-based24) rely on conformationalchanges reported by FRET. One of the cameleon sensors, lynD-3cpV25, is membrane-tethered. It consists of a calcium-sensing
domain sandwiched between two fluorescent proteins (CFP andcircular permuted (cp)Venus). About 30% changes in both donorand acceptor fluorescence have been reported for lynD3cpV uponan intracellular calcium concentration increase25.
Our 2PPM lynD3cpV observations (Fig. 5 and SupplementaryTable 2) showed that at low calcium concentrations, the CFPmoiety is in a fairly well-defined orientation with respect tothe cell membrane (rmax = 1.5; Fig. 5a). In contrast, the cpVenus moiety showed little LD (rmax = 1.07) in resting state cells.Upon an increase in intracellular calcium concentration throughstimulation by ATP, LD in cpVenus increased (rmax = 1.2).Upon removal of ATP, cpVenus LD returned to original values
(Fig. 5b,c and Supplementary Video 4). LD of CFP remainedconstant (data not shown). Calibration of cpVenus LD bycontrolling intracellular calcium concentration allowed char-acterization of the construct (saturated cpVenus rmax = 1.42,dissociation constant (Kd) = 0.64 M, Hill coefficient of 3.0;Supplementary Note) and determination of calcium concen-trations during ATP stimulation (0.40.6 M in different cells;mean = 0.495 M; rmax = 1.151.20) (Fig. 5d). These valuesare in very good agreement with results we obtained by FRET(Kd = 0.71 M, Hill coefficient of 2.6, ATP-induced calciumconcentrations 0.40.6 M, with mean of 0.505 M), althoughthe confidence intervals for calcium concentration valuesdetermined in individual cells were considerably larger in
2PPM experiments than in FRET experiments (Fig. 5d andSupplementary Discussion).
Our results are consistent with the lynD3cpV design anddemonstrate that even small changes in LD can be reproduciblyobserved, quantified and used to infer both structural and func-tional information. During ATP stimulation, cpVenusrmax/rmax =~0.15, corresponding to F/F of 7% in both the Fh and Fvchannels, in opposite directions. Both Fh and Fv are measured
virtually simultaneously, so although photobleaching adverselyaffects both values, it has little effect on the Fh/Fv ratio. Even themodest observed response size should (lynD3cpV responserate permitting) allow 2PPM observations of calcium spikes of13 ms (Supplementary Discussion).
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a bFg | 2PPM imaging o intracellularcalcium concentration through conormationalchanges in the calcium sensor lynD3cpV.(a) CFP signal o lynD3cpV. (b) cpVenusluorescence beore application o ATP (let),during application o ATP (center) and aterATP removal (right). Coloring is as inFg .All scale bars, 5 m. () Plot o cpVenus LD
(expressed as rand log2(r)) o the outlinedsections (inset) o the cell shown in a and b,as a unction o time. Triangles and squaresdenote data rom the indicated horizontally andvertically oriented sections o the membrane,respectively. Dashed traces indicate s.e.m.,n = 160200 pixels. The 40-s period opresence o ATP is indicated by a bar. () LDo cpVenus and FRET o lynD3cpV as a unctiono intracellular calcium concentration. Errorbars, s.e.m.; n = 1530 cells. The curve shownis a prediction or intermediate values oKd (0.68 M) and Hill coeicient (2.8) obtained rom LD and FRET measurements. Top inset, intracellular calciumconcentrations or six typical cells stimulated by ATP, determined by FRET (horizontal axis) and 2PPM (vertical axis). Error bars, s.e.m., n = 60400 pixels with|| < 3 and n = 10,00013,000 pixels used or FRET measurements. Bottom inset, experiment in , interpreted in terms o intracellular calcium concentration.
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discussion
The 2PPM method is applicable to many protein targets andfluorescent proteins (Supplementary Tables 1 and 2) in vari-ous cell types and organisms (including Saccharomyces cerevisiae,Caenorhabditis elegans and Drosophila melanogaster;Supplementary Fig. 5). Apart from membrane proteins, themethod is also applicable to cytoskeletal proteins and poten-
tially even to cytoplasmic proteins (after anchoring to the cellmembrane or cytoskeleton, or after photoselection). The tech-nique can be very sensitive (potentially allowing observationsof cellular processes with sub-millisecond temporal resolution,Supplementary Discussion), allows multiplexing and is resilientto bleaching artifacts. As 2PPM requires only one fluorescenttag (unlike FRET), many existing fluorescent proteintaggedconstructs are likely to act as 2PPM probes (similarly to theconstructs used in this study). The information 2PPM provides(fluorophore orientation and its changes) is largely complemen-tary to that provided by other methods, such as FRET. The 2PPMapproach can be used in rational development of both 2PPM andFRET-based probes.
In a basic form, 2PPM can easily be implemented on anytwo-photon microscope using a simple polarization modula-tor (Supplementary Fig. 3b). Such a setup allows observing LDin constructs with rmax > ~1.5. More sophisticated equipment(Supplementary Fig. 3c) allows detection of LD in most fluores-cent proteintagged membrane proteins, and observation andmonitoring of even very rapid processes.
Unlike other techniques, 2PPM relies on the shape and orienta-tion of the observed cell. Thus, cells with long sections of outlineoriented horizontally or vertical ly are more suitable for measure-ments than others. We have not found this to be a substantialdrawback (Supplementary Fig. 4), and in the future it is likely tobe mitigated by advances in polarization modulation and software.
Quantification of 2PPM data does require accounting for cellshape, but our results show that our procedure (SupplementaryFig. 6) allows accurate quantification of biophysical properties(Fig. 5d and Supplementary Discussion).
In principle, 2PPM is also capable of providing quantitativeinformation about membrane-protein structure, includingdetermining the orientation, with respect to the cell mem-brane or cytoskeleton, of the fluorescent protein (or anotherfluorescent moiety) attached to the studied protein. Suchdeterminations are currently not possible because of ourlimited knowledge of the micro- and nanoscopic geometryand dynamics of the cell membrane of living cells, the detailedoptical parameters of our imaging system and the nature of
two-photon absorptivity tensors of fluorescent proteins. Untilthese parameters are determined, information presentedin Supplementary Figure 2 can serve as a crude guide tostructural interpretation of 2PPM results.
Owing to its conceptual and experimental simplicity, robust-ness, wide applicability, availability of probes and high valueof information it can provide, we believe that 2PPM couldbecome an important method for visualization and analysisof molecular processes in living cells. Many phenomena thatare at present out of reach of imaging techniques, such as theinvestigation of G proteinGPCR interactions and observingindividual action potentials in neurons, may soon becomeobservable using 2PPM.
methods
Methods and any associated references are available in the onlineversion of the paper at http://www.nature.com/naturemethods/.
Note: Supplementary information is available on the Nature Methods website.
AcknowledGments
We thank L. Nedbal, Z. Benedikty, R. Uhl, M. Buenemann, Z. Peterlin andJ. Leps or discussions; C. Seebacher and A. Reshak or assistance withimaging; T. Bergmann, K. Tosnerova and members o the Institute o PhysicalBiology cell culture acility or technical assistance; R. Axel or inspiration;and G. Miesenboeck (Oxord University), M. Buenemann (Philipps UniversityMarburg), A. Tinker (University College London), R. Tsien (University oCaliornia, San Diego), M. Asahina-Jindrova (Institute o Parasitology,Academy o Sciences o the Czech Republic), C. Berlot (Geisinger Clinic),J. Blahos (Institute o Molecular Genetics, Academy o Sciences o the CzechRepublic), K. Deisseroth (Stanord University), S. Engelhardt (TechnicalUniversity Munich), N. Gautam (Washington University in St. Louis), A. Gilman(University o Texas, Dallas), S. Ikeda (US National Institute on Alcohol Abuseand Alcoholism), M. Jindra (Institute o Entomology, Academy o Scienceso the Czech Republic), T. Knopel (RIKEN Brain Science Institute), Y. Kubo(National Institute or Physiological Sciences, Japan), J. Ludwig (University oSouth Bohemia), R. Miller (Northwestern University), M. Rasenick (Universityo Illinois at Chicago), T. Montgomery, H. Sitte and T. Steinkellner (MedicalUniversity o Vienna) and M. Wildwater (Utrecht University) or constructs,
cells and animals. The research was supported by the European Commission(FP7 Marie Curie International Reintegration grant PIRG-GA-2007-209789MemSensors (J.L.), FP6-2005-Health project LSHG-CT-2007-037897Autoscreen (J.L.)), Columbia University Science Fellowship to J.L., McKnightInnovation in Neuroscience Award (S.J.F. and J.L.), Czech governmentinstitutional grants MSM6007665808, MSM6007665801 and AVOZ60870520(J.L.), EU Structural Funds grant CZ.1.07/2.3.00/09.0203 (J.L. and S.T.),University o South Bohemia ellowship (A.B.) and J.L.s personal savings.
Author contriButions
J.L. conceived the idea, carried out mathematical modeling and analyses,perormed initial microscopy experiments, developed image-processing sotware,directed the project and wrote the manuscript. A.B. perormed microscopyexperiments, prepared constructs, analyzed data and devised experimentalstrategies. S.T. developed sotware or quantitative analysis. S.J.F. contributedinspiration, consultations and unding.
comPetinG FinAnciAl interests
The authors declare competing inancial interests: details accompany theull-text HTML version o the paper at http://www.nature.com/naturemethods/.
Pb a p://.a./a/.
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/p/x..
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3. Piston, D.W. & Rizzo, M.A. FRET by uorescence polarization microscopy.Methods Cell Biol.8, 415430 (2008).
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doi:10.1038/nmeth.1643nAture methods
online methods
Mathematical modeling. We developed a mathematical model ofa spherical and a cylindrical cell (Supplementary Fig. 1) based ongeometrical optics and similar to published models10,11. Briefly,the surface of the cell contained idealized fluorophore molecules,each possessing a single absorption and emission TDM with iden-tical orientations. Angles and (spherical cell), or an angle
and ay coordinate (cylindrical cell) defined the position of afluorescent molecule on the surface of the model cell. We definedthe orientation of the TDM for each fluorophore molecule by anangle between the TDM and a normal to the cell membrane,and an angle describing rotation along an axis normal to thecell membrane. We approximated excitation polarization by asingle, linear polarization in the focal plane. The model took intoaccount collection of fluorescence by a high-numerical-aperturelens. We carried out modeling for a range of discreet values of,for Gaussian distributions ofdescribed by a mean value of0and an s.d., , and for other distributions. We performed somemodeling of individual confocal or two-photon slices, but we pre-ferred to model z-dimension stack projections, to avoid effects
of different cell sizes. For two-photon excitation, we assumed acosine to the fourth power relationship of the rate of absorptionon the angle between the electric field vector of the excitation lightand the two-photon pseudo-TDM. The models were implementedusing Mathematica and Perl. Images were generated using thePerlMagick Perl module.
Constructs.DleGFP12 was a gift from G. Miesenboeck. FromdleGFPwe derived the cleGFPand ileGFPconstructs throughremoval of one of the membrane targeting tags by PCR (Phusionpolymerase, New England Biolabs (NEB)) using suitable primers(cleGFP_Fand cleGFP_R for cleGFP, and ileGFP_Fand ileGFP_Rfor ileGFP; Supplementary Table 3). We purified PCR products
by agarose gel electrophoresis, extracted the DNA from the gel(QIAexII gel extraction kit, Qiagen), phosphorylated the DNA(T4 polynucleotide kinase, NEB), circularized it (T4 DNA ligase,NEB) and transformed it into Escherichia coli (DH5, Invitrogen),using standard or manufacturer-recommended procedures. Foreach construct, we grew two bacterial colonies in 5 ml of LBmedium with 100 mg l1 ampicillin. We isolated the plasmids(QIAquick Spin kit, Qiagen) and verified sequences of the insertsby DNA sequencing (Agowa).
Other constructs were gifts from M. Buenemann (Gi1-Leu91-YFP, Gi1-Leu91-CFP, Gi2-Leu91-YFP, Gi3-Leu91-YFP,Go-Leu91-YFP, Gs-Gly72-YFP, 2aAR-YFP, 2aAR-CFP,a2A adenosine receptorYFP, 2AR-CFP and 2AR-YFP),
A. Tinker (GAP43-CFP-Gi1, GAP43-CFP-Gi2, GAP43-CFP-Gi3, GAP43-CFP-Go and GAP43-YFP-Go), Y. Kubo(mGluR1-i1-YFP, mGluR1-i2-YFP and mGluR1-C-tail-YFP), R. Miller (G1-YFP), S. Ikeda (G1, G2 and G2-CFP),M. Rasenick (Gs-D71-GFP), A. Gilman (Gi1-Ala114-YFPand Gi2-Ala114-YFP), N. Gautam (Gi2-Leu91-CFPand Go-Gly92-CFP), C. Berlot (Gq-Phe124-GFP, Gs-Gly72-CFPandPKC-DsRed), J. Blahos (mGluR2-GFP), S. Engelhardt (1AR-Cer/YFP), T. Knopfel (VSFP 3.1, Addgene plasmid 18951),K. Deisseroth (opto-1-AR-YFPand opto-2-AR-YFP; Addgeneplasmids 20947 and 20948), E. Boyden (FCK-ChR2-GFP andFCK-Halo-GFP; Addgene plasmids 15814 and 14750, respec-tively) and R. Tsien (SuperGluSnFR and lynD3cpV).
Mammalian cell culture. We cultured HEK293 cells at 37 Cunder an atmosphere of 95% air, 5% CO2, in Dulbeccos modifiedEagles medium with Glutamax I and high glucose (Invitrogen),supplemented with 10% fetal bovine serum. Before observa-tion, we typically plated cells on 8-chamber microscopy slides(-Slides, Ibidi) and transfected them using Lipofectamine 2000(Invitrogen), according to the manufacturers protocol. We per-
formed microscopy experiments 2448 h after transfection. Weperformed G-protein activation and calcium-imaging experimentsin flow chambers (-Slide I0.8 Luer slides, Ibidi), using a peristalticpump (Minipuls3, Gilson). We washed cells with HEPES-bufferedHanks balanced salt solution (pH 7.4) and stimulated them withnorepinephrine (()-norepinephrine (+)-bitartrate salt; Sigma)at a final concentration of 1 M for G-protein activation, orwith ATP (Sigma) at a final concentration of 10 M for calciumimaging. To calibrate lynD3cpV responses, we applied calciumchlorideEGTA buffers containing ionomycin (Sigma, 5 M) and1 nM to 39 M of free calcium for 30 min before imaging.
Polarization fluorescence microscopy. Polarization microscopy
was performed on a customized laser-scanning confocal micro-scope iMic (Till Photonics) equipped with a Yanus beam scan-ner (Till Photonics), a 488-nm argon laser (LGK 7812-1, Zeiss)for single-photon confocal imaging and a tunable pulsed tita-nium:sapphire laser (Chameleon Ultra II with GVD compensa-tion, Coherent) operated at 800 nm (CFP) or 960 nm (GFP, YFPand DsRed) for two-photon imaging. We used a UApoPlan/IR60, numerical aperture (NA) 1.2 water-immersion objectivelens (Olympus). For single-photon confocal imaging, we used acombination of a long-pass dichroic beam splitter (FF495-Di02,Semrock) and a Brightline 500/24 (Semrock) emission filter. Fortwo-photon imaging (with non-descanned detection), we used along-pass dichroic (FF705-Di01, Semrock) and a suitable emis-
sion filter (Brightline 479/40 for CFP, Brightline 500/24 for GFPand Brightline 542/27 for YFP; all Semrock), combined with aninfrared-blocking filter (HQ700SP-2P, Chroma). Fluorescence wasdetected by a photomultiplier (R6357, Hamamatsu Photonics),operated at 700900 V, providing 16-bit output.
A polarization modulator (Supplementary Fig. 3) allowedrotating polarization of the excitation beam. In our initial experi-ments (Figs. 2 and 3, Supplementary Fig. 4 and SupplementaryVideo 1) we used a simple, manually operated polarization modu-lator (Supplementary Fig. 3b) consisting of a Glan-laser polar-izing beam splitter (CVI Laser) and a rotatable half-wave plate(488 nm zero-order, or 6901,080 nm achromatic; Thorlabs).We acquired, successively, two images of the same cell, with the
polarization of the excitation beam oriented horizontally and ver-tically in the reference frame of the acquired image. All imageswere acquired at 100200 nm pixel size (typically, 100 nm) and10 s pixel1 acquisition time.
In our later experiments (Figs. 45, Supplementary Figs. 56,and Supplementary Videos 24) we used a rapid polarizationmodulator (RPM) (Supplementary Fig. 3c) custom-made byBME Bergmann. The RPM consisted of a Pockels cell (RTP-3-20-AR800-1000, Leysop) and a high-voltage driver synchronized withthe microscope, so that polarization of the excitation beam wouldalternate (between horizontal and vertical) between acquisitionof subsequent pixels. Typically, we acquired an image at 50 nm 100 nm pixel size and 10 s pixel dwell time. We split the resulting
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doi:10.1038/nmeth.1643 nAture methods
image into two images, one consisting of odd-numbered pixels ofthe original image (acquired with horizontal polarization) and theother consisting of even-numbered pixels of the original image(vertical polarization). We imaged and quantitatively analyzed atleast 15 cells for each construct or combination of constructs.
Image processing. We performed basic image processing with
ImageJ, using standard ImageJ tools and in-housedevelopedmacros. We subtracted background of acquired images andadjusted brightness (but not contrast). We colored correspond-ing images acquired with horizontal and vertical polarizationmagenta (equal intensity blue and red) and green, respectively,and merged them into a composite image. When desired, theresulting image was colored using a color LUT designed to showa suitable range ofFh/Fv ratios while keeping the overall bright-ness constant. This procedure allowed simultaneous visualizationof LD (of any size) and total fluorescence intensity. For small
values of LD (r< 1.5), we applied a small (
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Nature Methods
Two-photon polarization microscopy reveals protein structure
and function
Josef Lazar14, Alexey Bondar1,2, Stepan Timr5 & Stuart J Firestein4
Supplementary Figure 1 Mathematical models.
Supplementary Figure 2 Results of mathematical modelling for two-photon excitation.
Supplementary Figure 3 Setup for two-photon polarization microscopy.
Supplementary Figure 4 A 2PPM image of HEK293 cells expressing dleGFP.
Supplementary Figure 5 Examples of cells and constructs showing linear dichroism.
Supplementary Figure 6 Quantitation of linear dichroism.
Supplementary Table 1 G-protein constructs
Supplementary Table 2 NonG-protein constructs
Supplementary Table 3 Primers
Supplementary Note Linear dichroism of a two-state system.
Supplementary Discussion Signal-to-noise analysis.
Note: Supplementary Videos 14 are available on the Nature Methods website.
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0
y
x
z
y
x
z
y
a b c
Supplementary Figure 1: Mathematical models.
(a) Model of a spherical cell. Position of the fluorophore on the surface of the cell is described
by angles and . (b) Model of a cylindrical cell. Position of the fluorophore on the surface
of the cell is described by coordinates and y. (c) Definition of variables describing the orienta-
tion of the fluorophore (transition dipole moment): mean tilt angle 0, standard deviation , and
rotational angle. (d) Behavior of a linearly polarized laser beam used for single-photon excita-
tion, passing through an objective lens (geometrical optics approximation). Polarization of the
beam remains perpendicular to the direction of light propagation. In the focal area, the present
directions of polarization add up in a vector fashion, restoring the original polarization of thelaser beam. Fluorescence excitation occurs throughout the light double cone created by the
objective lens. Observed area can be restricted by use of a confocal pinhole. (e) Behavior of a
linearly polarized laser beam used for two-photon excitation, passing through an objective lens
(geometrical optics approximation). Similar to d, but with excitation occurring invariably only in
the focal area.
Focal point:
Elsewhere:
=
Focal point:
Elsewhere:
=
d e
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0
5
10
20
45
0 30 60 90
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0
10%
20%
30%
40%
0()
log2
(r)/0 (
r/r)/0
0
5
10
20
45
0 30 60 90-2
0
2
4
6
8
10
12
14
16
1/4
1
4
16
64
256
1024
4096
16384
0()
log2
(r)
r
dc
b
a
Supplementary Figure 2: Results of mathematical modeling for two-photon excitation.
(a) Simulated images of a fluorescently labeled spherical cell a projection of a z-stack, for
TDM tilt angle 0 values 0, 22.5, 45, 67.5, and 90. Direction of polarization and coloring of
corresponding fluorescence is indicated by double-headed arrows. Linear dichroism (non-gray
color) is present for all shown 0 values. (b) Same as in a, but for a cylindrical cell. (c) Graph
of observed LD expressed as r (r= Fh/F
v) and log
2(r), as a function of0 and for experimental
arrangement in b. LD (r 1) is generally present, except when 0 = 50-55 or is very high(45). (d) Graph of expected fractional changes in dichroic ratio (r/r) upon a change in mean
tilt angle 0, for experimental arrangement in b. The graph, in effect, shows the percentage
change in rupon a change in the mean tilt angle 0 by 1, for different starting values of0 (x-
axis) and for different standard deviations () of the Gaussian distribution of tilt angles. Even for
wide distributions of ( = 20), a 1 change in 0 typically leads to a sizeable (2-4%) change
in r.
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laserpolarization
modulator
detector
scanning mirrors
dichroic mirror
objective lens
a
b c
Supplementary Figure 3: Setup for two-photon polarization microscopy.
(a) Schematic diagram of a two-photon polarization microscope. (b) A simple polarization
modulator composed of a Glan-laser polarization beamsplitter and a manually rotatable half-
wave plate. (c) A rapid polarization modulator (RPM) based on a Pockels cell, driven in syn-
chrony with scanning of the microscope.
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Supplementary Figure 4: A 2PPM image of HEK293 cells expressing dleGFP.The image was created by merging images acquired with horizontal and vertical polarization
(colored magenta and green, respectively). Polarization of the excitation beam was rotated
manually between acquisition of individual images. No background subtraction, brightness
or contrast adjustments were applied. Scale bar: 10 m.
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1.3
1.3
1
r
1.3
1.3
1
r
1.3
1.3
1
r
6
6
1
r
10
10
1
r
1.3
1.3
1
r
1.3
1.3
1
r
1.3
1.3
1
r
1.3
1.3
1
r
1.3
1.3
1
r
f g h i j
a b c d e
Supplementary Figure 5: Examples of cells and constructs showing linear dichroism.
Coloring as in Figs.2-5. Scale bars: 5 m. a-f, HEK293 cells. (a) Protein kinase C-DsRed (C-
terminal fusion)1. The top, non-activated cell shows cytoplasmic localization of fluorescence and
no LD, unlike the bottom, activated cell (rmax = 1.5, 0 < 52). (b) a2A-adenosine receptor-YFP (C-terminal fusion)2; rmax = 1.5, 0 > 52. (c) Metabotrapic glutamate receptor mGluR1-YFP
(intracellular loop 1 insertion)3; rmax = 1.5, 0 >> 52. (d) 2a-adrenergic receptor-CFP (C-terminal
fusion)4, rmax = 1.5, 0 > 52. (e) VSFP3.1, an engineered sensor of membrane voltage5, rmax =
1.5, 0 > 52. (f) Microtubule associated protein tau-GFP (C-terminal fusion)6. LD is visible both in
cytoplasmic and in membrane associated microtubules (rmax = 1.5, 0 > 52). (g) DleGFP7
expressed in a rat hippocampal neuron (rmax = 1.5, 0 < 52). (h) Yeast S. cerevisiae expressing
potassium channel TOK1-GFP (rmax = 1.5, 0 < 52)8. (i) An epithelial seam cell of a live C.
elegans worm, expressing pleckstrin-homology domain-GFP (rmax = 1.5, 0 < 52). (j) Epithelium
of fruitfly D. melanogasterexpressing E-cadherin-GFP (rmax = 1.5, 0 > 52)9.
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db
a
r
5
3
1
1-1 0 0.5-0.5 1.5-1.5
r
0
3
2
1
01
2
-2-1
-2-1
01
20
4
0
/2
-/2
- /2 0/2
0
/2
-/2
c
Supplementary Figure 6: Quantitation of linear dichroism.
(a) Analysis of geometry of an ileGFP expressing cell, a single optical section. From left to
right: an image used for construct characterization, processed as in Fig. 2; pixels judged to be
part of the cell outline; a spline approximating the cell outline; the same spline, colored accord-
ing to orientation (angle ); pixels of the cell outline colored according to the orientation (angle
) of the closest point on the spline, with color bar shown. (b) Graph of LD as a function of cell
outline orientation (LD/CSO relationship), for the cell in a. The data was fitted by a curvepredicted for a particular combination of fluorophore tilt angle 0 and tilt angle distribution
width (0 = 0.7, = 0.1). (c) Three-dimensional reconstruction of an ileGFP expressing cell,
shown as a triangular mesh, and colored according to cell surface orientation (angles , ),
with color bar shown. (d) Graph of LD as a function of cell surface orientation, for the cell in
c. The data was fitted by a surface predicted for the same combination of0 and as in b.
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Supplementary Table 1: G-protein constructs
When expressed aloneWhen co-expressed
with G, GG-protein construct
Design /
fluorescent
proteininsertion site
LD rmax 0 n LD rmax 0 n
GAP43-CFP-Gi11020-AA tag
CFP Gi1- < 1.05 N/A 20 + 2.0 < 52 25
Gi1-Leu91-YFP11 91-92 + 2.8 > 52 38 + 3.1 > 52 33
Q204L-Gi1-Leu91-YFP11
91-92 + 2.1 > 52 25 + 2.9 > 52 30
Gi1-Leu91-CFP12 91-92 + 2.0 > 52 24 + 3.1 > 52 20
Gi1-Ala114-YFP13
114-115 + 2.1 > 52 30 + 3.2 > 52 30
GAP43-CFP-Gi21020-AA tag
CFP Gi2- < 1.05 N/A 35 + 2.1 < 52 37
Gi2-Leu91-YFP14 91-92 - < 1.05 N/A 30 - < 1.05 N/A 25
Gi2-Ala114- YFP13 114-115 + 1.1 > 52 16 + 1.1 > 52 15
GAP43-CFP-Gi31020-AA tag
CFP Gi3- < 1.05 N/A 22 + 2.1 < 52 18
Gi3-Leu91-YFP14 91-92 + 2.0 > 52 17 + 3.2 > 52 18
GAP43-CFP-Go10 20-AA tag CFP Go - < 1.05 N/A 15 + 1.6 < 52 15
GAP43-YFP-Go1020-AA tag
YFP Go- < 1.05 N/A 20 + 1.6 < 52 22
Go-Leu91-YFP14 91-92 - < 1.05 N/A 52 + 1.7 < 52 62
Go-Gly92-CFP15 92-93 - < 1.05 N/A 15 - < 1.05 N/A 15
Gs-Asp71-GFP16 71-82 - < 1.1 N/A 15 + 1.3 < 52 15
Gs-Gly72-CFP17 72-85 - < 1.05 N/A 20 + 1.8 < 52 25
Gs-Gly72-YFP2 72-85 - < 1.1 N/A 15 - < 1.1 N/A 15
Gq-Phe124-GFP1 124-125 + 1.8 < 52 25 + 1.8 < 52 25
G1-YFP18 N-terminal - < 1.05 N/A 15 + 1.4 > 52 20
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Supplementary Table 2: Non-G-protein constructs
Construct LD rmax 0 n
2aAR-CFP4 + 1.7 < 52 35
2aAR-YFP4 + 1.3 < 52 30
2AR-YFP4 -
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Supplementary Table 3: Primers
Primer name Sequence
cleGFP_F TTTAATCTGTGTTGTAACTC
cleGFP_R GATGGAGGCGTTCAACTAG
ileGFP_F ACGACCCTAATGTGTACCGATTCT
ileGFP_R CCGCTTCCCTTTAGTGAG
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SUPPLEMENTARY NOTE
LD of a two-state system
The composition of a mixture (AB) of two states (A, B) can be inferred from the dichroic
ratio of the mixture (rAB), if the dichroic ratios of the individual components (rA, rB) of
the mixture are known. IfxA,xB are the fractions of the protein present in the form A and
B, respectively, and we assume that the total amount of fluorescence (F= FA + FB) is
approximately independent ofxA andxB (FA =xA . F; FB =xB . F), we can write:
vA
AF
r hAF
, andvB
BF
r hBF
. (Eq. 1, 2)
Thus,AAA
vArrr
F vAAvAAhAFFxFFF
, (Eq. 3)
and therefore Fr
FA
vA1
xA (Eq. 4)
Similarly, it can be shown that
Fr
FB
vB1
xA1 , F
rF
A
hA1
xr AA , and F
rF
B
hB1
xr AB )1( . (Eq. 5, 6, 7)
Thus, the dichroic ratio of a two-component system is:
)1)(1()1()1)(1()1(
1
)1(
1
11
AABA
BAABAA
B
A
A
A
BA
vBvA
hBhAAB
rxrxrrxrrx
Fr
xF
r
x
F
r
F
rFFFFr
)1( BAAA rxrx
(Eq. 8)
)(1 BAAAAB
rrxrr
)()1( BAAAB rrxrr (Eq. 9)
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)(1 BAAAAB
rrxrr
)()()()1( BAABAABBAABAB rrxrrxrrrxrrr (Eq.10)
)(1)(1 BAAAB
BAAA
BABrrxr
rrrxr
rr
)1)(()()( BBAABAABAAB rrrxrrxrrxr
(Eq.11)
The fraction of the component A can then be determined:
)1)(( )1)((
ABBA
Arrr
x
ABAB rrr
)(BAABAB rrxrr
(Eq. 12)
For values ofrA and rB similar to each other [specifically, for (rA-rB) considerably smaller
than (1+r
A)], Eq. 11 can be approximated by a simple linear relationship,
(Eq. 13)
and the fraction of component A then is:
)(
)(
BA
BABA
rr
rrx
(Eq. 14)
Apart from determinations of composition of mixtures, the above equations can
also be used for determining Kd, by substituting forxA in Eq. 12 from a suitable
equilibrium equation [such as the Hill equation we used for determining the Kd of
lynD3cpV,xA = [Ca2+
]n
/ (Kdn
+ [Ca2+
]n) ]. Alternatively, Kd values can be determined
by applying a standard mathematical description developed for ratiometric FRET
imaging24
to ratiometric 2PPM data (Fh/Fv). For a first order equilibrium reaction we can
write:
[Ca2+
]
vA
vB
ABA
BABd
FrrK
Frr(Eq. 15)
The term FvB/FvA is not easily experimentally accessible. However, if we assume (as we
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did in Eqs. 1-14) that the total fluorescence intensity (Fh + Fv) is the same for forms A
and B, we can approximate FvB/FvA by (rA + 1)/(rB + 1). For a system described by a Hill
equation we can then write:
[Ca2+
]n
1
)(B
A
ABA
BABn
drrr
K 1rrr
(Eq. 16)
Eq. 16 is equivalent to a combination of Eq. 12 and the Hill equation.
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SUPPLEMENTARY DISCUSSION
Signal-to-noise analysis
Calibration of photomultiplier detector response through Poisson noise analysis
has allowed us to interpret pixel intensities in terms of photon counts. Typically, during
the pixel dwell time (10 s) used by our setup, 100-200 photons were detected in each
pixel within the cell outline. The 95% confidence interval (95%CI) for a single
measurement and Poisson distribution of 150 events is 127-177. Thus, a single pixel
allows measurement of fluorescence intensity with ~20% accuracy. A Poisson
distribution of the mean value of 150, being far from 0, can be approximated by a normal
distribution with a mean of 150 and variance of 150 (thus, with both the standard
deviation and standard error equal to 150 = ~12). For values ofr= Fh/Fv close to 1 we
can estimate the standard deviation ofrto be 2 standard deviation of individual
fluorescence measurement/mean fluorescence intensity = 1.41 12 / 150 = 0.11.
Therefore, from a single pixel we know the value ofrwithin ~22%, with 95% confidence.
A short stretch (0.5 m) of the cell outline contains about 100 pixels, allowing
measurement ofrto 2.2% accuracy with 95% confidence. The acquisition time for 100
pixels with two polarization states is 2 ms, indicating that 2PPM is capable of
distinguishing between two states differing in rby ~5% in 2 ms. In molecular systems
displaying a larger change in r, the temporal resolution of 2PPM can be well below 1 ms.
Our experimental results (Figs. 4, 5) are in excellent agreement with this analysis.
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Forrmax determination, apart from the photon noise issues analyzed above, noise
and errors stemming from geometrical approximation of cell shape need to be considered.
Our data (Fig. 5d) indicates that the 95%CI forrmax in a single cell is typically 8-12% of
the mean (including 2-3% caused by photon noise). Averaging of several cells allows
narrowing the CI. While the 95%CIs for intracellular calcium concentrations determined
by FRET are typically ~40 smaller than for concentrations determined by 2PPM, this
needs to be considered in context. The FRET determinations used 6,000 longer
illumination time and ~50,000 larger cell area from which quantitative data was being
acquired. Improvements in polarization modulation and image processing software
(allowing using larger parts of cells to be used forrmax determination), and other
enhancements should allow very fast and accurate determinations ofrmax and other
biophysical properties in individual cells.
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