J.-A Spitz

R Yasukuni

N Sandeau

M Takano

J.-J Vachon

R Meallet-Renault

& R B Pansu
email: pansu@ppsm.ens-cachan.fr

Dr Robert B Pansu

Wide-field single photon counting device for fluorescence intensity, lifetime and timeresolved anisotropy imaging microscopy

Keywords: Fluorescence, anisotropy, FLIM, tr-FAIM, single photon counting, Quadrant anode, wide-field imaging

A single photon counting system for FLIM and fluorescence anisotropy wide-field imaging is described and characterized in this paper. The two polarizations of the fluorescence are divided by a Glan prism and acquired at the same time by the Q A detector. Fluorescence

decay profiles can be reconstructed for any desired area up to each pixel and used to calculate time resolved fluorescence anisotropy decays.

Introduction

Biological and physical sciences have an increasing interest in fluorescence spectroscopy imaging. Fluorescence emission can give access to different parameters such as intensity but also lifetime and anisotropy (Lakowicz 1999;[START_REF] Valeur | Molecular Fluorescence : Principle and Applications[END_REF]. Indeed, the spectroscopy of fluorescence is a powerful tool to probe viscosity, structural change, functional information and more generally speaking to probe local environment [START_REF] Fleming | Chemical application of ultrafast spectroscopy[END_REF].

Ion indicators where the fluorescence lifetime depends on the chelation state have been found and are used to measure calcium concentration [START_REF] Schoutteten | Development of intracellular calcium measurement by time-resolved photoncounting fluorescence[END_REF]. FLIM is also used to measure protein contact and deformation through FRET [START_REF] Förster | Transfer mechanisms of electronic excitation[END_REF]. Indeed, the presence of an absorbing dye within a few nanometers of the fluorescent protein induces a reduction of the fluorescence lifetime [START_REF] Millar | Time-resolved fluorescence spectroscopy[END_REF]. The early application of the principle has been the building of Cameleon, a construction that uses intramolecular FRET to measure Ca [START_REF] Miyawaki | Fluorescent indicators for Ca2+ based on green fluorescent proteins and calmodulin[END_REF]. Anisotropy is a parameter that is used for more general puposes. It measures the randomization of direction of the transition dipole of the emitter. Most of the time this randomization is due to the rotational dynamics of the fluorescent label, however it can also be due to the energy transfer in a FRET process [START_REF] Tramier | Restrained torsional dynamics of nuclear DNA in living proliferative mammalian cells[END_REF]. Quite often a change in the movement of the fluorescent label can be predicted or expected when a biological event occurs and it can be used to measure protein dimerization through FRET between identical labels (Homo FRET) [START_REF] Gautier | Homo-FRET microscopy in living cells to measure monomer-dimer transition of GFP-tagged proteins[END_REF].

There are three main FLIM techniques: phase fluorimetry, time gated set-ups and single photon counting systems (SPCS) [START_REF] Herman | Fluorescence Lifetime Imaging Microscopy[END_REF]. The first two are widely used due to the development of CCD cameras [START_REF] Wang | Fluorescence Lifetime Imaging Microscopy (FLIM) : Instrumentation and Applications[END_REF][START_REF] Gadella | Fluorescence lifetime imaging microscopy (FLIM): Spatial resolution of microstructures on the nanosecond time scale[END_REF][START_REF] So | Time-Resolved Fluorescence Microscopy Using Two-photon Excitation[END_REF][START_REF] So | New time-resolved techniques in two-photon microscopy[END_REF]. Although, the latter remains more unconventional, it seems more respectful to the sample because of its increased sensitivity. In the most common SPCS FLIM set-ups [START_REF] Buurman | Fluorescence lifetime imaging using a confocal laser scanning microscope[END_REF], the laser scans the image pixel by pixel which slows down the acquisition process. The use of wide-field imaging detectors for full parallel pixel acquisition has not been extensively developed [START_REF] Emiliani | Low-intensity two-dimensional imaging of fluorescence lifetimes in living cells[END_REF]. Moreover, instead of sampling the detection, which significantly reduces the sensibility, each emitted photon is taken into account.

Furthermore, time resolved fluorescence anisotropy imaging has been described. Jovin et al. developed a technology in which the phase delay and intensity ratios between the polarized components of the fluorescence signal are recorded, leading to estimations of rotational correlation times and limiting anisotropies. This set-up was successfully applied to rotational dynamics studies in solution and emFRET in bacteria expressing EGFP [START_REF] Clayton | Dynamic fluorescence anisotropy imaging microscopy in the frequency domain (rFLIM)[END_REF]. However, in their experiments, the two different polarizations are acquired successively. French et al. are able to image the rotational motility of a fluorophore thanks to a time gated fluorescence lifetime imaging system [START_REF] Siegel | Wide-field time-resolved fluorescence anisotropy imaging (TR-FAIM): Imaging the rotational mobility of a fluorophore[END_REF]. Time resolved fluorescence anisotropy has also been successfully applied to single molecule spectroscopy [START_REF] Ha | Polarization spectroscopy of single fluorescent molecules[END_REF][START_REF] Schaffer | Identification of single molecules in aqueous solution by time resolved fluorescence anisotropy[END_REF].

In our set-up, the whole decay profile of the two polarizations is acquired simultaneously with a single photon counting system. Thus, there is no sampling of the fluorescence decay. Moreover, the two polarizations are acquired at the same time, with the same sample, at the same position, with the same experimental conditions preventing us from artefacts such as instrument drift, evolution of the sample or photobleaching.

Figure 1

Materials and methods

The experimental device is shown on Fig. 1. The excitation source is an argon-ion laser pumped mode-locked Ti/sapphire laser (Tsunami by Spectra-Physics). Its output is repetitionlowered by a pulse-picker and frequency doubled in a BBO crystal to produce a 1.2 ps excitation source operating at a 4 MHz repetition rate, and which can be tuned from 430 to 500 nm. The laser beam enters the Nikon 2000 TE inverted microscope, being reflected toward the sample by the dichroic beamsplitter. The laser is focused on the back focal point of the objective and goes through the sample as a parallel beam, thus providing a wide-field excitation of the sample. the sample. Some kinds of histograms can also be constructed for selected areas of the image, thus giving the specific fluorescence decay of the selected area. For each pixel we also calculate the sum of all the delays between the laser pulse and the collected photons. When divided by the number of photons arrived on each pixel this sum of all the delays gives the average fluorescence lifetime as a FLIM image. This is a fast and robust way to make FLIM images.

The time resolved anisotropy function, r(t), is then calculated (without deconvolution of the instrument response function) from the Perrin equation :

⊥ ⊥ + - = GI I GI I t r 2 ) ( // // (1)
where G is the apparatus function (Cf. supra) and ⊥ I and // I are the perpendicular and parallel components of the fluorescence polarization.

Results and discussion

We present here the different aspects of the set-up characterization. First, we shall focus on the fluorescence lifetime and intensity measurements. Then, we will characterize the space resolution of this new detector. Finally we will discuss the measurement and imaging of fluorescence anisotropy. The pixels of an image of a rhodamine sample were sorted according their intensity and the lifetime distribution was fitted with a Gaussian whose width is the lifetime dispersion.

Time measurement

Lifetime measurement correction.

The crude FLIM image of a homogeneous sample (Rhodamine 6G (Magde et al. 2002), 10 -4 M in water) is shown on Fig. 3a. It shows a lifetime between 3 ns (black pixel) and 3.6 ns (white pixel), with more white pixels in the middle of the image. This homogeneous sample should show a sharp distribution in fluorescence lifetime. Thus, when the center of the image seems to have a longer lifetime, the periphery shows a shorter one. The artificial delays, that are observed, are due to electronics. Indeed for each avalanche, the propagation time of the induced current pulse through the multichannel plate to reach the discriminator depends on the location of the avalanche. To correct those constant time transit variations, we use a time transit correction map. To build up this map, we use a rhodamine sample in water that has a homogeneous life time on the whole sample and can be thus used as a reference. We calculate the difference between the time measured on each pixel and the average value, which is the expected lifetime; this difference will then be automatically subtracted to all future FLIM images.

Dispersion of the average fluorescence time.

If we look at Fig. 3c, we see a uniform value for the measure of fluorescence lifetime, but a remaining dispersion (Fig. 4). We shall show that this residual dispersion is due to photon statistics.

The precision of average fluorescence time measurements depends upon the number of photons collected by each pixel of the image. In the case of a monoexponential decay (e.g. rhodamine), the distribution P(t) of the photon arrival time is k.exp(-kt) were 1/k is the fluorescence lifetime. The expected value of the mean arrival time of N photons is 1/k and the variance of these arrivals times is 1/k_. The variance of the mean arrival time of N photons will be

) ? /( 1 N k
. This variance will tend to zero as N approches infinity. Thus, the number of photon per pixels has been counted and an average fluorescence time distribution has been build according to this number of photon per pixels. We get a family of Gaussians whose widths give the lifetime dispersion as a function of the number of photons (Fig. 5). The width scales linearly with N / 1 and extrapolates to 39 ps. This shows that the dispersion of fluorescence time is due to photon statistics and the extrapolated value to infinite photon count gives the quality of the correction by the transit time map.

Temporal resolution

The temporal resolution of the set-up is limited by our detector. To determine it, we use a 1.2 ps pulse and measure the time response of our detector (Fig. 6). The middle height width of the recorded pulse is around 310 ps. This is the shortest event we can efficiently measure and it gives us an idea of our temporal resolution. Global fluorescence decays can also be corrected from the transit time deviation. After this correction, the full width at half maximum of the pulse reaches the value of 150 ps. It can be reduced to 130 ps only if the center of the detector is used. This time resolution agrees with the one expected from the diameter of the holes in the MCPs.

Time shift from the microscope objectives

The use of 4 different objectives leads to another small time shift from one objective to another because, though objectives are designed to perform with same work distance, the lenses sizes are different. This explains why the way through the x40 is shorter than the other (-75 ps) whereas the x100 induces an extra time of 65 ps. Again, those shifts are automatically corrected to set all pulses at the same point.

Intensity measurements

Gain correction

Some areas of our detector can present different gains. The lighting of the sample may also affect the intensity image because some areas might be more lighted than others. As previousy mentioned, a software correction is necessary to supplement these sensibility variations (Fig. 7). The gain factor map is calculated from a rhodamine in aqueous sample. 7a), we can notice small dark spots which are areas of the detector that are less sensible than the average.

N.B. 2:

The overload on the periphery of the image is not due to reflections on the inner walls of our set-up neither to accumulation of miscalculated photons thanks to the help of the fifth surrounding anode (Fig. 8).

Dead time

Once a photon reaches the anode, it has to be proceeded by the set-up. During this dead-time, any other photon will not be taken into account. This dead-time is determined by sorting the acquired photons according to their delay relative to the previous photon (Fig. 9). Thus, we measure a dead time of 2.15 µs.

Saturation

The histogram (data not shown) of the amplitude of avalanches is independent of count rate.

Thus the saturation of the count rate is not due to a saturation of the MPC channel. The saturation due to the 2.15 µs dead time of the charge amplifiers should be 465 kHz. The measured saturation rate of 72 kHz (Fig. 10) might be due to the data transfer later in the process.

Spatial resolution

The determination of the spatial resolution of the device was carried out by imaging isolated fluorescent nanolatex. These latexes, from Molecular Probes (F-8787), have a diameter of 20 nm, which is below the resolution. The size of the smallest spots gives us the spatial resolution. The latexes are spin-coated on a microscope slide after dissolution (0.2% in mass) in a 1% PolyVinyl Alcohol aqueous solution according to the protocol described by R. The smallest fluorescent marks, corresponding to isolated nanolatex particle, are fitted by a series of 2-dimension Gaussians whose widths are plotted in a function of the altitude on Fig. 12. The lowest point of the resultant curve corresponds to the focus plan and the size of the spot (200 nm) is the spatial resolution of the imager. The Gaussian half-width of 200 nm corresponds to an Airy radius of 400 nm. The pixel size is smaller than the resolution limit and does not limit the overall spatial resolution of the set-up. NB: The dissymmetry of the curve Fig. 12-b is due to the imperfectly corrected spherical aberration of our set-up.

Méallet

Anisotropy Delay due to the set-up

The two different polarizations of the emitted fluorescence have different courses through the set-up. Indeed, the vertical component is reflected by the Glan prism and then by the pentaprism. Consequently, the optical path way of this polarization is longer than the other, leading to an extra delay of 160 ps (4,8 cm Fig. 13). Before any calculations on these decays, such as anisotropy calculation, this shift is corrected by computer post-treatment. A typical corrected FLIM image of the two polarizations of rubrene fluorescence is presented on Fig. We have studied the effect of the depolarization of the anisotropy of a solution of rubrene in squalane (n'=1,4474 [START_REF] Tripathi | Densities, Viscosities, and Refractive Indices of Mixtures of Hexane with Cyclohexane, Decane, Hexadecane, and Squalane at 298.15K[END_REF]) with these increasing collection angles. (Fig. 15, 16 and Table 1). The anisotropy measured in cuvette within a calibrated spectrofluorimeter has been added with a Numerical Aperture of 0. The predicted anisotropy value has been calculated by a full-vectorial modeling which is based on a method proposed by Enderlein [START_REF] Enderlein | Theoritical study of detecting a dipole emitter through an objective with high numerical aperture[END_REF]. The method permits the calculation of the electric field (Ei) (in the image space) emitted by a fluorophore (i) in the object space. It depends on the position and the orientation of the emitting dipole. The index of the fluorescent solution, the polarization of the excitation beam and the characteristics of the microscopes (NA, magnification) and of the fluorophores are taken into account too. In this case, the emitted field is projected along the two perpendicular directions of polarization (one is parallel to the polarization excitation beam). [START_REF] Axelrod | Carbocyanine dye orientation in red cell membrane studied by microscopic fluorescence polarization[END_REF]) is observed as previously stated with a different configuration [START_REF] Schoutteten | Characterisation of a Time resolved Photon Counting Confocal Fluorescence Microscope[END_REF] but does not prevent anisotropy measurement up to a collection angle of 50° where it can be neglected as reported by Seigel et al [START_REF] Siegel | Wide-field time-resolved fluorescence anisotropy imaging (TR-FAIM): Imaging the rotational mobility of a fluorophore[END_REF].

The time evolution of polarized fluorescence intensity is of two types // I and ⊥ I [START_REF] Fleming | Chemical application of ultrafast spectroscopy[END_REF])

)) ( 2 1 )( exp( 0 // t r t I I rot + - = τ (3) )) ( 1 )( exp( 0 t r t I I rot - - = ⊥ τ (4)
When high collection angles are used, the collected intensity with a vertical (resp.

horizontal) analyzer is a linear combination of // I and ⊥ I . Thus, the characteristic rotational correlation times are not affected by the collection angle used.

Anisotropy in thin films

Measurements of anisotropy in films will depend also on the collection angle but with different relations since the radiation pattern is no longer toroidal. Spin-coated 50-nm films of a fluorescent dye (PM567 30 µg.g -1 in 10 % PMMA in toluene, 1) 10 s 1000 rpm, 2) 50 s 3000 rpm) have been studied with the different objectives (Fig. 17). The relaxation of the anisotropy observed in such a film is not due to the Brownian motion of the excited state in the polymer film but to the Förster resonance energy transfer (FRET) from the excited molecule to one of its neighbour. The angular distribution of the transition moment after one FRET jump can be calculated. For a given distance R the jump probability is proportional to

[ ] 2 1 0 1 0 2 ) . ( ) . )( . ( 3 p p p u p u r r r r r r - = κ
(5). The angular distribution ρ(θ,φ) of the transition dipole after one jump is given by averaging __ over u r . This average gives a distribution ρ(θ,φ)=(3+cos_(θ)) which corresponds to a reduction of anisotropy down to a value of 4% of the original value [START_REF] Agranovich | Electronic Excitation Energy Transfer in Condensed Matter[END_REF]. Some authors show that this is zero (Berberan-Santos et [START_REF] Berberan-Santos | Fluorescence depolarization by electronic energy transfert in donor-acceptor pairs of like and unlike chromophores[END_REF]. Thus the rate of the anisotropy relaxation is the rate of the energy transfer to the first neighbour [START_REF] Förster | Transfer mechanisms of electronic excitation[END_REF][START_REF] Millar | Picosecond dynamics of electronic energy transfer in condensed phases[END_REF]) (6).

) exp( ) ( 0 τ t r t r - = (
Anisotropy decays have been fitted to this equation leading to the initial anisotropy (r 0 ) and the characteristic time of the energy transfer (_) gathered in Table 2. Apart from the highest numerical aperture, the anisotropy depolarization can also be neglected.

Conclusion

We describe a robust and useful set-up to measure fluorescence anisotropy imaging. The whole decay profile of the two polarizations is acquired simultaneously with a single photon counting system. Thus, there is no sampling of the fluorescence and the two polarizations are acquired at the same time, with the same sample, at the same position, with the same experimental conditions preventing us from artefacts such as instrument drift, evolution of the sample and photobleaching. Since FLIM can be estimated with a limited number of photons, FLIM images can be recorded with a single-photon counting system in less than one minute.

Correction maps are required for gain and transit time. These correction maps appear to be stable for a few months and recalibration of the set-up is easy on a few reference samples.

Overall, this device appears to be a powerful and sensible tool to do imaging in different fields such as cellular imaging (Fig. 18

  Photomultiplier (QA)

Figure 3

 3 Figure 3

Fig. 5 :

 5 Fig. 4: Histogram of the collected photon vs. lifetime before and after correction of time transit

Fig. 6 :

 6 Fig.6: Pulse and corrected pulse.

  Gain correction. a) Crude image of a rhodamine in basic water sample. b) Gain factor correction map calculated from another sample. c) Corrected image of the first sample using the gain factor correction map. N.B.: On the right part of the uncorrected image (Fig.

Figure 11 :

 11 Figure 11 :Images of spin-coated 20-nm f luorescent nanolatex in PVA film. (b) is the image in focal plane, (a) is the image 1.2 µm underneath and (c) is the image 5 µm over the focal plane.

Fig

  Fig. 12: a) 2-D Gaussian fit of the fluorescent spot of a 20 nm fluorescent nanolatex. b) Gaussian's width vs. altitude.

  14. No deconvolution is necessary because fluorophores used in this study have long fluorescent lifetimes.

Fig. 14 :Fig. 15 :

 1415 Photon

  Photon

Figure 17 :

 17 Figure 17 : Time-resolved anisotropy of PM567 in PMMA film with different numerical aperture. The anisotropy has been calculated according to Eq. (1) from the decays recorded using five dif ferent microscope objectives. The laser pulse has been superimposed to the figure. The angular distribution ρ(θ,φ) of the transition dipole after one jump is given by averaging

Fig. 1 :Fig. 2 :Fig. 3 :

 123 Fig. 1: Experimental setup.

Fig. 4 :Fig. 5 :

 45 Fig. 4: Histogram of the collected photons vs. lifetime before and after correction of time

Fig. 6 :

 6 Fig. 6: Pulse and corrected pulse.

Fig. 7 :

 7 Fig. 7: Gain correction. a) Crude image of a rhodamine in water sample. b) Gain factor

Fig. 8 :Fig. 9 :Fig. 10 :Fig. 11 :

 891011 Fig. 8: Position of the anodes on the detector surface.

FigFig. 13 :

 13 Fig. 12: a) 2-D Gaussian fit of the fluorescent spot of a 20 nm fluorescent nanolatex. b)

Fig. 14 :Fig. 15 :

 1415 Fig. 14: FLIM image of the two polarization components of the fluorescence of rubrene

Fig. 16 :

 16 Fig. 16: Time resolved anisotropy of rubrene in squalane with different numerical

Fig. 17 :

 17 Fig.17: Time resolved anisotropy of PM567 in PMMA film with different numerical

Fig. 18 :

 18 Fig. 18: Intensity image of a NIH 3T3 cell. Actin cytoskeleton is stained with phalloïdine-

Table 1 : Time zero anisotropy (r 0 ) of rubrene in squalane with different numerical aperture (NA); calculated anisotropy (r C ); rotational correlation time (_ rot )

 1 ), chemical sensing, µTAS, biochip diagnostic…

	Obj	N.A.	r 0	r c	_ rot (ns)
	0	0	0.297	-	2.65
	10	0.3	0.281	0.318	2.66
	40	0.6	0.272	0.311	2.52
	60	0.95	0.283	0.293	2.50
	100	1.45	0.234	0.244	2.66

Table 2 : Time zero anisotropy (r 0 ) of PM567 in PMMA films with different numerical aperture (NA and characteristic time of the energy transfer (_)

 2

Effect of the collection angles

Since we intend to use different scales of sample, we use different microscope objectives (x10, x20, x40, x60 and x100). Those objectives have different numerical aperture (resp. 0.3, 0.45, 0.6, 0.95 and 1.45). It is well known that measured anisotropies depend on the collection angle. For high collection angles, we start to collect the light emitted by the x-oriented population. Thus the observed anisotropy is reduced. This collection angle (u) is a function of the numerical aperture of the objective and of the refractive index in the fluorescent solution (n').

' sin n NA u =

(2)

i. B -Effect of the numerical aperture of the objectives