Multiple frequency fluorescence lifetime imaging microscopy

Authors


Dr Philippe I. H. Bastiaens Cell Biophysics Laboratory, Imperial Cancer Research Fund, WC2A 3PX London, UK. Tel: +44 (0)171 269 3082; fax: +44 (0)171 269 3094; e-mail: p.bastiaens@icrf.icnet.uk

Abstract

The experimental configuration and the computational algorithms for performing multiple frequency fluorescence lifetime imaging microscopy (mfFLIM) are described. The mfFLIM experimental set-up enables the simultaneous homodyne detection of fluorescence emission modulated at a set of harmonic frequencies. This was achieved in practice by using monochromatic laser light as an excitation source modulated at a harmonic set of frequencies. A minimum of four frequencies were obtained by the use of two standing wave acousto-optic modulators placed in series. Homodyne detection at each of these frequencies was performed simultaneously by mixing with matching harmonics present in the gain characteristics of a microchannel plate (MCP) image intensifier. These harmonics arise as a natural consequence of applying a high frequency sinusoidal voltage to the photocathode of the device, which switches the flow of photoelectrons ‘on’ and ‘off’ as the sinus voltage swings from negative to positive. By changing the bias of the sinus it was possible to control the duration of the ‘on’ state of the intensifier relative to its ‘off’ state, enabling the amplitude of the higher harmonic content in the gain to be controlled. Relative modulation depths of 400% are theoretically possible from this form of square-pulse modulation. A phase-dependent integrated image is formed by the sum of the mixed frequencies on the phosphor of the MCP. Sampling this signal over a full period of the fundamental harmonic enables each harmonic to be resolved, provided that the Nyquist sampling criterion is satisfied for the highest harmonic component in the signal. At each frequency both the phase and modulation parameters can be estimated from a Fourier analysis of the data. These parameters enable the fractional populations and fluorescence lifetimes of individual components of a complex fluorescence decay to be resolved on a pixel-by-pixel basis using a non-linear fit to the dispersion relationships. The fitting algorithms were tested on a simulated data set and were successful in disentangling two populations having 1 ns and 4 ns fluorescence lifetimes. Spatial invariance of the lifetimes was exploited to improve the accuracy significantly. Multiple frequency fluorescence lifetime imaging microscopy was then successfully applied to resolve the fluorescence lifetimes and fluorescence intensity contributions in a rhodamine dye mixture in solution, and green fluorescent protein variants co-expressed in live cells.

Introduction

Time-resolved fluorescence decays provide information about the state of a fluorescent molecule and its immediate environment. The fluorescence lifetime of a molecule is inversely proportional to the sum of all the deactivation pathways out of the excited state, consequently it is sensitive to environmental conditions such as pH, ionic strength and hydrophobicity and excited state reactions such as fluorescence resonance energy transfer (FRET), molecular quenching and triplet formation. Furthermore, unlike steady-state fluorescence intensity, the fluorescence lifetime is independent of fluorophore concentration and light path length, an intrinsic property which can be exploited in samples such as living cells, where these variables cannot be controlled experimentally. Fluorescence decay measurements can be performed directly in the time domain using pulsed light sources and various high speed gating techniques, or in the frequency domain using sinusoidally modulated excitation sources and homodyne or heterodyne detection methods. In recent years both the time and frequency domain techniques have been developed further to enable imaging of fluorescence lifetimes in a microscope ( Lakowicz & Berndt, 1991; Clegg et al., 1992 ; Gadella et al., 1993 ; Gadella et al., 1994 ; Dong et al., 1995 ; Muller et al., 1995 ; So et al., 1995 ; Szmacinski & Lakowicz, 1995; Periasamy et al., 1996 ; Carlsson & Liljeborg, 1997; Schneider & Clegg, 1997; Squire & Bastiaens, 1999). Fluorescence lifetime imaging microscopy (FLIM) has been applied for elucidating many aspects of cell physiology ( Lakowicz et al., 1994 ; Gadella & Jovin, 1995; Sanders et al., 1995 ; Bastiaens & Jovin, 1996; Bastiaens & Squire, 1999; Ng et al., 1999 ), where the highly heterogeneous nature of the cell environment makes the interpretation of fluorescence intensity especially problematic. In frequency domain FLIM, nanosecond fluorescence lifetime determination at every pixel of an image was made possible by the use of image intensifiers as frequency mixing devices for homodyne/heterodyne detection. For any one experiment both the phase and modulation of sinusoidally modulated fluorescence are recorded at a single excitation frequency, from which both the phase (τφ) and modulation (τM) fluorescence lifetimes are calculated at each pixel. These are only equal to the true fluorescence lifetime for mono-exponential homogeneous lifetime samples. Often, however, the sample measured contains various quantities of differing lifetime species or species in a multiple of lifetime states, the composition of which may also differ at every location in the image. At any single frequency and at any particular location within the image the phase and modulation fluorescence lifetimes measured are a weighted average of all the individual lifetime components. As the modulation frequency is increased or decreased the phase and modulation lifetimes measured approach either the shortest or longest lifetime component in the sample, respectively. In order to determine the true lifetime composition within the sample, the phase and modulation must be recorded at multiple frequencies to generate pairs of dispersion curves, where the reciprocal of the frequencies are in general chosen so as to span the full lifetime range in the sample (typically tens to hundreds of megahertz for nanosecond fluorescence lifetimes). A minimum of N frequency measurements is required to discern N lifetime components ( Weber, 1981). The approach whereby phase and modulation measurements are obtained sequentially over a set of modulation frequencies has been extensively applied for the lifetime analysis of solutions using a point detector ( Gratton & Limkeman, 1983; Lakowicz & Maliwal, 1985). This approach, however, has not found application in FLIM, principally because the sequential collection of lifetime images at every frequency is prohibitively costly, both in terms of data collection times and in terms of the total time that the sample is exposed to the excitation light. Both these points are especially critical in relation to microscopical measurements, because the samples under observation are often dynamic in nature (i.e. the movement of fluorescently labelled proteins within the spatial environment of a living cell) and far more sensitive to the effects of photobleaching than cuvette samples, where large sample volumes and diffusion ensure that the fluorophores at the point of illumination are continuously replaced. More recently, point detection instruments have been introduced employing digital acquisition systems for the simultaneous collection of data over many harmonic frequencies ( Feddersen et al., 1989 ; Verkman et al., 1991 ; Watkins et al., 1998 ). Here, the principles of parallel data acquisition are applied in the microscope, enabling the simultaneous measurement of phase and modulation images at a multiple of harmonically separated frequencies. Multiple frequency fluorescence lifetime imaging microscopy (mfFLIM) is made possible by exploiting the higher harmonic content in the gain characteristics of an image intensifier modulated at its photocathode. These frequencies are then available for simultaneous homodyne frequency mixing with matched harmonics in the fluorescent signal. By taking a series of phase-dependent images over a full period (0–360°) of the fundamental, all the harmonics in the signal can be sampled at once. This requires that the Nyquist sampling criterion is satisfied for the highest harmonic component present. A Fourier analysis of the resulting phase dependent images gives the phase and modulation at each of the matching frequencies. These can then be fitted to dispersion relationships for the phase and modulation in order to determine the fluorescence lifetime composition of the sample at each pixel. In this work a pair of standing wave acousto-optic modulators was used to obtain four or more harmonic amplitudes in the excitation field ( Piston et al., 1989 ). By recording mfFLIM data at only five frequencies, the composition of a rhodamine dye mixture, and a cell co-expressing different green fluorescent fusion proteins were discerned.

Theory

Principle of homodyne multitiple frequency fluorimetry

A full description of phase and modulation fluorimetry incorporating higher frequency terms has been covered thoroughly elsewhere ( Clegg & Schneider, 1996; Squire & Bastiaens, 1999). In brief, any excitation field E(t) repetitively modulated at a fundamental frequency ω can be described by a Fourier expansion with amplitudes En and phases Θn at each harmonic frequency . The fluorescence response F(t) to excitation with such light contains the same harmonic content with amplitudes Fn and phases Θ′n. However, each harmonic (n) is phase shifted by Δφn = Θn − Θ′n and demodulated by Mn = MF,n/ME,n relative to the excitation (ME,n = En/E0 and MF,n = Fn/F0 are the relative modulation depths of the excitation and fluorescence at each harmonic). Both the phase shift and demodulation vary as a function of the fluorescence lifetime composition of the sample according to the dispersion relationships:

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where αq is the fractional contribution (ΣQq = 1αq = 1) to the steady state fluorescence from the qth emitting species. For the simultaneous measurement of phase and modulation at multiple frequencies using the homodyne method the electronic mixing signal G(t) must contain higher harmonic terms matching those in the fluorescence F(t). The application of a low frequency filter to the product of the fluorescent and electronic signals results in an output D(k), which varies as a function of phase setting (k) given by:

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where QE is the quantum efficiency of the detected fluorescence signal, G0 is the average amplitude of the electronic mixing signal and Gn its amplitude for every frequency harmonic, φn is the total phase from the fluorescence and electronic signal, and kΔϕ is the adjustable portion of the electronic signal phase which can be sequentially incremented (k = 1, 2, 3 …) for phase sampling. The total number of phase points sampled is chosen to satisfy the Nyquist criterion for the highest harmonic component N in the signal, i.e. k > 2N. Typically, the total number of harmonics is limited by the bandwidth of the detection system. An inspection of Eq. (2) shows that the phase-dependent signal D(k) contains the amplitudes and phase content of the fluorescence at each of the mixing frequencies. An experimental determination of the phase shift and demodulation terms at each frequency (as functionally defined by Eq. (1)) can thus be obtained from a comparison of the fluorescence phase sampled data with a phase sampled signal acquired from a sample with no intrinsic excited state lifetime, i.e. a reflecting sample such as a piece of aluminium foil. For such a case the phase sampled data are functionally described by Eq. (2), with the average amplitude of the fluorescence signal F0 and harmonic amplitudes Fn replaced by the average excitation signal E0 and harmonic amplitudes En, respectively. Furthermore, φn gives the total phase from the electronic signal only.

Experimental set-up

In order to achieve homodyne detection at a multitude of harmonic frequencies simultaneously they must first be experimentally introduced into both the excitation field and the electronic mixing signal.

Generation of a multi-frequency homodyne mixing signal in a microchannel plate image intensifier

Phase and modulation fluorimetry in a microscope has been made possible by the use of microchannel plate (MCP) image intensifiers as devices for frequency mixing. Such devices amplify a light image incident upon its photocathode surface by electron cascades within microchannels of the MCP ( Kume et al., 1988 ). The electron cascade is then converted into an amplified light image by excitation of a photoluminescence surface at the output of the device. By modulating the gain characteristics of these devices it is possible to obtain homodyne or heterodyne signals at every image pixel, where the slow response of the phosphor screen acts as a low pass filter. To date, only fluorescence lifetime imaging microscopes have been described which perform a single frequency measurement at a time.

In this work, the simultaneous homodyne detection at a multitude of harmonic frequencies was achieved by exploiting the higher harmonic content present in the gain characteristics of a MCP image intensifier modulated at its photocathode by a sinusoidal voltage. The experimental determination of the photoelectron gain function (PGF) for an image intensifier (Model C5825; Hamamatsu Photonics) as a function of photocathode voltage offset is shown in Fig. 1. Here, the image average at the phosphor screen output of the device resulting from a constant photocathode (PC) illumination was used as a measure of the PGF (see experimental configuration in the upper right of Fig. 1a). The figure shows that at positive voltages the device is in an ‘off’ state with a sharp switch to the ‘on’ state for a small negative offset. This arises because the application of a positive voltage at the photocathode prevents the transfer of negatively charged photoelectrons to the MCP. Thus, the application of a zero mean sinusoidal voltage effectively leads to an approximate square wave modulation of the gain characteristics as the sinusoidal voltage alternates in polarity. By increasing the dc component of the sinus (i.e. by adjusting the offset) it is possible to reduce the duration of the ‘on’ state of the device relative to its ‘off’ state, leading to a square pulse modulation of the gain ( Fig. 1b) with a subsequent increase in the amplitude of the higher harmonic content. In theory, as the duration of the ‘on’ state goes to zero, the relative modulation depth in the gain at all frequencies approaches 400%. This type of behaviour is shown in Fig. 2(b–e). For each harmonic the changes in the gain characteristics of the image intensifier are plotted as a function of the relative voltage bias (defined as the photocathode offset voltage divided by the amplitude of the applied sinus voltage). These changes were obtained from the relative modulation depth of phase sampled data taken from sinusoidally modulated laser light imaged onto the photocathode. For each plot in turn the frequency of the photocathode voltage ω′ was set such that a progressively higher harmonic term in the gain matched the excitation frequency, nω′ = ω. An inspection of Eq. (2) shows that, as the frequency and amplitude of the excitation remained unchanged, the relative modulation depth in the sampled data gives the relative modulation in the gain multiplied by a common scaling factor. From these plots it can be seen that, within the bandwidth of the image intensifier, more frequencies are made available for homodyne mixing with the input signal as the relative bias voltage is increased. However, the subsequent reduction in the amplitude of the ‘on’ voltage with increasing offset at the photocathode leads to a reduction of image resolution. This occurs because photoelectrons are less strongly accelerated in the weaker electric field between the photocathode and MCP and are thus capable of larger deviations from a direct trajectory.

Figure 1.

 V. (b) From the PGF the effective gain of the MCP image intensifier (lower plot) in response to a biased sinusoidal voltage at the photocathode (upper plot) is projected.

Figure 2.

5 image intensifier measured as a function of the relative voltage bias on the photocathode. The gain characteristics have been measured from the relative modulation depth of phase sampled sinusoidally modulated laser light imaged onto the photocathode of the image intensifier. (a) The normalized average and (b–e) relative amplitudes for the first four harmonic terms in the gain characteristics of the image intensifier.

Generation of an excitation waveform with higher harmonic content

Standing wave acousto-optic modulators (SW-AOM) provide a means of modulating a continuous wave laser in a sinusoidal manner at high frequencies (tens to hundreds of megahertz). A number of these can be employed in series to simultaneously modulate the excitation light at the individual frequencies of the AOMs, and their differences and sums ( Piston et al., 1989 ). In this work, three AOMs were available with approximately ± 25% tunability about centre frequencies of 40 MHz, 80 MHz and 160 MHz. Each AOM, however, operates efficiently only at well-defined discrete resonant frequencies: for the 40 MHz AOM the resonances are typically 200 kHz apart with a finesse of approximately 2.66. Careful choice of driving frequency for each AOM is thus required in order to obtain efficient excitation modulation at frequencies corresponding to a harmonic set. Furthermore, considering that each AOM results in over 50% loss of light intensity, combinations of only two AOMs were employed at any one time, giving a minimum of four harmonics in the excitation field. In order to increase the total number and span of frequencies (about 20–360 MHz) available for data analysis, the phase-dependent data from two experiments sets were combined, where in each experiment the 40 MHz or 160 MHz AOM was used in combination with the 80 MHz AOM. Combining the 40 MHz and 80 MHz AOMs resulted in a set of excitation modulations weighted towards low frequencies relative to the set obtained with the 80 MHz/160 MHZ AOM combination. Typical examples of phase sampled excitation light from a reflecting sample and its relative harmonic content for both a ‘low’ and ‘high’ frequency set are shown in Fig. 3.

Figure 3.

20.976 MHz. The relative voltage bias on the photocathode of the image intensifier was set at about 0.9.

Experimental configuration

The experimental configuration for mfFLIM required a few hardware components in addition to the standard FLIM configuration previously described in detail ( Squire & Bastiaens, 1999), and these are shown in Fig. 4. Here, each combination of two AOMs was driven by the amplified output of two frequency synthesisers (Marconi 2023). These in turn were phase locked to a master synthesiser used to modulate the photocathode voltage of the MCP image intensifier at a fundamental frequency matching the lowest frequency component in the excitation field. Computer control of the relative phase of the master synthesiser enabled the relative phase in the image intensifier gain to be controlled. In this way the phase-dependent image at the phosphor screen output of the image intensifier could be sampled by recording an image at successive phase settings over a full period (0–360°) of the fundamental harmonic in the gain. A cooled CCD camera (Quantix, Photometrics) was used for acquiring phase-dependent images.

Figure 4.

. Schematic for mfFLIM. The amplified outputs from two phase-locked frequency synthesisers are used to drive a combination of two standing wave AOMs, giving a set of excitation modulations at frequencies from a harmonic set. The resultant fluorescence with equivalent harmonic content is imaged onto the photocathode of a MCP image intensifier. A master frequency synthesiser is used to modulate the voltage on the photocathode of the MCP at a frequency corresponding to the lowest frequency component in the excitation. The approximate square pulse response in the effective gain of the device has higher harmonic content, which matches that of the fluorescent signal. These harmonics are mixed simultaneously with the harmonics in the fluorescence signal. High frequency components are filtered by the slow time response (ms) of the phosphor. The remaining phase-dependent signal contains all the information on the phase and amplitude of the fluorescence at each harmonic. By acquiring a set of phase-dependent images at the output of the image intensifier using a CCD camera, all the harmonic content in the homodyne signal can be sampled at every pixel in the image. The master frequency synthesiser is used to step the phase (Δϕ) of the gain between acquired images.

Numerical methods

Numerical analysis of mfFLIM phase-dependent images

A two-step approach was applied for the determination of fluorescence decay parameters at each pixel of an image. Firstly, a Fourier decomposition of the phase sampled data was performed to determine the phase shift and demodulation at each harmonic frequency, followed by a fit of the thus obtained phase shift and demodulation data to the dispersion relationships (Eq. (1)) using a non-linear fitting routine.

Fourier decomposition

Linearization of Eq. (2) by standard trigonometric identities gives the constant (dc), cosine (an) and sine (bn) components of the phase-dependent signal:

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where

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By direct comparison of Eqs (2) and (3) it is seen that dc = QEG0F0 gives the average amplitude of the phase-dependent signal and acn = QEGnFn/2 gives the amplitudes at each of the harmonics. As previously described ( Squire & Bastiaens, 1999), the cosine (an), sine (bn) and dc terms in the Fourier expansion given by Eq. (3) may be obtained on a pixel-by-pixel basis from a set of phase sampled images, either by the application of a discrete Fourier transform (DFT) or by fitting to a Fourier expansion ‘model’, i.e. a band-limited form of Eq. (3), using a singular value decomposition (SVD) algorithm. For each harmonic, the phase shift Δφn and demodulation Mn are calculated from the Fourier amplitudes (dc, an, bn) in the phase sampled fluorescence signal relative to a phase sampled zero lifetime sample (i.e. a scattering or reflective sample) according to:

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Where ΨE,n and ME,n are the phase and relative modulation of the excitation light at each harmonic. These were calculated from the results of averaging each phase sampled image of the excitation field reflected from a piece of aluminium foil and applying a Fourier analysis.

For generating phase shift and demodulation images at each harmonic the use of an SVD routine was chosen in preference to a DFT. This enabled error images of the Fourier components to be calculated from the residuals of fitting the phase sampled data to a truncated Fourier model ( Faunt & Johnson, 1992). These error images are then used in the non-linear fit of the phase shift and demodulation images to the dispersion relationships given by Eq. (1) (see below). A number of criteria need to be considered for deciding which of the harmonic terms to include in the truncated Fourier model. Normally all possible harmonic components are included in the signal up to the band-limit of the detection system. In this work, however, the highest frequency is limited by the AOMs, where frequency mixing between AOM outputs may also result in missing harmonics.

Non-linear fit to dispersion relationships

At each frequency both the phase shift and demodulation are dependent on the true fluorescence lifetime composition of the sample. These fluorescence decay parameters can be determined from a fit to the dispersion relationships (Eq. (1)) ( Gratton & Limkeman, 1983; Lakowicz & Maliwal, 1985). This was achieved using a Levenberg–Marquardt non-linear fitting routine ( Press et al., 1991 ) written in C for the image processing package SCIL Image (version 1.3, TNO Institute of Applied Physics, Delft, The Netherlands). Here, phase shift and demodulation images were simultaneously fitted on a pixel-by-pixel basis by minimizing the χ2 goodness of fit criterion:

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where images of the variances in the phase shift σ2Δφn and demodulation σ2Mn were estimated by applying error propagation to images of errors in the Fourier amplitudes. Approximate errors in the fitting parameters (αq, τq) were obtained from the diagonal elements of the covariance matrix returned by the Levenberg–Marquardt non-linear fitting routine.

Dramatic improvements in the fit could be achieved by exploiting prior knowledge about the fluorescent system. A pixel-by-pixel minimization of Eq. (6) leads to an individual set of lifetimes τq with corresponding fractions αq in each pixel. In many experiments it can be assumed that the lifetime values do not vary significantly over the different pixels. This knowledge can be used to reduce the number of free parameters using, for example, a global fitting approach ( Beechem, 1992). A simple, although less precise, method of exploiting this a priori knowledge utilizes a two-stage fitting approach for α determination at each pixel. Firstly, each of the phase-dependent images are averaged in order to obtain a single data point at each phase. This has the effect of decreasing the variance of the noise by the total number of pixels in the image, which comes at the expense of lost spatial information. This averaged phase data series can then be fitted as described above in order to obtain the lifetimes with the corresponding total fractional intensity. Using this knowledge of the lifetimes a second round of fitting can be performed on images. This may be achieved by substituting the estimated lifetimes back into the dispersion relations (Eq. (1)) and solving for the fractions αq in each image pixel. It is then possible to transform Eq. (1) to a set of linear equations that can be solved, for instance, by SVD. In this work, however, we simply fixed the lifetimes in a pixel-by-pixel minimization of Eq. (6). This fitting procedure has been termed a ‘lifetime invariant fit’.

Results

Simulated mfFLIM data

Both the SVD routine, for fitting phase sampled images to a Fourier expansion model (with errors) and the Levenberg–Marquardt routine, for fitting phase shift and demodulation images to the dispersion relationships (Eq. (1)), were tested on simulated data sets. By use of Eq. (3), two sets of 32 phase sampled reference images (11.25° phase separation) were generated, measuring 50 × 50 pixels. In order to closely simulate an experimental data set, the amplitudes for the cosine and sine components in each case were taken from the experimental data shown in Fig. 3. The first five most significant harmonic amplitudes were used for constructing a model of the detected excitation light, with all other Fourier components set to zero. The frequencies corresponding to each Fourier term in the model were set in order to match those shown in the experimental data and were: 21.077 MHz, 42.154 MHz, 63.231 Mhz, 105.385 MHz, and 126.462 MHz for the ‘low’ frequency set of modulations, and 80.244 MHz, 160.488 MHz, 240.732 MHz, 320.976 MHz and 481.464 MHz for the ‘high’ frequency set, respectively. The sample was modelled as a mixture of two fluorophores, giving an ideal bi-exponential fluorescence decay function. The simulated detected fluorescence signal from the sample was obtained by the convolution of this function with the model of the detected excitation field. In this way two sets of 32 phase sampled fluorescence images were generated using the harmonic content of the simulated reference data. Spatial variations in the composition of the fluorescent sample were modelled according to the (50 × 50 pixel) parameter images shown in the first row of Fig. 5c. Fluorescence lifetimes of τ1 = 4 ns and τ2 = 1 ns were applied, with the relative fluorescence contribution of the 4 ns component (α1) set to 0.23 (α2 = 0.77) within the 10 pixel wide ring and 0.7 (α2 = 0.3) outside of it. A quantum efficiency of unity was assumed for detection of the fluorescence signal, and Poisson noise with a photon-conversion factor (1/β) of 1/2 ( Verveer & Jovin, 1997) was then added to the phase sampled fluorescence and reference images. The β factor was calculated using the relationship β = σ2/I, where the variance and average intensity were obtained from a statistical analysis of 50 reflection images on a pixel-by-pixel basis. Every fourth image in the phase-dependent fluorescence data from both the ‘low’ and ‘high’ frequency sets is shown in Fig. 5a.

Figure 5.

0 pixel phase-dependent images of a mixture of two mono-exponential fluorescent lifetime species (τ1 = 4 ns and τ2 = 1 ns). The relative modulation amplitudes and corresponding frequencies used for simulating the detected excitation light were set from the five most significant terms in the relative amplitude spectrum shown in Figs 3a and b. The relative fluorescence intensity contributions of each species inside and outside of the 10 pixel wide ring were: α1 = 0.23 (α2 = 0.77) inside and α1 = 0.7 (α2 = 0.3) outside. The parameters defining the fluorescent composition of the sample are shown in the top row of panel (c). (b) The first and third rows show phase shift and demodulation images calculated from the results of fitting a Fourier expansion to the phase-dependent data in panel (a). The residuals resulting from a non-linear fit of the phase shift and demodulation images to dispersion relationships are shown below their respective data sets. (c) The resulting parameters and errors estimated from the fit are shown in the second and third row. A bi-exponential fluorescence decay model was assumed in the fit. (d) The fractional fluorescence intensity (α1) and associated error calculated from a lifetime invariant fit to the combined low and high frequency sets.

The phase shift and demodulation images calculated from fitting a Fourier expansion model to the phase sampled data resulting from the ‘low’ and ‘high’ frequency excitation sets are shown in Fig. 5b. As expected, the relative degree of noise in the phase shift and demodulation images was largest where the relative modulation in the Fourier amplitudes of the reference was smallest. The fluorescence lifetime parameters resulting from a non-linear fit of this data to the dispersion relationships are shown in Fig. 5c and are in excellent agreement with the original parameters used in the simulation. Furthermore, the fit residuals ( Fig. 5b) are seen to be randomly distributed about zero. Error images generated from the fit are also shown, demonstrating a difference in the size of errors inside and outside the ring. The error for τ1 is larger inside the ring than outside owing to the low fraction of α1 inside the ring. This situation is reversed for τ2, where the error is largest outside the ring, in agreement with the low fraction of α2 (i.e. 1–α1) in that part of the image. These results are also summarized in Table 1a, where a statistical analysis of the fitting and error images inside and outside of the ring are compared. The average values of the lifetime components are accurately recovered and, as expected, the averages of the error images match the standard deviation in the fit well. Table 1b also summarizes the results of fitting to a reduced data set of five phase shift and demodulation images derived from phase-dependent data corresponding to the ‘low’ frequency excitation set alone. Here again the lifetime parameters are well recovered, with errors between two and three times as large as those derived with the combined phase shift and demodulation data sets. When a lifetime invariant fitting procedure (see numerical methods) was applied, to both the combined and reduced data sets in turn, the errors in the estimated parameters improved by at least one order of magnitude in both cases. The map of α1 and errors from the lifetime invariant fit of the combined data sets are shown in Fig. 5d, demonstrating that the original parameters used in the simulation are recovered with a high degree of fidelity.

Table 1.  . Fit parameters of simulated data for a low (a) and a combined (b) frequency set. 1 Average value of parameter within the structure. The value in parentheses was obtained with the lifetime invariant fit procedure.2 Standard deviation of parameter within the structure. The value in parentheses was obtained with the lifetime invariant fit procedure.3 Error in parameter within the structure calculated from the fit. The value in parentheses was obtained with the lifetime invariant fit procedure. Thumbnail image of

From these results the power of the lifetime invariant fitting procedure is clearly demonstrated, as it enables lifetime parameters to be estimated with relatively low error even from phase shift and demodulation data corresponding to a limited set of modulation frequencies. This is especially important for fluorescence lifetime work in live cell samples, because the consequent reduction in the sampling requirement enables data to be acquired quickly and the total exposure time limited, thus minimizing problems associated with cell movement and photobleaching.

mfFLIM measurements of a rhodamine dye mixture

The mfFLIM configuration and fitting routines were tested on an equiMolar (1 μm) solution of rhodamine 6G and rhodamine B in distilled water. The sample was pipetted onto a glass coverslip-bottomed Petri dish (MatTek Corporation) and images were acquired using a Zeiss 40× ph2 LD air objective. The 514 nm line of the argon/krypton mixed gas laser was used for excitation of the sample. The light was modulated by two AOMs acting in series: either the 40 MHz and 80 MHz AOMs tuned to modulate at 42.154 MHz and 63.231 MHz (including the sum and difference mixing frequencies) for a low frequency excitation set, or the 80 MHz and 160 MHz AOMs tuned to 80.244 MHz and 160.488 MHz (and sum and difference mixing frequencies) to give a high frequency excitation set, respectively. The sample was epi-illuminated and the fluorescence collected using a filter set comprising a 565 nm long pass dichroic in combination with a 610/75 nm band pass emission filter (Chroma Technology Corporation, ). For the ‘low’ and ‘high’ frequency sets the photocathode of the MCP was modulated at a fundamental frequency of 21.077 MHz and 80.244 MHz, respectively, with a relative voltage bias of about 0.9, and 32 phase sampled images were collected in each case (i.e. 11.25° phase steps between images). Reference images were obtained by phase sampling reflected light from aluminium foil illuminated with the modulated laser light. The averaged phase-dependent data of the reference resulting from illumination with the ‘low’ and ‘high’ frequency set and their relative harmonic content are shown in Fig. 3. All phase-dependent images were corrected for dark current and stray light by subtracting an image acquired in the absence of excitation field illumination. No significant photobleaching was observed in the fluorescence signal, owing mainly to the large diffusional volume of the sample.

Two sets of images showing phase sampling of the fluorescence from the rhodamine sample illuminated with excitation light modulated with a set of ‘low’ and ‘high’ frequencies can be seen in Fig. 6a, where every fourth phase sampled image is shown. The phase shift and demodulation images resulting from fitting both sets of phase sampled images to a Fourier expansion model have been combined and are shown in Fig. 6b. The phase shift and demodulation, together with their error images, were fitted to the dispersion relationships, where a bi-exponential fluorescence decay model was assumed. The fit parameters and error images estimated from these data are shown in Fig. 6c. The fitting procedure was also applied to a reduced data set corresponding to the five phase shift and demodulation images derived from phase-dependent data from the ‘low’ frequency excitation set alone. The results of this fit are summarized in Table 2a. Here, the fluorescence lifetimes recovered for the rhodamine B/6G mixture were in reasonable agreement with the literature values of 1.5 ns and 4 ns, respectively ( Lakowicz & Berndt, 1991). Furthermore, a relative intensity contribution of 73% was recovered for α1, which was in excellent agreement with a 71% value calculated from independent intensity measurements of rhodamine 6G and rhodamine B alone; taken using the same filter set as for the mfFLIM experiment.

Figure 6.

G and rhodamine B in distilled water. (a) Two sets of phase sampled fluorescent images (181 × 154 pixel) from the dye mixture excited at 514 nm with laser light modulated using a combination of AOMs to give a low and high set of harmonic frequencies, respectively (as shown in Fig. 3). (b) The first and third rows show phase shift and demodulation images calculated from the results of fitting the phase dependent data to a Fourier expansion model. The residuals resulting from a non-linear fit of the phase shift and demodulation images to the dispersion relationships are shown below their respective data sets. (c) The resulting parameters (α1, τ1, τ2) and errors estimated from the fit are shown the second and third row of this panel. A bi-exponential fluorescence decay model was assumed in the fit.

Table 2.  . Fit parameters of rhodamine B/6G mixture for a low (a) and combined (b) frequency set. 1 Average value of parameter in the image. The value in parentheses was obtained with the lifetime invariant fit procedure.2 Standard deviation of parameter in the image. The value in parentheses was obtained with the lifetime invariant fit procedure.3 Error in parameter in the image calculated from the fit. The value in parentheses was obtained with the lifetime invariant fit procedure. Thumbnail image of

The fit to the combined phase shift and demodulation data sets ( Table 2b) resulted in lower values for the recovered lifetimes of rhodamine B/6G and an overestimate of α1 ( Table 2). This may well arise because at the higher frequencies found in the combined data sets, both the phase shift and demodulation are weighted towards shorter lifetimes. In a bi-exponential fit of data exhibiting an additional short lifetime component with significant amplitude these high frequency data points exert a downwards influence on the estimated fluorescent lifetimes. This could be accounted for by refining the fitting model to include additional lifetime components. However, with few frequencies the increase in the number of parameters is likely to lead to a much worse definition of the minimum in error space. It may be more effective to judiciously select a set of low modulation frequencies such that the small amplitude, short lifetime components often observed in fluorescent samples are effectively filtered out.

The results of applying a lifetime invariant fitting procedure to the phase shift and demodulation data are also summarized in Tables 2a and b. The fluorescent lifetime parameters recovered show good agreement with their conventionally fitted counterparts but, as expected, have much smaller errors.

These results demonstrate in practice that with as few as five phase shift and demodulation images the populations of a binary mixture can be resolved, especially if the lifetime invariant fitting procedure is employed.

mfFLIM measurements of two co-expressed green fluorescent fusion proteins in live cells

We investigated whether mfFLIM could be used to disentangle the cellular distributions of co-expressed green fluorescent proteins (GFPs) with differing lifetimes ( Pepperkok et al., 1999 ). HeLa cells were plated on Matek Petri dishes in MEM supplemented with 5% foetal calf serum. These were microinjected in the nucleus with cDNA encoding plasmids for the yellow fluorescent protein (YFP5), which distributes diffusively throughout the cell, and a Golgi resident green fluorescent fusion protein (NA-GFP5) ( Pepperkok et al., 1999 ). Dishes of cells were washed and submerged in CO2 independent medium (GibcoBRL, ) before mfFLIM measurements at 37 °C. The GFP variants were excited with the 488 nm argon/krypton laser line. The detection filter block contained a dichroic beamsplitter 505LP (Chroma) in combination with a High Q bandpass emission filter 515/50 BP (Delta Light & Optics). A Zeiss Plan-Apochromat 100 ×/1.4 NA ph3 oil objective was used. In order to reduce the data sampling time to below 10 s phase-dependent data ( Fig. 7a) were acquired for a single set of excitation frequencies only. In this way photobleaching and artefacts due to movement of the live sample were minimized. The excitation light was modulated by the 40 MHz and 80 MHz AOMs tuned to 39.175 MHz and 117.525 MHz, respectively, and the photocathode of the MCP was modulated at the fundamental frequency of 39.175 MHz with a relative voltage bias of about 0.9. Phase sampled reference images were collected in the same manner as described above. A Fourier analysis of this data showed significant harmonic amplitudes at five frequencies: 39.175 MHz, 78.350 MHz, 117.525 MHz, 156.700 MHz and 195.875 MHz. For the cell samples, two times 16 phase-dependent images at 22.5° phase steps and 300 ms exposure were collected forwards and backwards over a full phase cycle of the fundamental. In this way any photobleaching could be corrected to first order from the image average at each phase setting ( Gadella et al., 1993 ). As only a single set of excitation frequencies was used, a lifetime invariant fitting procedure was employed for fitting phase shift and demodulation assuming a bi-exponential fluorescence decay. By using this approach we have reasonably assumed that the fluorescent lifetimes of the GFPs were pixel invariant parameters in contrast to the relative populations. The images of the fractions α1 and associated error resulting from this fit are shown in Fig. 7c. Multiplying the average dc image (top image in Fig. 7d) by the α1 and α2 (1–α1) images gave fluorescent intensity estimates for the cytosolic/nuclear YFP5 and Golgi resident NA-GFP5, respectively (shown by the middle and bottom images of Fig. 7d). These are seen to properly reflect their expected distributions in the cell. The results of the fit gave a recovered lifetime of 3.62 ns for YFP5, which is in good agreement with phase (τφ = 3.69 ns) and modulation (τM = 3.60 ns) values measured at 80.218 MHz, published previously ( Pepperkok et al., 1999 ). This is to be expected, as the similarity in the phase and modulation lifetimes is indicative of a homogeneous fluorescent state. On the other hand, previous phase and modulation lifetime measurements for NA-GFP5 showed heterogeneity in their values (τφ = 2.05 ns, τM = 2.40 ns), indicating the presence of a sub-population with shorter lifetimes. This could account for the lower recovered lifetime of 1.56 ns obtained for NA-GFP5 in this work. However, despite the use of only a bi-exponential decay model the intensity of the coexpressed GFP mutants were still effectively disentangled.

Figure 7.

5 MHz. (b) The first and third rows show phase shift and demodulation images calculated from the results of fitting the phase-dependent data to a Fourier expansion model. The residuals resulting from a non-linear fit of the phase shift and demodulation images to the dispersion relationships are shown below their respective data sets. (c) The resulting fractional intensity α1 and error image estimated from the non-linear fit. A bi-exponential fluorescence decay model was assumed in the lifetime invariant fit, where lifetimes of 3.64 ns and 1.56 ns were recovered for YFP and NA-GFP5, respectively. (d) The average fluorescence intensity (dc) and estimated intensities of NA-GFP5 (dc-NAGFP5) and YFP5 (dc-YFP5), calculated from the multiplication of the dc image with the images of the fractional fluorescence contributions (α1 and α2).

Discussion

We have demonstrated that multiple frequency fluorescence lifetime imaging can be performed by utilizing the higher harmonic content present in the gain of a MCP due to approximate square pulse modulation. Each of these harmonics is available for homodyne mixing with an equivalent set of frequencies in the fluorescence emission. These harmonic sets were obtained by modulating the excitation using a combination of AOMs. In this work mfFLIM has been performed by simultaneous detection of phase and modulations at multiple harmonic frequencies in contrast to sequential acquisition at individual frequencies. The parallel data acquisition mode has been implemented owing to several practical advantages over the sequential acquisition mode. First, there is no need for pure sinusoidal modulation of the excitation or detection, which is difficult to achieve in practice. Second, the modulation depths in the parallel acquisition mode are exceeding the theoretical 50% for sinusoidal modulation up to a factor of 4, resulting in better lifetime definition. Third, phase reproducibility at each of the sampled N frequencies is not a necessary requirement and therefore a single reference measurement is sufficient in contrast to N reference measurements in sequential mode. Fourth, the average signal (dc) is sampled only once in parallel acquisition mode in contrast to N times in the sequential mode, resulting in a reduction of the minimal data set which satisfies the Nyquist criterion by N − 1, where N is the number of sampled frequencies.

It was shown that with as few as five harmonic frequencies the populations of two fluorescent entities could be separated. mfFLIM enables the composition of fluorescence mixtures to be directly quantified, as multiexponential decay models can be fitted to the data. Practical examples of applications are the quantification of: (1) the distributions of multiple co-expressed GFPs in cells as examplified above, or (2) the populations of interacting molecules by the measurement of FRET through donor lifetimes ( Gadella et al., 1994 ; Bastiaens & Squire, 1999; Ng et al., 1999 ). In the latter case, the lifetimes in the presence and absence of acceptor are obtained at each pixel, the division of which gives directly the true FRET efficiency for the interacting pair. From the returned fractional intensity (α) image the efficiency of molecular association can be determined at each pixel.

Improvements to the current mfFLIM approach may be achieved by implementing hardware and software modifications in a number of ways. At present, 50% light loss at each of the AOMs and the difficulty in matching resonances to a harmonic set restricts the number of frequencies at which the excitation can be modulated. Although this may be overcome, in part, by combining the results of two or more independent measurements employing differing frequency combinations, this comes at a cost of increased data acquisition time. The number of frequencies available in the excitation could be increased significantly by using the higher harmonic content in the excitation of high frequency pulsed light sources such as a mode-locked laser ( Alcala et al., 1985 ; Watkins et al., 1998 ) or by the use of a pulsed Pockels cell coupled to a CW laser ( Verkman et al., 1991 ). These frequencies could be matched with pulsed high frequency modulation on the MCP, resulting in a broader spectrum of harmonic frequencies available for the simultaneous homodyne detection in one set of measurements. Additionally, in comparison to sinusoidal modulation of the photocathode, pulsing with a strong voltage should also result in an improved spatial resolution of the image intensifier. With these proposed set-ups, however, the higher harmonic content present in the excitation would require more sampling to avoid aliasing. This might not always be desirable due to associated longer acquisition times and increased level of photobleaching, especially in live samples. In this case, a restricted set of modulation frequencies, as applied in this work, might be optimal in combination with further improvement in the data analysis. This could be achieved by exploiting the notion that the pixels in an image can be conceived as individual experiments which are connected by a common set of physical laws. Inter-relationships between decay parameters at each pixel can be encoded in a global fit of the image in order to reduce significantly the fitting errors. For example, for a mixture of two fluorophores with homogeneous decays or a single fluorophore in two states, the lifetimes are pixel invariant and could be linked in the double exponential decay model over the whole image where the amplitudes are left uncoupled. This results in a reduction of 2P2–2 independent fitting parameters for a P × P image. The global fitting approach might therefore be expected to bring significant improvements in quantifying the distributions and populations of states of fluorescent bio-molecules in cells as measured by mfFLIM.

Acknowledgements

P.J.V. was supported by a long-term EMBO fellowship.

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