Appl. Phys. B 63, 517-523 (1996) Applied Physics B and Optics

© Springer-Verlag 1996

Detection and characterization of single molecules in aqueous solution

C. Zander 1, M. Sauer 2, K. H. Drexhage 1, D.-S. Ko 2'*, A. Schulz 3, J. Wolfrum 3, L. Brand 3, C. Eggeling 3, C. A. M. SeideP'**

lInstitut fiir Physikalische Chemic, Universit~it-Gesamthochschule Siegen, Adolf-Reichwein-Strage 2, 57068 Siegen, Germany 2Physikalisch-Chemisches Institut, Universifiit Heidelberg, Im Neuenheimer Feld 253, 69120 Heidelberg, Germany 3Max-Planck-Institut fiir Biophysikalische Chemic, Am Fagberg 11, 37077 G6ttingen, Germany

Received: 13 June 1996

Abstract. Using a confocal microscope with a single- photon avalanche photodiode as detector, we studied photon bursts of single Rhodamine 6G (R6G) and Rho- damin B-zwitterion (RB) molecules in aqueous solution by excitation of the lowest excited singlet state $1 with a frequency-doubled titanium:sapphire laser. Multichan- nel scaler traces, the fluorescence autocorrelation function and fluorescence decay times determined by time-corre- lated single-photon counting have been measured simul- taneously. The time-resolved fluorescence signals were analyzed with a maximum likelihood estimator. Fluores- cence lifetime patterns in steps of 100 ps were generated by convolution with the excitation pulse. The lifetime of the $1 state was derived from the Kullback-Leibler minimum discrimination information. We are able to demonstrate for the first time identification of two different single dye molecules via their characteristic fluorescence lifetimes of 1.79 _ 0.33 ns (RB) and 3.79 +_ 0.38 ns (R6G) in aqueous solution.

Over the past few years, several fluorescence-based tech- niques have evolved with sufficient sensitivity to detect single molecules in solution [1-11]. A serious problem with single-molecule detection in the visible wavelength region is the background signal generated by Raman and Rayleigh scattering as well as by fluorescence of impurities in the solvent. To reduce the background signal, it is imperative to use ultrapure solvents and well-suited op- tical filter systems. In addition, Raman scattering can be strongly minimized by reducing the detection volume [3]. The detection of single fluorescent molecules in solution

*On leave from Department of Physics, Mokwon University, Taejon, 301-729, Korea **Corresponding author

Dedicated to Prof. F. P. Schiller on the occasion of his 65th birthday.

using a small volume of 10-1Sl defined by a confocal microscope was pioneered by Rigler and coworkers [3-6]. The use of an extremely small open volume element (10-1Sl and below) in combination with confocal epi- illumination improves the signal-to-noise ratio by orders of magnitude without measurable photodestruction of the dye molecules under study [9, 10]. These improvements have led to the detection of single molecules in water excited by a diode laser emitting at 632 nm [12] as well as single-molecule detection by observing their fluores- cence after two-photon excitation [13]. The results ob- tained in recent years let us expect many diagnostic ap- plications on the single-molecule level in the near future [14-18].

Soper et al. [6] first reported the measurement of spectroscopic properties at the single-molecule level. In these experiments, the differences in the spectral emission properties of individual molecules of Rhodamine 6G (R6G) and Texas red in combination with two separate detectors were used to distinguish the two dyes. The identification of different dye molecules on the single-mol- ecule level by measuring their characteristic lifetimes of the first excited singlet state S~ via fluorescence decay times (fluorescence lifetimes) was suggested frequently, but it has not been realized up to now. Previous experiments using a time-resolved fluorescence detection had detection volumes in the pl range in order to obtain molecular transit times sufficiently long making single-molecule detection possible [1, 2, 6-8].

In this article, we present first results of time-resolved fluorescence identification of single molecules in water combining a confocal microscope with the technique of Time-Correlated Single-Photon Counting (TCSPC). For our experiments, we used two rhodamine dyes (R6G and Rhodamin B-zwitterion (RB)), which differ only slightly in their spectral properties. For excitation we employed a frequency-doubled titanium:sapphire laser providing pulses in the fs region. The detection was performed with a single-photon avalanche photodiode and two different kinds of PC-boards for time-correlated single-photon counting.

518

A~'~rgon ion laser ~ ~ T i : S a p p h i r e

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MCS ] SPC-300 [NIMmodules/PClCorrelator [

~ SPAD

MO

GP

L3

0

L1

FDC

L 2

RM, A ~

Sample

Fig. 1. Setup for confocal time-resolved identification of single molecules. L1 : lens (f= 60 mm); FDC: frequency- doubling crystal (BBO 2 mm); Lz: lens (f = 80 mm); RM: blocking of residual IR radiation by a resonator mirror; A: attenuator; L3: lens (f= 250 ram); GP: fused silica glass plate; MO: microscope objective ( x 100, NA = 1.4); IF: interference filter 565-DF-50; PH: pinhole (100 gin)

1 Experimental

In our experiment (Fig. 1), a titanium:sapphire laser (Mira 900, Coherent, Palo Alto, CA) pumped by an argon ion laser (Innova 415, Coherent, Palo Alto, CA) served as the excitation source. The pulse width of the tita- nium: sapphire laser was approximately 300 fs at a repeti- tion rate of 76 MHz. The wavelength of the laser was adjusted to 1028 nm.

To ensure that only light at a wavelength of 514 nm reaches the microscope, a resonator mirror (RM) (No. 0163-49-03, Coherent, Palo Alto, CA) was placed behind the frequency-doubling crystal (FDC) (BBO, 2 mm) to block the residual IR radiation. Using an attenuator (A), the power was adjusted to 370 ~tW at the sample. The laser beam was prefocused by the lens L3 ( f = 250 mm) and sent into the microscope by a fused silica glass plate (GP). Inside the microscope, the beam was focused onto the sample by an oil-immersion objective (MO) (SPlanapo x 100, NA = 1,4; Olympus, Tokyo, Japan). The diameter of the focus was adjusted to approximately 1 gin. The fluorescence emitted by dye molecules was collected by the same objective and detected by a single-photon counting avalanche photodiode (SPAD) (SPCM 200; EG&G, Canada). A 100 ~tm pinhole (PH) was placed in the image plane to block out-of-focus signals. An interfer- ence Filter (IF) (565-DF-50, Omega Optical, Brattleboro, VT) was used to suppress laser light and Raman scattered photons. The signal of the SPAD was amplified and registered by four different devices: (i)a PC-adapter counter (CTM-05, Keithley, Taunton, MA) for multichan- nel scaler traces of the fluorescence signal in the ms time range; (ii) a PC-card (SPC-300, Becker&Hickl GmbH, Berlin, Germany) for time-correlated single-photon counting with a minimal integration time of 10 ms for the fluorescence decay curves; (iii)time-correlated single- photon counting with conventional N1M modules (constant fraction discriminator Tennelec 454, time-to- amplitude converter Tennelec 862 and an analog-to-

digital converter Silena 7423 UHS-S) with a home-made PC-card which allows the measurement of fluorescence decay curves with a fixed photon number; and (iv) a real-time correlator card (ALV-5000/E, ALV, Langen, Germany) for fluorescence correlation spectroscopy. Time-correlated single-photon counting was performed in the reversed mode, i.e. the signal of the SPAD was used to start the clock of the time-to-amplitude converter and the reference signal of the titanium: sapphire laser was used as the stop signal. Using the PC-card SPC-300, the fluores- cence signal was collected in up to 100 histograms with an integration time of 10 ms. On the other hand, the home- made PC-card collects a constant number of photons (100-200) in a sequence of histograms.

The solutions for single-molecule experiments were prepared in double-distilled water by diluting 10-6M stock solutions with the appropriate amount of solvent down to the required concentration of l x t0-11M for Rhodamine 6G and Rhodamine B (Radiant Dyes, Germany). To ensure the formation of the Rhodamin B- zwitterion (deprotonated form of Rhodamine B with slightly blue-shifted spectral properties and a longer flu- orescence lifetime compared to the protonated form), 50 gl of the base triethylamine was added to 100 ml of the dye solution. Samples were transferred to the microscope support by a microscope slide with a small depression and covered by a conventional cover glass. The fluorescence lifetimes of bulk solutions were measured with the setup described above at a concentration of 1 x 10 8 M.

2 Results and discussion

2.1 Multichannel scaler trace

We used a MultiChannel Scaler (MCS) to monitor the time-dependent fluorescence fluctuations due to single- molecule transits through our detection volume. Poisson statistics predicts, for such low concentrations, that the

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519

Fig. 2. Fluorescence signals observed from rhodamine 6G excited by a frequency-doubled titanium: sapphire laser (514 nm, 370 gW). Data acquisition was performed at a speed of 1000 data points per second (1 ms integration time). (a) Rhodamine 6G (10 pM in water). The inset shows an expanded view of the fluorescence bursts. (b) Pure water

number of molecules fluctuates predominantly between 0 and 1 in a femtoliter detection volume. Figure 2a shows the time-dependent fluorescence signals of a 10 -11M Rhodamine 6G solution with fluorescence burst rates of up to 140 photons in 1 ms (140 kHz). For comparison, the background signal of pure water is given in Fig. 2b.

With our experimental setup, an average background level of approximately 2 kHz was obtained, which arises mainly from Raman scattered photons. On the basis of this background, we calculate a signal-to-noise ratio of up to 70 in water for an integration time of 1 ms.

2.2 Fluorescence correlation spectroscopy

We used Fluorescence Correlation Spectroscopy (FCS) as a method to provide precise statistical characteristics with respect to an average molecule number in the detection volume and an average diffusion time [9, 19-22]. The fluorescence signal I(t) was analyzed by the normalized intensity autocorrelation function G,(z~) assuming a three-dimensional Gaussian intensity distribution of the exciting laser beam. The intensity is given by I(r,z) = Io e x p ( - 2rZ/cog)exp( - 2z2/zg) with the 1/e 2 radius COo for the radial direction (r) and the 1/e 2 radius z0 for the axial direction (z). If intersystem crossing, triplet decay and translational diffusion are the only noticeable processes that cause fluorescence fluctuations in the meas- ured fluorescence I(t) about the average intensity ( I ) , then G,(~o) can be expressed by (t) E20, 23]:

(I(t + zo)I(t)> G,(z~) = ( i>2

(1 - IB/I) 2 = 1 + ( 1 - A + A e ~°/~*)

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Fig. 3. Normalized fluorescence autocorrelation function G,(~c) with time trace (inset) for 10- ~ M Rhodamine 6G in water. Re- corded data and fitted curve (Eq. (1)) with weighted residuals [23]. The following parameters were obtained with a background inten- sity of 2 kHz and a signal intensity of 4.2 kHz: baseline: 1.001; N: 0.033; ~D: 172 gs (COo: 0.45 pm); Zo/~Oo: 20; A: 0.108; zt: 3 ps

Here N is the average number of molecules in the detec- tion volume, A is the average fraction of molecules in the excited triplet state with a triplet correlation time zt, D is the translational diffusion coefficient and Zv = co~/4D is the characteristic time for diffusion. Furthermore, the am- plitude of the autocorrelation function will be influenced by the ratio of background IB to the total signal intensity I [23]. A typical normalized fluorescence correlation func- tion of 10 11M Rhodamine 6G solution is shown in Fig. 3.

520

Fitting of this curve with (1) using a Marquardt- Levenberg least-squares algorithm yields an average num- ber of molecules N of 0.033 (for parameters see Fig. 2), which shows that we detect predominantly single-mole- cule events. Assuming a diffusion coefficient D = 3 x 10-6 cm2s-1 [-20] for Rhodamine 6G, we can estimate from the characteristic diffusion time of 170 gs a three- dimensional Gaussian detection volume (V = (~/2)3/2co 2 Zo) of a few femtoliters. At a power of 370 gW of the exciting laser, intersystem crossing to the triplet state occurs for an average part of 11% of the molecules.

2.3 Time-resolved fluorescence spectroscopy

Our MCS and FCS data clearly prove that we have achieved a detection efficiency which should make pos- sible a real-time detection and identification of single molecules in water by time-resolved fluorescence spectro- scopy.

As indicated by the data in Table 1, the spectroscopic characteristics of Rhodamine 6G and Rhodamin B-zwit- terion meet several criteria for a time-resolved identifica- tion in aqueous solution. Both dyes are easily excitable with our frequency-doubled Ti:sapphire laser and exhibit fluorescence lifetimes which are well distinct. Figure 4 shows a three-dimensional plot of the fluorescence inten- sity vs the fluorescence time scale in ns and the macro- scopic time scale in ms, which was measured with the PC-card SPC-300 for a 10 11M aqueous solution of Rhodamine 6G. The corresponding time-integrated fluo- rescence signal trace with a bin width of 10 ms is given by the projection on the ms-time axis.

If a dye molecule passes the detection volume, up to 320 counts are collected, whereas about 20 counts are collected for background in the detection window of 12.6 ns.

For the following detailed statistical analysis of a few hundred detected photons in a fluorescence burst, we need an optimal estimation procedure to obtain fairly reliable fluorescence lifetimes. The Rao-Cram6r theorem found in the statistical literature states that in general the variance of an estimate cannot be smaller than a well-defined limit. The Maximum Likelihood Estimator (MLE) and the X 2 estimator (least-squares) reach this limit and are therefore called efficient estimators [24-28]. Considering small sig- nal intensities, as in our case, it could be shown by in- formation theory that a log-likelihood-ratio test has the lowest error or misclassification probability [29]. K611ner et al. [25, 27, 28] used the MLE successfully for fluores- cence pattern recognition and tested the efficiency by comparing the experimental error probability with the theoretical misidentification probability. Following the principal ideas of K611ner, we developed an algorithm which takes into account the experimental conditions

Table 1. Spectroscopic properties of the Rhodamine dyes used for the single-molecule identification. The wavelengths correspond to the maxima of the absorption and emission bands for the So-S ~ transitions

Solution "~abs [nm] Ae~ [nm] v [ns]

Rhodamine 6G Water 526 556 3.89 Rhodamin Water (basic) 554 577 1.73 B-zwitterion

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Fig. 4. Fluorescence decay curves of bursts due to single-molecule transits in a 10 21 M aqueous solution of Rhodamine 6G measured with the PC- card SPC-300. 3D plot of the fluorescence intensity vs the fluorescence time scale (ns) and the macroscopic time scale (ms). The corresponding time-integrated fluorescence trace with a bin width of 10 ms is given by the projection on the ms-time axis

521

needed for a real-time single-molecule detection and uses the entire measured signal including fluorescence, back- ground and stray light.

Since we have obtained our time-resolved fluorescence data by time-correlated single-photon counting, the counts are accumulated in channels. The distribution of N signal counts in k channels is best described by a multi- nomial distribution, where n~ is the number of detected photons in channel i. For this case, we use the MLE in (2) to determine fluorescence lifetimes of bursts on the basis of a minimum reduced 21" (Kullback-Leibler minimum discrimination information) [31] using different fluores- cence lifetime probabilities rni(r) (see below),

21" - k - 1 - f ~ n~ in , (2)

where m~ is the probability of a distinct fluorescence life- time pattern that a count will fall in channel i and f is the number of fitted parameters. Normalization of 2I* by the degrees of freedom (k - 1 - f ) leads to the reduced 21", which is 1 for an optimal fit and behaves similar to the reduced Zr 2 known from least-squares estimators.

A fluorescence lifetime pattern M appropriate for (2) is generated in several steps. Let us consider a monoex- ponential fluorescence decay and assume that the instru- ment response function (laser, detection system, and elec- tronics) may be described by a 5-pulse. The probability Pi of finding a count in channel i is then given by (3), where p~ depends on the number of channels k, the fluorescence lifetime r and on the finite measurement window T ex- pressed as a reduced time window (in numbers of lifetimes) r = T/z and where ~Pi = 1 (multinomial distribution):

e r/k -- 1"] pi(z, T,k) = e ir/k \ i--e;/ (3)

Recent experiments with time-resolved fluorescence detection have been performed with time-gated fluores- cence detection which analyze only a part of a fluores- cence decay [1, 2, 6, 8, 11]. These techniques do not use all emitted photons by disregarding the maximum of the fluorescence decay. Because the number of emitted and detected fluorescence photons in experiments with single molecules is limited by the diffusion time, the lifetime of the triplet state, and the photostability of a dye, it is crucial for an efficient molecule identification to measure and to analyze the entire fluorescence decay. Hence, the Instrument Response Function (IRF) has to be measured to generate a realistic fluorescence lifetime pattern which can be compared with a measured decay by the MLE. In reconvolution analysis, the normalized fluorescence life- time probabilities ci are obtained in (4) by convolution of the probability of the normalized IRF d with p of our lifetime model for a 6-IRF (3) [30]:

(d ® p('c, T, k))i ci(z, T, k) = ~ = l(d ® p(z, T,k)),

Emin(i.f) djPi _j(z, T, k) j=o

12_.j=o ajPi_Ar, T,k)" (4)

Taking a fraction u of constant background u into ac- count, (5) gives the multinomial probability M(z, T, k, u) for the probability mz(z, T, k, u) of the channel i:

U mi( 'c , T,k,u) = ~ + (1 -- u)ci('c, T, k). (5)

The IRF was obtained from laser light scattered at the boundary layer of the microscope slide. To define the fraction of background contained in the fluorescence decay curve, we added up all fluorescence decays of the single-molecule bursts. By doing this, we obtained a flu- orescence decay of good signal quality which allows the precise determination of several parameters. In the analy- sis of the integrated measurement with the MLE, the background fraction u and the shift s of the IRF with respect to the fluorescence decay were allowed to vary freely beside z. The values for the parameters u and s with a minimal 2I* and optimal-weighted residuals were kept constant in the further analysis of the individual decays; i.e. the only remaining adjustable variable is the para- meter of interest r.

The idea behind our analysis procedure is to generate a set of fluorescence lifetime patterns in steps of r of 0.1 ns

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Fig. 5. Normalized fluorescence decay curves of bursts (right axis) of single Rhodamine molecules (10 pM in water) with the number of detected photons N. The thin line is the normalized Instrument Response Function (IRF) (left axis). Seven channels of the peak were used for convolution (Eq. (5)). The fit (bold line) has been performed with a maximum likelihood estimator (Eqs. (2) and (5)) with a con- stant background fraction u. The insets show the dependence of 2I* on the fluorescence lifetime r (Eq. (2)). (a) Rhodamine 6G T: 3.7 ns; u: 0.05; 2I*: 0.982; N: 317. (b) Rhodamin B-zwitterion ~: 1.8 ns; u: 0.15; 2I*: 0.880; N: 160

522

and to study the dependence of 2I* on r (inset in Fig. 5a and b).

By collecting the values of ~ with a minimal 2I* for individual single molecules, we obtained a distribution of individually determined fluorescence lifetimes (Fig. 6).

The average fluorescence lifetimes of 1.79 + 0.33 ns for Rhodamin B-zwitterion and 3.79_+0.38 ns for Rho- damine 6G are in good agreement with the lifetimes from Table 1, whereby the obtained fluorescence lifetime distri- butions are centered around the lifetimes obtained from our bulk measurements. Furthermore, the 2I* surfaces give an impression on the individual error defined by the width of the minimum. Comparing the depth of the 21" surfaces for rhodamin B-zwitterion and rhodamine 6G, it is obvious that the depth of the 2I* minima for rhodamine 6G is smaller because the size of 12.6 ns of the actual fluorescence time window T is smaller than the optimal value of approximately 6 lifetimes [251, Using more than 250 single-molecule transits of both Rhodamine 6G and Rhodamin B-zwitterion, we were able to demonstrate that an unequivocal identification due to different fluorescence lifetimes of single molecules in water is possible by collect- ing more than 100 counts (Fig. 6). As a lower limit for the average statistical variance of the measured lifetimes, the variance of a lifetime for a fluorescence decay with no background and with an instrument response function described by a ~-pulse is given by (6) [24]:

1 r2 k 2 //_e{~/k)(1 _ e-~) k2 )-1 v a r ( z , T , k ) = ~ ~ ( 1 - e ~ ) U ~ 1} 2 (e ~ - 1 } "

(6)

The dependence of the variance on the number of detected photons N is calculated from (6) and is plotted as solid

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Fig. 6. Plot of the values of the fluorescence lifetimes ~ obtained by the maximum likelihood estimator for single Rhodamine 6G and Rhodamin B-zwitterion molecules as a function of detected photons N. 250 data sets were analyzed with (2) and (5). The data sets were recorded as specified for the MCS and FCS measurements. The dependence of the variance on the number of detected photons N is calculated from (6) and is shown by lines (for details see text)

lines in Fig. 6. As expected, most of our measured values for the lifetime lie within this 68% interval.

3 Conclusions

For the first time we have demonstrated the identification of single rhodamine dye molecules in water by their characteristic fluorescence lifetimes. This was achieved by using confocal microscopy in combination with the technique of time-correlated single-photon counting. Our results suggest that even more than two dyes are distinguishable on the single-molecule level by their characteristic lifetimes using the newly developed efficient maximum likelihood estimator procedure in combination with fast signal processing. Hence, this technique is ideally suited for biological mult iparameter applications on the single-molecule level, e.g. D N A sequencing, tumor and antigen diagnostics [1, 2, 7, 8, 14, 18].

Acknowledgments. We are grateful to J. Troe for generous support of this work. C.E. and C.S. thank R. Rigler, J. Widengren and U. Mets for the introduction into fluorescence correlation spectro- scopy. We also thank M. Brinkmeier for providing the optical filter used in the experiments. We would like to thank the Bundesminis- terium fiir Bildung und Forschung for financial support under grants 0310793 A, 0310158 A and 0310806. The financial support of Boehringer Mannheim GmbH is also gratefully acknowledged•

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