Fluorescence Cross-Correlation Spectroscopy as a Universal Method

Fluorescence cross-correlation spectroscopy (FCCS) has been proposed and developed as a protein detection assay for several years. Here, we combine ...
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Anal. Chem. 2009, 81, 5614–5622

Fluorescence Cross-Correlation Spectroscopy as a Universal Method for Protein Detection with Low False Positives Abigail E. Miller,†,‡ Christopher W. Hollars,‡,§ Stephen M. Lane,‡,| and Ted A. Laurence*,‡ Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, California 94550, and Center for Biophotonics Science and Technology, University of California, Davis, Sacramento, California 95817 Specific, quantitative, and sensitive protein detection with minimal sample preparation is an enduring need in biology and medicine. Protein detection assays ideally provide quick, definitive measurements that use only small amounts of material. Fluorescence cross-correlation spectroscopy (FCCS) has been proposed and developed as a protein detection assay for several years. Here, we combine several recent advances in FCCS apparatus and analysis to demonstrate it as an important method for sensitive, quantitative, information-rich protein detection with low false positives. The addition of alternating laser excitation (ALEX) to FCCS along with a method to exclude signals from occasional aggregates leads to a very low rate of false positives, allowing the detection and quantification of the concentrations of a wide variety of proteins. We detect human chorionic gonadotropin (hCG) using an antibody-based sandwich assay and quantitatively compare our results with calculations based on binding equilibrium equations. Furthermore, using our aggregate exclusion method, we detect smaller oligomers of the prion protein PrP by excluding bright signals from large aggregates. Fluorescence cross-correlation spectroscopy (FCCS) is generally applicable to antibody-based protein detection using a sandwich assay format, with two independent antibodies labeled with fluorophores of different colors1-4 (see Figure 1). In contrast, single color fluorescence correlation spectroscopy is not easily applicable to general protein detection, since it requires a large change in diffusivity upon binding (a large change in size).5 Sandwich assays are commonly used in an enzyme-linked immu* To whom correspondence should be addressed. Ted Laurence, Physical and Life Science Directorate, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA 94550. Phone: (925) 422-1788. E-mail: [email protected]. † University of California, Berkeley. ‡ Lawrence Livermore National Laboratory. § Currently at Midwest Research Institute, Kansas City, Missouri 64110. | University of California, Davis. (1) Ruan, Q.; Tetin, S. Y. Anal. Biochem. 2008, 374, 182–195. (2) Stoevesandt, O.; Brock, R. Nat. Protoc. 2006, 1, 223–229. (3) Rodbard, D.; Feldman, Y. Immunochemistry 1978, 15, 71–76. (4) Rodbard, D.; Feldman, Y.; Jaffe, M. L.; Miles, L. E. M. Immunochemistry 1978, 15, 77–82. (5) Haustein, E.; Schwille, P. Curr. Opin. Struct. Biol. 2004, 14, 531–540.

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nosorbent assay, or ELISA.6,7 An ELISA detects protein via a sandwich between antibodies attached to a substrate and a second antibody labeled with an enzyme. This labeling enzyme allows the production of an optical or electrochemical response after washing away unbound antibodies.8,9 In contrast to an ELISA, FCCS lifts this assay off any surface, simplifying the protein detection process by performing only a single step of mixing reagents and eliminating complications from nonspecific surface binding, which also complicates other alternative detection methods such as surface plasmon resonance.10,11 With FCCS, there is no need for the enzyme and its substrate. The observable in FCCS is the correlated signals caused by the diffusive motion of the antibody-antigen-antibody sandwich. Two color FCCS has been used to monitor a variety of binding events.12,13 It has also been applied to enzyme kinetics, such as oligonucletide cleavage14,15 and protease cleavage16,17 as well as the detection of a protease cleavage reaction.18 In living cells, two color FCCS has been applied to measuring and monitoring calcium activity in cells using calmodulin.19 It has recently been used to probe protein traffic through a mechanosensitive membrane channel, MscL.20 Also, two color FCCS can measure coincident events such as cellular trafficking, for example, when two parts of cholera toxin are located in the same part of the cell.21 These (6) Stryer, L. Biochemistry, 4th ed.; W. H. Freeman and Co.: New York, 1995. (7) Lequin, R. M. Clin. Chem. 2005, 51, 2415–2418. (8) van Weemen, B. K.; Schuurs, A. H. W. M.; Oostermeijer, M. W.; Raymakers, H. H. T. FEBS Lett. 1974, 43, 215–218. (9) Engvall, E.; Perlmann, P. Immunochemistry 1971, 8, 871. (10) Vareiro, M. L. M.; Liu, J.; Knoll, W.; Zak, K.; Williams, D.; Jenkins, A. T. A. Anal. Chem. 2005, 77, 2426–2431. (11) Masson, J.-F.; Battaglia, T. M.; Cramer, J.; Beaudoin, S.; Sierks, M.; Booksh, K. S. Anal. Bioanal. Chem. 2006, 386, 1951–1959. (12) Schwille, P.; Meyers-Almes, F. J.; Rigler, R. Biophys. J. 1997, 72, 1878– 1886. (13) Bacia, K.; Kim, S. A.; Schwille, P. Nat. Methods 2006, 3, 83–89. (14) Schwille, P.; Meyer-Almes, F. J.; Rigler, R. Biophys. J. 1997, 72, 1878– 1886. (15) Kettling, U.; Koltermann, A.; Schwille, P.; Eigen, M. Proc. Natl. Acad. Sci. U.S.A. 1998, 95, 1416–1420. (16) Kohl, T.; Haustein, E.; Schwille, P. Biophys. J. 2005, 89, 2770–2782. (17) Kohl, T.; Heinze, K. G.; Kuhlemann, R.; Koltermann, A.; Schwille, P. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 12161–12166. (18) Fouldes-Papp, Z.; Rigler, R. Biol. Chem. 2001, 382, 473–478. (19) Kim, S. A.; Heinze, K. G.; Waxham, M. N.; Schwille, P. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 105–110. (20) van der Bogaart, G.; Krasnikov, V.; Poolman, B. Biophys. J. 2007, 92, 1233– 1240. (21) Bacia, K.; Majoul, I. V.; Schwille, P. Biophys. J. 2002, 83, 1184–1193. 10.1021/ac9001645 CCC: $40.75  2009 American Chemical Society Published on Web 06/12/2009

Figure 1. Fluorescence cross-correlation spectroscopy (FCCS) may be used with labeled antibodies to detect unlabeled protein antigens. Black line: cross-correlation of labeled antibodies without antigen hCG. Red line: cross-correlation from labeled antibodies with 0.75 nM hCG.

are just a few examples of the problems being probed by FCCS that required labeling of the molecules of interest. Klenermen and colleagues have applied coincident event analysis, which is similar to FCCS, to detect and quantify DNA, for which they were able to achieve detection at the femtomolar level.22,23 They also have applied this method to the detection of a virus, which has multiple binding sites for an antibody.24 We introduce the use of alternating laser excitation, ALEX,25 to FCCS-based protein detection, which eliminates the effects of spectral cross-talk of fluorophores, to reduce the possibility of false positives. The use of alternating lasers in FCCS was first performed in Thews et al.26 to eliminate cross-talk between two fluorescence proteins; similar methods were used in Takahashi et al.27 It was also demonstrated in Muller et al.28 using two interleaved pulsed lasers. In Laurence et al.,29 ALEX was used to detect a small population of DNA sliding clamps on DNA when fluorescence resonance energy transfer (FRET) was unable to detect the interaction. It has not yet been used in one area of great impact: antibody-based protein detection via FCCS. We show that, even with two fluorophores well-separated spectrally, a large decrease in spurious cross-correlations is obtained, greatly reducing the possibility of false positives. The cleaner cross-correlation (22) Li, H. T.; Ying, L. M.; Green, J. J.; Balasubramanian, S.; Klenerman, D. Anal. Chem. 2003, 75, 1664–1670. (23) Orte, A.; Clarke, R.; Balasubramanian, S.; Klenerman, D. Anal. Chem. 2006, 78, 7707–7715. (24) Li, H. T.; Zhou, D. J.; Browne, H.; Balasubramanian, S.; Klenerman, D. Anal. Chem. 2004, 76, 4446–4451. (25) Kapanidis, A. N.; Lee, N. K.; Laurence, T. A.; Doose, S.; Margeat, E.; Weiss, S. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 8936–8941. (26) Thews, E.; Gerken, M.; Eckert, R.; Zapfel, J.; Tietz, C.; Wrachtrup, J. Biophys. J. 2005, 89, 2069–2076. (27) Takahashi, Y.; Nishimura, J.; Suzuki, A.; Ishibashi, K.; Kinjo, M.; Miyawaki, A. Cell Struct. Funct. 2008, 33, 143–150. (28) Muller, B. K.; Zaychikov, E.; Brauchle, C.; Lamb, D. C. Biophys. J. 2005, 89, 3508–3522. (29) Laurence, T. A.; Kwon, Y.; Johnson, A.; Hollars, C. W.; O’Donnell, M.; Camarero, J. A.; Barsky, D. J. Biol. Chem. 2008, 283, 22895–22906.

signals we obtain allow us to quantitatively compare our results with expected results calculated using supplier-quoted binding constants. We measure the FCCS-ALEX response of two model systems: human chorionic gonadotropin (hCG) and the prion protein (PrP). hCG is a hormone widely tested for in pregnancy tests6 based on an ELISA assay. PrP aggregates to form oligomers, fibrils, and finally plaques in the brain30-32 that are associated with CreutzfeldtJakob disease (CJD) in humans, scrapie in sheep, and bovine spongiform encephalopathy (BSE), also known as “mad cow” disease.33-35 FCCS can be applied to detect PrP monomers and oligomers.36 We also develop a simple method to eliminate the effects of large aggregates from cross-correlation curves. It is based on combining correlations calculated on short time sections, eliminating those sections with the brighter “bursts” of fluorescence. It is a variation on the methods we developed for obtaining correlations from selected, minor species.37 It allows the exclusion of aggregates from the correlations and also helps determine if the cross-correlation signal is due to smaller aggregates or monomers. We also apply photon arrival-time interval distribution (PAID) analysis38 to verify these results. PAID shows that the antibody sandwich is 20-50% brighter than the unbound antibodies, indicating occasional multiple antibody binding. This suite of analytical tools is applied to the detection of smaller PrP aggregates and may assist in the analysis of earlier stages in prion aggregate formation. THEORY We use a quantitative model to predict the response of FCCS measurements on antibody-antigen sandwich assays. The overall equilibrium reaction is A + B + P T AP + BP + APB A and B are the two antibodies, and P is the antigen protein. There are several species in solution. First, the observable double labeled antigen APB is present, but there are also the single antibodyantigen complexes AP and BP, as well as the unbound antibodies and antigen A, B, and P. The reaction can be broken down to four reactions for which we know or can measure the equilibrium constant. A + P T AP

(1)

(30) Murphy, R. M. Biochim. Biophys. Acta: Biomembranes 2007, 1768, 1923– 1934. (31) Baskakov, I. V.; Breydo, L. Biochim. Biophys. Acta: Mol. Basis Dis. 2007, 1772, 692–703. (32) Cancellotti, E.; Barron, R. M.; Bishop, M. T.; Hart, P.; Wiseman, F.; Manson, J. C. Biochim. Biophys. Acta: Mol. Basis Dis. 2007, 1772, 673–680. (33) Westergard, L.; Christensen, H. M.; Harris, D. A. Biochim. Biophys. Acta: Mol. Basis Dis. 2007, 1772, 629–644. (34) Watts, J. C.; Westaway, D. Biochim. Biophys. Acta: Mol. Basis Dis. 2007, 1772, 654–672. (35) Wadsworth, J. D. F.; Collinge, J. Biochim. Biophys. Acta: Mol. Basis Dis. 2007, 1772, 598–609. (36) Fuji, F.; Horiuchi, M.; Ueno, M.; Sakata, H.; Nagao, I.; Tamura, M.; Kinjo, M. Anal. Biochem. 2007, 370, 131–141. (37) Laurence, T. A.; Kwon, Y.; Yin, E.; Hollars, C. W.; Camarero, J. A.; Barsky, D. Biophys. J. 2007, 92, 2184–2198. (38) Laurence, T. A.; Kapanidis, A. N.; Kong, X.; Chemla, D. S.; Weiss, S. J. Phys. Chem. B 2004, 108, 3051–3067.

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B + P T BP

(2)

[B0] ) [B] + [BP] + [APB]

(10)

A + BP T APB

(3)

[P0] ) [P] + [AP] + [BP] + [APB]

(11)

B + AP T APB

(4)

Each equilibrium constant can be written in terms of the concentration of its product divided by the concentrations of its reactants: [A][P]/[AP] ) K1

(5)

[B][P]/[BP] ) K2

(6)

[A][BP]/[APB] ) K3

(7)

[B][AP]/[APB] ) K4

(8)

The equilibrium constants alone do not determine the concentrations of each species. The calculation must also follow the laws of conservation of mass. The final concentrations for each species can be summed as the initial concentrations of each unbound antibody, A and B, and antigen, P: [A0] ) [A] + [AP] + [APB]

(9)

This creates six equations; the equilibrium constant equation for reaction 4 is redundant since it can be obtained from combining reactions 1, 2, and 3, and six unknowns. This system of equations was solved numerically (using the FindRoot function in Mathematica, Wolfram Research) to determine all six final concentrations as a function of initial antigen concentration with five adjustable parameters: the two initial antibody concentrations and the three independent equilibrium constants (Figure 2). Except where specified otherwise, the equilibrium constants for reactions 1 and 3 are assumed to be the same for reactions 2 and 4, based on the assumption that the second antibody does not affect the binding for the first and vice versa. The final concentration of each species can be plotted as a function of the initial antigen concentration, displaying the wellknown peaked response of sandwich assays (Figure 2A). The case shown is for the binding constants from the specification sheets for the two hCG antibodies used in this study, ME.107 and ME.109, 5 × 10-11 and 2.5 × 10-11 M, respectively. The antibody concentrations are set at 1 nM each (as we use in experiments). When [P0] is less than 1 nM (the antibody concentrations), most of the antigen is bound by both antibodies. However, once

Figure 2. Calculated equilibrium concentrations can help determine binding affinities, as well as distinguish between nonideal binding situations. (A) Theoretical equilibrium concentrations for A, B, P, AP, BP, and ABP as a function of initial antigen concentration. Parameters are initial antibody [A0] ) [B0] ) 1 nM and the equilibrium constants for hCG antibodies provided by the supplier (25 and 50 pM). (B) Effect of decreased binding affinities on concentration of antibody-antigen sandwiches, [APB]. Black: theoretical maximum for [A0] ) [B0] ) 1 nM, with K1 ) K2 ) 0. Blue: same as the blue curve in part A. Red curves: binding constants K1 and K2 increased simultaneously by factors of 3, 10, 30, and 100 over hCG values in part A. (C) Effect of lower concentrations of antibodies. This could occur if a fraction of the labeled antibodies is inactive, lowering the effective concentration of the antibodies. The black and blue lines are the same as in part B. Green lines: lower [A0] ) [B0] to 0.3 and 0.1 nM. (D) Effect of competition between antibody binding, i.e., if the binding of one antibody reduces the binding affinity for the second antibody. The black and blue lines are the same as in part B. Cyan lines: lower K3 and K4 in relation to K1 and K2 by factors of 10 and 100. The different effects shown here (B-D) can be distinguished by comparing the measured [APB] as a function of [P0]. 5616

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[P0] is near the antibody concentration, [P] increases rapidly: the antibodies are nearly all bound, leaving free antigen. Because of this saturation, the concentration of antibody-antigen sandwiches has an inflection point after which [APB] decreases with increasing [P0]. The height and position of this inflection point depends on the binding constants of the antibodies, the initial concentrations of the antibodies, and on any effects one antibody has on the binding of a second (Figure 2B-D). The blue and black lines show [APB] as a function of [P0] for the hCG antibody binding constants (from Figure 2A) and the theoretical minimum binding constants (K1 ) K2 ) K3 ) K4 ) 0), respectively. In each case, [A0] ) [B0] ) 1 nM. For tight binding, as calculated for each of these three curves, there is a sharp inflection in the [APB] curve matching the antibody concentration. If the binding constants are increased (indicating weaker binding), the inflection is less sharp and shifts to lower [APB] and higher [P0]. In Figure 2B, the red lines show calculations modified from the hCG curve (blue line), multiplying the binding constants for the hCG antibodies 3, 10, 30, and 100 times. These calculations show what to expect for weaker binding constants. On the other hand, if the binding constants remain the same but the concentrations of the antibodies are decreased, the hCG curves shift to the lower left (green lines, Figure 2C). The lines to the lower left are found by decreasing [A0] and [B0] by factors of 3 and 10. Moving to the lower left as shown might be expected if significant fractions of the antibodies are inactive. For instance, if 2/3 of the antibodies were inactive, we would expect the results to follow the first green curve to the lower left of the blue curve. If binding one antibody decreases the affinity for the second (so that K3 and K4 are larger than K1 and K2), then the shape of the inflection in the curves changes. Increasing K3 and K4 above K1 and K2 for hCG by factors of 10 and 100 lead to the cyan curves shown in Figure 2D. The rapid decrease seen once [P0] increases above [A0] and [B0] is due to the preference of the antigen to bind only one antibody. The shapes of these curves can help determine what fraction of the antibodies are active, the strength of the interaction, and any interference between the antibodies. MATERIALS AND METHODS Labeling Antibodies with Fluorescent Dyes. For detecting hCG (Aldrich/Biodesign), antibodies ME.107 and ME.109 (Biodesign, Inc., Maine) were used, and antibodies 8B4 (Alicon Switzerland) and 6D11(Biodesign, Inc., Maine) were used for detecting wild type PrP. Alexa 488, Alexa 633, and Alex 647 (Molecular Probes, Invitrogen, Carlsbad, CA) were used to label the antibodies according to the labeling kit protocols from Molecular Probes. All experiments were done in phosphate buffered saline (0.01 M PBS which is NaCl, 0.138 M; KCl, 0.0027 M; pH 7.4, 0.02% NaN3). The quoted binding constants for each antibody were supplied by the manufacturers, Biodesign and Alicon. Actual binding constants at our conditions may be different. Fluorescence Cross-Correlation Measurements. hCG and PrP samples were investigated by fluorescence cross-correlation spectroscopy using a custom-built system based on an inverted optical microscope (Zeiss, Axiovert S100 TV), which makes use

Figure 3. ALEX FCCS experimental diagram: depiction of the optical layout used to collect fluorescence cross-correlation spectroscopy data. The alternating laser excitation (ALEX) occurs every 25 µs, and all red photons (655-745 nm) are collected at one detector and all green photons (515-555 nm) are collected at a second detector. With the use of only one laser at a time, alternating laser excitation separates leakage from the green fluorophore into the red detector temporally from the fluorescence of the red fluorophore.

of the 632.8 nm line of a helium-neon laser (Voltex, Inc., Colorado Springs, CO) and the 488 nm line from an argon ion laser (Coherent) as the excitation sources (Figure 3). The two lasers are directed through an opto acoustic modulator (AOTF 480622.5-.55, NEOS Technologies, West Melbourne, Florida) that alternates the lasers every 25 µs. The collimated laser beams are reflected into a 100× oil immersion objective with a numerical aperture of 1.45 (Zeiss, Planapochromat) using a dichromatic mirror (470/635 custom, Omega Optical, Inc., Brattleboro, VT). The focus of the laser beam is translated about 10 µm deep into solution, where it forms a tight spot of ∼1 µm3 volume that is experimentally verified with a standard dye. Fluorescence is collected by the same microscope objective, passed through the dichromatic mirror, and focused through a confocal pinhole of 150 µm diameter. Fluorescent light is then recollimated and split by a dichroic mirror (650DRLP, Omega Optical, Inc., Brattleboro, VT). The red beam is then passed through a longpass filter (655HQ, Chroma Technology Corp., Rockingham, VT) and a 700/90 bandpass filter (Chroma Technology Corp., Rockingham, VT) and focused directly onto a single-photoncounting avalanche photodiode (APD) (SPCM-AQR-14, PerkinElmer, Inc.) by means of a 25 mm focal length planoconvex lens (Newport Corp., Irvine, CA). The blue beam is passed through a 535/45 bandpass filter (Chroma Technology Corp., Rockingham, VT) and focused directly onto a single-photoncounting avalanche photodiode (APD) (SPCM-AQR-14, PerkinElmer, Inc.) by means of a 25 mm focal length planoconvex lens (Newport Corp., Irvine, CA). Photon events were recorded with a counter-timer card (NI-6602, National Instruments Inc., Austin, TX) that recorded the arrival time of each photon with 12.5 ns time resolution to the hard-disk drive of a personal computer system. Cross-correlation of recorded photon events from both APDs was performed using a custom-written program in LabVIEW (National Instruments Inc., Austin, TX), and fits were performed in Igor Pro (Wavemetrics, Inc., Lake Oswego, OR). Data was collected in 60-180 s sections. The time-averaged excitation power is 60 µW at 488 nm and 20 µW Analytical Chemistry, Vol. 81, No. 14, July 15, 2009

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at 633 nm for the hCG experiments and 20 µW at 488 nm and 25 µW at 633 nm for the PrP experiments. Fluorescence correlation measurements of 3 nM solutions of Alexa 488 and Alexa 633 were used to determine the size of the confocal detection volume for 488 and 633 nm excitation. We found that the detection volumes for both lasers were on average about 2.7 fL, with 20% variations typical (the 633 nm excitation volume was usually ∼10% larger). For verification of the overlap of the 488 and 633 nm excitation volumes, we used scattering from latex beads; the cross-correlation amplitude determined with ALEX was about 85% of the amplitudes of the autocorrelations. RESULTS Reducing False Positive Signals Using Alternating Laser Excitation. We add alternating laser excitation to a standard twolaser FCCS system25-29 to improve fluorescence cross-correlation spectroscopy by removing spurious cross-correlations. We alternate lasers over a period of 25 µs, with the laser lines at 488 and 633 nm, and the emission from each fluorescence probe collected at a separate detector (Figure 3). The lasers each excite a fluorophore, and the two fluorophores are chosen such that they are well separated in emission, minimizing emission overlap and possible energy transfer. The emission from the two probes can be separated both in wavelength and in time by alternating the excitation of the fluorophores, thereby allowing for the elimination of leakage between the two channels and decreasing false positives. The primary source of spurious cross-correlations in standard FCCS experiments is leakage of the green (blue-shifted) fluorophore into the spectral channel of the red fluorophore. ALEX separates that signal temporally from the emission from the red fluorophore. Because of the alternation period, we only probe correlation times longer than 25 µs; faster times are available if one uses pulsed lasers.28,39 We calculate several autocorrelations and cross-correlations from our data to demonstrate the improvement obtained by exclusion of the spurious cross-correlations. Each autocorrelation, calculated for the red and green channels (Figure 4A), is a reflection of all possible states that the labeled probe can be found in, from free in solution to all possible bound states. The crosscorrelations are calculated between the red and green channels (Figure 4B). For demonstrating the reduction in spurious cross-correlations, we calculate two different pairs of cross-correlations rather than just one (Figure 4B): the standard, total cross-correlations between all photons collected in each channel and ALEX correlations, which are the correlations between all red photons collected when there is only red excitation and all green emitted photons when only green emission occurs. In these experiments, by using Alexa 488 and Alexa 647 (or Alexa 633), we minimized spectral overlap. Even so, the advantage of the ALEX cross-correlation is clear, removing photons due to cross talk between the channels. Experiments without antigen can provide a “blank” which is subtracted from standard cross-correlations with antigen. However, this baseline can vary: compare the dotted cyan and black lines using standard, total cross-correlations performed under nominally identical conditions (Figure 4B). Errors in this “blank” subtraction affect the detected levels of antibody-antigen sand(39) Laurence, T. A.; Kong, X.; Jager, M.; Weiss, S. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 17348–17253.

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Figure 4. Cross-correlations using ALEX clearly distinguish between spurious and true cross-correlations in antibody-antigen sandwich assays. (A) Autocorrelations of signals from green and red fluorophores are shown. Amplitudes are consistent with ∼1 nM concentrations and a ∼2.7 fL detection volume. (B) Cross-correlations using ALEX (solid lines) provide a greater distinction between experiments with (red lines) and without (black lines) antigen present than do standard cross-correlations (dotted lines). It is possible to subtract experiments without antigen from experiments with antigen to subtract effects of leakage. However, variations in cross-correlations in different experiments (compare dotted black and cyan lines) provide additional measurement error in standard cross-correlations. Without antigen, ALEX-based cross-correlations (solid black and cyan lines) have no amplitude within measurement error. (C) Statistically significant detection of antigen can be obtained using ALEX-based crosscorrelations of a 3 min section of the 40 min measurements in Figures 1 and 2B.

wiches that are obtained using standard cross-correlations. This source of error is eliminated when using ALEX-based crosscorrelations, since there is no amplitude above measurement error without antigen (solid black and cyan lines, Figure 4B). We point out that, although we use 40 min experiments for our data, 3 min subsections of the data still provide statistically meaningful results (Figure 4C). For the remainder of the paper, “cross-correlation” will only refer to the ALEX cross-correlations, and the total crosscorrelations will no longer be used.

The autocorrelations are a reflection of all red- or all greenlabeled antibodies in solution, with no separation due to the state bound to an antigen or free in solution. In contrast, the crosscorrelations only occur when red-labeled antibodies and greenlabeled antibodies are either bound to each other or bound to the same antigen. There is a clear change in the cross-correlation when the labeled antibodies are in the presence of their antigen (Figure 4B,C). For the two antibodies, the cross-correlation occurs when both antibodies are bound to the same unlabeled, target molecule. The concentrations of the labeled components, bound and unbound, can be obtained from the amplitudes of the correlations. With calibration of the binding constants of the labeled antibodies or a calibration curve, the concentration of the antigen, the target molecule, can also be determined. Calculation of Concentrations of Labeled Species. The auto- and cross-correlations calculated from our data are fitted according to basic diffusion models to determine the concentration of the labeled antibodies and antibody-antigen sandwiches present in solution. The cross-correlations (Figure 1) are functions of the diffusion time of the complex and the concentration of the complex (antibody-antigen-antibody). The intercept of the curve is dependent on the concentration of the double labeled complex. The autocorrelations and cross-correlations of the red and green channels were fitted using a 2-D diffusion model:40

〈G(τ)〉 ) 1 +

1 N

(( )) 1

1+

τ τD

(12)

For the autocorrelations, we extract, using eq 12, the occupancies Ng and Nr for the green and red labeled antibodies. Each occupancy is the average number of labeled molecules in the confocal detection volume and is equal to N ) CAVf, where Vf is the focal volume, A is Avogadro’s number, and C is the concentration. The focal volume was determined by measuring the autocorrelations with free dyes Alexa 633 and Alexa 488 with known concentrations. For the cross-correlations, 1/N is replaced by (NX)/(NgNr), where NX is the occupancy for the antibodyantigen sandwiches.5,14 The diffusion time τD of a molecule depends on the size and shape of the molecule, the solution viscosity η, and the size of the focus of the laser beam.41,42 The diameter of the labeled species changes upon the binding of the antibodies and the antigen, thereby affecting the diffusion time in the autocorrelation. This effect is much harder to reliably detect and quantify than the amplitude of the cross-correlation and hence is not discussed further. Variable Number of Fluorophores Per Antibody. When antibodies are labeled using standard kits, there is not a constant number of fluorophores per antibody. This affects the occupancy values extracted using the auto- and cross-correlations. Having a variable number of fluorophores per antibody enhances the strength of the autocorrelation signal in comparison to the crosscorrelation signals. To see how this happens, consider the random (40) Rigler, R.; Mets, U.; Widengren, J.; Kask, P. Eur. Biophys. J. Biophys. Lett. 1993, 22, 169–175. (41) Haupts, U.; Maiti, S.; Schwille, P.; Webb, W. W. Proc. Natl. Acad. Sci. U.S.A. 1998, 95, 13573–13578. (42) Elson, E. L.; Magde, D. Biopolymers 1974, 13, 1–27.

variables ng and nr, which are the number of fluorophores per antibody, labeled with the green (g) or red (r) fluorophores. The average numbers of these fluorophores are 〈ng〉 ) µg and 〈nr〉 ) µr. Assuming the intensities from the labeled antibodies is proportional to the number of fluorophores and that the number of fluorophores follows a Poisson distribution (i.e., the number of possible sites is much greater than the actual number of labels), the autocorrelation amplitudes would be proportional to 〈ng2〉 ) µg2 + 1 and 〈nr2〉 ) µr2 + 1. This affects the occupancy extracted from eq 12. The autocorrelation of the g channel at zero time delay is 〈Ig2〉/〈Ig〉2, where Ig is the measured intensity. The number of fluorophores per antibody is statistically independent of the other factors, so its effect on the autocorrelation can be separated into a multiplicative factor: 〈ng2〉/〈ng〉2 )(µg2 + 1)/µg2. The occupancy N′ measured from an autocorrelation is related to the true occupancy N by this factor: N′ ) N(µg2 + 1)/µg2. A similar expression holds for the red channel. In contrast, the cross-correlation amplitudes would be proportional to 〈ngnr〉 ) µgµr. If the above corrections are not employed in the fit, the extracted occupancy N′X of the antibody-antigen sandwich will be suppressed. The true value NX may be obtained by multiplying by the factor: NX ) N′X((µg2 + 1)(µr2 + 1))/(µg2µr2). This effect is significant for the hCG experiments but not for the PrP detection experiments. Using absorption spectroscopy, we determined that ME.107 antibody was labeled with an average of 1.5 Alexa 488 fluorophores per antibody and ME.109 with 1.3 Alexa 633 fluorophores per antibody. For the hCG experiments, a correction factor of 2.3 was applied to the hCG data. For the PrP antibodies, 6D11 was labeled with an average of 5.2 Alexa 488 fluorophores per antibody and 8B4 with 5.2 Alexa 647 fluorophores per antibody. The correction factor was 1.08, which was deemed insignificant. hCG Detection and Quantification. We demonstrated the ability to measure the cross-correlations for an unlabeled antigen, bound to two different antibodies, over a range of concentrations from 10 nM (Figure 5). Human chorionic gonadotropin (hCG) was tested as an antigen with hCG antibodies ME.107 and ME.109. hCG is a well characterized glycoprotein made of two separate subunits of different amino acid sequences that interact noncovalently. ME.107 binds the β subunit with a binding constant of 5 × 10-10 M, and ME.109 binds the R subunit with a binding constant of 2.5 × 10-10 M; these binding constants were provided by the supplier and may have been obtained under conditions different from ours (BioDesign International). The exact location, in the amino acid sequence of the hCG, of the binding site of each antibody is unknown. Each correlation is the compilation of 40 min of collecting photons. The timeaveraged excitation power was 60 µW at 488 nm and 20 µW at 633 nm. The concentration was 1 nM for each antibody at all concentrations of the antigen, hCG, leaving the autocorrelations relatively constant. A concentration of 1 nM for each antibody was chosen to be at the highest concentration where bright single molecule events are visible, i.e., roughly one molecule in the focal volume at all times. The cross-correlation with no antigen present shows some variations (black circles, Figure 5), thereby defining our detection limit for this experiment. Analytical Chemistry, Vol. 81, No. 14, July 15, 2009

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Figure 5. Measured antibody-antigen sandwich concentrations as a function of initial antigen concentration. (A) The experimentally determined concentrations of hCG (red squares; black circles for no hCG present) and two possible fits that explain the lower-thanexpected concentrations: lower binding affinity (dotted red line; factor of 30 lower binding affinity, with an error of 30%) and competition (dotted cyan line; no satisfactory fit found). Using the data without hCG present, we determine a measurement limit of 20 pM for the concentration of detected APB antibody-target-antibody complex. The hCG detection limit is 100 pM (see Detection Limits in the Discussion). (B) Data from part A and PrP data (green triangles), compared to calculated antibody-antigen sandwich concentrations based on supplier-provided binding constants: the blue line is for hCG, and the green line is for PrP.

Adhesion of proteins is often a problem in lower concentration measurements. FCS-measured concentrations measured here for the antibodies were within 30% of expected values, usually somewhat less than expected. During the 40 min experiments, the signal levels dropped 20-30% typically; cross-correlations amplitudes did not drop more than this during that time. These effects were not predictable, and often no change was observed at all. To minimize adhesion, we mixed the measured solutions immediately prior to measurement. We scanned the surface of glass, but we did not notice any significant fluorescence levels from any proteins adhered to the glass surface. We performed measurements on surfaces coated with a modified PEG molecule, but we did not find any noticeable difference in our measurements. We also tried adding BSA to the buffer, and the most noticeable change was an addition of a background signal. The primary complication resulting from adhesion effects is a significant, approximately 30% contribution to the variations in concentrations measured (Figure 5A). The measurement errors shown in Figure 5 (typically ±10 pM) are determined by comparing 20 bootstrap samples of each data set.38 Each data set is subdivided into N 2 s sections. To obtain one bootstrap sample, N of the 2 s sections were randomly selected with replacement and averaged into the calculation of 5620

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the correlations (the same section can be selected multiple times or omitted). This procedure provides an error estimate for each given measurement but does not account for additional errors caused by variations in sample preparation such as pipetting errors or from adhesion effects; these factors lead to errors of around 30%. Using the data without hCG present, we determine a limit of detection of 20 pM of detected APB antibody-target-antibody complex (1 standard deviation above the highest measurement of the 0 nM hCG sample). This corresponds to a limit of detection of ∼100 pM for hCG under the current measurement conditions. The concentration of hCG-antibody sandwiches follows the expected profile of a sandwich assay as shown by the red squares, which represent the cross-correlation amplitudes after conversion to concentrations of the hCG-antibody sandwich, [APB]. We fitted the data in Figure 5A by scaling the calculations from Figure 2. We can exclude the possibilities that a large fraction of the antibodies are inactive and significant interference between the antibodies, since we were unable to obtain adequate fits (dotted cyan curve shown in Figure 5A for competitive binding was closer). However, the dotted red curve fit the data well. The fitted parameters indicate binding approximately 30 times weaker than specified by the supplier, with an error of 30%. Rather than 25 and 50 pM binding constants, we measure binding constants in the rage of 1-2 nM. This may either be due to differences in conditions (measurement conditions and methodology were not specified by the supplier), loss of binding efficiency due to fluorescent labeling (although with the low labeling of ∼1-2 labels per antibody this seems unlikely), or the binding constants were not as strong as specified. Even with the difference between our measured binding constants from those quoted by the supplier, we were able to cleanly and reproducibly obtain a binding curve that matches theory, allowing us to distinguish between possible nonidealities. PrP Detection and Quantification. Recombinant prion protein, PrP, was also tested as an antigen. For the detection of PrP, the same conditions were used as for the hCG experiments, namely, PBS buffer with each antibody at 1 nM. The antibodies used were 8B4, which binds residues 37-44 with a binding constant of 10-12 M and 6D11 which binds residues 93-109 with a binding constant of 4 × 10-11 M; these binding constants were provided by the supplier and may have been obtained under conditions different from ours (Alicon Switzerland). The time-averaged excitation power is 20 µW at 488 nm and 25 µW at 633 nm. We observe a population of aggregates under these conditions. The maximum detected PrP-antibody sandwich concentration is not in range of initial PrP concentration [P0] measured (Figure 5B, green triangles). The species detected via the cross-correlation was present at a lower concentration than the initial PrP concentration [P0], since the peak of the detected sandwich concentration peak is well above the antibody concentration and crossed above the theoretical limit. This can possibly be explained by depletion of [P0] via aggregation. Large aggregates are occasionally observed traversing the confocal detection volume (Figure 6A), causing correlated bursts in the green and red channels. The aggregates tended to be brighter with increasing PrP concentration (Figure 6B). It is possible to focus on these large aggregates and study their

Figure 6. Analysis of cross-correlations accounting for presence of PrP aggregates. (A) Large signals occur due to large PrP aggregates. We divide the acquisitions into 2 s time slices (black lines), which are rank-ordered in terms of maximum signal intensity over 10 ms windows. Correlations are calculated over various percentages of time slices. (B) The intensity of the signals from aggregates is higher for higher concentration PrP (25 vs 0.25 nM). (C) When excluding the slices with the top 1% of signal intensities (black line), the correlation drops dramatically (correlation with 0% excluded rises above graph range). For PrP, the cross-correlation drops further as more time slices are excluded. (D) For hCG, the cross-correlation amplitude does not drop when time slices are excluded: only the signal-to-noise decreases.

properties as others have done previously.43 However, we developed a way to probe what other smaller species are present by excluding these aggregates. To do so, we divided each 30-40 min acquisition into 2 s time slices (delimited by black lines in Figure 6A). Each 2 s time slice was then scored for the maximum number of photons nmax observed in either channel over any 10 ms time period. All time slices from the 30-40 min acquisition were rank ordered by nmax. We calculated the auto- and crosscorrelations over a predefined percentage of the 2 s sections. In Figure 6C, the cross-correlation calculated for a sample with [P0] ) 25 nM PrP is shown as a function of the percentage of sections retained. The most dramatic change occurs when decreasing from 100% to 99%, which excludes the large aggregates; the cross-correlation with 100% of the sections (not shown) is very high, going out of the range of the graph. With 99% of the sections, a normal FCS functional form is found. The concentrations shown in Figure 5 were extracted when 99% of the sections are retained. Even after exclusion of the large aggregates, our data suggest that the PrP detected via cross-correlations has often formed smaller aggregates. As the percentage of sections used in the analysis decreases from 99% to 25%, the amplitude of the crosscorrelation decreases significantly (Figure 6C). This suggests that the cross-correlations are associated with the brighter than average signals, i.e., small aggregates. That this is not simply an artifact of the analysis can be demonstrated by observing that the hCG cross-correlations do not decrease; only the noise level (43) Bieschke, J.; Giese, A.; Schulz-Schaeffer, W.; Zerr, I.; Poser, S.; Eigen, M.; Kretzschmar, H. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 5468–5473.

increases (Figure 6D). We used PAID analysis,38 which extends the cross-correlation analysis to determine molecular brightness of species in FCCS experiments, to help determine the extent of aggregation. We found that the species producing the crosscorrelation is brighter than the antibodies alone (by 20-50%), indicating that, on average, more than one antibody is attached to the species. No comparable increase was found with hCG. DISCUSSION Quantitative Comparisons Lead to Improved Understanding. We have brought several recent advances in FCCS to the area of protein detection via cross-correlation spectroscopy. The most important advantage of the current methodology is the use of ALEX to eliminate spurious cross-correlations. The elimination of the need to subtract blank samples to extract meaningful data allows us to exploit some of the natural advantages of FCS such as sample size and freedom from surfaces, while mitigating some of the disadvantages such as dynamic range. With the use of ALEX, the dynamic range of FCCS is extended lower due to the improvements in measurement error. With this improved data, as well as detailed calculations of expected response of the antibody sandwich system, we are able to detect that the antibodies perform as expected, albeit with weaker binding. We are able to exclude interference or competition between antibodies and the possibility of a large, inactive population. The data are consistent with a reduced binding strength, due to different buffer conditions, fluorescent labeling, or another cause. The ability to model the system using equilibrium binding equations allows us to determine that the behavior of the PrP system is anomalous, indicating aggregation. Using Analytical Chemistry, Vol. 81, No. 14, July 15, 2009

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this information, we are able to develop a method for monitoring correlations excluding the aggregates. We then use another methodology, PAID, to verify, using brightness, that there are small aggregated species. The ability to perform all of this analysis, and reach these conclusions, depends on the clean crosscorrelations obtained using ALEX. We were able to obtain these results with two different biochemical systems with a minimum of development. No surface passivation was necessary, only labeling of the antibodies. This shows the strength of the FCCS platform for general protein detection. Other groups have demonstrated user-friendly, portable systems.36 The additions here do not affect the possibility of such systems and also do not preclude the development of systems that make many simultaneous measurements to increase throughput. We found the intriguing result that, even when the large aggregates of PrP are excluded, the remaining cross-correlation signal has properties that suggest the presence of smaller aggregates. These may be related to small aggregates that may play a role in nucleating the aggregation process.44 The techniques developed here provide a valuable platform for studying these issues. Detection Limits. For the FCCS two antibody-antigen system, there are two detection limits, the instrumental limitation which is reflected in the concentration of measurable double labeled complex and the biological system limitation which is the amount of antigen detected for some initial antigen concentration. The detection limit for the system is how much of the double labeled complex can be detected. This can vary for the length of time over which the data is collected, because longer collection times result in less fluctuations in the cross-correlations thereby increasing the signal-to-noise of N. The threshold is determined by the noise in the cross-correlation of the labeled antibodies when no antigen is present, leading to a limit of approximately ∼20 pM under our conditions. In our experiments, we used a relatively low laser excitation intensity (10-40 µW) that allowed us to ignore issues such as triplet state-induced fluctuations and photobleaching. If the excitation intensity is increased, the signal-to-noise can increase dramatically (provided photobleaching remains unimportant), lowering the required acquisition time. We did not optimize our conditions for rapid acquisition but for simplicity. We expect that the 20 pM limit can be decreased further when optimizing for signal-to-noise. We show in Figure 4C that we can obtain meaningful results within 3 min. There is still significant optimization that can occur, but these results are already encouraging.

The detection limit for the initial antigen is set by the detection limit of the system and the binding constants of the antibodies. Experimentally it was found that for 30 min of data, the detection limits for hCG is ∼100 pM and for PrP it is ∼2 nM, which is unexpected for the PrP since it has stronger antibodies but the system is complicated by the protein aggregation. Again, longer collection times and increased excitation intensity lead to better resolution and lower detection limits. To push the detection limits to lower concentrations, the simplest solution is to collect for a longer time, but to still be considered a rapid method of analysis, the collection time for FCCS cannot be lengthened indefinitely. If FCCS can be extended into an array, either probing the same sample solution measured multiple times simultaneously or multiple samples all probed simultaneously, the detection limit can be lowered without compromising its ability to be a rapid method of analysis.

(44) Caughey, B.; Lansbury, P. T. Annu. Rev. Neurosci. 2003, 26, 267–298.

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CONCLUSIONS From the experiments with hCG and PrP, it is possible to use FCCS as a universal detection method for proteins limited only by the binding strength of the antibodies. The unknown concentration of a known protein can be determined via the application of standard analytical methods, such as a calibration curve. The detection limits for FCCS are demonstrated to be as low as ∼20 pM for the antibody-target-antibody complex, in less than an hour, and can be expected to reach femtomolar concentrations with longer detection times or higher excitation intensities. ALEX FCCS provides a straightforward method for the quantification of proteins in solution with low false positives. ACKNOWLEDGMENT We thank Man Sun Sy, Case Western Reserve University, and Jim De Yoreo, LLNL, for the gift of PrP. This work was supported by CBST, and DOE. A.E.M. was supported by the SEGRF program at LLNL. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. The Center for Biophotonics, an NSF Science and Technology Center, is managed by the University of California, Davis, under Cooperative Agreement No. PHY 0120999.

Received for review January 22, 2009. Accepted May 18, 2009.