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Biosciences Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
Reprint requests to: Liaohai Chen, Biosciences Division, Argonne National Laboratory, Argonne, IL 60439, USA; e-mail: lhchen{at}anl.gov; fax: (630) 252-5517.
(RECEIVED February 12, 2004; FINAL REVISION June 3, 2004; ACCEPTED July 2, 2004)
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Abstract |
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Keywords: phage–protein interaction; phage display; combinational libraries; M13 phage; T7 phage; fluorescence correlation spectroscopy; dissociation constants
Article and publication date are at http://www.proteinscience.org/cgi/doi/10.1110/ps.04695704.
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Introduction |
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TOPAbstractIntroductionResults and DiscussionMaterials and methodsReferences |
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Among the methods used to study the biointeractions, ranging from radioisotope labeling, Enzyme-Linked Immunosorbent Assay (ELISA), Surface Plasmon Resonance (SPR) to Microcalorimetry, Fluorescence Correlation Spectroscopy (FCS) has various unique advantages (Rigler and Elson 2001; Hess et al. 2002):
FCS has been extensively used to study the interactions of protein–protein and protein–small molecule (Schwille et al. 2000; Rigler and Elson 2001; Hess et al. 2002) both qualitatively and quantitatively. Rigler’s group first extended the FCS studies to the phage system, and was able to characterize the protein–M13 phage interactions a few years ago (Lagerkvist et al. 2001). To the best of our knowledge, there have been few reports of FCS studies on phage–protein interactions since then. Herein, we describe detailed, systematical FCS studies of the specific interactions of both M13 and T7 phage particles with the corresponding proteins with sizes ranging from 12 kDa (S-protein) to 150 kDa (IgG antibodies). Our results indicated that FCS is a very reliable tool to characterize protein–T7 interactions. For the M13 phage system, considering its filamentous structure (~800 nm in length and 8 nm in diameter), new measures have been developed to characterize protein–M13 interactions quantitatively by FCS. Although we could adapt the method established by Lumma et al. (2003), which was successful to probe the dynamics of a large semiflexible chain such as a 
-phage DNA by FCS, we used a simple approach of enlarging the confocal detection volume to accommodate the M13 phage and still used the standard FCS correlation function. In addition, we took the advantage of the large mass ratio between the phage and the protein; thus, were able to obtain the diffusion time of the protein–phage complex from the phage particle itself, and used it as a fixed parameter when fitting the autocorrelation curves of the protein–phage system. Under these conditions, we were able to reliably deduce the dissociation constant of the protein–phage interaction from the corresponding FCS spectra.
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Results and Discussion |
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TOPAbstractIntroductionResults and DiscussionMaterials and methodsReferences |
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), the T7 phage has an icosahedral shape with a diameter of ~50 nm. At the concentrations used in this study (~1 nM), purified T7 phages (via CsCl gradient) are well dispersed in the solution, and there was no evidence of aggregate formation. Because the overall dimension of T7 phage is much smaller than the confocal detection volume (the beam waist radii was estimated to be 500 nm), T7 phage systems were characterized using FCS setup with a conventional 50-µm pinhole and a 60x/1.2 NA, water immersion objective. The interaction of the S-peptide peptide with a 104 aa S-protein derived from pancreatic ribonuclease A has been well characterized in the literature with a nanomolar dissociation constant (Raines et al. 2000). By labeling the S-protein with Alexa-647 dye, the interaction of the S-protein and S-peptide-displayed T7 was examined by FCS.
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(0.19 msec). The diffusion time of Alexa-647 was then used to obtain the diffusion time of dye-labeled proteins via a two-component model.
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. The average values were used as fixed parameters for the FCS studies of the interaction between S-peptide-displayed T7 and S-protein.
Dye conjugation of the T7 phage was achieved by the reaction of succinimidyl ester of the red fluorescent dye Alexa-647 to the epsilon-amino groups of the lysine residues in T7 capsids. The labeled T7 phage were readily purified (removal of unreacted free dye) to ~98% using a gel filtration spin-column. To determine the diffusion time, 10 µL of 0.3 nM of Alexa-647-conjugated T7 phage in PBS buffer solution was placed on the top of the cover glass. At least five FCS spectra were recorded with an average counting rate of 20 KHz (laser power 250 µW). Again, we used the two-component model, while keeping the diffusion time of free dye a fixed parameter to fit the autocorrelation curves. The diffusion time of Alexa-647-conjugated T7 phage in PBS (3.8 msec), as deduced from each of five FCS spectra, is reported in Table 1. The diffusion time of T7 phage was used as a fixed parameter for the FCS study of the interaction between S-peptide-displayed T7 and S-protein.
Characterization of the interaction between S-peptide-displayed T7 and S-protein
To quantify the interaction of S-protein with S-peptide-display T7 phage, a stock T7 solution of 2.4 x 1011 phage per mL (0.4 nM) was used to prepare constant total volume mixtures of stock dye-S-protein with T7 and PBS buffer such that the concentration of dye-S-protein was held constant, at a variable T7 phage concentration. Unlabeled T7 was found to provide a weak fluorescent background of ~2 KHz; however, the amplitude contributed to G was negligible during FCS integration times used. After ~1 h of incubation at room temperature, ~30-sec duration FCS measurements were made. Figure 2 shows typical autocorrelation curves obtained for the free dye, dye-labeled S-protein and S-protein–T7 complex. The FCS autocorrelation curves were fitted with a three-component model. As before, the diffusion times from the previous measurements (free dye, dye-labeled protein, and phage particles), as well as the mole fraction of the free dye were held fixed in this model (Fig. 2, dotted line).
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This assumption was reinforced by the observation that the average counting rate as well as fluctuation amplitudes of the dye-labeled protein (both the S-protein and anti-T7 antibody) remain constant with increasing phage concentration (after deducting the weak autofluorescence of the phage particle). This suggested that a 1:1 stoichiometry of the binding reaction was observed. A higher binding stoichiometry between the fluorescent protein and the phage would lead to either a reduction of total fluorescence due to the self-quenching of the fluoreorphores on the phage when the interfluorophore distant is closed enough on the phage surface, or a larger counting rate fluctuation due to the increase of fluorescence per phage when the interfluorophore distant is far away on the phage surface. In addition, the fact that the dissociation constant deduced from FCS spectra is insensitive to the initial protein concentration also suggested a 1:1 stoichiometry of binding reaction when the initial protein concentration is less than 10 nanomolar.
Accordingly, data were analyzed by nonlinear least-squares fits to the three-component version of equation 1 using measured diffusion times of 0.19, 0.72, and 3.8 msec for the free dye and dye-S-protein and S-protein–T7 complex, respectively (Table 1). The derived mole fractions for the complex as a function of T7 concentration are shown in Figure 3A. The increased mole fraction of bound S-protein as the function of phage concentration clearly indicate the strong binding between S-protein and S-peptide displayed T7 phage at the given concentration. The dissociation constant for the complex was determined by first deducing the value of [P]0 – [T]0y and y/(1 – y) from Figure 3A and then fitting the data to equation 4 (Fig. 3B). The derived dissociation constant (kd) is 2.2 nM, which matches the literature value of the dissociation constant of the S-protein and S-peptide (Raines et al. 2000).
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Characterization of T7–T7 antibody interaction
The S-protein is a small protein with a molecular weight of 11.5 kDa. To examine the interaction of the T7 phage with relatively larger proteins, we chose to study the interaction of the T7 antibody and T7 phage particle. The commercial T7 antibody is a monoclonal antibody directed against a short peptide (11 amino acid, gene 10 leader peptide) from the amino-terminal of the T7 phage capsid protein. By conjugating the Alexa-647 fluorescence dye to the antibody, the interaction of the T7 phage and T7 monoclonal antibody were characterized by FCS. In brief, dilute samples of free dye (1 nM of Alexa-647), purified and dye-labeled antibody (2 nM), as well as purified and dye-labeled T7 phage (0.3 nM) were first analyzed by FCS to obtain their diffusion times (
j) and the free dye mole fraction of labeled antibody (shown in Fig. 4). From fitting the FCS curves (Fig. 4, dotted line), the diffusion times for the free dye, dye-labeled antibody, as well as dye-labeled T7 phage are 0.24 msec, 1.4 msec, and 3.8 msec, respectively. Subsequently, a series of fluorescence correlation curves for the T7 antibody–T7 phage complex were recorded with a constant concentration of dye-labeled antibody and variable T7 concentration ranging from 0.9 nM to 2.8 nM. The resulted fluorescence autocorrelation curves were fitted with the three-component model of equation 1 with the diffusion times of free dye, dye-labeled protein, and phage particles and free dye mole fraction held constant. The derived mole fractions dye-labeled antibody bound to the T7 phage as a function of the T7 concentration are shown in Figure 5A. The increased mole fraction of the bound anti-T7 antibody as the function of the phage concentration proves the strong binding between the antibody and antigen (T7) at the given concentration. The dissociation constant for the complex was determined by deducing the value of [P]0 – [T]0y and y/(1 – y) from Figure 5A and fitting the data to equation 4 (Fig. 5B). The derived dissociation constant (kd) is 1.4 nM.
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is deviated from the origin. A dissociation constant of 5.2 nM is obtained when the fitting curve was forced to pass through the origin. However, such a fitting line exhibited unacceptable deviation especially with the data point of a high phage concentration. This may imply that the dynamic range of equation 4 for the anti-T7–T7 system is quite small. Nevertheless, the dissociation constant for anti-T7 is in the range of the average dissociation constants of monoclonal antibodies, which are in the order of a micromole to nanomole (Bender and Gizeli 2003).
FCS studies for M13 phage system
Wild-type M13 and the interaction of the monoclone M13 antibody with M13 were used for the FCS study. As illustrated in Figure 1B, the filament-like M13 phage is ~800 nm in length and ~8 nm in diameter. Due to its filamentous shape, which can be easily tangled, M13 tends to aggregate at a higher concentration (Lagerkvist et al. 2001). In a typical FCS system, the beam waist radii for the detection volume are less than ~0.5 microns. Thus, the length of a M13 phage exceeds the FCS beam waist (wo) (see Discussion section), and cannot fulfill the condition of d < wo for FCS measurements. In addition to the above factors, the FCS study of M13 phage systems was somewhat more challenging because (1) M13, with a length/diameter aspect ratio of ~100, is not expected to be rigid in solution; thus, rotational motion may contribute to the autocorrelation function; (2) aggregates of labeled M13 could easily overwhelm FCS spectra, because even an individual aggregate of M13 can contribute large nonstatistical amplitude to G with contributions from ~100 nsec to fractions of a second. Consequently, such spectra cannot be reliably modeled by equation 1 (or other standard FCS relations). Because our FCS setup (same as most of the FCS setups nowadays, except the setup used in Dr. Enrico Gratton’s group) engage the use of a hardware correlator, the system does not have the option of editing large amplitude "spikes" in FCS fluctuations prior to autocorrelation. Although the "spikes" can be eliminated from G by some other means of discrimination (e.g., non-multiple methods; Muller et al. 2003), the simplest way to work around is to reject any FCS spectra, which contain a "large spike." Accordingly, several measures have been taken in our studies to address these issues; including (1) we used objective/pinhole combination (b) (i.e., a 40x/0.55 objective plus an 100-µm pinhole) with 633 nm excitation. The beam waist radius (wo) is ~0.8 micron, which is large enough to host an entire M13 particle; (2) we only used low concentration of M13 for FCS studies. Our TEM studies indicated that most of purified M13 particles (via CsCl gradient) remain monomeric when the phage concentration is less than ~1 nM or 1012 pfu/mL; (3) we eliminated any FCS spectra that has larger spikes in its count rate trace (our criterion is to reject spectra that contain spikes with amplitudes or temporal durations exceeding twice the values measured from the purified labeled receptor FCS spectra (during determinations) because these fluctuations are associated with phage aggregates).
Diffusion time determination for pure dye, anti-M13–dye conjugation, and M13 phage particles
The diffusion time determination procedure for pure dye and the dye-labeled antibody is the same as previously described in the T7 system except a 40x/0.55 objective and a 100-µm pinhole were used for M13 system. The diffusion times were 0.42, 2.5 msec for free dye and the dye-labeled antibody, respectively (Table 1). The preparation of Alexa-647-labeled M13 was described in the experimental section. The labeled phage was repeatedly purified by spin columns, and analyzed by FCS at 633 nm using the 40x/0.55 objective and the 100-µm pinhole. The obtained FCS spectra were analyzed with the two-component version of equation 1 with a fixed free dye diffusion time and yielded a diffusion time of ~8.2 msec for the M13 monomer (Table 2). The diffusion rate for M13 phage derived from the diffusion time measured and our instrument geometry factor matches the value measure by Rigler’s group at 1.34 msec (40x/1.2, 30-micron pinhole) (Lagerkvist et al. 2001).
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shows typical autocorrelation functions obtained for the free dye, labeled anti-M13, and anti-M13–M13 complex. After the acquisition of a series of fluorescence correlation curves with a constant concentration of dye-labeled antibody and variable M13 concentrations, data were analyzed by nonlinear least-squares fits to the three-component version of equation 1 using measured diffusion times of 0.42, 2.5, and 8.2 msec for the free dye and dye–anti-M13, and M13, respectively (Fig. 6, dotted line).
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. Specific binding (~20% mole antibody–M13 complex) was observed at subnanomolar concentrations of M13; however, the observed mole fractions of bound anti-M13 again did not vary significantly with the increase of M13 concentrations.
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. The interaction of the antibody and M13 phage particles at the nanomolar range was also confirmed by an enzyme-linked immunosorbent assay using the concentrations similar to the FCS measurement (data not shown). One possible explanation for the observation of flat binding as the concentration of the phage particle is increased is the antibody-induced phage aggregation. As the phage particle concentration increases, the aggregate concentration also increases. Indeed, we observed more spikes in the count rate traces as the phage concentration was increased. On the other hand, the "larger spike" phenomenon is barely observed in the pure dye-labeled M13 system. Because we had to avoid spikes in our FCS experiments, which were corresponding to the large, aggregated particles, the effective concentration of phage particles (monomer) was not necessary increased proportionately. On a separated study, the interactions of ATP binding M13 phage with Alexa-647-labeled ATP were examined by FCS with similar experimental conditions and identical setup. The mole fraction of bound ATP to the M13 phage was increased as a function of M13 concentration; thus, the dissociation constant of the ATP binding M13 phage was deduced to be 15 nM. The measured dissociation constant was confirmed by a fluorescence anisotropy experiment (L. Makowski, S. Mandava, J. Bahns, L. Chen, and D.J. Rodi, in prep.). Thus, the method described in this artricle is suitable for characterizing the M13 phage system.
General remarks
In agreement with Rigler’s report, we also found that to use FCS to characterize phage particles, it is extremely important to prepare samples of pure monomeric phage particles. The sample preparation steps must include prelayered cesium chloride density gradient centrifugation after PEG precipitation. Our TEM images indicated that most phage particles in nanomolar concentrations remain as monomeric after CsCl purification.
Although FCS measurements are relatively straight forward in most experimental circumstances, situations do arise that tend to complicate or obscure such measurements. For brevity, we list a few problems encountered, and discuss in greater detail those relevant to these experiments. Generally, problem areas tend to fall into three areas: (1) the sample (e.g., contaminants, solubility, turbidity, aggregation, etc.); (2) the FCS system (e.g., system geometry, alignment, detection volume, location of beam waist in the sample, detector afterpulsing, laser scatter, etc.); (3) the interpretation of the data (e.g., unidentified factors that adversely influence the shape of the autocorrelation function, G(), baseline drift, optical pumping effects such as photo-bleaching, triplet decay, blinking, or rotational structure, noise, laser scatter, large particles, background fluorescence, etc.). Such factors can introduce artifacts and adversely influence G(). In the worst cases, these can introduce ambiguities in the fitting procedure, particularly when more than a single independent parameter is involved. Control of such effects is critical when multicomponent systems (i.e., containing more than one fluorescent component) are involved, because these require the accurate independent determinations of diffusion times for each component. The major difference of this work from other work in terms of data analysis is that we measured the diffusion times of all components in the system as well as the mole fraction of free dye, and held them as fixed parameters to obtain the relative mole fractions of bound and free target molecules. We deduced the dissociation constants by taking advantage of the phage particle’s much larger mass than the target proteins; thus, its diffusion time can be determined from dye-labeled phage particles. Although this cannot be achieved when FCS is used to study protein–protein or protein–small molecule interactions, we found it is extremely important for the phage system. Otherwise, it is very difficult to deduce a reliable and repeatable mole fraction of bound target proteins using contemporary FCS.
One unique problem associated with FCS measurements of large (e.g., M13 phage) fluorescent particles results when one or more of the physical dimensions (d, long radius) of the particle exceeds one or more of the physical dimensions (wo) of FCS sample volume itself. Typically, FCS measurements satisfy the condition d << wo. However, when d is approaching wo, it becomes possible for a single large particle to completely "fill" the sample volume in one or more dimensions (at the complete exclusion of other particles), while only a fraction of the particle is ever actually being observed by the FCS system, although it is only the fluorescently labeled portion of the particle that is actually imaged. Although this is less problematic when the labeled particle is rigid, it can be a problem when the labeled particle is flexible (i.e., dynamic conformation changes) because it is then possible for a small fluorescently labeled portion of the particle to enter and leave the FCS sample volume without translational diffusion of the entire particle (i.e., without translation of the particle’s center of mass). This can call into question the validity the derived diffusion time because it no longer relates to bulk translational diffusion of the particle. To address this problem, the observation volume was increased sufficiently to observe the motion of the entire particle in all three dimensions. However, to keep N (the number of observed particles) constant, increases in the system volume would need to be compensated for by proportionate reductions in sample concentration, thus leading to the analysis of increasingly more dilute (and less biologically relevant) solutions as the particle size is increased. In addition, for G to remain statistically significant, sample integration time would need to be increased proportionately. Furthermore, as diffusion times increase, laser intensity would need to be reduced to minimize optical pumping effects (e.g., photobleaching, triplet formation, etc.) during particle residence time. It is worth noting that when d is approaching wo, the possibility of optically hindered diffusion, trapped Brownian motion becomes more probable (Osborne et al. 1998; Chirico et al. 2002).
Conclusions
We have performed FCS measurements of labeled phage diffusion times, and determined equilibrium dissociation constants for labeled complexes of T7 and M13 phage. Although experiments with T7 were relatively straightforward, two major complications were encountered with M13: (1) difficulties obtaining a sample suitable for determining for the M13 monomer; (2) volume sampling appropriate for M13 translational diffusion. Modifications to experiments and methodology are discussed to handle key problems associated with the FCS of large M13 phage particles.
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Materials and methods |
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Conjugation of phage particles, as well as anti-M13 and anti-T7 tag monoclonal antibodies with Alexa-647 dye
Purified phage particles as well as anti-M13 and anti-T7 tag monoclonal antibodies (Amersham Biosciences) were conjugated to the Alexa-647 dye by using an Alexa-647 labeling kit from Molecular Probes according to the protocols provided. In brief, a 90-µL PBS buffer solution containing M13 or T7 phage particles (1012 pfu/ mL) was mixed with add 10 µL of 1 M bicarbonate (pH ~8.3). The resulting phage solution was transferred into a vial containing reactive dye (Alexa Fluor 647 carboxylic acid, succinimidyl ester). The mixture was gently agitated for one half hour in the dark at room temperature. Free dye was removed by size-exclusion spin column provided with the kit. The labeled phage particles were further purified using a gel filtration spin-column (Centrisep, Princeton Separations). For the conjugation of antibodies to the dye, a similar procedure was used with the following differences: 0.1-mg antibodies were resuspended in 450 µL PBS buffer and mixed with 50 µL of 1 M bicarbonate (pH ~8.3). The labeled proteins were finally eluated from free dye by size-exclusion spin column. The degree of labeling was calculated to be 4 moles of Alexa-647 per mole of antibody.
Observation of T7 and M13 phage particles under transmission electron microscope (TEM)
Electronic microscopic images were obtained from a Philips CM-120 transmission electron microscope, operated at 120 kV. The samples were supported on 400 mesh carbon coated grids, freshly glow discharged (Evaporator: Edwards Auto 306) for 45 sec. Specimens were negatively stained by applying a drop (5 µL) of phage particles to the grid. The grid was then washed with water, stained for 30 sec with aqueous solution of uranyl acetate (1%), and then wicked off with filter paper and allowed to dry. Micrographs were recorded on a Gatan CCD digital camera.
FCS setup
We set up a fluorescence auto correlation spectrometry base on a modified confocal/near field scanning optical (NSOM)/atomic force microscope (Nanonics-100, Nanonics), using an inverted microscope (IX 70, Olympus). A 5-mW Helium Neon laser (633 nm, Spectrooptics) was used for the excitation. The laser beam is directed to the microscope through a laser port equipped with a dichroic mirror. The beam output width is expanded to fill the back aperture of the microscope objective (a 60x/1.2 NA, water immersion, and a 40x/0.55 NA, Olympus) to provide a diffraction-limited spot. The fluorescence signal of the sample is collected with the same objective and is transmitted by a band pass filter (Chroma, Ltd.) to reduce the background signal. A pinhole (50 or 100 µm) was installed in an image plane of the microscope to discriminate against out of focus signals. The collected fluorescence light is then focused onto an avalanche photo diode (SPCM-AQR-15 (EG&G), Perkin-Elmer) detector. Autocorrelation functions are generated on line with a high-speed multiple tau digital correlator (ALV-6010, ALV-GmbH) and fitted off-line to the autocorrelation function equation. The diffusion time relaxation constant is related to the diffusion constant D by = wo2/4D, where wo is the lateral radius of the detection volume. The power of the laser beam could be adjusted with neutral density filters to provide high fluorescence signals per molecule, yet low enough to avoid significant photobleaching.
The geometric parameters for our home-built FCS apparatus were determined by using dilute (0.1–10 nM) standard dye (Alexa-647) with 633-nm excitation. A holographic filter (Kaiser Optical System) combined with a long pass ( > 645 nm) filter were used to block the reflect laser beam and transmit fluorescence (645–700 nm). FCS experiments were performed with objective/pinhole combinations: (a) 60x/1.2 (water immersion) objective with a 50-micron pinhole or (b) 40x/0.55 objective with an 100-micron pinhole. Ratios of measured diffusion times for free dye were found to be ~2.4 for (b) relative to (a). Combination (b) was used to prepare a sampling volume appropriate for measuring M13 phage diffusion. The beam waist radii were estimated to be ~0.5 and ~0.8 microns for (a) and (b), respectively.
FCS model
FCS measures fluctuations of the fluorescence intensity within minute (femtoliter) detection volumes and a temporal range from microsecond to seconds. The random fluctuations represented by the autocorrelation function of the fluctuation signal can be analyzed using equation 1 (Hess et al. 2002),
 | (1) |
where
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represent the relative fluorescence efficiencies Fj and molar fractions Yj of j; T is the triplet state lifetime; T is the triplet fraction; j is the characteristic diffusion time of component j; total detected signal; IB is the intensity of the uncorrelated background signal; 
0 and z0 are the radial and axial waist radii defining the detection volume; and 
is the compensate parameter for artificial effects in the autocorrelation (such as photobleaching) with time constants exceeding 1 sec.
FCS measurements
For all binding experiments, we measured the free dye first to determine its diffusion time using a one-component model, including the triplet term (equation 1). Because it was impossible to eliminate all free dye when purifying the dye labeled protein, we obtained the diffusion time of dye-labeled protein with a two-component model (equation 1) that contained the independently determined free-dye diffusion time as fixed parameter, assuming the fluorescence efficiencies (Fj) and triplet terms of Alexa-647 and Alexa-647-labeled protein are the same. For protein–phage complex systems, the FCS autocorrelation curves were analyzed with a three-component model. In this case, the diffusion times for the phage and phage–protein complex were also assumed to be the same due to the negligible mass difference between phage particles and protein–phage complexes. With predetermined diffusion times and free dye mole fraction held fixed in this model, the relative mole fractions of bound and unbound phage with target molecules in the solution were derived from nonlinear least squares fits to the experimental G().
Data analysis for dissociation constant measurements
To measure the dissociation constant of the dye labeled target protein (T) with phage particle (P), T and P were first incubated sufficiently long to reach equilibrium (0.5–1 h). Because it is cumbersome to produce a large quantity of purified phage and because phage particles [P] tends to aggregate (Xu et al. 2001) at higher concentrations (which is not suitable for FCS studies), all experiments associated with dissociation constant measurements are under the conditions of maintaining a constant concentration of T (in the order of nM) while varying the concentration of P in the approximate concentration range of 0.3 nM to 3 nM. Thus, the conventional pseudofirst-order condition ([P] >> [T]) used for binding studies could not be satisfied here. Under these conditions, the interaction between the target protein (T) and ligand displayed phage particles (P) can be described by equation 2 provided a 1:1 stoichiometry:
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The autocorrelation function can be expressed in a two- or three-component model (equation 1) [J = 1(free dye), 2(dye-labeled protein), 3(dye-protein: phage complex)]. Consequently, the mole fraction (y) of bound T can be derived from the fitting of the autocorrelation curve. The dissociation constant can be written as the following equation (equation 3):
 | (3) |
where [T]0 and [P]0 are the initial (total) concentrations of dye labeled target molecules and phage particles, respectively, and y is the fraction of bound target molecule against all target molecules in the solution:
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Rearrange equation 3 as equation 4:
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A plot of [P]0 – [T]0y against y/(1 – y) can be linearly fitted according to equation 4. Consequently, Kd can be determined from the slope of the plot.
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Acknowledgments |
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References |
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TOPAbstractIntroductionResults and DiscussionMaterials and methodsReferences |
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Castagnoli, L., Zucconi, A., Quondam, M., Rossi, M., Vaccaro, P., Panni, S., Paoluzi, S., Santonico, E., Dente, L., and Cesareni, G. 2001. Alternative bacteriophage display systems. Comb. Chem. High Throughput Screen. 4: 121–133.[Medline]
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Lumma, D., Keller, S., Vilgis, T., and Radler, J.O. 2003. Dynamics of large semiflexible chains probed by fluorescence correlation spectroscopy. Phys. Rev. Lett. 90: 218301–1–218301–4.[CrossRef][Medline]
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Rodi, D.J., Makowski, L., and Kay, B.K. 2002. One from column A and two from column B: The benefits of phage display in molecular-recognition studies. Curr. Opin. Chem. Biol. 6: 92–96.[CrossRef][Medline]
Schwille, P., Kummer, S., Heikal, A.A., Moerner, W.E., and Webb, W.W. 2000. Fluorescence correlation spectroscopy reveals fast optical excitation-driven in tramolecular dynamics of yellow fluorescent proteins. Proc. Natl. Acad. Sci. 97: 151–156.
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