Fluorescence Correlation Spectroscopy Study on the Effects of the

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Fluorescence Correlation Spectroscopy Study on the Effects of the Shape and Size of a Protein on Its Diffusion Inside a Crowded Environment Sujit Basak and Krishnananda Chattopadhyay* Protein Folding and Dynamics Laboratory, Structural Biology and Bioinformatics Division, CSIR−Indian Institute of Chemical Biology, 4 Raja S. C. Mullick Road, Kolkata 700032, India S Supporting Information *

ABSTRACT: Fluorescence correlation spectroscopy (FCS) has been commonly used to study the diffusional and conformational fluctuations of labeled molecules at singlemolecule resolution. Here, we explored the applications of FCS inside a polyacrylamide gel to study the effects of molecular weight and molecular shape in a crowded environment. To understand the effect of molecular weight, we carried out FCS experiments with four model systems of different molecular weights in the presence of varying concentrations of acrylamide. The correlation curves were fit adequately using a model containing two diffusing components: one representing unhindered diffusion and one representing slow hindered diffusion in the gel phase. A large number of measurements carried out at different randomly chosen spots on a gel were used to determine the most probable diffusion time values using Gaussian distribution analysis. The variation of the diffusivity with the molecular weight of the model systems could be represented well using the effective medium model. This model assumes a combination of hydrodynamic and steric effects on solute diffusivity. To study the effects of solute shape, FCS experiments were carried inside a urea gradient gel to probe the urea-induced unfolding transition of Alexa488Maleimide-labeled bovine serum albumin. We showed that the scaling behavior, relating the hydrodynamic radius and the number of amino acids, changes inside an acrylamide gel for both folded and unfolded proteins. We showed further that crowding induced by a polyacrylamide gel increases the resolution of measuring the difference in hydrodynamic radii between the unfolded and folded states.

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INTRODUCTION Cell cytoplasm consists of large number of constituents, such as different proteins and a network of cytoskeletal filaments, through which the movement of small macromolecules, proteins, and mRNAs diffuse to maintain cellular functions.1 These functions include gene transcription,2 signal transduction,3 and intracellular transport within the cell.4−6 Although the detailed understanding of cellular networking7 and intracellular interaction8 requires extensive and concerted applications of molecular and cellular biology, biophysics, spectroscopy, and imaging techniques, a significant amount of research effort has been already devoted to study the diffusion of small and large molecules in complex and crowded systems 9−11 to approximate biological systems more closely.12−14 Fluorescence recovery after photo bleaching (FRAP) and nuclear magnetic resonance (NMR) are two popular methods used for the diffusion measurements.15,16 However, the lack of complete recovery in FRAP experiments is a disadvantage.17,18 NMR, however, requires a relatively high concentration of the diffusing solute and is often affected by interfering background signals from the crowding substance.19 In contrast, fluorescence correlation spectroscopy (FCS) offers a potential alternative © 2013 American Chemical Society

with straightforward operation. Another advantage of FCS comes from its requirement of relatively less excitation power, resulting in less photodamage. FCS detects fluorescence signals and analyzes intensity fluctuations of fluorescent molecules in a small observation volume. The fluorescence intensity fluctuations can originate either from molecular diffusion in and out of the observation volume or from conformational fluctuations between multiple conformers with large differences in fluorescence profiles. The analyses of the intensity fluctuations because of molecular diffusion using a suitable correlation function provide an estimate of diffusion time (τD). The hydrodynamic radius of the diffusing molecule (rH) can be obtained from τD using the Stokes’ Einstein formalism.20,21 The analyses of the intensity fluctuations because of conformational dynamics result in the determination of the time constant (τR) of conformational dynamics provided that the value of τR is considerably less than τD (τR ≪ τD).22,23 Received: August 21, 2013 Revised: October 4, 2013 Published: November 1, 2013 14709

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normalized with the value of τD obtained with free Alexa488, which was measured under identical conditions.20 For a simple solution experiment involving one diffusing molecule (excluding the contributions of the triplet state), the autocorrelation function can be defined by the following equation30

FCS has been used extensively to study biomolecular interactions, aggregation, and protein conformational dynamics at single-molecule resolution.22,24−27 Nevertheless, one of the potential limiting factors of FCS detection arises from the assumptions related to the Stokes’ Einstein formalism. Because the diffusion time (τD) varies with the cube root of the molecular weight of the diffusing solute, the sensitivity of size discrimination for small protein−protein or protein−ligand complexes would be quite low. In addition, the constraint of the conformational dynamics measurements (τR ≪ τD) imposes a restriction on the time scale of detection. In this article, we used FCS to study the diffusion of several model molecules inside a polyacrylamide gel to get insight into the behavior of solute diffusion in a crowded environment. The data for diffusion inside a polyacrylamide gel could be represented well using the sum of two diffusion time values: fast and slow components corresponding to the free unhindered and hindered diffusion, respectively. To minimize the heterogeneity inherent to the diffusion measurements in an acrylamide gel, we used a Gaussian distribution fit of a large number of measurements at various randomly chosen spots. The use of the effective medium model, which combines the hydrodynamic and steric effects, fit the diffusivity data well. Using a urea-gradient-gel system and FCS, we further studied the urea-induced unfolding transition of a model protein, BSA. Our results showed that the scaling behavior between the hydrodynamic radii (rH) and the number of amino acids (Na) changes inside the acrylamide gel for both the folded and unfolded proteins. We showed that the resolution of hydrodynamic radius (rH) detection, which is one of the known limiting factors in solution measurements, could be enhanced significantly inside the polyacrylamide gel.

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G(τ ) = 1 +

1 1 N 1+

(

1 τ τD

1/2

) (1 + S ) 2τ τD

(1)

where τD denotes the diffusion time of the diffusing molecule, N is the average number of molecules in the observation volume, and S is the structural parameter that defines the ratio between the radius and the height. The value of S has been determined by FCS experiments with the free dye (Alexa488), and its values (typically around 5 and always less than 10 in all of the measurements described here) have been fixed for the analyses of the protein data. It should be noted that the correlation function data at the early time regions (faster than 10 μs) have been excluded in all of our data analyses to ignore the contributions of the triplet states. The validity of this method was checked in the case of all of the proteins in their diffusion measurements in free solution by including complete correlation traces up to 1 μs and by using the triplet component in the fit. We have obtained similar results with our model proteins using both the methods. For a more complex system containing multiple diffusing species (excluding the triplet state contributions), the correlation function can be defined by30 G(τ ) = 1 +

1 N

Ai 1 ⎛ τ ⎞⎞ ⎛ ⎞1/2 ⎜1 + ⎜ τ ⎟⎟ ⎜1 + S2⎜⎛ τ ⎟⎞⎟ ⎝ Di ⎠⎠ ⎝ ⎝ τ ⎝ Di ⎠⎠

∑⎛ i

(2)

where τDi is the diffusion time of the ith diffusing species present in the solution and Ai is its relative amplitude. It is important to note that

∑ Ai = 1 i

EXPERIMENTAL SECTION

The value of τD obtained by fitting the correlation function is related to the diffusion coefficient (D) of a molecule by the following equation

Bovine serum albumin (BSA), lysozyme, donkey antigoat IgG, and urea were purchased from Sigma Chemical Company (St. Louis, MO, USA). The chemicals for the polyacrylamide-gel experiments (e.g., acrylamide, bis-acrylamide, ammonium persulfate (APS), and N,N,N′,N′-tetramethylethylenediamine (TEMED)) were purchased from USB. I24C, a single cysteine mutant of the intestinal fatty acid binding protein (IFABP), was purified using a published procedure.28 Labeling of the Model Proteins with Alexa488Maleimide. All of the model proteins used in this study contain at least one free cysteine residue at the surface. These proteins were labeled with Alexa488Maleimide (Alexa488) using a published procedure.27 Briefly, Alexa488 was dissolved in DMSO and was then slowly added to a 1 to 2 mg/mL solution of the protein with constant stirring. The ratio between the dye and protein molar ratio was maintained at 10:1. The reaction mixture was incubated for 5 h at 4 °C, with shaking after every 30 min. The labeling reaction was stopped by adding excess βmercaptoethanol. Extensive dialysis followed by column chromatography using a Sephadex G20 column equilibrated with 20 mM sodium phosphate buffer (pH 7.5) was performed to remove excess free dye from the reaction mixture. FCS Experiments and Data Analyses. FCS experiments were carried out using a Zeiss ConfoCor 3 LSM (Carl Zeiss, Evotec, Jena, Germany) equipped with a 40× water-immersion objective (NA 1.2). Samples were excited with an argon laser at 488 nm. Low laser power (about 10 μW) was used to minimize photobleaching. A main dichroic filter was used to separate the fluorescence signal from the excitation line. The fluorescence signal was collected using two avalanche photodiodes (APD). A correlator card was used to calculate the correlation function from the photocurrent detected by the APD. Microscope correction collar and height were adjusted manually to correct for the refractive-index mismatch between the immersion solution and experimental environment.20,29 The protein data were

τD =

ω2 4D

(3)

The value of ω, which defines the size of the observation volume, has been calculated using FCS measurements with Rhodamine 6G, whose value of D has been well established (D = 4.2 × 10−10 m2 s−1). The value of the hydrodynamic radius (rH) can be obtained from D using the Stokes’ Einstein formalism (eq 4).

D=

kT 6πηrH

(4)

where η is the viscosity and k is the Boltzmann constant. Preparation of Urea Gradient Gel. The transverse urea gradient gel was prepared using a published procedure.31 The gradient gels were cast inside two clear glass square plates, and they were held in such a fashion so that after polymerization the gels were turned 90° and fit to the electrophoresis system. In this way, a gradient of urea concentration was established that was perpendicular to the direction of electrophoresis. The glass plates were held in place using three plastic spacers (1−3 mm thick). One of these spacers was at the bottom of the glass plates, and two other spacers were at the sides of the glass plates. After polymerization, these spacers were removed, and a new spacer was placed opposite to the bottom spacer. For each time of casting and electrophoresis, the edges were sealed with tape. For the urea gradient gel, one well of a standard gradient maker (GE healthcare) was filled with 10% acrylamide and the other well was filled with 10% acrylamide along with 10 M urea. The mixing of these two solutions was ensured using a rotating magnetic flea. In the polymerization process, ammonium persulfate and TEMED were used as an initiator and a polymerization catalyst, respectively. 14710

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Figure 1. Normalized correlation functions obtained by the FCS experiments with Alexa488IFABP, Alexa488Lys, Alexa488BSA, and Alexa488Antibody in free solution (a) and inside a 10% polyacrylamide gel (b, c). For panel b, the data was fit to a single-component diffusion model, and for panel c, the data was fit to a two-component diffusion model. The lines through the data corresponded to the fit lines. Representative residual distributions obtained with Alexa488BSA are shown at the bottom of each panel.

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RESULTS AND DISCUSSION

Table 1. Diffusion Parameters Obtained with the Model Systems in Freely Diffusing Solutiona

Because most of the analytical solutions and the measurement parameters of FCS experiments are valid for free, unhindered diffusion in dilute solutions, the application of this technique is expected to be complicated in the case of diffusion in crowded medium. In this study, we used FCS to study the translational diffusion of four model proteins of different molecular weights, namely, Alexa488-labeled IFABP (Alexa488IFABP, molecular weight 15.7 kDa), Alexa488-labeled lysozyme (Alexa488Lys, molecular weight 14.7 kDa), Alexa488-labeled BSA (Alexa488BSA, molecular weight 66.7 kDa), and Alexa488-labeled donkey antigoat IgG (Alexa488Antibody, molecular weight 150.7 kDa), inside the polyacrylamide-gel system. The model systems are globular proteins that provide a wide range of molecular weights. Measurements of Translational Diffusion of the Model Proteins in a Freely Diffusing Medium as Studied by FCS. FCS experiments were carried out with the model proteins in 20 mM sodium phosphate buffer at pH 7.4. The resulting correlation functions obtained with the FCS experiments under this buffer condition for all model systems could be fit successfully using eq 1 (Figure 1a). Equation 1 assumes free single-component diffusion of labeled molecules with the diffusion time of τD and the average number of particles of N. The goodness of the fits was established using residual distributions analyses (Figure 1a). Because intestinal fatty acid binding protein (IFABP) has a solved crystal structure, the molecular volume of IFABP (18 479 Å3)32 was used to calculate the rH value of IFABP (16.5 Å).33 Using the cube-root dependence of rH with the molecular weights, the expected values of rH of our model systems were calculated and are shown in Table 1. The experimental (from the values of τD obtained using FCS experiments) and the predicted (using the crystal structure of IFABP and assuming a cube-root dependence with the molecular weight) values of rH for the model systems matched well (Table 1). The present results establish that the use of a single-component diffusion model is sufficient

protein Alexa488IFABP Alexa488Lys Alexa488BSA Alexa488Antibody

diffusion coefficient in solution (m2 s−1) 1.16 1.08 0.62 0.49

× × × ×

10−10 10−10 10−10 10−10

experimental rH (Å)b

predicted rH (Å)c

19.9 21.4 37.6 47

16.5 21.5 36 47.3

a

FCS experiments were performed in 20 mM sodium phosphate buffer at pH 7.5 and room temperature. bThe values of experimental r H were determined using FCS data using Stokes’ Einstein approximation cThe values of predicted rH were determined using the crystal-structure volume of IFABP and assumed that the hydrodynamic radius has cube-root dependence with the molecular weight.

to describe the translational diffusion of all of the model systems in freely diffusing solution. Measurements of the Translational Diffusion of the Model Proteins by FCS in a Polyacrylamide Gel. The correlation functions obtained with the model proteins in the presence of 10% acrylamide are shown in Figure 1b. For all of the model systems, the correlation curves in the presence of polyacrylamide gels were found to be relatively more complex. The use of a single-component diffusion model failed to describe the correlation functions obtained with the model systems in the presence of a polyacrylamide gel (Figure 1b). This was evident by the nonrandom residual distribution observed for the fits using eq 1 (Figure 1b). Consequently, a model containing two diffusion components of equal brightness (i = 2 in eq 2 with A1 + A2 equal to 1) was used, which yielded a better fit (Figure 1c). The representative residual distributions obtained with the two diffusion components fit are shown in Figure 1c. Correlation data analyses using model free maximum entropy method (MEM) also supported the use of two diffusion components inside the polyacrylamide gel (representative MEM profiles are shown in Figure S1, Supporting Information). One of these diffusion components is fast, whereas the other one is relatively slow. The fast component 14711

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Figure 2. (a) Variations of τD,fast for Alexa488Lys and Alexa488Antibody with acrylamide concentration. (b) Variation of τD,slow (for Alexa488BSA) with bis-acrylamide concentrations. (c) Behavior of τD,slow distributions with the increase in acrylamide concentrations. (d) Variation of the most probable value of τD,slow (obtained using the Gaussian fit of the τD,slow distribution) with acrylamide concentrations; in the inset, the variation of the log of the most probable value of τD,slow with acrylamide concentration was found to be linear. (e) Correlation between τD0,cal and τD0,exp. The line through the data points shows the linear fit. (f) Variation of the diffusivity (Dg/D0) values with the volume fraction analyzed using the effective medium model. The color used are as follows: blue, Alexa488IFABP; black, Alexa488Lys; red, Alexa488BSA, and dark cyan, Alexa488Antibody.

concentration, whereas the value of τD,fast was not changed. Finally, the values of τD,fast and τD,slow (normalized by those observed with the free dye, Alexa488) inside the polyacrylamide gel remained unchanged for all of the proteins when the experiments were repeated in the presence of different pinhole diameters (Figure S2, Supporting Information). Note that the inherent assumption of equal brightness for both components could not be verified in the present measurements. The representative values of the amplitudes of the fast and slow components are shown in Figure S3 (Supporting Information). It can be envisaged that the inside of a polyacrylamide gel represents a heterogeneous system. Although it is difficult for us to identify all of the reasons for the variations, we assumed that the following are some of the important factors. (1) The inherent optical effects of the variation of refractive index and viscosity of the polyacrylamide gels. The effects of focal heights,

(with the diffusion time of τD,fast) is similar to the values of τD of the protein systems measured in free solution (Table S1 and Figure S1, Supporting Information).The values of τD,fast remained constant in all acrylamide concentrations (Figure 2a). In contrast, the slow component (with the diffusion time of τD,slow) corresponded to possible hindered diffusion as a result of multiple contact formation inside the gel matrix. A twocomponent model has been used in the literature to probe the diffusion of a dye molecule in mesoporous glass.34 An alternative description of the two-component behavior (solution phase and gel phase) in a polyacrylamide gel has also been reported.35,36 In a separate control experiment, the concentration of the cross-linker (bis-acrylamide) was varied, keeping the acrylamide concentration constant at 10%. The results obtained with Alexa488BSA (Figure 2b) show that the value of τD,slow increased with the increase in cross-linker 14712

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the solute protein molecules is profound, and the increase in τD, slow in crowded medium follows the following trend: Alexa488Antibody (150.7 kDa) > Alexa488BSA (66.7 kDa) > Alexa488Lys (14.7 kDa) ∼ Alexa488IFABP (15.7 kDa) It is important to discuss a number of different aspects regarding the present data. First, although we have used a model containing two diffusion components to analyze the data presented in this article, a different model of anomalous diffusion has been commonly used to study solute diffusion in a crowded environment.9,39 The anomalous diffusion model uses an exponent, the value of which decides if the solute experiences anomalous sub- or superdiffusion.40 We preferred the two-component diffusion model over anomalous diffusion because the former model yields a better residual distribution profile, at least with the present data (Figure S4). It should be noted that Dauty and Verkman used a simple diffusion model to fit their diffusion data in the presence of Ficoll-70.41 Additionally, Brazda et al. have found that the use of a twocomponent diffusion model was preferred (over the anomalous diffusion model) to analyze the diffusion of EGFP−retinoic acid receptor in HeLa cells using FCS.42 Second, it is important to consider the effect of the pore geometry into the increase in the diffusion time.43 It has been shown that the pore geometry could induce an entropic force field when it enters or exits the pore.44 This entropic force field may lead to controlled drift of particles at the edge of the pore.45 In contrast, when a particle travels parallel to the edge of the pore, it exhibits free diffusion. Use of the Effective Medium Model Is Satisfactory to Explain the Diffusion Data Inside a Polyacrylamide Gel. We used one of the popular methods, namely, the effective medium model, to explain the diffusion behavior of the model proteins inside a polyacrylamide gel. For this purpose, the values of τD,slow observed with different solutes in the presence of a 0, 2, 5, 7.5, 10, and 12.5% acrylamide gel were converted to diffusivity (Dg/D0) (the ratio of diffusion coefficient of a solute in presence and absence of a polyacrylamide gel, respectively) using the following equation

viscosity, and refractive indices on FCS detection have been shown to result in the variation in the diffusion time of the experimental systems,20,37 and these effects were minimized using the free dye, Alexa488Maleimide, as a control. (2) The inherent errors of FCS measurements at a given point in the gel. We minimized this effect using the average of 30 measurements of 10 s. (3) The difference between two points in a gel of the same concentration. This difference may originate from slight variations in the viscosity, refractive index, or depth between these two points or slight variations in the thickness of the gel between these two points. Another source of heterogeneity may arise from changes in the size and shape of the protein systems during the diffusion between different points inside the acrylamide gel. This is expected because there could be small changes in the pore sizes and polymer density in different portions of the gel even at the same concentration, resulting in a small difference in the crowding effect. Unfortunately, these effects cannot be minimized using the free dye as a control because that would require the simultaneous presence of the free dye at these same points along with the protein system under study, and this condition is extremely difficult to achieve. More importantly, because the effect of crowding changes with the molecular weight, this change may not be normalized using the free dye. To take these variations into account, we used a histogram-analysis method to determine the τD,slow values observed in each acrylamide concentration. In this method, we carried out about 100 separate FCS experiments at each acrylamide concentration. Each FCS experiment consisted of approximately 30 measurements of 10 s (to minimize the effects described in point 2 above). These 100 experiments were performed at different points chosen randomly. All of these data points were analyzed globally, and the histograms obtained using the values of τD,slow (which are normalized using the τD,slow of the free dye measured at the same experimental condition, see point 1 above) were fit using a Gaussian function. The peaks, which corresponded to the most probable value of τD,slow, were plotted with the acrylamide concentrations. A similar approach for analyzing FCS data in a heterogeneous system has been used before.38 Figure 2c shows the variation of the Gaussian distribution profiles of the τD,slow values of Alexa488BSA, which corresponds to the hindered diffusion in the gel phase, with the increase in acrylamide concentration, [C]. The acrylamide concentration, [C], dependence of the most probable values of τD,slow was plotted in Figure 2d. Because the dependence between the most probable values of τD,slow (denoted as τD,slow henceforth) and [C] shows an exponential increase, a plot of logτD,slow and [C] should be linear. τD,slow = A exp(k[C ])

Dg τ0 = D0 τg

(6)

where τ0 and τg correspond to the values of τD,slow in the absence and presence of acrylamide, respectively. The volume fraction of the polyacrylamide gel plus cross-linker (φ) in the gel was determined using the following equation, as described before35 vpmp φ= mpvp + (m w + mb)vwb (7)

(5)

where υp (the partial specific volume of polyacrylamide in water) and υwb (the partial specific volume of buffer in water) are 0.70 and 1.01 cm3/g, respectively.35 The parameters mp, mw, and mb correspond to the mass of polyacrylamide, water, and experimental buffer, respectively. One early model has been proposed by Ogston,46 which assumes that the polyacrylamide-gel system is composed of random straight and long fibers with negligible width. In this model, solute molecules are considered as hard spheres. The diffusion of the solute molecules in a fiber network takes place by directional movement in random unit steps without any collision with the polymer fiber. According to the Ogston model, the diffusivity, Dg/D0, can be related to the volume fraction of the fiber network in gel as

A linear variation between logτD,slow and [C] was been observed for all four model systems (inset of Figure 2d). The extrapolated values of τD,slow to zero acrylamide concentration (τD0,cal), which could be calculated from the intercepts of the linear fit, correlated very well (Figure 2e, correlation coefficient of 0.95) with the diffusion time values measured independently for the model systems in freely diffusing solution in the absence of acrylamide (τD0,exp). The FCS data indicate that the value of τD,slow of a solute molecule inside a polyacrylamide gel depends on at least two factors, namely, the extent of crowding and the size of the solute. The effect of crowding is evident because τD, slow increases exponentially with the acrylamide concentration, [C] (Figures 2d). The effect of the molecular weight of 14713

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⎛ R ⎞ = exp⎜ −φ−0.5 s ⎟ D0 Rf ⎠ ⎝

Equilibrium Unfolding Transition of Alexa488BSA as Studied by FCS Inside a Polyacrylamide Gel. We showed that FCS can be used to study the processes of diffusion inside a polyacrylamide gel. We also showed that the effect of molecular weight inside a polyacrylamide gel could be described using a model containing both hydrodynamics and steric factors. We wanted to explore further if this method could be applied to study the effect of molecular shape. A convenient way that one can change the molecular shape of a protein while keeping the molecular weight identical is by unfolding the protein. We studied urea-induced unfolding of a model protein, Alexa488BSA, inside the polyacrylamide-gel system. Another motivation behind this experiment was to find out if the combination of FCS and a polyacrylamide-gel system could be used to achieve higher resolution to study biologically important events. Figure 3a shows a typical trace of the behavior of Alexa488BSA inside a 0−10 M urea gradient polyacrylamide gel. Because the protein is fluorescently labeled, its observation did not need any staining or destaining procedures, and Figure 3a was obtained by observing the gel under visible light. Figure 3a showed a sigmoidal profile as the concentration of urea increased in the gradient gel. The protein moved slowly when it was unfolded compared to when it was in the folded state. This was expected because unfolding would lead to a more extended conformation of BSA. For the FCS experiments, the urea-gradient native gel shown in Figure 3a was divided and cut into 11 equal fragments of 0.7 cm, and each fragment represents one urea concentration. FCS experiments were carried out at different points in each fragment to develop the profile of the unfolding transition. The inset of Figure 3b shows the profiles of τD,slow histogram analyses obtained with Alexa488BSA in the presence different urea concentrations. Figure 3b shows the unfolding transition of Alexa488BSA measured inside the polyacrylamide gel using FCS. The unfolding transition obtained in solution using farUV CD is also shown in Figure 3b. Although the unfolding transitions were quite similar in nature, the protein seemed to be slightly more stable inside the polyacrylamide gel (urea unfolding midpoint of 6.5) than it was in free solution (midpoint of 5). The increase in protein stability in the presence of molecular crowding has been noted before for a number of protein systems.48,49 However, it is important to note that a small difference in the urea concentration was unavoidable in a urea gradient gel, which might also contribute to the observed increase in the measured midpoint inside the polyacrylamide gel. Nevertheless, the size of the fragments was maintained as small as was experimentally possible to minimize this effect. Variation of Hydrodynamic Radius of the Folded and Unfolded Proteins Inside the Polyacrylamide Gel. Figure 4a shows the variation of the hydrodynamic radii (rH) of the model systems in their folded and urea unfolded states with the number of amino acids (Na). The line through the data (Figure 4a) is a fit using the following equation

Dg

(8)

where Rs and Rf are the solute and fiber radius, respectively, in a polyacrylamide gel. The Ogston model considers only the hydrodynamic effect of polyacrylamide gel and does not recognize steric factors. Although it was the only model available for many years, the importance of incorporating the steric factors has been recognized in several models developed later. The effective medium model takes both the hydrodynamic and steric effects into consideration.47 In this model, the solute diffusion is represented by the following equation −1 ⎛ ⎛ R s ⎞2 ⎞ −0.84f 1.09 Rs 1 = ⎜1 + + ⎜ ⎟⎟ e D0 ⎜⎝ 3 ⎝ k ⎠ ⎟⎠ k

Dg

(9)

where 2 ⎛ R ⎞ f = ⎜1 + s ⎟ φ Rf ⎠ ⎝

where, Rs is the solute radius and Rf is the fiber radius. The value of k, the hydraulic permeability, was calculated using the following equation35 k−2 = (2.64 × 10−16cm 2) φ−1.42

(10)

Figure 2f shows the variation of D g /D 0 obtained experimentally using FCS data with the volume fraction of the acrylamide gel. The line through the data for each case represents the fit using the effective medium model (eq 9). The value of the fiber radius (Rf) has been determined previously for a polyacrylamide gel of identical conditions,35 and their value of 6.5 Å was fixed in all of the fits shown in the present article. The values of solute and pore size derived from the effective medium model are shown in Table 2. It is evident from Table 2 Table 2. Different Parameters Obtained Using the Effective Medium Model molecules Alexa488IFABP Alexa488Lys Alexa488BSA Alexa488Antibody

solute size (Å)a 21 23 31 42

(19.9) (21.4) (37.5) (47.1)

fiber size (Å)a 6.5 6.5 6.5 6.5

(fixed) (fixed) (fixed) (fixed)

pore size (Å)a 55 59 75 97

a

The values of pore size were determined from the following relation: pore size = 2(solute size + fiber size).52 The values of the hydrodynamic radii of these systems were measured by FCS experiments in freely diffusing solutions and are shown in parentheses.

that the calculated values of the solute size for all of the proteins are comparable to their hydrodynamic radii (in free solution), validating the fits with the effective medium model. The data presented in this article clearly suggest that the application of FCS can be extended to the protein diffusion inside polyacrylamide-gel systems. The use of a two-component diffusion model, which assumes equilibrium between molecules diffusing in free solution and in a crowded gel environment, is found adequate. The diffusion data inside the polyacrylamide gel can be represented by the effective medium model, which considers both the hydrodynamics and steric contributions to the diffusing solutes.

rH = A × Na α

(11)

where A is a proportionality constant, and α is an empirical scaling parameter whose value has been predicted to be 0.3 for the folded proteins in a poor solvent (like aqueous buffer) and 0.6 for the unfolded proteins in a good solvent (like urea).22,50 The variation of the present rH data obtained using FCS experiments with the folded (in aqueous buffer at pH 7.4) and unfolded proteins (in the presence of urea at pH 7.4) with Na 14714

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Figure 3. (a) Unfolding transition of Alexa488BSA inside a urea-gradient native gel. The unfolding trace was photographed using a digital camera (model Canon SX-90). (b) Variation of diffusion time (black) and ellipticity at 222 nm (red) with urea concentration. The ellipticity values were measured using a far-UV CD experiment with proteins under freely diffusing solution conditions (20 mM sodium phosphate buffer at pH 7.5). The diffusion time values were obtained using FCS experiments inside a urea-gradient polyacrylamide native gel. The variations of τD distributions with urea concentration are shown in the inset.

fits well using eq 11 and using the values of 0.3 and 0.6, respectively (Figure 4a). However, the use of these exponents

needs to be suitably modified if it is to be applied in a crowded solution (e.g., inside a polyacrylamide gel). To study further the effect of the change in shape in the absence and presence of acrylamide gel, the difference in rH between the unfolded (rH,U) and folded (rH,F) state of a protein has been determined as follows ωs = (rH,U) − (rH,F)

(12)

Figure 4b shows the variation of ωs with the increase in Na. Figure 4b clearly suggests that inside the polyacrylamide gel the parameter ωs increases with the increase in Na. In addition, the behavior of ωs is very different in freely diffusing medium. In the freely diffusing medium, the values of ωs increase initially and tend to saturate at high Na. This observation suggests that the increase in the number of amino acids (Na) results in the decrease in the resolution in measuring the difference in rH between the unfolded and folded states in freely diffusing solution. This is in contrast to the data inside the polyacrylamide gel, which clearly indicate that the crowding induced by the polyacrylamide gel leads to a large increase in the resolution of measuring the difference in rH because of the shape change. Additionally, the effect of crowding is even more prominent in the case of higher molecular weight (or higher Na). Although the present data clearly show that the presence of a polyacrylamide gel increases the value of ωs significantly at higher Na, a physical understanding is missing. However, it can be speculated that a large component of the retardation effect in the presence of a polyacrylamide arises because of the nonspecific interactions between the solute particles and the polymer matrix. Arguably, this effect would be more prominent in the case of a more extended unfolded state of the protein compared to the compact folded state. The effect of the presence of urea, which could also contribute to this effect by increasing the viscosity, can be ignored because of the normalization procedure used in the present study. The application of advanced microscopy techniques can provide important and interesting results to understand the molecular details of the diffusion behaviors of biological fluids in crowded medium in general and the effect of molecular shape in particular.

Figure 4. (a) Variations of rH,slow of the folded and unfolded proteins (in the presence of 10 M urea) with Na in freely diffusing buffer and inside a polyacrylamide gel. (b) Variations of ωs with Na under these conditions are also shown. The measurements inside the polyacrylamide gel were carried out using gel matrix made with 10% acrylamide and 0.8% bis-acrylamide.

in eq 11 does not work for the model systems inside the polyacrylamide gel. Instead, for both the folded and unfolded systems, the values of rH show a more direct dependence (α = 0.9 and 1.06 for the folded and unfolded systems, respectively) (Figure 4a). Although the application and validity of the polymer scaling law has been extensively studied for folded (in poor solvent) and unfolded proteins (in good solvent),51 it 14715

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CONCLUSIONS We used FCS to study the effect of molecular size and shape on the diffusion inside a polyacrylamide gel using a number of model systems. A combination of a histogram analysis and a two-component fit was used to determine the values of the most possible diffusion time of the model systems inside a polyacrylamide gel. The use of the effective medium model, which uses both hydrodynamic and steric factors, fits the solute behavior well inside the polyacrylamide gel. The presence of crowding enhances the resolution of hydrodynamic radius detection both for the size and shape changes.

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ASSOCIATED CONTENT

S Supporting Information *

Correlation functions obtained with different proteins using maximum entropy method analysis; variations of normalized τD,fast and τD,slow in the presence of different pinhole diameters; amplitudes of the fast and slow components obtained with BSA in the presence of varying concentrations of polyacrylamide; and residual distribution analysis of BAS inside a 12.5% polyacrylamide gel. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

We thank Professors Carl Frieden and Elliot Elson of the department of Biochemistry and Molecular Biophysics of the Washington University School of Medicine for their critical comments on the manuscript. This work was funded by a CSIR network project (UNSEEN). S.B. was supported by CSIRresearch fellowship. We thank Professor Siddhartha Roy, the director of the CSIR-Indian Institute of Chemical Biology, for his support.

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