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Combined SAXS/UV−vis/Raman as a Diagnostic and Structure Resolving Tool in Materials and Life Sciences Applications Sylvio Haas,*,† Tomás S. Plivelic,*,† and Cedric Dicko‡ †

MAX IV Laboratory, Lund University, P.O. Box 118, SE-22100 Lund, Sweden Pure and Applied Biochemistry, Lund University, P.O. Box 118, SE-22100 Lund, Sweden

‡

S Supporting Information *

ABSTRACT: In order to diagnose and fully correlate structural, chemical, and functional features of macromolecules and particles in solution, we propose the integration of spectroscopy and scattering on the same measuring volume and at the same time in a dedicated sample environment with multiple probes. Combined SAXS/UV−vis and SAXS/Raman information are employed to study the radiation damage effect in proteins in solution and the scattering from single wall carbon nanotubes (SWNTs) in SDS dispersion, respectively. In the first case, a clear correlation is observed between the time dependence of the radius of gyration (Rg) of the protein determined by SAXS and the turbidity of the protein solution extracted from simultaneous UV−vis measurements. In the second case, the ratio of bundled/isolated carbon nanotubes is obtained unambiguously through proper modeling of the scattering data and cross-validated with the Raman information. The uses of convex constraint analysis (CCA) and twodimensional correlation analyses (2DCOS and 2DHCOS) are introduced to fully explore the combination of data sets from different techniques and to extract unique insights from the sample. however, permeated the fields of materials, soft matter, and life sciences.1,9−12 In their unique setup, the SWING beamline at SOLEIL8 has pioneered the positioning of ancillary techniques where the X-ray interacts with the sample. Our present setup achieves the same, with the exception that the sample holder allows for other probes to be fitted. Direct combination of techniques without separation (i.e., simultaneous experiments) has received less attention regardless of the seminal paper by Bras et al.10 The approach1 often involves two probes at most in a dedicated sample environment. From a data quality point of view, the necessary compromise to accommodate different techniques simultaneously needs to outweigh the results from single experiments on optimized instruments. This is in most cases impossible; therefore, there is no good reason to perform techniques simultaneously unless one is dealing with systems that evolve in time or subject to an external perturbation (e.g., temperature, pH, etc.). In these cases, the loss of data quality, which is inevitable when combining experiments, is compensated by the synergy of having an accurate time correlation between the data sets. This advantage comes with the knowledge that the data is taken from the same sample volume, which in turn eliminates artifacts that could be introduced by sample variability (e.g.,

1. INTRODUCTION While the importance of structure−function relationships has been recognized and their correlation sought after, the underlying molecular mechanisms linking structure to function are elusive. The complexity of sample reactivity and polymorphism are only few reasons among others for such difficulties. A relevant way to approach the problem is the combination of techniques that can report on the structure and chemistry of the samples. This is a vast area, and we focus our effort on the combination of small-angle X-ray scattering (SAXS) with spectroscopic tools.1−3 Traditionally, hyphenated techniques4,5 are defined by the combination of a separation method such as liquid chromatography (LC), gas chromatography (GC), or capillary electrophoresis (CE) linked to spectroscopic detection techniques, e.g., Fourier-transform infrared (FTIR), photodiode array (PDA) UV−vis absorbance or fluorescence emission, mass spectroscopy (MS), and nuclear magnetic resonance spectroscopy (NMR), resulting in the introduction of various modern hyphenated techniques, e.g., CE-MS, GC-MS, LC-MS, and LC-NMR. The power of combining separation technologies with spectroscopic techniques has been demonstrated over the years for both quantitative and qualitative analysis of unknown compounds in complex natural product extracts or fractions. Recent efforts to combine LC and SAXS have also proven valuable to resolve structural ambiguities arising from the sample complex composition.6−8 However, very little combination of SAXS with solely in situ optical spectroscopy6−8 has, © 2014 American Chemical Society

Received: December 13, 2013 Revised: January 31, 2014 Published: January 31, 2014 2264

dx.doi.org/10.1021/jp412229j | J. Phys. Chem. B 2014, 118, 2264−2273

The Journal of Physical Chemistry B

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Raman, and UV−vis probes are arranged perpendicularly to the capillary long axis and pointing at the same sample volume, whereas the overlapping volume is given by the smallest spot size of all probes (SAXS = 200 × 200 μm2, UV−vis = 500 μm2 diameter, Raman = 85 μm2 diameter). An overview of the technical specification of each of the probes is given in Table 1.

chemical and structural inhomogeneity, environmental conditions, aging, etc.). The above advantage is then exploited by specific data analysis techniques, as illustrated in the present contribution. Briefly, linking structure to function heavily relies on understanding the link between spectral and structural features. Typical examples are extraction of secondary structures from vibrational or circular dichroism spectra,13,14 where the spectral features are correlated to known structure using databases. This approach, although popular and successful in most cases, has serious limitations when the system under investigation has unusual components and a mixture of these. To address the structure−function relationship challenges, the modern approach is to use self-modeling15,16 and correlation analysis.17 The former resolves the number of components and extracts their “pure” spectra and composition. The latter method allows for identification of the spectral features involved in changes experienced by the mixture of components. The combination of the two methods is thus demonstrated in this manuscript to highlight the integration of the techniques to extract unique insights from the samples. It is therefore our aim to implement and demonstrate the viability of combined techniques using state of the art fiber optics based spectrometers. The results presented in this contribution highlight the versatility and simplicity of the setup given the correct software−hardware integration. The potential of our approach is stressed in two case studies: bovine serum albumin (BSA) and single wall carbon nanotubes (SWNTs). In the first case, radiation damage and aggregation under high flux X-ray radiation are detected and studied by SAXS and UV−vis. In the latter case, the dispersion properties of SWNT in SDS are investigated and modeled.

Table 1. Overview of the Current Probes Specification Raman specification company/model B&W Tek Inc./i-Raman excitation wavelength 785 nm laser power 50−350 mW detector CCD-array Raman-shift range 175−3200 cm−1 resolution 3 cm−1 UV−vis specification company/model light source wavelength range optics detector beamline wavelength q-range beam size at sample flux 2D X-ray detector

Pharmacia/μPeak xenon flash lamp 190−600 nm monochromatic beam photodiode SAXS specification I911-4 at MAX IV Lab 0.91 Å 0.07−0.6 Å−1 200 × 300 μm2 ∼3 × 1011 ph/s Pilatus 1M, Dectris

The holder is equipped with a temperature control unit based on copper pipes and a thermostatted water bath. This option allows controlling the temperature of the sample in the range 10−70 °C. The full potential of the multiprobe environment can only be properly explored if the control environment is flexible but also user-friendly. Two Python based graphical user interfaces have been developed to control each spectrometer (Raman and UV−vis) via TCP/IP socket communication. The operating software of the beamline is SPEC (Certified Scientific Software). This macro based script language allows socket communication, making it suitable to communicate with other devices. Different operation modes were implemented in the current setup: simultaneous SAXS/UV−vis and SAXS/Raman. Combined UV−vis and Raman was not possible because the laser from the Raman system influences the UV−vis measurement. Therefore, UV−vis and Raman measurements were done in an alternating operation mode, by closing/opening the Raman laser shutter. 2.1.2. SAXS at the MAX IV Laboratory. The SAXS measurements were performed at the SAXS station at the MAX IV Laboratory.18 This fixed wavelength beamline at λ = 0.91 Å covers the scattering vector (q) range 0.007−0.6 Å−1 by off-centering the 2D X-ray sensitive detector (where q = (4π/λ) sin(θ) and 2θ the scattering angle). In the present case, the hybrid pixel X-ray detector Pilatus 1M (Dectris, Switzerland) was used. A focused beam with a rectangular spot size of approximately 200 × 300 μm2 (H × V) at the sample position was used during all measurements. The relative scattering intensities were scaled to absolute differential scattering cross section in cm−1 using Milli-Q water as standard reference and the empty quartz glass capillary scattering as corresponding

2. MATERIALS AND METHODS 2.1. Multiprobe Platform: SAXS/UV−vis/Raman. 2.1.1. Experimental Setup and Control. A custom-built sample holder with optical ports was constructed to fit at the SAXS beamline at the MAX IV Laboratory. Figure 1 shows a

Figure 1. Sketch of the basic concept behind the SAXS/UV−vis/ Raman multiprobe platform.

3D model of the holder together with the optical probes for Raman and UV−vis spectroscopy. The compact and portable design of the holder allows for online (at the SAXS beamline) or offline operations. The liquid samples are injected in exchangeable quartz glass capillaries with a nominal inner diameter of 2.0 mm and wall thickness of 0.01 mm. The SAXS, 2265



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⎧ y(υ , t ) − y ̃(υ) if tmin ≤ t ≤ tmax y ̃ (ν , t ) = ⎨ ⎩0 otherwise

background.19 The scattering vector calibration was done using a silver-behenate standard sample. The typical X-ray exposure time was 60 s. 2.1.3. Raman Spectroscopy. The Raman measurements were performed using an optical fiber based Raman spectrometer with backscattering geometry. The iRaman system from B&W Tek Inc. was equipped with a laser at wavelength 785 nm and maximum laser output power between 150 and 200 mW. The CCD-array-based spectrometer is calibrated for detecting Raman shifts between 175 and 3200 cm−1 at a resolution of 3 cm−1 in a single shot. The BAC100 laboratory Raman fiber optics probe produces a spot size of 85 μm in diameter at the sample surface and has a working distance of 5.9 mm. On the sample holder, this Raman probe is mounted from the top (see Figure 1). 2.1.4. UV−vis Spectroscopy. The UV−vis measurements were performed using a μPeak Monitor (Pharmacia, Uppsala, Sweden) for detection in the wavelength range 190−600 nm at a resolution of 1 nm. The equipment consists of a main unit and optical fibers. The source contains a beam splitter; one part of the incoming light is used as a reference spectrum, while the other part is guided to the sample holder using optical fibers. The optical system inside the spectrometer consists of a xenon flash lamp, condenser, block filter, grating, beam splitter, and detection unit (avalanche photodiode). The μPeak can operate in three different modes: single wavelength detection, three wavelength detection, and scanning mode. The main advantage of the μPeak compared to modern CCD-array-based devices is the larger dynamic range and high signal-to-noise ratio. On the sample holder, the UV−vis source optical fiber is mounted from the bottom left and the detection fiber from the top right at 30° from the vertical direction (see Figure 1). 2.2. Data Analysis. 2.2.1. Two-Dimensional Correlation Analysis. Two-dimensional correlation analysis, 2DCOS, is a technique17,20 where the spectral intensity is defined as a function of two independent spectral variables. By spreading the original data over the second dimension, the spectral resolution is enhanced, and the features not readily observable in the conventional spectra are emphasized. Moreover, it can probe the specific sequential order of the spectral intensity variations under external perturbations. A very intriguing method in 2D correlation spectroscopy is 2D heterospectral correlation analysis, 2DHCOS, in which two completely different types of spectra for a system are compared.17,20,21 The different spectra are obtained by using multiple spectroscopic probes under similar external perturbation. 2D heterospectral correlation analysis has become one of the most active areas of research in 2D correlation spectroscopy. Typically, the 2DCOS provides a pair of synchronous and asynchronous correlation spectra, which represent the overall similarity of the spectral intensity variations and the differences in dynamic behavior, respectively. Computation of the 2D correlation spectra: first of all, one needs a set of spectra measured on a system, which was induced by some external perturbation. Spectral intensities of this set can be expressed as I(υ, t), where υ is a spectral characteristic variable (wavenumber, wavelength, or Raman shift) and t is a parameter of an external impulse. That can be an evolution in time, temperature, pH, concentration, etc. Only a certain range of t can be measured, and therefore, a dynamical spectrum is implemented as

(1)

where ỹ(ν) is a reference spectrum of the system. An average spectrum is usually picked as a reference spectrum, but any reasonable spectrum can be chosen. The correlation spectrum is then defined as χ (υ1 , υ2) = ⟨y ̃(υ1 , t ) ·y ̃(υ2 , t )⟩

(2)

where the symbol ⟨ ⟩ is a cross-correlation function. This spectrum expresses a functional dependency between υ1 and υ2 during the interval of external variable t that is present. Using a complex number notation, the cross-correlation can be simplified and divided into synchronous, Φ, and asynchronous, Ψ, parts as follows: χ (υ1 , υ2) = Φ(υ1 , υ2) + i Ψ(υ1 , υ2)

(3)

Unfortunately, the direct computation of χ is very timeconsuming and therefore is used very rarely. Some simplification can be made when the data are equidistantly spaced, yielding for the synchronous spectra Φ(υ1 , υ2) =

1 y ̃(υ1)T ·y ̃(υ2) m−1

(4)

where m is the number of spectra equidistantly measured between tmin and tmax. For the asynchronous spectra, we further use the Hilbert− Noda matrix (N) as follows: ⎧0 for j = k ⎪ Njk = ⎨ 1 otherwise ⎪ ⎩ π ( k − j) Ψ(υ1 , υ2) =

1 y ̃(υ1)T Ny ̃(υ2) m−1

(5)

(6)

The heterocorrelation, 2DHCOS, is simply an extension of the above homocorrelation, 2DCOS, by treating υ1 and υ2 from different sources, e.g., SAXS and UV−vis. The UV−vis spectra were baseline subtracted prior to the calculation of the 2D correlation. The SAXS data were plotted as I(q)·q2 vs q (Kratky) to enhance the visualization. The generalized 2D correlation analysis was applied by the 2D Shige software, version 1.3 (Shigeaki Morita, Kwansei-Gakuin University, Japan, 2004−2005). The average spectrum was used to compute the dynamic spectra. In the 2D contour maps, the red-colored regions are defined as the positive correlation intensities, while the blue-colored regions represent negative correlation intensities. 2.2.2. Convex Constraint Analysis (CCA). The CCA21 is a modeling technique that assumes that a measured spectrum at time t is a weighted sum of pure-component spectra gTi (X) with weight coefficients Ci,tT that depends on time t. The index i indicates the component, T the technique (UV or SAXS), and X is λ or q depending on the method. The spectrum can be expressed as P

ftT (X ) =

∑ C(Ti ,t) × giT (X ) i

(7)

where P is the number of pure components. The parameters can be determined by chi-square χ2 minimization performing a 2266



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nonlinear regression of the experimental data set hTt (X), with time t = t0, ..., tN (N: number of spectra): N

χT 2 = (∑ htT (X ) − t=1 N

= (∑ htT (X ) − t=1

N

∑ ftT (X ))2 t=1 N P

∑ ∑ CiT,t × giT (X ))2 t=1 i=1

(8)

Three generic constraints were included in the nonlinear regression:22 (a) Unity constraint: The sum of weights CTi,t for each time t must be unity: ∑Pi=1 CTi,t = 1. (b) Positive constraint: The weights must be positive real numbers: CTi,t ≥ 0 ∀ i, t. (c) Volume constraint: The points {CTi,t|i = 1, ..., P; t = t0, ..., tN} must be an element of the P-dimensional Euclidean space with the smallest volume. In a typical analysis, different numbers of components P are cross-checked to determine the most suited solution. 2.3. Samples and Experiments. 2.3.1. Radiation Damage Experiment. Combined measurements of SAXS and UV− vis spectroscopy were performed on a 5 mg/mL BSA solution in 10 mM, pH 7.0 sodium phosphate (NaP) buffer. The BSA powder was obtained from Sigma-Aldrich and used directly without further purification. Prior to use, the BSA solution was centrifuged for 15 min at 14 000 rpm in 1.5 mL eppendorf tubes. The SAXS exposure time was 60 s, and during that time, the UV−vis light absorbance at 280 nm was recorded simultaneously with a time resolution of 1 s. After each SAXS pattern, a “full” UV−vis spectra has been taken (200−600 nm). The measurement sequence has been measured in total for 2 h. The Raman spectra were not included, since no signal from BSA was detectable. 2.3.2. Carbon Nanotube Experiment. The SWNTs (SigmaAldrich, reference number 636797) were initially dispersed in 1% SDS (35 mM) solution and sonicated for 1 h (100 W, 42 kHz sonication bath). The dispersed solution was centrifuged at 12 000 rpm (25 000 g) for 1 h in a Sorvall RC6-plus centrifuge (ThermoFischer). A SWNT concentration series using nominal concentration cSWNT = 0, 1.25, 2.5, 5.0, and 10 mg/mL was prepared for analysis.

Figure 2. UV−vis spectra (a) and SAXS curves (b) of BSA as a function of the total X-ray exposure time on the sample. The inset in panel (a) shows that the turbidity increases with time, and the inset in panel (b) shows the pair-distance distribution function.

time, respectively. Changes of the protein solution due to X-ray radiation can be observed by both techniques. The inset graph in Figure 2a shows the evolution of the turbidity τ(λ, t) from each UV−vis spectrum, using the equation τ(λ , t ) = b(t )λ−m(t )

3. RESULTS AND DISCUSSION To illustrate the potential of the multiprobe platform, two example scenarios are presented. The first example emphasizes the diagnostic aspect of the multiprobe approach to investigate protein solutions, typically concentration calculation and X-ray induced radiation damage on bovine serum albumin (BSA). The second example deals with organic−inorganic interfaces, namely, the dispersion properties of single wall carbon nanotubes in sodium dodecyl sulfate (SDS). 3.1. Diagnostic and Structural Changes of X-ray Radiation Damage on BSA. Nowadays, a recurring issue in protein solution scattering experiments at synchrotron facilities is the risk of radiation damage of the protein due to the high photon flux from the source. This is monitored and can be overcome using different strategies (see, for example, Jacques et al.23). The absorbance spectra (UV−vis data) and the SAXS intensities I(q) are shown in Figure 2a and b as a function of

(9)

where λ is the wavelength, b a scaling factor, and m an exponent. Both b and m are time t dependent. The parameters b and m were determined for each kinetic data set (at time t) by a nonlinear regression of the measured absorbance spectra in the range λ = 320−375 nm. An increase of the turbidity with time has been clearly detected. The UV−vis spectra after correction for turbidity show no measurable differences in the aromatic region of the spectra. The signal associated with the backbone of the protein (below 230 nm) was not accessible from lack of suitable light transmission. A model free analysis of the SAXS pattern yielded a radius of gyration Rg and maximum dimension of the protein Dmax. Rg and Dmax at time t were determined by indirect Fourier transformation (IFT).24 IFT determines the pair-distance distribution function P(r), which is shown in the inset graph in Figure 2b. Dmax is given by the largest nonzero value in the P(r) function and Rg by the formula25,26 2267


The Journal of Physical Chemistry B Rg2 =

∫ p(r )r 2 d r 2 ∫ p(r ) d r

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and UV−vis kinetic series. For the investigated system, only two pure components, P = 2, gave physically meaningful results of the CCA. The weights (composition in %) are shown in Figure 5 for the convex constraint analysis of UV−vis and

(10)

In the present case, the quantity Rg has to be understood as an average size parameter of the system because the monodisperse behavior of the protein solution (initial state) is affected with time due to the radiation damage effect (see Figure S1, Supporting Information). The time evolution of Rg and Dmax is shown in Figure 3. Both quantities are continuously increasing with time following

Figure 5. Convex constraint analysis, CCA, of the transition from the initial native protein (component 1) toward the radiation damaged protein state (component 2). The identical crossing point indicates that both probes simultaneously detect the same structural change.

SAXS, respectively. A roughly linear transition from the pure component 1, which represents the initial protein state, toward the pure component 2, which represents the last measured radiation damaged protein state, can be seen for both methods. The SAXS derived pure-component curves 1 and 2 reveal a radius of gyration of 33.23 and 49.96 Å, respectively. The Rg value of 33.23 Å for component 1 corresponds to the known size of native BSA.27 The coincidence of the two crossing points in Figure 5 indicates that both probes (SAXS and UV− vis) simultaneously detected the same structural changes. The smooth linear transition indicates that the radiation damage of BSA is a continuous process and does not comprise a measurable intermediate transition state; otherwise, the number of components must be larger than 2. To assert the impact of the simultaneous multiprobe approach, the same experiments without UV−vis measurements were repeated. The behavior of the radius of gyration as a function of the X-ray dose didn’t show significant differences between the tests (see Figure S2, Supporting Information). To fully exploit the combination of techniques, we need to also combine the data. To do so, we choose the generalized two-dimensional correlation spectroscopy (2DCOS) framework. Figure 6 shows the 2DCOS synchronous and asynchronous correlation map for the SAXS data (Figure 6a and b) and the UV−vis data (Figure 6c and d), respectively. The intensity of a synchronous correlation map represents the simultaneous occurrence of coincidental changes of two spectral intensity variations. The synchronous map is symmetric, and the intensity of peaks located at the diagonal position corresponds to the autocorrelation function. Those peaks are referred to as autopeaks. The magnitude of the autopeak reflects the extent by which a spectral region changes. For example, in Figure 6a and c, we observe two comparable autopeaks at 0.03 and 0.07 Å−1 for the SAXS and one strong autopeak (below 240 nm) and one weak autopeak (300 nm) in the UV−vis spectra. The off-diagonal peaks, cross-peaks, represent the simultaneous or coincidental changes observed in the spectral region of interest. While the sign of the autopeak is always positive, the cross-peaks can be either positive or negative. Typically, the cross-peak has a positive intensity (here

Figure 3. Comparison of the time evolution of the radius of gyration Rg and the maximum dimension Dmax of the protein.

approximately the same power law. For this reason, the Rg parameter can be used as an indicator of size changes of the protein. Besides the increasing size of the BSA due to being exposed to X-rays, the overall shape changes as well, indicated by the evolution of the P(r) function with time (see Figure 2b). The occurrence of larger distances in P(r) with time can be interpreted as something similar to an unfolding process and/or to an aggregation process. The comparison of the time evolution of Rg and turbidity is summarized in Figure 4. As Rg increases, the turbidity exponent m also increases with approximately the same power law. The linear correlation between the radius of gyration and the turbidity exponent means that both techniques detected the same structural changes induced by X-ray radiation. The last statement can be proved quantitatively by independent convex constraint analysis (CCA) of both SAXS

Figure 4. Comparison of the radius of gyration Rg of the protein with the exponent of the turbidity m. A clear correlation can be observed as a function of the X-ray exposure time on the sample. 2268



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Figure 7. Shown are the synchronous (a) and asynchronous (b) spectra of the hetero 2D correlation analysis (2DHCOS) of SAXS and UV−vis. The red color indicates positive correlation peaks, while the blue color, negative correlation peaks.

correlation between 0.07 Å−1 and the peak below 240 nm. This suggests that the change in UV−vis below 240 nm, namely, unfolding,28 is directly related to the change in signal at 0.07 Å−1 in the SAXS. The overall change at 0.03 Å−1 is a consequence of these changes. Interestingly, Figure 6b (asynchronous map for the SAXS) suggests that the change at 0.03 Å−1 occurs before the change at 0.07 Å−1. This would mean that the radiation damage effect on BSA proceeds by first an increase in overall size without a significant change in conformation, followed by some change in conformation and increase in size. This particular series of events is reminiscent of a nucleation event prior to elongation in fibrillar systems. Earlier work on X-ray induced radiation damage29−31 suggests that the indirect effects of radiation, i.e., the reaction of radical and nonradical products of water radiolysis with the protein, are mainly responsible for radiation damage. In our experiment, we cannot observe the effects of radicals, but the likely small (catalytic) changes in the side chain residues (UV spectra) may be indicative of such radical activities. The quantitative analysis of protein solution SAXS experiments needs the information of the protein concentration. The advantage of combining SAXS and UV−vis at the same volume is the possibility to determine the protein concentration from UV−vis in real time. A similar approach is also reported in the literature by David and Perez.8 The protein concentration can be determined from UV−vis using the well-known Lambert− Beer law. The concentration c in mg/mL is given by

Figure 6. On the left side are shown the synchronous spectra of SAXS (top) and UV−vis (bottom). On the right side are the corresponding asynchronous spectra. The red color indicates positive correlation peaks, while the blue color, negative correlation peaks.

in red) if the correlated spectral features increase or decrease together. On the other hand, a negative sign (here in blue) of the cross-peak intensity indicates that one of the correlated spectral features increases while the other one decreases. A look at Figure 6a and c shows that the cross-peaks are negative, which means that the changes in the autopeak happen in opposite directions. For example, in the SAXS data, the correlated intensity at 0.03 Å−1 increases, while the intensity at 0.07 Å−1 decreases. The UV−vis correlation map is not as clear because of the first autopeak truncation (not visible below 240 nm) and the large intensity difference between the two autopeaks. Nevertheless, the changes below 240 and 300 nm are correlated and happen in opposite directions. The strength of the 2DCOS analysis comes from the use of the asynchronous maps. The changes here are indicative of sequential or successive but not coincidental changes in spectral intensities. The asynchronous map does not have any autopeak and consist exclusively of cross-peaks. The asynchronous crosspeak develops only if the intensities of the two spectral features change out of phase with each other (e.g., delayed or accelerated). The sign of an asynchronous peak becomes positive (here red) if the change happens before and vice versa (blue intensity) if the change happens after. Looking at Figure 6b and d, we observe cross-peaks in the asynchronous maps of the SAXS and UV−vis. Figure 6b shows a positive cross-peak at 0.03 Å−1 and a negative cross-peak at 0.07 Å−1. This suggests that the change at 0.03 Å−1 occurs before the change at 0.07 Å−1. Figure 6d reveals that the change below 240 nm occurs after the change at 300 nm. To gain some further understanding on how the SAXS information correlates with the UV−vis, we implement a twodimensional heterospectral correlation (2DHCOS). The 2DHCOS synchronous and asynchronous maps can be calculated, with the exception that the synchronous map does not show any autopeaks. Figure 7 shows the 2DHCOS of the SAXS and UV data combined. In Figure 7a, the synchronous map, we observe that the changes below 240 nm in the UV spectra are negatively correlated to the change at 0.03 Å−1 and positively correlated to the change at 0.07 Å−1 in the SAXS. In the asynchronous map (Figure 7b), we observe only a positive

c[mg/mL] =

10(A 280 − A320) ⎡ 100 mL ⎤ εpercent⎢⎣ g cm ⎥⎦L[cm]

(11)

where A280 and A320 are the absorbance and the background for a wavelength of 280 and 320 nm, respectively, L is the mean path length in cm, and εpercent is the percent extinction coefficient of the protein in units of 100 mL g−1 cm−1 (e.g., εBSA percent = 6.67[100 mL/g cm]). For the investigated system, a BSA concentration of 3.75 mg/mL was determined from the absorbance spectra of the initial state and cross-checked with a conventional laboratory device (3.73 mg/mL). We further tested the dynamic range of our techniques by estimating the UV−vis spectra of a dilution series of lysozyme (see the Supporting Information, Figure S3). We found that down to 0.45 mg/mL we could measure a lysozyme solution by SAXS and UV−vis with a useful signal-to-noise ratio. 3.2. SDS-Dissolved Single Wall Carbon Nanotubes (SWNTs). The organic−inorganic interfaces are important 2269



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frequency ω+G and ω−G. Bundled carbon nanotubes add another two more components of frequency ω+E2 and ω−E2. The G-band of the highest concentration sample was fitted with four sharp Lorentz profiles (fwhm ∼6−15 cm−1), as shown in Figure 9. The determined Raman shifts of all four modes correlate well with previously reported values.33

aspects in designing complex functional materials. Between them, the interactions of organic substances with carbon nanotubes are of major interest due to the prospects to design efficient biosensors for medical applications. To illustrate the potential of the multiprobe platform, we investigated the decoration of single wall carbon nanotubes (SWNTs) by sodium dodecyl sulfate (SDS) in solution. Simultaneous SAXS and Raman spectra of approximately the same sample volume were recorded (UV−vis spectra were also taken but didn’t show any relevant information in the detectable range). Figure 8a shows the solvent corrected

Figure 9. Analysis of the G-band peak of the highest SWNT concentration. The peak was fitted with four Lorentzian peaks, where two peaks correspond to isolated/bundled SWNTs and the other two only to bundled SWNTs.

The occurrence of the E2 modes indicates that isolated and bundled SWNTs were present in the system. The ratio of isolated to bundled SWNTs cannot be determined from Gband analysis. Instead, it can be established by the ES22 resonant level excitation of semiconductor SWNTs that could be measured with UV−vis spectroscopy. Unfortunately, this is out of the current implemented UV−vis spectrometer range. Alternatively, the radial breathing modes (RBMs) of isolated and bundled nanotubes can be used. The RBMs are found at frequencies of 167 and 180 cm−1, but the low intensities of the Raman signal in that region prevented a quantitative analysis of those modes. Nevertheless, a different approach can be used on the basis of the scattering data. As a second step, the SAXS curves were analyzed using the information obtained by Raman. The pure SDS solution sample (buffer) was modeled assuming ellipsoidal core−shell nanoparticles together with hard sphere structure factor, as mentioned in the literature.34 The best fit of the experimental data is shown in Figure 8b. The sizes of the core semi axes are 10.5 and 16.1 Å. The shell thickness was found to be 12.4 Å, which is in agreement with the reported values.35 To fit the SAXS data of the SWNT dispersions, a multicomponent model was used

Figure 8. Raman spectra (a) and SAXS curves (b) for the different concentration of SWNTs. (a) The Raman spectra indicate that the SWNTs are semiconducting rather than metallic. (b) The symbols are the experimental data points and the lines the fittings.

Raman intensity for the different SWNT concentrations. The different Raman modes of semiconducting SWNTs can be readily indexed in each spectrum, with the best signal-to-noise ratio found for the highest concentration case of 10 mg/mL. The corresponding SAXS curves are shown in Figure 8b, including the pure SDS solution, which had no Raman signal. To derive the proper structural model of the organic−inorganic interface and assembly, both SAXS and Raman spectra were quantitatively analyzed and combined. As a first step, the Raman G-band, associated with the transverse vibration modes of carbon atoms, was analyzed to determine the aggregation state of the SWNTs.32 Isolated carbon nanotubes reveal two components of the G-band of

I(q , c) = ISDS(q , c) + ISWNT(q , c)

(12)

The first component ISDS(q, c) is free SDS in solution and described by the same model as the pure SDS sample c ISDS(q , c) = NSDS FECS2(q , rA , rB , ηSDS , ηsolvent)S(q)

(13)

The sizes rA, rB and electron densities ηSDS, ηsolvent for this component were kept fixed for all samples. The subindex c indicates the SWNT concentration dependency. The analytic expression for the form factor of ellipsoidal core−shell particles FECS2 as well as the hard sphere structure factor S(q) can be found elsewhere.36 NcSDS takes into account the number density of free SDS in solution. Since a small fraction of SDS can be 2270



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bounded to the carbon nanotubes, such a quantity is dependent on the SWNT concentration. NcSDS needs to be kept as a fitting parameter in eq 12. The second component ISWNT(q, c) was assumed to be long cylindrical core−shell objects (core = SWNT, shell = SDS) with a constant shell size ΔSSWNT and electron density values for the phases (ηSWNT, ηSDS, ηsolvent) ISWNT(q , c) =

∫

Table 2. Overview of the Particle Number Density Derived from SAXS cSWNT (mg/mL) 0.00 1.25 2.50 5.00 10.00

Pbi(R , ri , rb , Nic , N bc)

× FCCS2(q , R , ΔSSWNT , ηSWNT , ηSDS , ηsolvent)S(q) dR

4.23 3.95 3.77 3.41 2.41

± ± ± ± ±

0.02 0.02 0.02 0.03 0.03

NSWNT bundled (×106 cm−3) 0.39 0.74 1.29 2.73

± ± ± ±

0.03 0.03 0.03 0.06

NSWNT isolated (×106 cm−3) 0.05 0.08 0.16 0.33

± ± ± ±

0.01 0.01 0.01 0.02

increasing SWNT concentration as expected. The ratio of bundled to isolated SWNTs decorated with SDS was found approximately as a factor of 10. This stems from the calculation of the total number density of nanotubes Ntotal = Nisolated + Nbundled which must be proportional to the total amount of carbon in the solution. Therefore, a cross-check of the obtained total number density can be done by comparing the number density with the amplitude of the Raman D-band, which is proportional to the carbon amount. The Raman D-band was fitted with a Lorentz profile, and the resulting amplitude is shown in Figure 11 together with the total number density of

(14)

The expression of the form factor of cylindrical core−shell particles FCCS2 can be found elsewhere.36 For the core radius, a bimodal log-normal size distribution Pbi was used (isolated and bundled SWNTs, respectively), where Nci and Ncb are the SWNT concentration dependent number densities. The bimodal size distribution was normalized according to the following expression:

∫ Pbi(R , ri , rb , Nic , Nbc) dR = Nic + Nbc

NSDS (×108 cm−3)

(15)

The mean length of the cylindrical shaped objects was fixed at 7500 Å (Sigma-Aldrich). Note that a distribution for the length parameter does not affect the fit result significantly because the scales involved are out of the accessible q-range. Therefore, the only fitting parameters for the model were the number densities for the pure SDS, isolated, and bundled SWNT/SDS (NCSDS, NCi , NCb ) as well as the core radius ri = risolated and rb = rbundled and the shell thickness ΔSSWNT. Within the error bar, all curves could be fitted simultaneously by such a structural model, as shown in Figure 8b. In this case, simultaneous means that the size parameters are assumed to be the same for the different SWNT concentrations. The volume weighted size distributions of the different components are summarized in Figure 10. The two log-normal distributions correspond to the isolated and bundled versions of the SWNTs, respectively. In addition, schematic cross sections are depicted. The obtained particle number densities from the simultaneous nonlinear regression of the SAXS curves are given in Table 2. The excess of pure SDS is slightly reduced with

Figure 11. Comparison of the total number density of the SWNT particles obtained from SAXS with the Raman amplitude of the Dband as a function of the SWNT concentration. Within the error, both quantities are proportional to each other, indicating a consistent description of the system.

SWNTs as a function of the SWNT concentration. Within the error, both quantities are proportional to each other, which confirms the obtained parameters of the SAXS analyses. It is important to stress at this point that without the combination of techniques the structures would not be resolved.

4. CONCLUSION We developed a multiprobe sample environment, which combines SAXS with spectroscopic methods like UV−vis absorbance and Raman spectroscopy. The simultaneous measurement of the probes at the same sample volume with minimal time delay allows a quantitative linking of structure to function properties of biomolecules or colloidal particles in solution. We also propose the use of self-modeling and correlation analysis (CCA, 2DCOS, and 2DHCOS) to enhance the interpretation and integration of the data from the different techniques. It is important to note that modeling, of at least three probes results, allows for the determination of the number of components in a mixture, their spectral character-

Figure 10. The volume weighted size distribution of the particles. The blue lines are the size parameters of the pure SDS micelles, while the red line is the shell thickness of the SWNT/SDS particles. The two distributions (red curves) correspond to the isolated (solid) and bundled (dotted) SWNTs, respectively. 2271



Article

(7) Perez, J.; Nishino, Y. Advances in X-Ray Scattering: From Solution Saxs to Achievements with Coherent Beams. Curr. Opin. Struct. Biol. 2012, 22, 670−678. (8) David, G.; Perez, J. Combined Sampler Robot and HighPerformance Liquid Chromatography: A Fully Automated System for Biological Small-Angle X-Ray Scattering Experiments at the Synchrotron Soleil Swing Beamline. J. Appl. Crystallogr. 2009, 42, 892−900. (9) Caetano, B. L.; Santilli, C. V.; Meneau, F.; Briois, V.; Pulcinelli, S. H. In Situ and Simultaneous Uv-Vis/Saxs Abd Uv-Vis/Xafs TimeResolved Monitoring of Zno Quantum Dots Formation and Grwoth. J. Phys. Chem. C 2010, 115, 4404−4412. (10) Bras, W.; Derbyshire, G. E.; Bogg, D.; Cooke, J.; Elwell, M. J.; Komanschek, B. U.; Naylor, S.; Ryan, A. J. Simultaneous Studies of Reaction Kinetics and Structure Development in Polymer Processing. Science 1995, 267, 996−999. (11) Briois, V.; Belin, S.; Villain, F.; Bouamrane, F.; Lucas, H.; Lescouëzec, R.; Julve, M.; Verdaguer, M.; Tokumoto, M. S.; Santilli, C. V.; Pulcinelli, S. H.; Carrier, X.; Krafft, J. M.; Jubin, C.; Che, M. New Insights for Materials Science Characterisation Using Different Complementary Techniques Combined with X-Ray Absorption Spectroscopy. Phys. Scr. 2005, T115, 38−44. (12) Bras, W.; Ryan, A. J. Small-Angle X-Ray Scattering and WideAngle X-Ray Scattering Experiments Combined with Thermal and Spectroscopic Analysis Techniques. J. Mol. Struct. 1996, 383, 309−314. (13) Wolfgang Kabsch, C. S. Dictionary of Protein Secondary Structure: Pattern Recognition of Hydrogen-Bonded and Geometrical Features. Biopolymers 1983, 22, 2577−2637. (14) Sreerama, N.; Woody, R. W. Estimation of Protein Secondary Structure from Circular Dichroism Spectra: Comparison of Contin, Selcon, and Cdsstr Methods with an Expanded Reference Set. Anal. Biochem. 2000, 287, 252−260. (15) Hamilton, J. C.; Gemperline, P. J. Mixture Analysis Using Factor Analysis. Ii: Self-Modeling Curve Resolution. J. Chemom. 1990, 4, 1− 13. (16) Juan, d. A.; Tauler, R. Factor Analysis of Hyphenated Chromatographic Data: Exploration, Resolution and Quantification of Multicomponent Systems. J. Chromatogr. 2007, 1158, 184−195. (17) Noda, I.; Ozaki, Y. Two-Dimensional Correlation Spectroscopy. Applications in Vibrational and Optical Spectroscopy; John Wiley & Sons, Ltd: Chichester, U.K., 2005. (18) Labrador, A.; Cerenius, Y.; Svensson, C.; Theodor, K.; Plivelic, T. The Yellow Mini-Hutch for SAXS Experiments at MAX IV Laboratory. J. Phys.: Conf. Ser. 2013, 425, 072019. (19) Orthaber, D.; Bergmann, A.; Glatter, O. Saxs Experiments on Absolute Scale with Kratky Systems Using Water as a Secondary Standard. J. Appl. Crystallogr. 2000, 33, 218−225. (20) Noda, I. Advances in Two-Dimensional Correlation Spectroscopy. Vib. Spectrosc. 2004, 36, 143−165. (21) Perczel, A.; Park, K.; Fasman, G. D. Analysis of the Circular Dichroism Spectrum of Proteins Using the Convex Constrain Algorithm: A Practical Guide. Anal. Biochem. 1992, 203, 83−93. (22) Perczel, A.; Hollosi, M.; Tusnady, G.; Fasman, G. D. Convex Constraint Analysis: A Natural Deconvolution of Circular Dichroism Curves of Proteins. Protein Eng. 1991, 4, 669−679. (23) Jacques, D. A.; Guss, M. G.; Svergun, D. I.; Trewhella, J. Publication Guidelines for Structural Modelling of Small-Angle Scattering Data from Biomolecules in Solution. Acta Crystallogr., Sect. D: Biol. Crystallogr. 2012, D68, 620−626. (24) Hansen, S. Bayesapp: A Web Site for Indirect Transformation of Small-Angle Scattering Data. J. Appl. Crystallogr. 2012, 45, 566−567. (25) Müller, K.; Glatter, O. Practical Aspects of the Use If Indirect Fourier Transformation Methods. Makromol. Chem. 1982, 183, 465− 479. (26) Guinier, A. La Diffraction Des Rayons X Aux Tres Petits Angles: Applications a L’etude De Phenomenes Ultramicroscopiques. Ann. Phys. 1939, 11.Sér. 12.1939, 161−237. (27) Mylonas, E.; Svergun, D. I. Accuracy of Molecular Mass Determination of Proteins in Solution by Small-Angle X-Ray Scattering. J. Appl. Crystallogr. 2007, 40, S245−S249.

istics, and volume fractions. This type of a generalized convex constrained analysis, without assuming the number of components, will make the multiprobe sample platform invaluable for routine to advanced characterization of nanostructured materials in solution. The performed examples, X-ray induced radiation damage on protein solutions, and dispersion properties of carbon nanotubes illustrate the quantitative information gain by combining different methods and building a robust structural model. However, it should be mentioned here that a major issue in combining different methods is the sample preparation, in particular, the concentration values to be studied and their impact on the signal-to-noise ratio in all different probes. We are confident that suitable conditions can be found for most of the systems by performing a concentration series. We anticipate that the multiprobe characterization approach will appeal to a broader audience and leads to new insights into how complex systems behave in solution.

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ASSOCIATED CONTENT

S Supporting Information *

Figure S1: the SAXS patterns of the X-ray induced radiation damage of BSA in the Guinier representation (log I vs q2 plots). Figure S2: the X-ray dose dependency of the radius of gyration. Figure S3: Lysozyme UV−vis concentration series. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Author Contributions

S.H., T.S.P., and C.D. designed the experiment, S.H. and C.D. performed the experiment and analyzed the data, and S.H., T.S.P., and C.D. wrote the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The MAX IV Laboratory is acknowledged for beamtime access (project number 20120171). S.H. is supported by a postdoctoral grant of the MAX IV Laboratory. The MAX IV Laboratory is acknowledged for financial support.

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REFERENCES

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