Characterization of Porous Materials by Fluorescence Correlation Spectroscopy Super-resolution Optical Fluctuation Imaging.

Experimental Application of fcsSOFI to Agarose and Liquid

Crystals. fcsSOFI analysis was applied to image heterogeneous pore distributions and diffusion within agarose hydrogels, which are used broadly in cell culture growth, electrophoretic and chromatographic separations, 9 , 36 and 3D immunoassays 37 ( Figure 2 ). Imaging the nanoscale pore structure of agarose by traditional methods is challenging due to the high water content, which undoubtedly leads to the disparity in pore sizes reported in the literature. 36 , 38 – 40 We therefore compared fcsSOFI analysis to diffraction-limited imaging and to SPT analysis of diffusing 100 nm carboxylate fluorescent spheres in agarose. Wide-field total internal reflection fluorescence (TIRF) microscopy was used for imaging (see Methods ), and a blank coverslip with the spheres in water was used as a control. Indeed, the heterogeneity in spatial and diffusion features of the agarose could be discerned by the fcsSOFI approach ( Figure 2 ). In comparison to the control sample in which diffusion occurred with no preferred spatial distribution, in 1% and 2% agarose, the probes stochastically diffused in the pores ( movies S4 – S6 ). The 1% average image did not resolve any structures due to fast diffusion and low SBR, whereas the 2% average image shows the diffraction-limited position of emitters that are primarily trapped within pores ( Figure 2a – c ). In contrast, fcsSOFI analysis revealed the heterogeneous distribution of bright areas, where beads are free to diffuse (i.e., pores) and dark areas devoid of diffusing beads (high density agarose), and successfully mapped the pore structure for both fast-moving and slow-moving/stationary probes( Figure 2d – f ). Quantitative characterization of the spatial and diffusion properties in the 1% agarose environment showed that the fcsSOFI approach does a better job, as compared to diffraction-limited imaging and SPT, in discerning pore sizes and heterogeneous diffusion properties ( Figure 2b , e , h ). First, the fcsSOFI image in Figure 2e resolved pores at a 150-fold higher contrast compared to the diffraction-limited image in Figure 2b (SBR ∼300 and ∼2 for the fcsSOFI and average images, respectively). This result demonstrates the high sensitivity of correlation analysis to low signal fluctuations. Next, the fcsSOFI analysis in Figure 2e was used to determine that there are primarily two pore populations with diameters of 240 ± 90 and 1000 ± 500 nm ( Figure S11a ). SPT analysis identified only short trajectories due to the low signal and high density of emitters (mean trajectory length = 4 points; Figure 2h and Figure S11c ) and yielded a smaller average pore size of 150 ± 130 nm ( Figure S11a ). Interestingly, if ensemble methods were used, instead of identifying the underlying heterogeneous pore distribution, a normal distribution with diameter of 240 ± 90 nm would be extracted, 39 agreeing well with one previous report. 40 Finally, for the diffusion properties, correlation analysis finds an average of log ( D / nm 2 ⋅ s − 1 ) = 4.8 ± 0.8 , in agreement with expectations based on FCS ( Figure S11b ). 41 SPT also accurately finds log ( D / nm 2 ⋅ s − 1 ) = 5.3 ± 0.3 . However, fcsSOFI analysis super-resolves the spatial heterogeneity of diffusion coefficients (arrows, Figure 2e ). Smaller diffusion coefficients seem to arise from increased confinement within the agarose, where diffusion becomes anomalous ( Figure S10 ). Another possibility, albeit unlikely in this case, is that there are motions in the axial direction that are not incorporated in the correlation curve fitting decay model. In contrast, it is difficult to visualize the relationship between the heterogeneous diffusion coefficients and the porous structure with a map of overlapping, short trajectories in the SPT figures. Further quantitative discussion of the experiments with 2% agarose is included in the Supporting Information , where fcsSOFI analysis may not be the preferred method for analysis of stationary emitters that are trivial to track. fcsSOFI analysis was also demonstrated to achieve super-resolved structural details from 1D diffusion of perylene diimide (DTPDI) single-molecule fluorophores within lyotropic liquid crystal gels ( Figure 3 ). Liquid crystals can controllably self-assemble into complex phase-segregated structures for applications in biological and electronic transport and electro-optical displays. 42 – 45 While SPT has been applied to diffusion in 1D-aligned liquid crystals 11 , 42 and polydimethylsiloxane nanochannels, 46 optimizing appropriate experimental conditions is a challenge. In contrast to fluorescent beads, single-molecule emitters present an additional challenge due to photobleaching, which reduces the total signal observed during the measurement. Rapid diffusion also causes difficulty in linking frame-to-frame positions to form trajectories. SPT fails in cases like the data exhibited in movies S7 and S8 due to photobleaching and fast diffusion. Despite the limited amount of signal, fcsSOFI analysis reveals the 1D spatial alignment of pores in F127 and C12EO10 liquid crystals ( Figure 3c , d ). Due to fast diffusion and low SBR, the diffraction-limited average images entirely miss this 1D spatial alignment ( Figure 3a , b ). For F127, analysis of the diffusion coefficients was very similar to previous reports ( log ( D / nm 2 ⋅ s − 1 ) = 4.7 ± 0.3 ), 42 whereas SPT failed to localize molecules due to the low SBR ( Figure 3e ). For C12EO10, the low SBR posed challenges in curve fitting ( Figure S12d ). However, estimation of diffusion coefficients by SPT in C12EO10 was not possible due to short trajectories ( Figure 3f ). Further work with higher SBR and extended dye lifetimes could improve confidence in the results of fluorophore diffusion in lyotropic liquid crystals.

METHODS Diffusion Simulation. All simulations and analysis were written in MATLAB 2011b. For the simulation, we define our pixel size to be 50 nm and frame rate to be 25 Hz to be similar to experimental conditions. Each emitter is represented by a two-dimensional Gaussian point spread function with a full width at half-maximum of 317 nm, approximately the diffraction limit for a 637 nm excitation wavelength. The intensity of the emitter is taken from a Poisson distribution of intensities to simulate shot noise. The background of the image is taken from a random normal distribution to simulate readout noise. For simulations of 1D diffusion, the emitters are allowed to traverse in pores separated at a subdiffraction limit ( Figure 2a , f ) by 300 nm. Continuous boundaries were used at the edges. For 2D diffusion, pore maps with features separated by variable numbers of pixels were provided, as shown in Figures S9a and S10a . Random 1D and 2D walks were used to simulate diffusion. For each step, the magnitude of the displacement is based on a user-defined diffusion coefficient and distribution width, and the step size was sampled from a normal distribution and added to the particles’ previous location. 52 Three types of diffusion were simulated to demonstrate the versatility of the technique: Brownian (random walk), Brownian under flow (biased random walk), and anomalous diffusion (Lévy walk, step size taken from a power distribution). The number of emitters, diffusion constant, and SBR were also varied. A total of 5000 frames were analyzed in each simulation. See movies S1 – S3 for example simulations. Experimental Agarose Data. Carboxylate-modified polystyrene beads of 100 nm size (orange fluorescent, max abs/em: 540/560 nm, Invitrogen) were diluted by a factor of 1:500 concentration in 1% and 2% (w/w) agarose (type I low EEO, Sigma-Aldrich) in molecular biology grade water (Hyclone, VWR) heated to 80 °C. The anionic carboxyl group on the emitter beads would be expected to have minimal interaction with the anionic agarose. 41 Further discussion on the selection of possible emitters, including mixtures, for fcsSOFI is provided in the Supporting Information . Glass coverslips (no. 1, 22 × 22 mm, VWR) were cleaned for 90 s in a bath of 4% (v/v) H 2 O 2 (Fisher Scientific, Radnor, PA) and 13% (v/v) NH 4 OH heated to 80 °C. The slides were further cleaned under O 2 plasma (PDC-32G; Harrick Plasma; medium power) for 2 min. A custom-sized silicon template (43018M, Grace BioLabs) was placed on the coverslip, and a 30 μ L aliquot of the bead/agarose solution was added. The chamber was covered with an additional coverslip to avoid dehydration, and the agarose gelled at room temperature. An in-house constructed wide-field TIRF microscope was used to measure samples after equilibration on the microscope stage for 15 min. The beam of a solid-state 532 nm laser (Coherent, Compass 315M-100SL) was focused at the edge of a 1.45 numerical aperture, 100× oil-immersion objective (Carl-Zeiss, alpha PlanFluar) for through-the-objective TIRF microscopy. Further details of the microscope setup have been previously reported. 53 The generated evanescent wave at the coverslip/agarose interface had an approximate intensity of 10 μ W/cm 2 . The low intensity was used to limit the observation volume in the axial dimensional (∼85 nm) to avoid 3D effects on the projected 2D observation. Data were recorded with an electron-multiplied charge-coupled device (Andor, iXon 897) for 1000 frame intervals with an acquisition time of 10 ms and frame rate of 25 Hz. Experimental 1D C12EO10 and F127 Samples. The triblock copolymer Pluronic F127 having the formula PEO 100 PPO 65 PEO 100 was obtained from Anatrace, while decaethylene glycol monododecyl ether (C12EO10) was obtained from Sigma-Aldrich. Both were used as received. Aqueous gels of F127 and C12EO10 were prepared by first adding an appropriate amount of either to a clean, disposable glass vial. An aliquot of HPLC-grade water was then added, followed by an aliquot of n -butanol in the case of F127. The final dye-doped F127 gel composition was 47.5% F127, 38.6% water, 9.9% butanol, and 4.0% ethanol (see below) by weight. The final dye-doped C12EO10 gel composition was 53.7% C12EO10, 44.1% water, and 2.2% ethanol (see below) by weight. These gels were extremely viscous. They were mixed by repeated inversion and centrifugation. Air bubbles formed in the gels during mixing were removed by repeated centrifugation for several hours over a period of several days prior to use. N,N ′-Bis(tridecyl)perylene-3,4,9,10-tetracarboxylic diimide (DTPDI) was employed as the probe dye in both samples. The dye was obtained from Sigma-Aldrich and was used as received. A 96 nM solution of the dye in ethanol (HPLC-grade) was used to prepare dye-doped samples. The final dye concentration was ∼5 and ∼3 nM in the F127 and C12EO10 gels, respectively. Fluidic channels were used for encapsulation and flow alignment of the F127 and C12EO10 samples, as described previously. 42 These were prepared by casting uncured poly-(dimethylsiloxane) (PDMS, Sylgaard 184) onto a prefabricated glass mold. A rectangular fluidic channel of 0.5 mm depth, 2.5 mm width, and 15 mm length was obtained after curing the PDMS and separation from the mold. Inlet and outlet holes 1.5 mm in diameter were subsequently punched in the ends of the channel. The PDMS monolith was next cleaned in an air plasma (5 min) along with a microscope coverslip (FisherFinest Premium). The PDMS monolith was then contacted to the coverslip to form the completed fluidic cell. All Movie data were collected by imaging through the coverslip. Gels were loaded into the fluidic channels by first drawing them into a glass capillary. The capillary was next contacted to the cell inlet, and the gel infused into the channel. The viscous gels were flowed into the channels at a linear flow velocity of ∼0.5 mm/s. The small dimensions of the channel and the high viscosities of the gels ensure that channel loading occurred within the laminar flow regime. Optically clear gels were obtained in all cases. After filling, the inlet and outlet holes were sealed using standard, two-part 5 min epoxy. All samples were characterized within a few hours of preparation. The ambient temperature during sample characterization ranged from 20 to 22 °C. Verification that the gels comprised flow-aligned cylindrical micelles was obtained by comparing gel composition to their published phase diagrams, 54 , 55 by small-angle X-ray scattering in the case of F127 and by observation of 1D dye diffusion along the flow alignment direction in the microscope. All DTPDI tracking experiments were performed on a wide-field fluorescence microscope operated in pseudo-TIRF mode. This system has been described previously in detail. 56 It employs an inverted epi-illumination microscope (Nikon TiE) with closed-loop focus stabilization. Light from a blue diode laser (488 nm) was used to excite dye fluorescence. The excitation light was first passed through a spinning optical diffuser before being reflected from a dichroic beamsplitter (Chroma, 505 DCLP) and focused, off-axis, into the back aperture of an oil-immersion objective (Nikon Apo TIRF 100×, 1.49 numerical aperture). The incident laser power was maintained at