Quantitative Interpretation of the Optical Textures of Liquid Crystals

Publication Date (Web): March 1, 2000 ... The procedure is a simple one to perform, requiring use of a CCD camera and a polarized white light source. ...
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Langmuir 2000, 16, 3529-3536

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Quantitative Interpretation of the Optical Textures of Liquid Crystals Caused by Specific Binding of Immunoglobulins to Surface-Bound Antigens Justin J. Skaife and Nicholas L. Abbott* Department of Chemical Engineering, University of Wisconsin, Madison, Wisconsin 53706 Received August 16, 1999. In Final Form: December 13, 1999 We report a quantitative analysis of the change in optical appearance of a supported film of liquid crystal that is induced by specific binding of an immunoglobulin (IgG) to a surface-bound antigen. We interpret the optical appearance to indicate the amount of bound IgG and thus the concentration of IgG in solution. The procedure is a simple one to perform, requiring use of a CCD camera and a polarized white light source. We use the average gray scale brightness of the optical appearance of the supported liquid crystal to construct an optical response curve as a function of the amount of anti-biotin IgG bound to surfaceimmobilized biotin. We interpret the optical response curve using a model based on statistical binding of antibody to the surface and a cooperative response of the nematic liquid crystal to the bound antibody. Because the amount of bound antibody is largely controlled by mass transport of the antibody to the surface and thus the concentration of IgG in solution, the optical appearance of the liquid crystal can be correlated to the concentration of IgG in solution. We measured changes in the gray scale brightness of the liquid crystal over 2 orders of magnitude of concentration of IgG in solution (1-100 nM). Our results also suggest that convection and geometry can be used to increase the dynamic range and sensitivity of the liquid crystal to the concentration of IgG in solution.

Introduction The goal of the work reported herein is to investigate the dependence of the orientation of a liquid crystal, and thus the optical signal transduced by the passage of light through the liquid crystal, on the amount of protein bound specifically to a surface on which the liquid crystal is supported. Whereas our past work has established that liquid crystals can be used to detect threshold amounts of proteins bound at surfaces,1 here we report that the optical textures of liquid crystals can be interpreted quantitatively to indicate the amount of bound protein. The capability to quantify the amount of protein specifically bound to a surface by using liquid crystals offers the basis of simple procedures to determine, for example, the concentration of proteins in solution. The work described in this paper is motivated by the potential usefulness of rapid, simple, and label-free procedures that (i) permit direct measurement of the concentration of biomolecules in solution and (ii) do not require competitive binding of a second species. Diagnostic assays, for example, that permit direct measurement of immunoglobulins within a sample, have potential uses in blood analysis and tests for a variety of diseases and for measurement of markers of cardiac function.2,3 Whereas current technologies for detection of antibodies in solution generally rely on competitive assays with labeled antibodies (enzymes, radioisotopes, fluorescent markers, latex beads, gold spheres, etc.) or labeled anti-antibodies, the labeling of antibodies is time-consuming and expensive, and in some cases the presence of the label can interfere with the binding characteristics of the antibody to the * To whom correspondence should be addressed. E-mail: abbott@ engr.wisc.edu. Fax: 608-262-5434. (1) Gupta, V. K.; Skaife, J. J.; Dubrovsky, T. B.; Abbott, N. L. Science 1998, 279, 2077. (2) Van Oss, C. J.; van Regenmortel, M. H. V. Immunochemistry; Dekker: New York, 1994. (3) Harlow, E.; Lane, D. Antibodies: A Laboratory Manual; Cold Springs Harbor Laboratory: Cold Springs Harbor, New York, 1988.

antigen.4-6 A second area of potential impact of methods that permit direct measurement of biomolecules in solution is protein microarrays. Protein microarrays that make possible the imaging of specific binding of proteins to ligands hosted on surfaces with a spatial resolution of tens of micrometers have potential uses in the molecular profiling of cancer and the elucidation of signal transduction pathways in cells.7-9 Whereas microarray technologies for DNA are well established, similar methods that permit profiling of the protein composition of cells, for example, do not exist. Methods based on surface plasmon reflectivity (SPR) and matrix-assisted laser desorption-ionization (MALDI) mass spectrometry have been developed for imaging protein arrays.10-16 Both SPR and MALDI, however, involve the use of complex instrumentation (particularly when dealing with arrays) and require specialists for reliable operation. Laser ablation mass spectrometry, in addition, is a serial procedure. The work reported here is motivated by the proposition that liquid crystals can be used as surface-sensitive agents to quantify the specific binding of proteins and other (4) Koertge, T. E.; Butler, J. E. J. Immunol. Methods 1985, 83, 283. (5) Steinmetz, I.; Reganzerowski, A.; Brenneke, B.; Haussler, S.; Simpson, A.; White, N. J. J. Clin. Microbiol. 1999, 37, 225. (6) Cocchi, J. M.; Trabaud, M. A.; Grange, J.; Serres, P. F.; Desgranges, C. J. Immunol. Methods 1993, 160, 1. (7) Marshall, A.; Hodgson, J. Nature Biotechnol. 1998, 16, 27. (8) Cheng, J.; Sheldon, E. L.; Wu, L.; Uribe, A.; Gerrue, L. O.; Carrino, J.; Heller, M. J.; O′Connell, J. P. Nature Biotechnol. 1998, 16, 541. (9) Ramsay, G. Nature Biotechnol. 1998, 16, 40. (10) Heaton, R. J.; Haris, P. I.; Russel, J. C.; Chapman, D. Biochem. Soc. Trans. 1995, 23, 502s. (11) Schofield, D. J.; Dimmock, N. J. J. Virol. Methods 1996, 62, 33. (12) Haussling, L.; Ringsdorf, H.; Schmitt, F.-J.; Knoll, W. Langmuir 1991, 7, 1837. (13) Shivashankar, G. V.; Libchaber, A. Appl. Phys. Lett. 1998, 73, 417. (14) Fitzgerald, M. C.; Smith, L. M. Annu. Rev. Biophys. Biomol. Struct. 1995, 24, 117. (15) Schieltz, D. M.; Chou, C. W.; Luo, C. W.; Thomas, R. M.; Williams, P. Rapid Commun. Mass Spectrosc. 1992, 6, 631. (16) Caprioli, R. M.; Farmer, T. B.; Gile, J. Anal. Chem. 1997, 69, 4751.

10.1021/la991101h CCC: $19.00 © 2000 American Chemical Society Published on Web 03/01/2000

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biomolecules to surfaces without the need for labels, by using simple laboratory procedures, and with a spatial resolution of tens of micrometers on patterned surfaces.1 Whereas our past work has demonstrated that procedures based on liquid crystals can permit direct detection of a threshold concentration of IgG in solution as well as permit the imaging of IgG bound within ∼10 micrometer-sized areas of a surface presenting antigen,1 here we address the question of whether the optical appearance of the liquid crystals can be interpreted quantitatively so as to indicate the amount of IgG bound to the surface and thus the concentration of IgG in solution. We report that simple quantitative measures of the optical appearance of liquid crystals, such as gray scale analyses of the optical appearance, can be used to indicate the amount of bound IgG and thus the concentration of IgG in solution. We interpret the optical response curve using a model based on statistical binding of antibody to the surface and a cooperative response of the nematic liquid crystal to the bound antibody. The experiments we report revolve around the behavior of nematic liquid crystalline phases at surfaces. Numerous past studies have demonstrated that the orientations of liquid crystals can be influenced by their contact with surfaces through a variety of long- and short-range forces that act between liquid crystals and surfaces.17-22 Our experiments are based on surfaces prepared by the deposition of semitransparent (thickness of 10-20 nm) films of gold onto glass microscope slides.23 The gold films are prepared by deposition of a vapor of gold from a fixed direction of incidence and at an angle of incidence from the normal of 50°.24,25 A thin layer of titanium (thickness of ∼10 nm) is deposited onto the glass microscope slide prior to deposition of the gold, so as to promote adhesion between the gold and the glass substrate. By using atomic force microscopy, we have measured the gold grains within obliquely deposited gold films to be elongated in one direction.24 The lateral dimensions of the gold grains (∼10-30 nm) were measured to be greatest in a direction perpendicular to the plane of incidence of the gold vapor during deposition of the gold film. The root-mean-square curvature of the gold grains was also determined to be smallest when measured in the same direction.24 The anisotropic structure of the gold film induced by the oblique deposition of the gold causes liquid crystals placed onto these films to adopt a preferred azimuthal direction.25 Our past studies have demonstrated that the orientations of liquid crystals supported on obliquely deposited films of gold can be manipulated by forming self-assembled monolayers (SAMs) of organosulfur compounds on these surfaces.1,23-30 In particular, by using mixed SAMs formed from octanethiol (C8SH) and biotin-(CH2)2[(CH2)2O]2NHCO(CH2)11SH (BiSH), we have demonstrated ampli(17) Jerome, B. Rep. Prog. Phys. 1991, 54, 391. (18) Flanders, D. C.; Shaver, D. C.; Smith, H. I. Apply. Phys. Lett. 1978, 32, 597. (19) Ong, H. L.; Hurd, A. J.; Meyer, R. B. J. Appl. Phys. 1985, 57, 186. (20) Ong, H. L. Mol. Cryst. Liq. Cryst. 1985, 144, 17. (21) Wolff, U.; Greubel, W.; Kruger, H. Mol. Cryst. Liq. Cryst. 1973, 23, 187. (22) Dubois, L. H. Annu. Rev. Phys. Chem. 1992, 43, 437. (23) Drawhorn, R. A.; Abbott, N. L. J. Phys. Chem. 1995, 99, 16511. (24) Skaife, J. J.; Abbott, N. L. Chem. Mater. 1999, 11, 612. (25) Gupta, V. K.; Abbott, N. L. Langmuir 1996, 12, 2587. (26) Gupta, V. K.; Abbott, N. L. Science 1997, 276, 1533. (27) Gupta, V. K.; Abbott, N. L. Phys. Rev. E 1996, 54, R4540. (28) Miller, W. J.; Abbott, N. L.; Paul, J. D.; Prentiss, M. Appl. Phys. Lett. 1996, 69, 1852. (29) Gupta, V. K.; Miller, W. J.; Pike, C. L.; Abbott, N. L. Chem. Mater. 1996, 8, 1366. (30) Shah, R.; Abbott, N. L. J. Am. Chem. Soc. 1999, 121, 11300.

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fication and transduction of biospecific interactions between proteins (avidin and anti-biotin IgG) and biotin by using liquid crystals.1 In the absence of bound protein, the mixed SAM (∼25% BiSH in the mixed SAM) uniformly aligns a nematic liquid crystal in a direction that is parallel to the plane of incidence of the gold during deposition of the gold film and parallel to the surface of the gold film. This orientation of the liquid crystal was observed using polarized light microscopy (transmission) as a uniform optical texture. Following immersion of the mixed SAM in an aqueous solution containing proteins that bind specifically to biotin, such as avidin or anti-biotin IgG, we observed the optical appearance of the liquid crystal to be nonuniform when observed over areas with dimensions of ∼100 µm or greater. By performing a series of control experiments (blocked avidin and nonspecific IgG), we demonstrated that protein molecules specifically bound to the surface can erase the anisotropy in the surface introduced by oblique deposition of the gold film and thereby cause nonuniform optical textures of liquid crystals. These past studies, however, did not attempt to interpret the optical textures formed by the liquid crystals in terms of the amount of protein specifically bound to the surface or the concentration of protein in solution. The goals of the research reported in this paper were five-fold. First, we aimed to establish a simple procedure that would permit control over the amount of IgG specifically bound to the SAMs used in our studies. Second, we aimed to determine the qualitative dependence of the orientations of supported liquid crystals on the amount of bound IgG. In particular, we aimed to determine if the orientations assumed by liquid crystals supported on the SAMs were continuous or discontinuous functions of the amount of bound protein. Third, we aimed to establish quantitative measures to describe the change in the optical appearance of the liquid crystals with the amount of bound protein. Fourth, we aimed to construct a simple model that would describe the optical response of the liquid crystal to the amount of IgG specifically bound to the SAM and subsequently test the model against experimental measurements. Fifth, we aimed to identify processes that control the amount of IgG bound to the SAMs as a function of the concentration of IgG in solution, and thus understand the origin of the optical response of the liquid crystals to the concentration of IgG in solution. Experimental Section Materials. Octanethiol (99%) (C8SH) was purchased from Aldrich (Milwaukee, WI). The biotinylated thiol, biotin-(CH2)2[(CH2)2O]2NHCO(CH2)11SH (BiSH), was synthesized using procedures reported in the literature.31 The liquid crystal, 4-cyano4′-pentylbiphenyl (5CB), was obtained from EM Sciences (New York, NY). All aqueous solutions were prepared using deionized water with a resistivity > 18 MΩ cm (Milli-Q System, Millipore, Bedford, MA). Affinity-isolated goat anti-biotin immunoglobulin G (anti-biotin IgG) and goat anti-FITC immunoglobulin G (antiFITC IgG) were obtained from Sigma BioScience (St. Louis, MO). The dissociation constant, kd, of biotin and anti-biotin IgG in bulk solution is ∼10-9 M.1,32 Solutions of the IgG were prepared in 25 mM PBS buffer (pH 7.35) using 100 mM NaCl, 0.01 wt % NaN3 as a preservative, and 0.004 wt % Triton X-100 purchased from Sigma (St. Louis, MO). Preparation of Films of Gold. Films of titanium (thickness ∼ 10 nm) and gold (thickness ∼ 20 nm) were evaporated onto clean glass substrates with an electron beam evaporator (CHA/ Telemark, Fremont, CA). The rates of deposition of the metals (31) Spinke, J.; Liley, M.; Schmitt, F. J.; Guder, H. J.; Angermaier, L.; Knoll, W. J. Chem. Phys. 1993, 99, 7012. (32) Bagci, H.; Kohen, F.; Kuscuoglu, U.; Bayer, E. A.; Wilchek, M. FEBS Lett. 1993, 322, 47.

Optical Textures of Liquid Crystals were 0.02 nm/s, and the metals were deposited at an angle of incidence of 50° from the normal. A detailed description of these procedures, including procedures for the cleaning of the glass microscope slides, can be found in a recent publication.24 Following the deposition of each batch of gold films, we performed several experiments to confirm the quality of the films. First, we formed SAMs from hexadecanethiol on the surface of the films and confirmed that nematic phases of 5CB were anchored uniformly in a direction parallel to the plane of incidence of the gold (see below for procedures). Second, we used ellipsometry to measure the optical thickness of a SAM formed from hexadecanethiol on the gold film. Films of gold on which the optical thickness of the SAM deviated from ∼2.3 nm by >0.3 nm were not used in further experiments. Formation of SAMs. Self-assembled monolayers were formed on the surfaces of the gold films by immersion of the films into ethanolic solutions containing both octanethiol (C8SH) and the biotinylated thiol (BiSH). The concentrations of C8SH and BiSH were 22 and 44 µM, respectively. After 8 h of immersion at room temperature, the slides were removed, rinsed with ethanol, and then dried under a stream of N2. By measuring the ellipsometric thickness of the SAMs, we estimate SAMs formed by this procedure to contain ∼25% BiSH.1,33 Binding of Proteins. Aqueous solutions of IgG were prepared by pipetting a volume of reconstituted stock solution of IgG (0.1 mg/ml) into ∼3 mL of PBS buffer (25 °C) containing 0.004 wt % Triton X-100 held in a small polypropylene vial. The concentration of IgG in solution was calculated by weighing the stock solution and buffer. We note that 3 mL of a 10 nM solution of IgG contains approximately ∼2 × 1013 molecules of IgG. Because adsorption of a monolayer of IgG onto a 2 cm2 area of a surface would remove ∼1.3 × 1012 molecules from solution,34 we concluded that nonspecific adsorption of IgG from solutions containing 10 nM or less IgG can potentially deplete the IgG in solution to levels that would influence the extent of binding of IgG to the surface of SAMs used in our experiments. For this reason, we used Triton X-100 to minimize the nonspecific adsorption of IgG to the surface of the vial as well as to the SAMs. We used IgG solutions immediately following their dilution. The binding of IgG was performed by placing a mixed SAM formed from BiSH and C8SH into a plastic vial filled with the aqueous solution of IgG for 30 min (without stirring) at 25 °C (Figure 1). Immediately following removal of the SAM from the solution, the samples were rinsed with water for ∼10 s and exposed to a stream of N2 to displace water from the surface. By using ellipsometry, we found that rinsing of SAMs for 5-45 s did not change the amount of IgG bound to the SAMs. Control experiments using a nonspecific IgG (anti-FITC IgG) demonstrated that rinsing of the mixed SAM for 10 s was sufficient to remove nonspecifically adsorbed protein (and Triton X-100). Fabrication of Liquid Crystal Cells. Mixed SAMs supporting bound IgG were assembled into liquid crystal cells in order to observe the optical appearance of liquid crystal on the SAMs. The liquid crystal cells were fabricated by spacing two SAMs (facing each other) apart by ∼10 µm using thin strips of Mylar (Figure 1). The cell was placed on a warm surface (at 40 °C) and gently heated with a hot air gun for approximately 10 s. 5CB, heated into its isotropic phase (∼35 °C), was spontaneously drawn into each cell by capillary action (10 s). The cell was allowed to sit on the hot plate for 30 s after injection and then removed and cooled to room temperature. During cooling, the 5CB changed from its isotropic state to the nematic state. The optical appearance of the sample was observed in transmission using (33) The amount of BiSH present in the SAM was estimated by linear interpolation of the height of the pure component SAMs (∼4 and ∼1 nm for pure BiSH and C8SH, respectively). (34) We have measured the maximum amount of bound protein, h, to be ∼4 nm and assume this to be a complete monolayer for our system. The volume, V, of an individual IgG molecule is 4 nm × 10 nm × 15 nm (Silverton et al.).35 The maximum surface density, Γmax, for our system is given by

Γmax )

h ) 6.6 × 1011 proteins/cm2 V

A 2 cm2 area could potentially require ∼1.3 × 1012 molecules for a complete monolayer.

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Figure 1. Schematic illustration of the experimental procedure used to transduce the specific binding of IgG to surface-bound antigens. (A) A mixed SAM of BiSH and C8SH is immersed in a solution of IgG for 30 min at 25 °C. (B) The mixed SAM is rinsed with water to remove unbound IgG and buffering salts. Excess water is displaced from the surface by using a stream of N2. (C) The mixed SAM is cut in two and assembled into a liquid crystal cell. The optical texture of the liquid crystal is examined using polarized light transmitted through the cell.

Figure 2. Intensity of polarized light transmitted through a supported film of liquid crystal during rotation between crossed polarizers: (filled circles) liquid crystal supported on a mixed SAM formed from BiSH and C8SH (Figure 4, 0 nm); (open circles) liquid crystal supported on a mixed SAM with bound IgG (Figure 4, 2.9 nm). a polarizing light microscope (under crossed polars). The settings of the microscope (light source and aperture) were kept constant in all experiments (see below). The procedure we used to characterize the appearance of the liquid crystal involved two steps. First, the sample was aligned in the microscope with the deposition direction of the gold film parallel to the axis of the polarizer. This arrangement results in the extinction of light transmitted through the sample in cases where 5CB is uniformly anchored on the mixed SAM. The sample was then rotated between cross-polarizers, and the intensity of light transmitted through the sample was measured. A plot of the modulation of the intensity of transmitted light for both uniform and nonuniform optical textures is shown in Figure 2. Maximum extinction of the light transmitted through a uniform cell between crossed polars occurs when the optical axis of 5CB is parallel to either axis of the polarizer or analyzer. Little modulation in the intensity of

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transmitted light is observed when the liquid crystal is nonuniformly oriented by the surface (Figure 2). Image Capture and Analysis. Images of the optical appearance of the liquid crystal were captured with a CCD camera (DXC-151A, Sony, Park Ridge, NJ) and frame grabbing software (Mediagrabber, Rasterops Inc., Santa Clara, CA) that was attached to a polarized light microscope (BX60, Olympus, Melville, NY). A quantitative comparison of the textures was made using computer software (NIH Image, Bethesda, MD) to calculate the average luminance (average pixel value on a scale of 0-255) of the image after conversion of the image from color to gray scale. Consistent settings of the microscope light source (50% of maximum intensity, 50% open aperture, and no condenser) and CCD camera (0 dB gain, no auto color correction, and open shutter) were used to permit the comparison of values of luminance between samples. The raw luminance of each sample (S) was corrected for the minimum luminance of an image of the liquid crystal supported on a mixed SAM (no bound protein; Smin) and normalized by the corrected, maximum luminance of images of liquid crystals supported on SAMs on which proteins were bound (Smax). Variations in Smin and Smax were found to be small (∼2-3%) from batch to batch of samples. The equation used to calculate the normalized and corrected luminance (optical output) is given by

L(%) )

(

)

S - Smin ‚ 100 Smax - Smin

(1)

Ellipsometry. We measured the optical thickness of the mixed SAMs and of the IgG bound to the mixed SAMs by using ellipsometry. Ellipsometry was performed using thick (thickness of 50 nm) films of gold because thick gold films are optically reflecting. The thick films of gold were deposited on glass microscope slides while rotating the microscope slides to avoid the introduction of anisotropy into the gold films. Obliquely deposited films of gold possess anisotropic optical constants that make interpretation of the ellipsometric measurements more complex than when using gold films deposited without a preferred direction. The procedures used to form mixed SAMs on thick films of gold, and to bind IgG to the mixed SAMs, were the same as that used on thin films of gold. We measured the ellipsometric constants at three locations on each sample using a Rudolph AutoEL II ellipsometer (wavelength 632 nm, angle of incidence 70°, Rudolph Tech., Flanders, NJ). Ellipsometric constants of the bare gold surfaces were determined immediately after removal of the gold films from the evaporator. A simple slab model was used to interpret the ellipsometric constants when the mixed SAM, or mixed SAM supporting bound protein, was formed on the surface of the gold film. The slab (SAM and protein) was assumed to have an index of refraction of 1.46.

Results and Discussion Control of the Amount of IgG Bound on the Mixed SAM. Our first goal was to demonstrate a simple experimental procedure that would permit control over the amount of IgG bound to a mixed SAM formed from BiSH and C8SH. We used ellipsometry to characterize the amount of bound IgG following immersion of mixed SAMs into aqueous solutions containing between 1 and 400 nM IgG for 30 min (Figure 3). We measured the thickness of the bound layer of IgG to reach an asymptotic value of ∼4.0 nm for high concentrations of IgG in solution (>300 nM). We point out that the experimental measurements shown in Figure 3 do not describe an equilibrium adsorption isotherm. For example, the amount of IgG bound to the surface at low concentrations can be increased substantially by immersing the surface into the IgG solution for periods >30 min or by providing convection (stirring). As discussed below, mass transport plays a significant role in determining the amount of IgG bound at concentrations below ∼100 nM in our experiments. The solid straight line shown in Figure 3 is an estimate of the amount of IgG that binds to the surface under mass-

Figure 3. Ellipsometric thickness of IgG bound to a mixed SAM formed from BiSH and C8SH as a function of the concentration of IgG in bulk solution. The curved line passing through the experimental data points is drawn to guide the eye. The straight line (solid) is the ellipsometric thickness of bound IgG under conditions of mass-transfer-limited binding of the IgG.

transfer-limited conditions (see below for details). The principal conclusion drawn here from the experimental measurements shown in Figure 3 is that manipulation of the concentration of IgG in solution provides a simple and convenient means to control the amount of IgG specifically bound to the mixed SAMs. Qualitative Nature of the Anchoring of 5CB As a Function of the Amount of Bound IgG. We used mixed SAMs formed from BiSH and C8SH that supported varying amounts of bound IgG to determine the dependence of the anchoring of 5CB on the amount of bound IgG (Figure 4). Following immersion of a mixed SAM into PBS buffer (containing Triton X-100 but not IgG), we observed the optical appearance of the liquid crystal to be uniform. When the optical axis of the liquid crystal was aligned parallel to either the polarizer or the analyzer of the microscope, the polarization of the incident light was not changed by transmission through the sample. The optical appearance of the liquid crystal was, therefore, uniformly dark when viewed through crossed polars (Figure 4; 0 nm). Rotation of the same sample between crossed polars led to a strong modulation in the intensity of light transmitted through the sample (Figure 2). We observed bound IgG to first perturb the uniform orientation of the liquid crystal when the amount of bound IgG was measured to be 0.6 nm by ellipsometry (Figure 4; 0.6 nm). On these samples, the uniform optical appearance was disrupted by a low density of disclination lines. These disclination lines scatter light and can be seen without the use of polarizers. By estimating the volume of an IgG molecule to be 4 nm × 10 nm × 15 nm,2,35 we calculate the density of IgG molecules on these surfaces to be ∼1000 molecules/µm.34 On mixed SAMs supporting ∼2.0 nm or more of bound IgG, the optical appearance of the supported liquid crystal was measured to be highly nonuniform across the sample (Figure 4; 2.3, 2.4, 2.6, and 2.9 nm). Rotation of these samples between crossed polars led to no measurable modulation in the intensity of light transmitted through the sample (Figure 2), thus indicating that there was no preferred azimuthal orientation of the liquid crystal within the sample. The IgG bound to the mixed SAM erases the anisotropic structure of the mixed SAM/gold interface responsible for the uniform alignment of the liquid crystal in the absence of bound IgG. Inspection of Figure 4 reveals that the change from uniform to nonuniform anchoring of the liquid crystal as a function of the amount of bound IgG is a gradual one. (35) Silverton, E. W.; Navia, M. A.; Davies, D. R. Proc. Natl. Acad. Sci. U.S.A. 1977, 74, 5140.

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Figure 5. Average luminance of a film of liquid crystal supported on a mixed SAM formed from BiSH and C8SH as a function of the amount of anti-biotin IgG bound to the mixed SAM (solid line). The lines are predictions of a model with coherence lengths of 55 nm (dotted line), 550 nm (dotted-shortdashed line), and 5 nm (dotted-long-dashed line). See text for details.

Figure 4. Optical images of films of liquid crystal supported on mixed SAMs formed from BiSH and C8SH as a function of the amount of anti-biotin IgG bound to the mixed SAMs. The ellipsometric thickness of the bound layer of IgG is indicated in the top left corner of each image. The size of each sample was ∼1 mm × 1 mm. The images are obtained through crossed polars.

The fraction of the image that is dark (uniformly anchored IgG) decreases with increasing amount of bound IgG. We confirmed that the gradual change in optical appearance seen in Figure 4 was the result of IgG bound to the SAM by specific interactions between the biotin and IgG and not due to nonspecific adsorption of the IgG. The control experiment was performed by measuring the anchoring of liquid crystal on a mixed SAM that had been immersed into a solution containing a 500 nM solution of anti-FITC IgG. We observed the optical texture of the liquid crystal to be uniform on this sample, thus confirming that specific binding of IgG to biotin is responsible for the change in optical appearance of the liquid crystal shown in Figure 4. The colors of the liquid crystal shown in Figure 4 arise from optical interference of the white light upon transmission through the liquid crystal.36 Because these colors depend on the thickness and orientation of the film of liquid crystal confined between the two SAMs, we do not attempt to interpret them in this paper. By systematically changing the thickness of the cells containing the liquid crystal, below we demonstrate that the thickness of the cell does not greatly influence the index we use in this

paper to characterize the nonuniformity of the anchoring of the liquid crystal. Image Analysis. The work we report in this section demonstrates the gradual change in the optical appearance of the liquid crystal shown in Figure 4 to be usefully indexed by the average luminance of the image. This measure of the optical appearance of the liquid crystal is calculated from the image as the average value of the brightness of the pixels of the image (on a scale of 256). This choice of index is not unique and does not necessarily represent the optimal means of characterizing the change in features seen in Figure 4. Figure 5 shows a plot of the luminance of the images shown in Figure 4 as a function of the ellipsometric thickness of IgG bound to the SAM. The principal result extracted from Figure 5 is the observation that the average luminance increases as a sigmoidal function of the amount of bound IgG. At low amounts of bound IgG, 0.25 nm, the average luminance increased with concentration, as did the nonuniformity of the optical appearance of the liquid crystal. When the amount of bound IgG was >2.5 nm, the average luminance fluctuated about the maximum value of ∼1. Whereas the thickness of a film of liquid crystal does, in general, change the color of its appearance (see discussion above), we found the thickness of the films of liquid crystal used in our experiments not to significantly affect the gradual change in the nonuniformity of the optical texture as characterized by the average luminance. Figure 6 is a plot of the optical output (average luminance) of a typical nonuniform sample as a function of the thickness of the film of liquid crystal. The cell used to confine the liquid crystal was fabricated with a 50 µm spacer at one end of the cell and no spacer at the other end. The films of liquid crystal reported elsewhere in this paper are approximately 10 µm thick with a standard deviation of about 1 µm. Figure 6 clearly demonstrates that the optical output of a typical nonuniform cell varies (36) Interference colors result from the transmission of particular wavelengths of light when using a white light source of illumination. The extent of transmission of a particular wavelength of light depends on the retardation, ∆nd, where ∆n is the birefringence and d is the thickness of the birefringent film. Light propagating through the liquid crystal will be extinguished under conditions where ∆nd ) jξ, j ) 0, 1, 2, ..., where ξ is the wavelength of light. Interference colors are divided into orders according to the magnitude of the retardation: 0-550 nm (first order); 550-1100 nm (second order); 1100-1650 nm (third order).

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Figure 6. Average luminance of a film of liquid crystal supported on a mixed SAM formed from BiSH and C8SH as a function of the thickness of the film of liquid crystal.

little over a wide range of cell thicknesses. Between 8 and 12 µm, the variation in average luminance is only several percent. Model of Optical Response of Liquid Crystal to Bound IgG. We propose a simple model to describe the change in optical appearance of the liquid crystal as a function of the amount of bound IgG. This model is based on two propositions. First, we propose that local variations in the number density of bound IgG molecules exist due to the statistics of adsorption of the protein. Here we described these variations by the statistics of random adsorption of the IgG at the surface, although other factors may also influence the distribution of IgG on the mixed SAM (such as variations in the local structure and composition of the SAM). We hypothesize that spatial variations in the local number density of bound IgG molecules will cause the anchoring of the liquid crystal to become a function of lateral position on the surface. Second, we propose the response of the liquid crystal to be a cooperative one that reflects the local density of molecules. This local density is calculated over an area that is characterized by a coherence length of the liquid crystal on the surface (λ). Figure 7 is a cartoon that illustrates the essential elements of the model. Figure 7A conveys the fact that an IgG molecule (∼10 nm × 15 nm × 4 nm) is large compared to the amplitude of roughness of the gold film (∼1-2 nm) but comparable in size to the wavelength of the gold grains (∼10-30 nm). Binding of the IgG to the SAM supported on the gold film can, therefore, erase the anisotropic structure of the gold film that is measured by AFM or STM and plausibly lead to nonuniform anchoring of the liquid crystal on the IgG-laden surfaces. Figure 7B depicts the statistical binding of IgG within areas of the surface that are defined by the coherence length of the liquid crystal. We use this coherence length to capture the fact that the liquid crystal responds to areaaveraged properties of the surface. We assume that the density of IgG molecules within the area defined by the coherence length must exceed a certain threshold for the local orientation of the liquid crystal to depart from the uniform one observed in the absence of bound protein. We note at this point of the discussion that a number of past studies of the anchoring of liquid crystals on chemically and topologically inhomogeneous surfaces have concluded that patterned surfaces will lead to spatial variations in the orientations of liquid crystals out to distances from a surface that are comparable to the wavelength of the pattern on the surface.19-22 For example, surfaces patterned with submicrometer (∼10 nm) patches that caused either uniform planar or perpendicular (homeotropic) anchoring on homogeneous surfaces were observed to orient bulk nematic liquid crystals with a

Figure 7. Schematic illustration of the lengths involved in the process of transduction of binding of IgG at a surface by a liquid crystal. The patches in part C represent areas of liquid crystal possessing a uniform azimuthal orientation (each shade of gray represents a different direction). The patches in part D represent larger domains of liquid crystal which possess an orientation controlled by a cooperative effect between the smaller domains in part C. See text for details.

uniform tilt from the patchy surface. Our experimental situation differs from this past work for a number of reasons. For example, a mixed SAM completely covered by IgG does not uniformly orient a liquid crystal. A mixed SAM supporting a partial monolayer of IgG can be viewed as a surface consisting of two types of “patches”: areas of mixed SAM that cause a uniform orientation of the liquid crystal and areas defined by coherence lengths (λ) which orient liquid crystal in a random azimuthal direction (near the surface) (Figure 7C). For the case where the coherence length is small compared to the wavelength of light, the domains shown in Figure 7C will not be imaged directly by optical microscopy. Instead, the orientations will define an effective medium with optical properties that reflect the distribution of orientations. Furthermore, with increasing distance from the surface, we expect a coarsening of the domain structure of the liquid crystal with a maximum domain size comparable to the thickness of the film of liquid crystal (Figure 7D). The optical appearance of the liquid crystal is, therefore, a complex quantity that reflects variations in the structure of the liquid crystal across the cell.37 An approximate mathematical description of the model can be derived from consideration of statistical adsorption of n proteins to a surface. The surface can be viewed as being composed of N regions of the size λ2. By assuming statistical adsorption of molecules of IgG to the surface, (37) The optical appearance of the liquid crystal is a complex quantity that could be described by many indexes (i.e. standard deviation of image brightness, amplitude of modulation in image intensity upon rotation between crossed polars, etc.). We chose to quantify the optical appearance by measuring the average gray scale brightness of the image due to its simplicity.

Optical Textures of Liquid Crystals

Langmuir, Vol. 16, No. 7, 2000 3535

we evaluate the probability of finding k proteins in each area of size λ2, as given by the binomial distribution38

Pk,n )

n! N-n(N - 1)n-k k!(n - k)!

(2)

For large n and N, this expression can be approximated by the Poisson distribution39

n e ( N) ) k

Pk,n

-n/N

(3)

k!

We define

n ) Γxmax N

(4)

where Γ is the fraction of the surface occupied by protein (0 e Γ e 1) and xmax is the maximum number of proteins that can be bound in an area λ2 of the surface. We point out that Γ is an area-averaged occupancy of the surface that is characterized in our experiments by a measurement of the ellipsometric thickness of bound protein. The maximum number of proteins that can be hosted in an area λ2 of the surface is given by

xmax ) F0λ2

(5)

where F0 is the maximum areal density of protein molecules that can be bound to the surface. The number of proteins per area λ2 of the surface is calculated as

k ) δxmax

(6)

where δ is the local fraction of the surface covered by protein. Note that the statistics of random adsorption cause variation in the value of δ for each area λ2. Equation 3 then becomes

[ΓF0λ2][δF0λ ]e-[ΓF0λ ] 2

P(δ, Γ) )

[δF0λ2]!

2

(7)

where P is the probability of finding a surface coverage, δ, in a given area of λ2 of the surface when the average coverage of protein over the entire surface is Γ. We propose that the local anchoring of liquid crystal in an area λ2 of the surface will be described by a random azimuthal orientation when the coverage of protein within the area exceeds a threshold, δ*. We calculate the percentage of areas that assume a local orientation that differs from the uniform orientation of liquid crystal in the absence of bound protein as Y(Γ)

Y(Γ) )

∫δ*1 P(δ) dδ

(8)

A plot of Y(Γ) versus Γ provides an estimate of the response of the near-surface region of liquid crystals to the coverage of protein on the surface. As discussed above, the optical response obtained by the propagation of light through the film of liquid crystal involves processes of average wavelengths comparable to those of light. These processes are complex and beyond the scope of the simple model (38) Jaeger, R. C. Introduction to Microelectronic Fabrication; Addison-Wesley Pub. Co.: New York, 1988. (39) Haberman, R. Elementary Applied Partial Differential Equations; Prentice Hill: Englewood Cliffs, NJ, 1987.

described here. Here we approximate the optical response of the liquid crystal as Y(Γ). The shape of the response Y(Γ) depends on two parameters, δ* and λ. We estimate the critical surface coverage that causes a change in anchoring, δ*, from the experimental response curves corresponding to the coverage of the surface by protein that gives rise to a 50% signal. A value for δ* of 0.4 was obtained from the data in Figure 5. Figure 5 also shows a family of response curves calculated from the model using coherence lengths of 5, 55, and 550 nm. A small coherence length results in a more gradual response, while a steplike response is seen when using large coherence lengths. By comparing the model and experimental data, we estimate the coherence length of the experimental system to be ∼55 nm. The principal proposition emerging from the above model is that heterogeneity of a surface, here introduced by the statistics of random adsorption of the IgG molecules on the surface, can lead to a continuous response of the liquid crystal to the amount of bound IgG (when averaged over the total area of the sample). This proposition is a useful one to consider because it suggests routes to the engineering of surfaces that will permit control over the response of the liquid crystal to the amount of bound protein. For example, the model predicts that deliberate introduction of heterogeneity will expand the range over which the liquid crystal responds to the average amount of bound protein (i.e., control of sensitivity and dynamic range). We also point out that in a separate study we have measured the response of liquid crystals to the conversion of SAMs terminated in carboxylic acid groups to SAMs terminated with sodium carboxylate salts.30 In these studies, the change in orientation of the liquid crystal was observed to be a discontinuous function of the extent of conversion of acid to salt. This observation is consistent with the qualitative predictions of the above-described model because the number of acid groups per unit area of SAM is several orders of magnitude greater than the number of proteins bound per unit area in the studies described in this paper. In our model, the continuous response of the liquid crystal results from the variance (heterogeneity) of the surface composition calculated within an area defined by a coherence length, and the variance decreases with increasing number of bound/ converted species within that area. Mass-Transfer Analysis. We conclude this paper by examining the factors that control the amount of IgG bound to the mixed SAM after its removal from solutions containing different concentrations of IgG. Identification of these factors is important because they influence the optical response of the liquid crystal to the concentration of IgG in solution (Figure 8). We have examined the role of mass transport in determining the amount of bound IgG as a function of the concentration of IgG in solution. First, we estimate the rate of mass transfer using a simple scaling analysis. The diffusion length, L, needed to form a monolayer of IgG is given by

L)

Φmax Cbulk

(9)

where Φmax is the surface density of bound IgG and Cbulk is the concentration of IgG in bulk solution. Equation 9 reveals that formation of a monolayer of IgG with a density of ∼104 molecules/µm2 from a 500 nM solution of protein will require a diffusion length of 10-100 µm. The time

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Langmuir, Vol. 16, No. 7, 2000

Skaife and Abbott

Φ(t) 2 ) Cbulk xtD ≈ Cbulk1.12xtD Φmax xπ

Figure 8. Average luminance of a film of liquid crystal supported on a mixed SAM formed from BiSH and C8SH as a function of the concentration of IgG in solutions into which the mixed SAM was immersed for 30 min.

required for this process of diffusion can be approximated as

t)

L2 D

(10)

where D is the diffusivity of the protein in bulk solution and t is the time required for the species to reach the surface and form a monolayer. If we assume the areal density of an IgG monolayer to be ∼104 molecules/µm2 and the diffusivity of the protein in bulk solution to be ∼1 × 10-7 to 1.0 × 10-6 cm2/s, we calculate the time required to form the monolayer of IgG from a 5 nM solution to be >30 h.40,41 The diffusion time for the 30 nM solution of IgG is ∼1 h. This estimate is in agreement with the ellipsometric data in Figure 3, which indicate that we do not form a complete monolayer of bound IgG on mixed SAMs immersed into 5 and 30 nM solutions of IgG for only 30 min. The diffusion equation can be readily solved to provide an estimate of the amount of IgG bound after 30 min by making the assumption that the concentration of IgG in solution near the surface is zero (i.e. that binding of protein to the surface proceeds much faster than diffusion) and that far from the surface the concentration is constant.42 This solution, which has been used for past descriptions of protein adsorption,2,41,42 gives a result that is similar to the simple scaling laws given above. (40) Duschl, C.; Sevin-Landais, A.-F.; Vogel, H. Biophysical J. 1996, 70, 1985. (41) Schmitt, F.-J.; Haussling, L.; Ringsdorf, H.; Knoll, W. Thin Solid Films 1992, 210, 815. (42) Bird, R.; Stewart, W.; Lightfoot, E. Transport Phenomena; John Wiley & Sons: New York, 1960.

(11)

Figure 3 shows the prediction of eq 11 as a function of time. The mass-transfer estimate (solid line) in Figure 3 was calculated by multiplying the fractional coverage (eq 11) by the height of a full monolayer (∼4 nm, estimated from the asymptotic height in Figure 3 (dotted line)). Our experimental measurements fall near this line for concentrations of IgG < 30 nM. At high concentrations of IgG in bulk solution, the amount of bound IgG is less than the mass-transfer limited amount of IgG. By using ellipsometry, we estimate the composition of the mixed SAM to be ∼25% BiSH and ∼75% C8SH, thus creating a surface with >5 × 106 biotin groups/µm2. This density of biotin groups is several orders of magnitude greater than the maximum number density of molecules of IgG that could be hosted within a monolayer on a surface (∼1 × 104 to 5 × 104 molecules/µm2). This comparison suggests that there is no shortage of biotin groups at the surface of the mixed SAM for binding of IgG but that the kinetics of binding are likely slowed by factors such as steric crowding on the surface once the surface density of molecules of IgG exceeds a threshold. The simple mass-transfer analysis reported above leads to several useful conclusions. First, the optical response of the liquid crystal to the concentration of IgG in solution is largely determined by mass transport. Second, control of the diffusion length by using, for example, microfluidic channels will likely permit manipulation of the response of the liquid crystal to the concentration of IgG in solution (e.g., high levels of sensitivity to the concentration of IgG in solution). Conclusions The principal conclusion of the work reported in this paper is that simple measures of the optical appearance of films of liquid crystals that are anchored on proteins specifically bound at surfaces can be used to indicate the amount of bound protein. This result suggests that liquid crystals may offer simple procedures that permit quantitative amplification and transduction of biospecific interactions at surfaces. We also suggest a simple model that describes the dependence of the optical appearance of the liquid crystal on the amount and distribution of specifically bound protein. Acknowledgment. This research was supported by funding from the Office of Naval Research (Presidential Early Career Award for Science and Engineering to NLA) and the Center for Nanostructured Interfaces (NSF-DMF 9632527) at University of WisconsinsMadison. LA991101H