Langmuir 2008, 24, 8821-8832
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Quantifying Nanoparticle Adhesion Mediated by Specific Molecular Interactions Jered B. Haun and Daniel A. Hammer* Department of Bioengineering, UniVersity of PennsylVania, 210 South 33rd Street, Philadelphia, PennsylVania 19104 ReceiVed February 22, 2008. ReVised Manuscript ReceiVed April 24, 2008 Receptor-mediated targeting of nanometric contrast agents or drug carriers holds great potential for treating cardiovascular and vascular-associated diseases. However, predicting the ability of these vectors to adhere to diseased cells under dynamic conditions is complex due to the interplay of transport, hydrodynamic force, and multivalent bond formation dynamics. Therefore, we sought to determine the effects of adhesion molecule density and flow rate on adhesion of 210 nm particles, with the goal of identifying criteria to optimize binding efficiency and selectivity. Our system employed a physiologically relevant ligand, the vascular adhesion molecule ICAM-1, and an ICAM-1 specific antibody tethered to the nanoparticle using avidin-biotin chemistry. We measured binding and dissociation of these particles in a flow chamber as a function of antibody density, ligand density, and flow rate, and using a transportreaction model we distilled overall kinetic rate constants for adhesion and detachment from the binding data. We demonstrate that both attachment and detachment of 210 nm particles can be correlated with receptor and ligand valency and are minimally affected by shear rate. Furthermore, we uncovered a time-dependent mechanism governing particle detachment, in which the rate of detachment decreases with contact time according to a power law. Finally, we use our results to illustrate how to engineer adhesion selectivity for specific molecular targeting applications. These results establish basic principles dictating nanoparticle adhesion and dissociation and can be used as a framework for the rational design of targeted nanoparticle therapeutics that possess optimum adhesive characteristics.
Introduction Targeting of therapeutic or imaging agents to the vasculature via specific molecular interactions offers numerous advantages over conventional systemic treatments, including decreased incidence of adverse side effects and reduced total dosage. Furthermore, use of a polymer- or lipid-based delivery carrier can afford protection of sensitive agents, controlled release, and high payload capacity. Due to the potential that these magic bullet therapies hold, considerable research throughout the last decade has resulted in nanoscale vectors directed to molecular targets on tumors as well as inflamed vascular cells associated with atherosclerosis, stroke, myocardial infarction, thrombosis, and autoimmunity.1–3 Although these vectors are designed to bind specifically due to incorporation of monoclonal antibodies, short peptides, or endogenous ligands, the adhesion dynamics of these carriers or similar ones under flow has not been addressed. Delivery carrier binding within the bloodstream is complex due to the combined effects of transport, hydrodynamic force, and multivalent bond formation dynamics. Therefore, the targeting potential of a delivery carrier cannot be fully realized unless the binding performance is characterized under hydrodynamic flow conditions similar to the vascular circulation. Optimization of adhesion can be used in conjunction with intelligent carrier design and agent selection to engineer efficacious targeted therapies. For the ideal targeting scenario in which a molecular determinant is expressed exclusively on the surface of cells in the pathological state, optimization of carrier adhesion would simply entail maximizing the binding efficiency. This could be * To whom correspondence should be addressed. Telephone: (215) 5736761. Fax: (215) 573-2071. E-mail:
[email protected]. (1) Cuenca, A. G.; Jiang, H.; Hochwald, S. N.; Delano, M.; Cance, W. G.; Grobmyer, S. R. Cancer 2006, 107, 459–466. (2) Ding, B. S.; Dziubla, T.; Shuvaev, V. V.; Muro, S.; Muzykantov, V. R. Mol. InterVentions 2006, 6, 98–112. (3) Sinha, R.; Kim, G. J.; Nie, S.; Shin, D. M. Mol. Cancer Ther. 2006, 5, 1909–1917.
accomplished by utilizing the highest binding rate adhesion receptor in the highest copy number possible. However, targeting scenarios can also involve a molecular target that is basally expressed on normal cells and up-regulated in the diseased state. In this case, we are interested in the selectivity of binding of carriers to diseased versus normal cells. Consequently, carrier adhesion should be optimized for maximum selectivity through appropriate tuning of binding efficiency. Since the design of carriers depends upon the clinical situation, we sought to establish general criteria for engineering adhesion efficiency and selectivity. This information is useful not only for preventing unintended drug exposure or improving imaging sensitivity, but also to reduce financial costs as well by determining minimum design constraints for carrier concentration and targeting receptor coating density. Intracellular adhesion molecule (ICAM)-1 is expressed basally on normal vascular endothelium, but inflammation results in upregulation of expression and, within the microvasulature, leukocyte recruitment via activated LFA-1 integrins.4,5 Therefore, ICAM-1 represents a potential delivery target for which adhesion selectivity is necessary. Since ICAM-1 has been directly linked to pathological settings such as atherosclerosis, autoimmune disorder, transplant rejection, and cancer, it has been used in numerous delivery carriers.6–8 However, these ICAM-1-directed carriers were not developed to selectively bypass normal endothelium in favor of inflamed cells. Estimates for ICAM-1 expression on quiescent endothelial cells in Vitro have been reported at 150-300 sites/µm2, while values are greater than (4) Sumagin, R.; Sarelius, I. H. Am. J. Physiol.: Heart Circ. Physiol. 2007, 293, H2786–2798. (5) Springer, T. A. Cell 1994, 76, 301–314. (6) Sakhalkar, H. S.; Dalal, M. K.; Salem, A. K.; Ansari, R.; Fu, J.; Kiani, M. F.; Kurjiaka, D. T.; Hanes, J.; Shakesheff, K. M.; Goetz, D. J. Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 15895–15900. (7) Eniola, A.; Hammer, D. A. Biomaterials 2005, 26, 7136–7144. (8) Muro, S.; Dziubla, T.; Qiu, W.; Leferovich, J.; Cui, X.; Berk, E.; Muzykantov, V. R. J. Pharmacol. Exp. Ther. 2006, 317, 1161–1169.
10.1021/la8005844 CCC: $40.75 2008 American Chemical Society Published on Web 07/17/2008
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1000 sites/µm2 during cytokine induced inflammation.9–11 Through intelligent design, this window in ICAM-1 expression between normal and diseased states may be exploited. Here, we employ a receptor-targeted delivery system to quantitatively assess multivalent nanoparticle adhesion under physiological shear flow conditions. We use a model delivery carrier comprising 210 nm diameter polystyrene spheres decorated with monoclonal antibody specific for ICAM-1, and measure adhesion to ICAM-1-coated glass substrates in parallel-plate flow chamber binding assays. In these experiments, the antibody density, ICAM-1 density, and shear rate are systematically varied to quantitatively determine their effect on particle recruitment efficiency and bound state stability. To analyze binding profiles, we utilize a transport-reaction model to track free and bound particle species, account for transport phenomena, and define multivalent kinetic parameters for attachment and detachment. Our results provide a direct correlation between adhesion molecule densities and the rates of nanoparticle attachment and detachment, thus establishing criteria necessary to predict adhesive behavior within the context of specific targeting applications. In addition, we observed that the rate of particle detachment decreases with time, presumably due to an adhesion strengthening mechanism that acts on the time scale of minutes. Finally, we demonstrate how our model antibody-directed delivery carriers can be tailored for optimum selectivity of ICAM-1-related diseases, which in our case would require use of a low antibody density. This work demonstrates a set of methods to test and evaluate multivalent nanoparticle adhesion dynamics, which can be used to engineer the binding of nanometric targeted drug or contrast agent delivery carriers.
Materials and Methods Proteins. Biotinylated anti-human ICAM-1 (clone BBIG, mouse IgG1 κ) and control (anti-mouse integrin RMβ2, rat IgG2b) monoclonal antibodies, ICAM-1/human IgG1 Fc chimera, and control human IgG1 Fc were purchased from R&D Systems (Minneapolis, MN). Protein G was from Pierce (Rockford, IL). Horseradish peroxidase (HRP)-conjugated rat anti-mouse κ-light chain monoclonal antibody was obtained from Invitrogen (Carlsbad, CA). Mouse anti-human ICAM-1 monoclonal IgG1 antibody (clone 15.2) was from Ancell (Bayport, MN), and HRP-conjugated rat anti-mouse IgG1 monoclonal antibody was from BD Biosciences (San Jose, CA). Bovine serum albumin (BSA) was purchased from Sigma (St. Louis, MO). Particle Functionalization. Neutravidin-coated, yellow-green fluorescent, 210 nm diameter polystyrene FluoSpheres (Invitrogen) were diluted to 5 × 109 particles/mL concentration using 20 µL of Block-Aid (Invitrogen) and sonicated for 5 min per the manufacturer’s instructions. This was followed by dilution with phosphate-buffered saline (PBS) containing 1% BSA (PBS+) and addition of biotinylated antibody (control, anti-ICAM-1, or combination) to yield a solution of particles at 108/mL and total antibody at 10 µg/mL final concentration. This mixture was then incubated for at least 1 h at room temperature on an end-to-end rotator. Unbound antibody was removed by size-exclusion chromatography using Sephacryl S-500 ¨ KTA HR gel filtration media with PBS as the running buffer and an A Basic high-performance liquid chromatography (HPLC) system (GE Healthcare, Piscataway, NJ). For flow experiments, peak fractions were collected, analyzed for concentration using a fluorescence plate reader at 485 nm excitation/527 nm emission, pooled to attain the necessary number of particles, and diluted with PBS+ to 107/mL concentration. Particle concentration was determined based on a calibration curve constructed from the stock particle solution. Particle Characterization. Antibody surface density was assessed by enzyme-linked immunosorbent assay (ELISA) using an HRP(9) Dustin, M. L.; Springer, T. A. J. Cell Biol. 1988, 107, 321–331. (10) Lomakina, E. B.; Waugh, R. E. Biophys. J. 2004, 86, 1223–1233. (11) Hentzen, E. R.; Neelamegham, S.; Kansas, G. S.; Benanti, J. A.; McIntire, L. V.; Smith, C. W.; Simon, S. I. Blood 2000, 95, 911–920.
Haun and Hammer conjugated anti-mouse κ-light chain specific monoclonal antibody. Since this reagent binds exclusively to mouse antibody light chains, it provides a direct measurement of anti-ICAM-1 binding sites. Briefly, 1 mL of antibody-functionalized particles from peak elution fractions was incubated with 10 µL of secondary antibody-HRP at room temperature for 1 h and purified again using size-exclusion chromatography. Three peak elution fractions were analyzed by loading 50 µL into opaque 96-well tissue culture treated polystyrene plates in triplicate. Plates were incubated with 0.2 mL of StartingBlock (Pierce) per well for 1 h prior to sample addition to prevent deactivation of HRP enzyme by adsorption to the plate walls. Particle fluorescence was assessed at 485 nm excitation/527 nm emission before addition of 50 µL of Amplex Red fluorescent peroxidase substrate (Invitrogen) to each well. The ELISA reaction was allowed to proceed for 10 min at room temperature before measurement of fluorescence at 544 nm excitation/590 nm emission. The fluorescence signal from yellow-green particles was negligible using this filter set. Calibration curves were prepared from stock solutions of particles and biotinylated HRP (Invitrogen) and were used to convert the respective fluorescence intensities to the number of HRP molecules per particle. This was then converted to anti-ICAM-1 binding site density per area of particle (nr) by assuming a 1:1:1 ratio of binding site to anti-κ light chain antibody to HRP. ICAM-1 Substrate Preparation. Substrates for parallel-plate flow experiments were prepared using glass coverslips (24 × 50 mm2, #1.5, Fisher) that were silanized with 3-aminopropyltrimethoxysilane (Sigma) to improve protein adsorption. Silanization entailed washing with Piranha solution (66.7% concentrated sulfuric acid and 33.3% hydrogen peroxide) for 1.5 h, extensive rinsing with Milli-Q water, oven drying at 90 °C, and overnight incubation with an open pool of silane within an evacuated glass vacuum desiccator (Jencons, Bridgeville, PA). Silane-treated coverslips were fitted with modified FlexiPerm silicone gaskets (three wells cut to create a single rectangular well, Sigma), washed with adsorption buffer (0.1 M NaHCO3, pH 9.2), and incubated for 2 h at room temperature with a saturating concentration of protein G in adsorption buffer (100 µg/mL, 0.7 mL). Substrates were then washed three times with PBS to remove excess protein G before introduction of a saturating solution of Fc protein (Fc control, ICAM-1/Fc, or mixture) in PBS (100 nM, 0.7 mL). Fc protein was reacted for at least 1 h at room temperature before removal immediately prior to use by three rapid washes with SuperBlock (Pierce). ICAM-1 Substrate Characterization. ICAM-1 surface density was assessed by ELISA using an HRP-conjugated anti-mouse IgG1 antibody. Eighteen mm circular glass coverslips were used so that the ELISA reaction could be carried out in 12-well plates (BD Falcon). Piranha wash and silanization were performed as described above. Protein G adsorption and Fc protein binding was also similar; however, single-well FlexiPerm gaskets were used and all volumes were scaled down to 0.2 mL to preserve the same surface area to volume ratio. After Fc protein incubation, substrates were blocked with ice-cold StartingBlock (Pierce) for approximately 10 min while gaskets were removed. This was followed by incubation with icecold PBS containing anti-ICAM-1 antibody (2 µg/mL, 0.5 mL) for 1 h at 4 °C and three washes with ice-cold PBS. Identical incubation and wash sequences were then performed using HRP-conjugated anti-mouse IgG1 monoclonal antibody (1:500 dilution, 0.5 mL). After the final wash step, coverslips were placed in fresh 12-well plates and 100 µL of PBS was added to the top of each. The ELISA reaction was initiated by addition of 0.9 mL of TMB Turbo chromagenic peroxidase substrate (Pierce) and continued for 10 min at room temperature before quenching with 1 mL of 1 M sulfuric acid. Absorbance was measured at 450 nm using a plate reader and converted to number of HRP molecules by calibration with biotinylated HRP. ICAM-1 site density per area substrate (nl) was determined using the gasket surface area (0.77 cm2) and by assuming a 1:1:1:1 ratio of ICAM-1 to primary antibody to secondary antibody to HRP. Parallel-Plate Flow Chamber Assays. Particle binding was assessed under laminar flow using a parallel-plate flow chamber
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with a straight channel (0.01 in. high, 0.35 cm wide) cut from Duralastic silicone sheeting (Allied Biomedical, Ventura, CA). This chamber was similar to ones described previously,12 but it was modified to fit a 24 × 50 mm2 coverslip. The flow chamber was assembled with the ICAM-1-coated or control coverslips secured in the bottom section, and it was positioned on an inverted Nikon Diaphot microscope equipped with cooled charge-coupled device (CCD) camera, motorized stage, and standard fluorescein isothiocyanate (FITC) filter cube. Fluorescent images were captured at 40× magnification with an exposure time of 500 ms. The camera and stage were controlled using custom Labview (National Instruments, Austin, TX) programs developed in our laboratory. Particle binding experiments were performed analogously to typical Biacore assays, with a binding period followed by a washout period using buffer only to study detachment. Fluid flow was brought about using a syringe pump (Harvard Apparatus, Natick, MA), and particle solution or PBS buffer was selected using a threeway valve. The effect of fluid hydrodynamics was investigated using three flow rates, which corresponded to wall shear rates of 100, 400, and 1000 s-1. The physiological shear rate range is approximately 40-2000 s-1, and the values above are representative of flow within postcapillary venules, large arteries, and arterioles/capillaries, respectively.13 The wall shear rate γ˙ w was calculated from the volumetric flow rate Q using the following relation:
γ ˙w )
6Q H2W
(1)
where H is the chamber height and W is the chamber width. Binding experiments were conducted at constant flux to maximize the number of particles that could be used for each experiment. Thus, particle concentration was adjusted to 2.5 × 106 and 106 particles/mL using PBS+ prior to runs at 400 and 1000 s-1 shear rate, respectively. Eight total stage positions near the center line were tracked throughout both binding and detachment periods. The first position was 5 mm from the inlet, and the subsequent positions were spaced 3 mm apart down the axis. Complete imaging cycles were completed each minute during the binding period and with decreasing frequency (2-5 min) during the detachment period. Imaging was started once the particles reached the chamber; however, binding data was only used after the binding rate reached steady state. This required 2 min at 100 s-1 and 1 min at the higher shear rates. Binding Profile Analysis. Particle binding profiles were constructed by manually tracking adhesion and dissociation events from fluorescent microscopy images using overlays of consecutive images with a custom Labview program developed in our laboratory. Binding and detachment profiles represent the instantaneous bound particle count at each time point throughout binding and detachment experiments, respectively. Attachment profiles were also constructed based on the aggregate number of particles that had bound and thus do not reflect detachment. Using the measured field of view area, bound particle numbers were then converted to densities. Both time and bound particle density were initialized to the beginning of the steady state period, and data from each of the eight stage positions were averaged. We define the kinetics of multivalent particle adhesion using the following rate equation:
∂B ) kACw - kD B ∂t
(2)
where B is the bound particle density (#/area), Cw is the unbound particle concentration at the wall, t is time, and kA and kD are the kinetic rate constants for particle attachment and detachment, respectively. These multivalent kinetic rate constants describe the binding dynamics of a particle as an individual unit and therefore differ from monovalent kinetic forward (kf) and reverse (kr) reaction rates governing bond formation between receptors on the particle and ligands on the glass surface. Receptor and ligand densities do not appear in eq 2 because the number of bonds formed during a
docking event is unknown and will vary based on the number of molecules available to bind. While theory has been developed to account for the dependence of adhesion on available surface area by assigning a net flux based on the probabilities of reaching an unoccupied site and binding once there,14 we assessed particle binding only during early stages in which the surface coverage of bound particles was low, rendering this effect negligible. Since multivalent particles can continually form bonds while bound to the substrate, we posit that the detachment rate may decrease with contact time. Therefore, we propose the following power law to account for potential time-dependency in the detachment rate:
kD(t) )
k0D
(3)
(t ⁄ tref)R
where kD0 sets the magnitude of the detachment rate, R determines the functional form of the time dependence, and tref is a reference time that scales the total time and ensures that kD0 and kD have the same units. Since we do not have enough information to establish a physical basis for tref, we will arbitrarily use 1 s for the value. It should be noted that a constant detachment rate is obtained using R ) 0. Particle attachment data obtained during the binding period do not reflect detachment; thus, the attachment rate (kACw) can be determined by setting kD ) 0 in eq 2 and integrating to yield
BTotal ) kACwt
(4)
where BTotal is the aggregate number of particles bound per area. Thus, kACw is given by the slope of BTotal versus time. Isolation of kA from Cw requires knowledge of the particle concentration throughout the chamber, however, and this will be dealt with in a subsequent section. Likewise, the detachment constants kD0 and R can be directly obtained from detachment experiment data, in which case kA ) 0. Substitution of eq 3 into eq 2 and integration gives
[
B ) B0 exp
]
kD0 1-R 1-R (t - t ) 1-R 0
(5)
where B0 and t0 are the bound particle density and time at the start of the detachment period, respectively. Detachment dynamics can also be analyzed during the binding period by integration of eq 2 after substitution for the time-dependent kD in eq 3. An analytic solution is not possible for unknown R in this case, and therefore, integration must be performed numerically. Monte Carlo Simulation of Particle Detachment. The detachment analysis in the previous section is based on the notion that the behavior of a population of particles can be classified by its population average. For the case in which detachment is time-dependent, however, population behavior is the observed manifestation of the individual particle dynamics. Characterizing the diversity of responses across a population might be better served by tracking bound lifetimes for each particle throughout both experimental binding and detachment periods. Since this would require considerable effort experimentally, we devised a computer simulation that tracks particle histories and stochastically samples for detachment events. These simulations considered each particle as a discrete entity and did not seek to characterize adhesion molecule binding dynamics as others have accomplished previously.15–18 (12) Eniola, A. O.; Willcox, P. J.; Hammer, D. A. Biophys. J. 2003, 85, 2720– 2731. (13) Goldsmith, H. L.; Turitto, V. T. Thromb. Haemostasis 1986, 55, 415– 435. (14) Turitto, V. T. Ind. Eng. Chem. Fundam. 1975, 14, 275–276. (15) English, T. J.; Hammer, D. A. Biophys. J. 2004, 86, 3359–3372. (16) Hammer, D. A.; Apte, S. M. Biophys. J. 1992, 63, 35–57. (17) Chang, K. C.; Hammer, D. A. Langmuir 1996, 12, 2271–2281. (18) Kuo, S. C.; Hammer, D. A.; Lauffenburger, D. A. Biophys. J. 1997, 73, 517–531.
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Haun and Hammer
Simulations were constructed by dividing the experimental time into discrete time steps, ∆t, during which a constant number of particles, ∆B, were introduced into the system based on the observed attachment rate kACw. Detachment events were then sampled for by comparing a randomly generated number to the detachment probability
(( ) )
-κD0 PD ) 1 - exp(-κD∆t) ) 1 - exp ∆t tb β tref
(6)
[
]
(7)
where C is the free particle concentration, Vx is the axial velocity, and D is the particle diffusivity. Particle velocity normal to the direction of flow is omitted despite alignment of the gravitational force vector with the y-dimension because 210 nm particles will not appreciably sediment in the time that they are in the chamber. The flow profile within a parallel-plate chamber under conditions of fully developed and laminar flow is parabolic, given by
[ Hy - ( Hy ) ] ) γ˙ H[ Hy - ( Hy ) ] 2
Vx ) 6U
2
w
(8)
where U is the average velocity. The latter relation comes from eq 1 and the fact that average velocity is given by the volumetric flow rate divided by the chamber cross-sectional area. Particle diffusivity is given by the Stokes-Einstein equation
D)
kBT 6πµRp
2
[ ( )]
[
kBT ∂2C ∂2C ∂C + ) ∂x 6πµRp ∂x2 ∂y2
(9)
where kBT is the thermal energy, Rp is the particle radius, and µ is the solvent viscosity. Insertion of eqs 8 and 9 into eq 7 yields (19) Myszka, D. G.; He, X.; Dembo, M.; Morton, T. A.; Goldstein, B. Biophys. J. 1998, 75, 583–594. (20) Turitto, V. T.; Baumgartner, H. R. Trans. Am. Soc. Artif. Intern. Organs 1975, 21, 593–601.
]
(10)
The boundary conditions include (1) a constant particle concentration at the inlet equal to the starting concentration (C0)
C(t, x ) 0, y) ) C0
(11a)
(2) a convective flux condition at the outlet
∂C (t, x ) L, y) ) 0 ∂x
where κD is the detachment rate applicable to individual particles, κD0 and β are detachment parameters that arise from defining κD analogously to eq 3, respectively, and tb is the total time bound. If the random number was less than PD, the particle “detached” and tb was recorded. Otherwise, tb was updated by ∆t and the process was repeated during the subsequent time step. To simplify simulation structure, ∆B was set explicitly, and the same ∆B value was used for all experimental conditions regardless of attachment rate kACw. Consequently, the theoretical flow chamber area being observed varied between conditions in accordance with the attachment rate kACw. Profiles of bound and total bound particles were then constructed by summing the instantaneous and cumulative particle counts, respectively, at each time step and dividing by the area. For detachment experiment simulations, ∆B was set to zero and the number of bound particles remaining at the conclusion of the binding period was used as the initial condition. Transport-Reaction Model. To evaluate particle binding data in terms of multivalent kinetic rates, we developed a transportreaction model based on previous deterministic treatments of monovalent protein interactions and platelet adhesion under flow.19,20 A Cartesian coordinate system is used with the origin at the flow chamber inlet, x-axis parallel to the direction of flow, and y-axis normal to the ICAM-1-coated surface. Since the channel width is more than 1 order of magnitude greater than the height, particle concentration is assumed to be uniform across the width. Thus, particle concentration within the flow chamber is given by the twodimensional transient convective-diffusion equation
∂C ∂C ∂2C ∂2C + + Vx )D ∂t ∂x ∂x2 ∂y2
∂C y y ˙wH +γ ∂t H H
(11b)
and (3) a insulation/symmetry condition at the impenetrable, nonreactive top chamber surface
∂C (t, x, y ) H) ) 0 ∂y
(11c)
The fourth boundary condition defines the heterogeneous reaction at the ligand-coated chamber surface as stated by eq 2 and matches the reaction rate to the flux of particles to the wall. Therefore, the rate of bound particle accumulation is given by
∂B ∂C (t, x) ) kA C(t, x, y ) 0) - kD B(t, x) ) D (t, x, y ) 0) ∂t ∂y (11d) To simplify solution of eq 10, the governing equations were made dimensionless using the following parameters
ˆ≡ C C C0
B ˆ B≡ C0H
P≡
ξ≡
x L
η≡
˙wH2Rp 6UH 6πµγ ) D kBT
y H
ε≡
δA ≡
H L
kAH D
tD H2 kDH2 δD ≡ (12) D
τ≡
where P is the Peclet number, which relates convective and diffusive transport and δA and δD are the Damko¨hler numbers for attachment and detachment, respectively, which scale the kinetic rates to the diffusive transport rate. Inclusion of the scaling parameter ε normalizes the chamber dimensions, simplifying finite-element solution of the model. Substitution of the dimensionless parameters into eqs 10 and 11 yields
ˆ ˆ ˆ ∂2C ˆ ∂C ∂C ∂2C + Pε[η - η2] ) ε2 2 + 2 ∂τ ∂ξ ∂ξ ∂η ˆ(τ, ξ ) 0, η) ) 1 C
(13)
(14a) ˆ ∂C (τ, ξ ) 1, η) ) 0 (14b) ∂ξ ˆ ∂C (τ, ξ, η ) 1) ) 0 (14c) ∂η ˆ ˆ ∂C ∂B ˆ(τ, ξ, η ) 0) - δ ˆ (τ, ξ, η ) 0) ) (τ, ξ) ) δAC DB(τ, ξ) ∂η ∂τ (14d) Equation 13 was solved numerically subject to boundary conditions 14 using Comsol Multiphysics finite-element modeling software employing the two-dimensional transient convection-diffusion application. The one-dimensional reaction at the adhesive boundary was incorporated using the weak form boundary application, enabling formulation of the heterogeneous reaction with the low-level weak form instead of the PDE form. The domain was set to encompass the entire chamber from inlet to outlet, with nodes placed at each of the eight positions observed experimentally to track binding phenomena. The initial particle concentration was set to 1 to emulate the steady state nature of the experimental data. The domain mesh
Quantifying Nanoparticle Adhesion
Figure 1. Schematic diagram of nanoparticle binding system. Fluorescent particles (210 nm) coated with different densities of an antibody, antiICAM-1, were bound to ICAM-1 substrates under flow. Both attachment and detachment kinetics were measured as a function of shear rate, antibody density, and ICAM-1 density.
was generated with a maximum element size of 0.001 at the reactive boundary, with the size gradually increasing upward toward the top of the chamber. This ensured that computational energy was concentrated in the region of most interest. Statistics. ELISA results and bound particle densities are given ( the standard error for at least three independent experiments. Curve fitting results for attachment rate and attachment rate constant are given ( the standard error of the data, while all other curve fits are given ( the 95% confidence interval.
Results Characterization of Particle Receptor and Substrate Ligand Molecular Densities. Figure 1 illustrates the nanoparticle system employed in this paper. Polystyrene particles (210 nm) were functionalized with the BBIG anti-ICAM-1 antibody using avidin/ biotin chemistry. The maximum anti-ICAM-1 binding site density (nr) was measured by ELISA to be 3400 ( 50 µm-2, and this was titrated down to 1080 ( 170 and 410 ( 110 µm-2 by mixing with a biotinylated control antibody at equal mass concentration (Figure 2A). These densities correspond to 470 ( 6, 149 ( 24, and 56 ( 15 binding sites per particle, respectively. The antiICAM-1 antibody bound to the bead surface preferentially to control antibody, resulting in a nonliner dependence of the surface anti-ICAM-1 antibody to anti-ICAM-1 antibody mass ratio. This was likely due to a greater degree of biotinylation of the antiICAM-1 antibody relative to the control antibody. ICAM-1/Fc chimera was coupled to glass substrates using protein G, and the density was modulated using equimolar mixtures with an Fc control protein. ICAM-1 densities (nl) were measured by ELISA to be 8 ( 1, 14 ( 3, 21 ( 1, 41 ( 3, and 134 ( 6 sites/µm2 (Figure 2B). As with the antibodies above, Fc proteins did not partition equally, with the ICAM-1/Fc binding preferentially. ICAM-1/Fc was incubated at a ratio of 1.25%, 2.5%, 5%, and 10% with control to achieve the values listed above. Particle Binding and Detachment Profiles. Particle binding and detachment profiles from flow chamber experiments are shown in Figure 3. Each trace represents a different particle receptor density or substrate ligand density condition. Each part of Figure 3 represents a different shear rate. Binding experiments were conducted at a constant particle flux of 109 mL-1 s-1 (107/ mL at 100 s-1 shear rate, 2.5 × 106/mL at 400 s-1, or 106/mL at 1000 s-1) and were followed directly by a washout period at the same shear rate using buffer only. Particle adhesion was greater than background levels for all conditions tested and generally increased with the density of both receptor and ligand. Bound particle densities also decreased with shear rate. Once particles were omitted from the chamber, particle detachment was observed for all cases. Determination of Observed Attachment Rate (kACw) from Binding Experiments. Particle attachment profiles were constructed by tracking the total number of particles bound throughout
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the course of the binding experiments. These profiles were then fit by linear least-squares regression to obtain the attachment rate kACw in accordance with eq 4. (Attachment rate values for all conditions are listed in the Supporting Information, Table 1.) As indicated for the data at 100 s-1 shear rate, kACw varies linearly with nl (Figure 4A) and nr (Figure 4B) at low to intermediate adhesion molecule densities but saturates at higher values. Furthermore, plotting kACw versus the product of the densities nrnl (Figure 4C) collapsed the data onto a uniform curve. Thus, the rate of particle recruitment depends on the product of receptor and ligand density and hence the receptor/ligand encounter probability. Similar results were observed at 400 and 1000 s-1, as indicated in Figure 4D where kACw was plotted for all shear rates after normalization by the inlet concentration C0. Figure 4D also indicates that hydrodynamic flow positively influenced particle recruitment. Evaluation of Detachment Rate kD from Detachment Experiments. Detachment dynamics observed during detachment experiments were characterized by performing simultaneous twoparameter (kD0, R) curve fits according to eq 5. These fits resulted in a broad range of values for R extending from approximately 0.1 to 0.9. However, it was clear that R was nonzero, indicating that detachment rate was indeed time-dependent for multivalent nanoparticles. The distribution of R was narrowed considerably by focusing on the early stages of detachment in cases where particle dissociation stopped abruptly. After this adjustment was made, R ranged from 0.3 to 0.6 with an average of 0.34. Moreover, for nearly all of the 100 s-1 shear rate samples, in which inlet concentration and thus bound particle densities were greatest, R ranged between 0.3 and 0.4. Thus, we concluded that the same power law governs the effect of time on kD regardless of adhesion molecule density and shear rate. Single-parameter (kD0) curve fits were performed holding R between 0.3 and 0.4, and upon examination 1/3 most accurately reflected detachment profiles across all samples. Data fits with R ) 1/3 for representative samples can be found in Figure 5. These fits are remarkably accurate at predicting detachment, thus suggesting that we have uncovered a fundamental rate law for multivalent particle detachment. Values for k0D that were obtained from detachment experiments are given in Figure 6. (These values are listed in the Supporting Information, Table 2.) Statistical reliability is indicated by 95% confidence interval of the fit and does not include data error. Overall, confidence decreased as adhesion molecule density decreased and shear rate increased, reflecting the smaller sample sizes. Moreover, kD0 varied inversely with adhesion molecule density, suggesting dissociation was more likely at lower molecular adhesion densities. While kD0 varied with the amount of both molecules, kD0 was more strongly dependent on antibody density. This finding is illustrated in Figure 6A, where kD0 values at 100 s-1 shear rate are scaled by the product nr3nl to yield a uniform curve. An alternative way to represent this relationship is to plot kD0 versus 1/(nrnl1/3), which results in a straight line with a slope equal to 4.2 ( 0.4 (Figure 6B). A linear relationship between kD0 and 1/(nrnl1/3) was generally observed at higher shear rates as well (Figure 6C and D). However, the trend was more error prone due to a higher degree of error accompanying the smaller bound particle sample sizes. Because the slope values relating kD0 and 1/(nrnl1/3) were similar at each shear rate (4.2 ( 0.4, 5.1 ( 1.6, and 4.0 ( 1.3 at 100, 400, and 1000 s-1, respectively), it does not appear that hydrodynamic shear has a significant effect on nanoparticle detachment. Consequently, once tethered, nanoparticle stability is governed exclusively by the dynamics of molecular bond formation and dissociation.
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Figure 2. Particle receptor (A) and substrate ligand (B) densities as measured by immuno-ELISA. (A) Anti-ICAM-1 binding site densities measured using HRP-conjugated rat anti-mouse κ-light chain specific monoclonal antibody. Neutravidin-coated particles were incubated with 10 µg/mL total biotinylated antibody in 1%, 5%, and 100% ratios of anti-ICAM-1 antibody with a control. (B) ICAM-1 site densities measured using mouse anti-human ICAM-1 and HRP-conjugated rat anti-mouse IgG1 monoclonal antibodies. Substrates were prepared by first adsorbing protein G to silanized glass coverslips and then incubating with 100 nM total Fc at ICAM-1/Fc ratios of 1.25%, 2.5%, 5%, 10%, and 100%. Error bars represent the standard error of at least three independent measurements.
Figure 3. Bound particle density profiles measured in flow chamber binding and detachment assays using shear rates and inlet particle concentrations, respectively, of (A) 100 s-1 and 107/mL, (B) 400 s-1 and 2.5 × 106/mL, and (C) 1000 s-1 and 106/mL. Vertical dashed lines indicate the start of the detachment period. Error bars represent the standard error of at least three independent experiments.
Evaluation of kD from Binding Experiments. Binding profiles were evaluated subject to eq 2 using the time-dependent detachment rate constant defined in eq 3. (kACw values from this fit are listed in the Supporting Information, Table 1). Numerical solutions were obtained using the ordinary differential equation solver ODE45 in Matlab, with kD0 and R selected to match the binding data. Reasonable fits could be obtained for R ) 1/3; however, better fits could be achieved using R ) 3/4 (data not shown). Thus, during an attachment experiment, dissociation depends more strongly on time, which is consistent with a timedependent strengthening of adhesion. Monte Carlo Detachment Simulation. We have illustrated that multivalent particle dissociation is time- and historydependent, but we sought to find a self-consistent means of characterizing dissociation across all time scales. To this end, we developed a probabilistic simulation of particle detachment to recreate observed adhesion data. This simulation enabled isolation of detachment parameters that characterize individual
particle behavior and are thus applicable to both binding and detachment experiments. In these simulations, we could assign an individual particle detachment rate (κD) defined analogously to kD in eq 3, but instead use the parameters κD0 and β to clearly distinguish from the macroscopic quantities (k0D and R) evaluated previously. Simulations were conducted using Matlab with a time step of 1 s and ∆B ) 5, and the outputs from three independent simulations were averaged. In addition, the standard deviation was calculated to generate error bars for data fitting purposes. Particle attachment was set by values of kACw (Supporting Information, Table 1) that had previously been determined from binding experiments, and detachment was stochastically sampled based on the detachment probability defined by eq 6. Detachment parameters (κD0 and β) were then chosen to fit binding and detachment experiment data simultaneously. Based on matching the correct shape of the data, we concluded that good fits could be attained for all experimental conditions using β ) 3/4. In
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Figure 4. Attachment rates (kACw) measured during binding experiments based on total cumulative bound particles. Results obtained at 100 s-1 shear rate are plotted versus (A) substrate ligand density nl, (B) particle receptor density nr, and (C) the product of the densities nrnl, indicating a linear relationship at low and moderate values that saturates at high density. (D) Attachment rate scaled by inlet concentration C0 plotted versus nrnl for data at 100, 400, and 1000 s-1 shear rates, demonstrating positive dependence on hydrodynamic flow. Error bars indicate the standard error of at least three independent experiments.
Figure 5. Natural logarithm of detachment data from the detachment period after normalization by initial bound particle density B0. Results shown are representative fits using selected adhesion molecule densities at (A) 100, (B) 400, and (C) 1000 s-1 shear rates. Profiles were fit by regression analysis of eq 5 using the time-dependent kD defined by eq 3. Fit parameters included R ) 1/3 and kD0 values listed in the Supporting Information, Table 2. Colors and symbols represent the same receptor and ligand densities as those in Figure 3.
nearly all cases, however, the attachment rate had to be increased to successfully match observed binding and detachment experiment profiles. It is our belief that the discrepancy between experimental and simulation attachment rate arises from the manner in which experiments were conducted. As illustrated in Figure 7A, the simulation predicts a substantial population of particles that remain bound for only seconds to tens of seconds before detaching. Since images were captured every minute during experiments, most of these particles would not have been observed. Fits for all conditions can be found in Figure 7B-D,
with the corresponding values for adjusted attachment rate (kACwTotal) and κD0 provided in the Supporting Information (Tables 1 and 2). In most cases, only minor adjustments to the attachment rates were necessary. In addition, the deterministic binding experiment fits from the last section were performed again using kACwTotal for the attachment rate. This did not alter the value of R previously determined (3/4), but it did increase the best fit kD0 values (Supporting Information, Table 2). Upon comparison to kD0 values obtained from deterministic analysis of detachment experiments, these values were greater by approximately 80-
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Figure 6. Detachment rate constant (kD0) values obtained by regression analysis of detachment data in accordance with a time-dependent detachment rate (eq 5). (A,B) Results for kD0 at 100 s-1 shear rate. (A) kD0 plotted versus nr3nl to collapse all conditions onto a single curve that could be fit using a simple power law, demonstrating the difference in detachment sensitivity to receptor and ligand densities. The lowest adhesion molecule density data (indicated by *) deviated from the trend, and therefore, these points were not included in the power law fit. (B) Representation of the data in part (A) by transformation of the abscissa to 1/(nrnl1/3) in order to obtain a linear relationship. (C,D) Results at (C) 400 and (D) 1000 s-1 shear rates indicating that the same scaling relationship is valid and that the slope values were similar. These data at elevated shear rate were more error prone due to smaller sample sizes. Colors and symbols represent the same receptor and ligand densities as those in Figure 3. Error bars indicate 95% confidence intervals for regression analysis fits and do not include data error.
Figure 7. Stochastic detachment simulation results using the fundamental detachment rate constant κD. (A) Histograms of total time bound before detachment during binding experiments for a representative sample (nr ) 1080/µm2, nl ) 133.8/µm2, 100 s-1 shear rate). Results are presented as the percentage of detachment events within 10 s bins relative to the total number that detached during the experiment period. The histogram outline recreates the functional dependence of the observed detachment rate kD. (B-D) Simulation fits for all adhesion molecule densities at (B) 100, (C) 400, and (D) 1000 s-1 shear rates using a self-consistent time-dependent detachment rate applicable to both binding and detachment experiments and governed by power law β ) 3/4. Colors and symbols represent the same receptor and ligand densities as those in Figure 3. Error bars indicate the standard error of the experimental binding data and the standard deviation between three independent simulations for the fits.
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Figure 8. Transport-reaction model results for particle recruitment illustrating depletion of free particle concentration due to binding reaction and the effect on particle adhesion. (A) Representative results for nl ) 133.8/µm2 and 100 s-1 shear rate for (i) nr ) 410, (ii) nr ) 1080, and (iii) nr ) 3400 sites/µm2 samples demonstrating that attachment rate affects the extent of depletion but not the free particle concentration gradient height. (B) Representative results for nr ) 3400 and nl ) 133.8 sites/µm2 at (i) 100, (ii) 400, and (iii) 1000 s-1 shear rates illustrating that flow rate decreases both the extent of depletion and gradient height as a result of increased flux and decreased residence time, respectively. Net effect of depletion on (C) free particle concentration and (D) bound particle density for a representative sample (nr ) 3400, nl ) 133.8, and 100 s-1 shear rate) plotted versus chamber axial position for the region observed during experiments. Results are displayed at 1 min time intervals throughout the binding period. The eight “observed” axial positions from experiments are indicated by the red dots. (E) Bound particle density profiles with time for the same representative sample at the eight experimental axial positions.
fold. Again, this is consistent with the notion that, in an attachment experiment, detachment may occur rapidly as the particles have had a shorter residence time on the surface and hence a shorter time to secure adhesion, making dissociation more facile. Correspondingly, simulations led to a simple functional form for detachment that was self-consistent. This result, given in eq 15 below, yields a dissociation rate that is higher than that previously observed during detachment experiments and lower than that observed during binding experiments. This is reasonable, since this is a single rate that should span all dissociation dynamics. The scaling analysis for the detachment rate with respect to adhesion molecule densities is unchanged. Thus, the selfconsistent rate for dissociation is
κD )
κ′D0 nrnl1⁄3t1⁄3 b
(15)
where the constant κ′D0 is equal to 90 in this case but does include the effects of other parameters such particle size as well as receptor/ligand structural, chemical, and mechanical properties, and therefore is unique to this experimental system. Determination of Attachment Rate Constant kA. The attachment rate constant kA was isolated from the attachment rate kACw by finite-element solution of eq 13 subject to boundary conditions 14 using Comsol Multiphysics software. Since we had already characterized detachment rate, we focused on attachment by setting δD ) 0 and manually varying δA to match our calculation to the observed attachment rate (kACwTotal, Table 1 in the Supporting Information). Solutions utilized a 1 s time step and were carried out for a total of 14 or 20 min to emulate binding experiments. Equation 12 was used to convert between
dimensional and dimensionless forms of the attachment rate, and kA values are listed in Table 1 in the Supporting Information for all experimental conditions. The model indicates that a particle concentration gradient develops at the reactive boundary due to depletion of free particles from the near-wall region. The attachment rate did not affect the size or shape of the gradient profile, but it did influence the extent of particle depletion (illustrated in Figure 8A). Increasing shear rate was associated with decreases in both gradient zone size and depletion due to shorter residence time and greater particle flux, respectively (Figure 8B). At moderate to high attachment rates, particle depletion was sufficiently extensive to cause free particle concentration at the wall and the bound particle density to vary appreciably with chamber length (Figure 8C–E), which was observed in experiments as well (data not shown). As observed for the attachment rate in Figure 4, a linear relationship was observed between kA and the product of the adhesion molecule densities even at the highest densities employed (Figure 9). However, in this case, kA is truly linear with nrnl, suggesting the deviation at high molecular densities observed in Figure 4 was due to particle depletion in the bulk, which is properly characterized by our reaction-diffusion model, and not saturation of the binding rate. The attachment rate constant increased with shear rate, although the change was not statistically significant. Therefore, hydrodynamic flow does not appear to substantially alter the binding rate of 210 nm particles, at least at the conditions investigated. Linear regression analysis revealed the slopes of kA versus nrnl to be 8.0 × 10-7 ( 0.2 × 10-7, 9.8 × 10-7 ( 0.4 × 10-7, and 11.8 × 10-7 ( 0.3 × 10-7 µm5/s at 100, 400, and 1000 s-1, respectively.
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Figure 9. Attachment rate constants (kA) isolated using transport-reaction model fitting of adjusted recruitment rate data (kACwTotal, Supporting Information, Table 1) plotted versus the product of the adhesion molecule densities at (A) 100 s-1 and for (B) all shear rates, indicating a linearly proportional relationship with both nr and nl out to the highest adhesion rates. Error bars indicate the standard error from attachment rate fits propagated through the transport-reaction model.
Discussion Using a well-characterized nanoparticle system, we have discovered several basic tenets for the adhesion and dissociation of nanoparticles mediated by specific adhesion molecules. They are as follows: (1) The rate of adhesion is linearly proportional to the densities of both receptor and ligand, that is, nrnl. (2) The rate of dissociation is time-dependent and is most strongly affected by the density of receptors on the bead surface. The functional form for dissociation follows the law nr-1nl-1/3t-3/4. (3) The depletion of free particles from the region near the reactive surface can affect the appearance of attachment, especially at high molecular densities. While these fundamental rules have been elucidated with one molecular system, it remains to be seen in future work if these basic rules are ubiquitous across all adhesion chemistries. Attachment. Particle attachment rate was determined from the total number of particles bound during the experimental binding period per time, and the transport-reaction model was then used to isolate the attachment rate constant (kA). Linear relationships were observed between kA and both adhesion molecule densities for all conditions investigated, and plotting kA versus the product of the densities nrnl collapsed the data onto a single line. Hence, multivalent nanoparticle recruitment depends directly on adhesion molecule encounter probability. It is expected that the linear relationship between kA and nrnl will hold for other receptor-ligand pairs, although it remains to be seen how capture efficiency will vary with structural, chemical, and mechanical bond properties. Direct association between kA and nrnl has previously been proposed as an approximation to relate the bond forward reaction rate kf and observed cell adhesion rate in flow chamber experiments.21 Recently, this relationship was formalized based on an extension of theory developed for micropipet frequency assays and applied to neutrophil tethering.22 Shear rate did not significantly affect kA, indicating that the antibody–ICAM-1 on-rate is sufficiently fast (kf ) 1.6 × 105 M-1 s-1; ref 12) to secure nanoparticle binding at all shear rates tested. Moreover, this suggests that the minimum number of bonds required to tether the particles does not vary across the shear rate range investigated. Our estimate for the hydrodynamic force on a tethered 210 nm particle at the conditions employed ranges from approximately 0.001 to 0.01 pN (FMax ) 13.2µγ˙ wRp2; refs t (21) Chang, K. C.; Hammer, D. A. Biophys. J. 1999, 76, 1280–1292. (22) Yago, T.; Zarnitsyna, V. I.; Klopocki, A. G.; McEver, R. P.; Zhu, C. Biophys. J. 2007, 92, 330–342. (23) Goldman, A. J.; Cox, R. G.; Brenner, H. Chem. Eng. Sci. 1967, 22, 653. (24) Yago, T.; Wu, J.; Wey, C. D.; Klopocki, A. G.; Zhu, C.; McEver, R. P. J. Cell. Biol. 2004, 166, 913–923.
23 and 24). This is much lower than the force required to break a single antibody–antigen bond, which typically have bond strengths of 10-100 pN.25 Thus, it is possible that the minimum number of bonds needed for adhesion could be one. Detachment. Analysis of data from detachment experiments revealed that particle dissociation was time-dependent. This finding implies that initial particle tethering is a nonequilibrium state, from which additional bonds can form over time, thus reducing the probability of detachment. The temporal dynamics of detachment was modeled by incorporation of time into the detachment rate constant using a power law (eq 3). This timedependent detachment rate was then used to fit experimental data using two different approaches. The first was a macroscopic analysis of the behavior of entire particle populations, which entailed deterministic solution of the differential equations governing binding (eq 4) and detachment (eq 5) experiments. The second approach to evaluate particle detachment utilized stochastic simulations to track individual particle histories so that a fundamental detachment rate, κD, could be established. Unlike the observed kD obtained from macroscopic binding and detachment profile analyses, κD is intrinsic to each particle and thus applicable across all phases of particle binding. Using the simulation, we found that the time exponent, β, that governed particle detachment was 3/4 across all adhesion molecule densities and shear rate conditions investigated. Thus, it appears that adhesion strengthening reduces the probability of dissociation over time. The numerical coefficient, κ′D0, in the numerator of eq 15 is likely due to specific features of this system and may change as chemistry, particle size, and other system parameters are modulated. The rate of particle detachment varied inversely with both adhesion molecule densities, with an exponentially greater sensitivity observed for the density of antibody (third power). This finding was surprising considering that antibody density was much greater than ICAM-1 density in all cases. However, shape differences between the spherical particle and planar glass surface may reduce adhesion molecule accessibility. Shear rate did not significantly influence particle detachment, indicating that dissociation was entirely due to receptor/ligand bond chemistry. On the basis of the estimate for hydrodynamic force in the previous section, it is expected that fluid flow would not affect the dissociation of particles. Other factors potentially contributing to particle dissociation include the sparse ICAM-1 densities employed, which translate to an average of one to five binding sites within the particle cross-sectional area, and use of the protein G/human IgG1 Fc linkage to couple ICAM-1 to the glass surface, which provides a secondary mechanism for bond (25) Weisel, J. W.; Shuman, H.; Litvinov, R. I. Curr. Opin. Struct. Biol. 2003, 13, 227–235.
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Figure 10. Selectivity of nanoparticle binding. (A) Extent of depletion effects illustrated by plotting the attachment rate constant kA and observed attachment rate (kACw/C0) versus nrnl for the data at 100 s-1 shear rate. (B,C) Calculation of carrier delivery to endothelial ICAM-1 expressed at normal (nlN ) 150/µm2) and inflamed (nlD ) 150/µm2) densities. Attachment rate was determined for both ligand density cases out to the maximum antibody density obtained experimentally (3500/µm2), and the transport-reaction model was used to determine the resulting attachment rate. Transportreaction model solutions were obtained assuming exposure of a 10 cm long section of vessel to a bulk carrier concentration of 107/mL for 10 min. The attachment rate was then used along with the appropriate detachment rate (calculated κD0 based on molecule density, β ) 3/4) in the stochastic simulation to assess particle detachment during the 10 min binding period and for 10 min following. (B) Density of carriers delivered to the diseased case (BD) and the difference compared to the normal case (BD - BN) given as a function of antibody density. Depletion effects lead to a saturation of delivery to diseased cells as well as a decrease in the difference in delivery between the two cases for carriers with antibody densities greater than 20% of the maximum. (C) Selectivity for the diseased case as measured by the ratio of densities (BD/BN), indicating decay from the maximal value (nlD/nlN) due to depletion effects. However, a small deviation is observed at approximately 10% of the maximum receptor density due to an abrupt change in the scaling of detachment rates with nr.
dissociation. Utilizing protein G was advantageous for orienting ICAM-1 molecules into the flow field, however, and orientation has been shown to influence both the rates of encounter and binding between surface-bound adhesion molecules.26 Depletion Effects and Disease Targeting. Solutions from our transport-reaction model revealed that particle recruitment was sufficiently fast at high adhesion molecule densities to extensively deplete free particle concentration near the reactive surface. This is significant because, as Figure 10A illustrates, particle depletion decreased the observed adhesion level (indicated by kAC/C0) from that which was theoretically possible (dictated by kA). At low adhesion molecule densities, the observed and theoretical profiles overlap because particle depletion is minimal. However, as adhesion efficiency increases, the observed attachment rate is reduced to about one-third of the value without depletion. Thus, adhesion molecule valency can drive particle adhesion from reaction-limiting to transport-limiting conditions. This aspect can have drastic implications for designing targeted delivery carriers, especially for cases in which the disease determinant is expressed on both normal and diseased tissues. Since kA varies linearly with nrnl, the selectivity of the carrier for the diseased case relative to normal is invariably given by the ratio of the ligand expression levels. However, depletion effects will be experienced to a greater extent at the diseased site, potentially reducing selectivity unless adhesion efficiency is appropriately controlled. To illustrate how our results for nanoparticle attachment and detachment, as well as potential effects of particle depletion, (26) Huang, J.; Chen, J.; Chesla, S. E.; Yago, T.; Mehta, P.; McEver, R. P.; Zhu, C.; Long, M. J. Biol. Chem. 2004, 279, 44915–44923.
translate to carrier delivery within the context of a physiologically relevant targeting scenario, we predicted the number of particles that would be recruited to normal and inflamed vascular endothelium via ICAM-1. For this calculation, we first determined kA and κD0 at the ICAM-1 expression levels reported for normal and activated endothelial cells in Vitro, 150 and 1000 sites/µm2, respectively,9–11 over the range of receptor densities that we could attain experimentally (up to 3500/µm2). The transportreaction model was then used to determine the observed attachment rate by assessing delivery over a 10 cm long section of flow chamber/blood vessel surface for 10 min with a bulk particle concentration of 107/mL. Finally, based on the attachment rate, the calculated κ0D value, and β ) 3/4, the stochastic simulation was used to account for binding over 10 min. Due to the possible saturation of the detachment rate suggested by Figure 6A, κD0 was not allowed to exceed 0.05 s-1. Figure 10B displays the predicted carrier density that would be delivered to diseased endothelium (BD) as a function of receptor density and suggests that delivery is ultimately limited by particle depletion effects. Furthermore, this result indicates that a carrier with half-maximal antibody density would still maintain 90% of the maximum delivery potential. Also included in Figure 10B is the difference in carrier density between the diseased and normal cases (BD BN), which demonstrates there is a clear maximum in BD - BN at an anti-ICAM-1 bead surface density of 20% of the maximum; increases in density beyond this value would diminish the effectiveness of the carrier. An alternative way to plot selectivity, BD/BN, is plotted in Figure 10C, demonstrating that selectivity is a decreasing function of receptor coverage. However, since overall carrier binding is low at low receptor coverage, the most
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meaningful design criteria for the carriers is derived from Figure 10B. It is clear that intermediate levels of receptor expression (from 10% to 30% of maximum) provide a significant extent of binding and establish selectivity. We sought to characterize the binding dynamics of nanoparticles functionalized with monoclonal antibody due to the extensive use of antibodies in targeting strategies. In addition, numerous monoclonal antibodies have previously been developed and tested in clinical trials as stand-alone therapies for cancer as well as inflammatory and immune diseases,27–29 providing a ready pool of potential targeting receptors if the use of antibodies could be validated. Here, we have demonstrated that a particular antibody is efficient at bringing about adhesion of 210 nm particles to its counter-ligand ICAM-1 at high antibody densities (thousands of sites/µm2). In addition, we demonstrated that antibody density could be tuned to provide optimally selective delivery to ICAM-1 on diseased endothelium relative to normal cells. Therefore, this antibody would be an effective targeting receptor for treating ICAM-1-related diseases with nanoscale delivery carriers. It remains to be seen how the particle binding rate can be related to the kinetics of binding of the antibody-antigen bond (kf ) 1.6 × 105 M-1 s-1, kr ) 1.1 × 10-4 s-1) as well as to the bond’s mechanics and structure. Computational methods such as adhesive dynamics can be used to relate the adhesion behavior observed here to the molecular binding properties, which can then be used for predictive mapping to identify ideal molecular binding characteristics.15,16 This work was conducted under idealized flow conditions, including a fully laminar flow field and dilute solution limit. As such, correlating the principles determined herein to in ViVo carrier delivery would require consideration for numerous factors present within the vascular circulation. For instance, we assumed that particle transport normal to the direction of flow takes place exclusively by diffusion. Due to vessel branching and other features encountered within the vasculature, though, particle solutions will experience turbulent mixing. Additionally, physical interactions with blood components, particularly red blood cells,
can alter the distribution and transport rate of particles. For instance, red blood cell collisions have been shown to enhance the diffusivity of platelets and polymer microparticles and cause margination to the vessel wall.30–32 Consequently, the use of whole-blood flow chamber assays or intravital microscopy would be beneficial to incorporate additional factors relevant for in ViVo targeting to identify appropriate optimization criteria. Finally, obtaining accurate information regarding disease determinant expression levels and temporal profiles in ViVo is an important but nontrivial task, and it will likely require development of novel imaging techniques. In summary, we have developed techniques to measure multivalent nanoparticle adhesion, including methods to analyze binding isotherms and extract multivalent kinetic rates. Using these techniques, we characterized the attachment and detachment behavior of a 210 nm particle as a function of particle receptor density, substrate ligand density, and shear rate. Our results indicate that multivalency increases the probability of encountering binding partners and stabilizes the bound state through multiple anchoring linkages, which in the latter case was observed as a decrease in particle dissociation rate with time. Furthermore, we established that, at high adhesion efficiency, particle depletion effects can limit adhesion, which can play a critical role in the design of delivery carriers. This led us to the counterintuitive conclusion that certain targeting cases may call for submaximal adhesion efficiency, or receptor valency, to optimized carrier delivery.
(27) Imai, K.; Takaoka, A. Nat. ReV. Cancer 2006, 6, 714–727. (28) Andreakos, E.; Taylor, P. C.; Feldmann, M. Curr. Opin. Biotechnol. 2002, 13, 615–620. (29) Kaneider, N. C.; Leger, A. J.; Kuliopulos, A. FEBS J. 2006, 273, 4416– 4424.
(30) Grabowsk.Ef; Leonard, E. F.; Friedman, L. I. Ind. Eng. Chem. Fundam. 1972, 11, 224. (31) Turitto, V. T.; Benis, A. M.; Leonard, E. F. Ind. Eng. Chem. Fundam. 1972, 11, 216. (32) Tilles, A. W.; Eckstein, E. C. MicroVasc. Res. 1987, 33, 211–223.
Acknowledgment. We thank E. D. Johnston, M. J. Paszek, M. T. Beste, A. D. Trister, and W. F. Liu for technical assistance and helpful discussions. This work was supported by Unilever Research US, NSF BES 0314265 and NIH CA 115229. Supporting Information Available: Table of attachment rate values, table of detachment rate values, and table of parameter values used for the transport-reaction model. This material is available free of charge via the Internet at http://pubs.acs.org. LA8005844
