Nonspecific Colloidal-Type Interaction Explains Size-Dependent

Nonspecific Colloidal-Type Interaction Explains Size-Dependent Specific Binding of Membrane-Targeted Nanoparticles Anders Lundgren,*,†,‡ Björn Agnarsson,† Ronald Zirbs,‡ Vladimir P. Zhdanov,†,§ Erik Reimhult,‡ and Fredrik Höök*,† †

Department of Physics, Chalmers University of Technology, Gothenburg 412 96, Sweden Department of Nanobiotechnology, University of Natural Resources and Life Sciences, Vienna 1190, Austria § Boreskov Institute of Catalysis, Russian Academy of Sciences, Novosibirsk 630090, Russia ‡

S Supporting Information *

ABSTRACT: Emerging biomedical applications such as molecular imaging and drug delivery often require directed binding of nanoparticles to cell-membrane receptors. The specific apparent affinity of such ligand-functionalized particles is size-dependent, an observation so far solely attributed to multivalent receptor−ligand interaction. We question the universality of this explanation by demonstrating that the binding kinetics also depends on weak, attractive colloidal-type interaction between nanoparticles and a lipid membrane. Applying label-free single-particle imaging, we correlate binding of nanoparticles targeted to a cell-mimetic lipid membrane with the distribution of nontargeted particles freely diffusing close to the membrane interface. This analysis shows that already a weak, kBT-scale attraction present between 50 nm gold nanoparticles and the membrane renders these particles an order of magnitude higher avidity compared to 20 nm particles. A stronger emphasis on nonspecific particle−membrane interaction might thus be required to accurately predict nanoparticle targeting and other similar processes such as cellular uptake of exosomes and viruses. KEYWORDS: targeted nanoparticles, lipid−membrane interaction, DLVO interaction, single-particle imaging, light-scattering, quartz crystal microbalance

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NPs increases markedly with increasing their diameter from 20 nm to about 50 nm.2−6 Although this can potentially be related to size-selectivity in active (clathrin-dependent)7,8 and passive (receptor-mediated wrapping-dependent)9,10 cellular uptake, the correlation between cellular uptake and binding avidity and the fundamental questions how and why the latter depends on the actual NP size itself remain open for studies and discussions. Due to multivalent interaction between NP-conjugated ligands and receptors in the lipid membrane, the rate constants for detachment, koff, of targeted NPs are orders of magnitude lower compared to those for the corresponding monovalent interaction.3,11,12 The commonly observed increase in binding avidity with increasing NP size has, therefore, been explained as an effect of the NP curvature on the number of ligand−receptor

igand-functionalized or, in other words, targeted nanoparticles (NPs) have high potential in biomedicial applications including drug delivery, hyperthermia therapy, and vaccine development and as contrast agents in imaging. They are also used as molecular markers and for identification and purification of cells, proteins, and nucleic acids. Furthermore, NP-targeting is reminiscent of the biological recognition of viruses and exosomes by membrane receptors, which means that it can serve as an experimentally accessible model for these important biological processes. The successful targeting of NPs interacting biospecifically with a lipid membrane and their subsequent internalization into the cell depend on their binding avidity,1 which in this context can be quantitatively characterized by the NP-membrane association constant. It is therefore important to understand how this feature relates to the physiochemical properties of NPs. In particular, the influence of NP size on the interaction between targeted NPs and receptors in the cellular membrane has received considerable attention. The corresponding studies have repeatedly shown that the cellular uptake of targeted gold © 2016 American Chemical Society

Received: June 23, 2016 Accepted: October 26, 2016 Published: October 26, 2016 9974

DOI: 10.1021/acsnano.6b04160 ACS Nano 2016, 10, 9974−9982

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RESULTS AND DISCUSSION To study the effect of size-dependent colloidal interactions on the NP binding kinetics at physiological salt conditions, we ensured that the differently sized gold NPs were stabilized by functionalization with dense PEG brushes, displaying controlled density of peripheral biotin ligands. A 10-fold excess of thiolated PEG (5 kDa) was added to citrate-stabilized gold NPs in water,17 yielding grafting densities of 1.0 and 0.8 nm−2 for 18 and 51 nm NPs, respectively (Supporting Information Figure 2). Despite the 20% difference in grafting density, the equilibrium brush thicknesses were observed to be essentially identical for large and small NPs, both having dense, approximately 10 nm thick shells (Figure 1a,b). As theoretically

bonds that can be formed between a NP and receptors in the lipid membrane,3,11,13 since larger NPs have larger contact areas. In contrast, the influence of the specific binding rate, characterized by the binding rate constant, kon, on the avidity in general and the efficiency of NP targeting in particular, has generally been overlooked. Considering that bond formation is the initial event required for all downstream cellular processing of NPs, including uptake, this assumption could be problematic. For example, while the multivalent ligand−receptor interaction considerably increases the residence time for a NP once bound to its targeted interface,1,14−16 kon for the preceding NPreceptor binding is often lower than the corresponding rate constant for binding of free ligand to the same receptor.14,16 Since the avidity is determined by the ratio of the “on” and “off” rate constants, low binding rates, therefore, tend to counteract the effect of multivalent interaction on the equilibrium binding level. However, more importantly, when the effect of multivalency is so strong that NP binding is effectively irreversible, i.e., the avidity is very high, NP binding can still be very slow; in the experimental or clinical practice, targeting can indeed be limited by the specific binding rate of the NPs to the cell-membrane receptors. The role of NP size on the outcome of targeting applications can therefore not be fully anticipated by an analysis of NP equilibrium-binding levels, and accordingly the bond-formation process and thereto related NP dynamics close to the membrane interface have to be scrutinized in detail. This question is in this work addressed by investigating how size-dependent, weak colloidal interaction between a ligandfunctionalized NP and a lipid membrane tunes their specific binding rate and accordingly influences the specific avidity. The approach taken was to correlate the binding rate constants, kon, measured upon exposure of a receptor-modified lipid membrane to targeted gold NPs of different sizes (51 and 18 nm in diameter) with the size-dependent, weakly attractive force caused by the DLVO-type (Derjaguin, Landau, Verwey, and Overbeek) interaction between similar but nontargeted NPs and the lipid membrane. Although the latter interaction indeed is expected to directly influence the equilibrium spatial distribution of the NPs in close proximity to the interface, an experimental quantification of this phenomenon is very challenging for the NP-size range of interest. To tackle this challenge, we created a lipid membrane on the surface of an optical waveguide, thus allowing simultaneous imaging of scattering intensities from thousands of individual NPs diffusing in the evanescent light field close to the membrane interface. The exponential decay of the illumination intensity with the distance from the lipid-bilayer-modified substrate allowed determination of the spatial distribution of the individual NPs in solution near the membrane. In this way it was possible to experimentally confirm the theoretically determined NP− membrane interaction potential, which was used here to aid a detailed interpretation of the measured association kinetics of targeted NPs, including both specific interactions between surface-conjugated ligands and receptors at the lipid membrane and size-dependent colloidal interactions treated in the framework of the extended DLVO theory. Thus, our findings provide an additional tool for designing targeted NP systems and offer quantitative insights into how specific interactions in biological systems can be strongly modulated by nonspecific DLVO-type interaction.

Figure 1. Preparation and characterization of ligand-functionalized nanoparticles. (a) Gold-core NPs with PEG brush shells were prepared with a mixed monolayer of α-carboxy-, α-methoxy-, and α-biotinyl-ω-mercapto-poly(ethylene glycol) (MW 5000 Da) by self-assembly in water solution. (b) Size-distributions of core−shell NPs determined with scanning electron microscopy (core diameters) and dynamic light scattering (core + shell diameters). (c) Number of biotinylated ligands per NP as a function of the fraction of α-biotinyl-ω-mercapto-poly(ethylene) glycol present during self-assembly according to titration with biotin (5fluorescein) for particles with core diameter 18 nm (blue) and 51 nm (red).

predicted,18 this equalization is attributed to the larger volume that becomes available per PEG chain for NPs with higher curvature. The number of biotin molecules per NP was varied from 2 to >200 (the corresponding densities are ∼10−4 nm−2 and ∼10−1 nm−2, respectively) by changing the molar ratio of biotinylated to nonbiotinylated PEG during assembly of the shell. The presence of peripheral biotin was confirmed by direct observation of streptavidin binding using electron microscopy (Supporting Information Figure 4) and further quantified by titration with biotin (5-fluorescein) (Figure 1c). The binding of NPs to supported lipid bilayers sparsely modified with mobile streptavidin receptors was measured using quartz crystal microbalance with dissipation monitoring (QCM-D). The corresponding kinetics for NPs with different degrees of biotin functionalization display linearly increasing binding during the first 90 s after injection (Figure 2a,b). The biotin−streptavidin ligand−receptor pairs have a very low unbinding rate,19 making binding essentially irreversible (no unbinding was detected, even in the case when NPs were bound via a single ligand−receptor bond). For this reason, and since the surface concentration of streptavidin receptors, cSA, in these experiments was kept low, the observed association rate can unambiguously be represented as dc NP/dt = koncSAC NP 9975

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Figure 2. Binding curves and binding rate constants for membrane-targeted NPs. Binding of NPs with core diameters of (a) 18 nm and (b) 51 nm and various degrees of biotin functionalization (in TRIS-buffer 10 mM, pH7.4, 100 mM NaCl). In these plots, the frequency shift measured with QCM-D is indicated on the left axis, and the corresponding NP surface concentration, cNP, normalized to the surface concentration of streptavidin receptors, cSA, and the NP bulk concentration, CNP, is indicated on the right axis. (c) Corresponding binding rate constants, kon, determined for NPs with core diameter 18 nm (blue) and 51 nm (red) for different peripheral concentration (nm−2) of biotin ligands. The average number of biotin molecules per NP is indicated within parentheses. The error bars represent the results from at least three experiments.

where cNP and CNP are the surface and bulk concentrations of NPs, respectively. The corresponding rate constant, kon, relating to the probability of bond formation when a NP encounter a receptor, was found to increase approximately linearly with concentration of biotin ligands on the NPs (Figure 2c), but saturated at higher ligand densities (≳0.01 nm−2). This saturation correlates with the onset of extensive multivalent interaction between many biotin ligands on a single NP with several streptavidin receptors on the lipid bilayer and subsequent depletion of streptavidin available for binding (Supporting Information Figure 7). Notably, for NPs with only a few (∼2) biotin ligands, NPs with 51 nm cores had close to 1 order of magnitude higher kon than 18 nm core NPs (Figure 2c). Given that the ligand density in fact is significantly smaller for the large NPs, this result appears at first sight contradictory. To scrutinize this observation, the NP association kinetics will, therefore, in the following section be analyzed in further detail. Nanoparticle Binding Rate in the Kinetically Controlled Regime. Our observation that the binding rate is proportional to the ligand surface concentration on NPs shows that the binding process is kinetically controlled rather than globally limited by NP diffusion. Indeed, from the linear regime in the plot of kon as a function of ligand concentration on the NP surfaces (Figure 2c), kon can be extrapolated to a value in the range between 106−107 M−1 s−1 for densities approaching full monolayer coverage of NP-grafted ligands. This value is in good agreement with literature data for the binding rate of free biotin to streptavidin.19 For the case of NPs with submonolayer ligand coverage, the measured rate of bond formation is accordingly related to a combination of the probability that conjugated ligands encounter a receptor on the bilayer interface and the rate of the bond formation itself. While the latter depends on the ligand and receptor properties, including, e.g., the relaxation time of the polymer tether,20 the encounter probability is expected to depend on NP size. To rationalize the dependence of kon on various factors, we therefore introduce a coarse-grained model (Figure 3 and section 3 of the Supporting Information), in which the NP is represented by a sphere of radius R displaying biotin molecules (ligands) with surface coverage θB. We neglect deformation of the PEG shell (because this costs energy and accordingly an appreciable deformation is unlikely) and assume that binding occurs during contact of the NP periphery with a streptavidin receptor represented by a sphere with radius ρ. The location of the NP with respect to the streptavidin molecule is characterized by the distance r between the

Figure 3. Scheme of the interaction between biotin-functionalized NP and a streptavidin receptor at the lipid interface, where R is the particle hydrodynamic radius, filled red circles denote biotin ligands, d is the diameter of the patch with area A on the periphery of the particle explored by each polymer end segment, ρ is the radius of the streptavidin receptor, and r is the distance between the projections of the particle and receptor centers to the lipid membrane.

projections of their centers to the membrane interface and the minimal separation z between the NP periphery and the same interface. For R ≫ ρ the minimal separation can be approximated by z = 2ρ − r2/2R, showing that bond formation is possible at r ≤ r* ≡ 2(ρR)1/2. Neglecting the effect of NP rotation (because NPs are relatively large and their rotation is slow) as well as in-plane diffusion of streptavidin receptors in the lipid membrane [because NPs diffuse sufficiently faster than the streptavidin receptors (Supporting Information Figure 9)], the attachment rate constant can be obtained by integration over the contact surface with r ≤ r* as r

kon ∝ θB

∫0 * rdr ∝ θBr*2 ∝ θBρR

(2)

These expressions correspond to the kinetically limited association of homogeneously distributed NPs and, in this limit, may in fact be applicable in a wide range of NP-rotation and streptavidin-diffusion rates. In our context, we note that the biotin surface coverage can be represented as θB = σA, where σ is the ligand surface concentration and A is the area explored by a biotin molecule attached to the end segment of the polymer spacer, which may depend on the NP radius.21 For the smaller NPs under study, A can be approximately twice that of the larger NPs (Supporting Information Figure 10). This means that the explicit size dependence indicated by relation (eq 2), which already is too weak to explain the experimental 9976

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ACS Nano observations, may vanish, and we would expect kon to be proportional to the biotin surface concentration and almost independent of NP size. However, since the nonspecif ic NP− membrane interaction is expected to depend strongly on NP size,22 we therefore hypothesized that the large contrast in the association rate de facto observed for binding of differently sized NPs may relate to weak attraction between the larger NPs and the lipid membrane. This colloidal-type interaction results in size-dependent, nonhomogeneous distribution of NPs near the membrane interface and in this way influences the association rate. Diffusing Nanoparticles Are Transiently Trapped in the Vicinity of the Lipid Membrane. The influence of nonspecific forces on binding rate constants has previously been elaborated in the context of biomolecular interactions on cell surfaces.23,24 Whereas for molecules the columbic interaction is considered most important, attractive van der Waals interaction is longer-ranged for NPs and may, at physiological ionic strengths, dominate the colloidal interaction between the NPs and the lipid membrane.22 In combination with very short-ranged and strongly repulsive steric and hydration forces, the attractive van der Waals interaction can give rise to a weak well in the NP−membrane separationdependent interaction potential, U(z), with minimum at a few nanometers separation from the membrane interface, where diffusing NPs can be transiently entrapped.25 This would lead to a nonuniform distribution of NPs in the vicinity of the membrane, and accordingly the probability of finding a NP at separation z from the membrane interface would be proportional to the Boltzmann factor, exp[−U(z)/kBT]. Taking this into account, expression (eq 2) for the binding rate constant should be extended to

Figure 4. Detection and analysis of light scattered by membranebound and diffusing NPs. (a) Scattering intensities for individual NPs were measured under an up-right microscope in a droplet of buffer applied on top of a planar waveguide chip, on which the glass core had been modified with a supported lipid bilayer displaying streptavidin receptors. Scattering data were simultaneously obtained from snapshots of surface-bound biotinylated NPs (red in the cartoon) and diffusing nonbiotinylated NPs (yellow in the cartoon); the latter indicated by red arrows in the micrograph. (b) Distribution of normalized scattering intensities, 6 I0 /⟨ 6 I0 ⟩, for individual core−shell NPs with core diameter 51 ± 5 nm bound to the lipid bilayer. The distribution of normalized scattering intensities was fitted by a Gaussian distribution with standard deviation σ = 0.1, indicated by the gray dashed curve. (c) Distributions of normalized scattering intensities for diffusing NPs, measured in buffer with 11 mM salt and 110 mM salt, respectively. To eliminate ambiguities in the image analysis only diffusing NPs with high normalized scattering intensity, 6 I / ⟨ 6 I ⟩ > 0.75, were analyzed. (d) Graphical interpretation of i 0 NP redistribution in the vicinity of the lipid bilayer in response to shift in buffer ionic strength and corresponding estimated interaction potentials, U(z), where z is the separation between the periphery of the PEG brush and the lipid bilayer. The full interaction potential was determined in accordance with the extended DLVO theory.

r

kon ∝ θB

∫0 * exp[−U(z(r))/kBT ]rdr

(3)

where z(r) is defined as above. From the exponential dependence of kon on U(z), it is clear that already a small difference in the interaction potential will result in orders of magnitude higher attachment rates, as indeed observed for the larger NPs under study (Figure 2c). For micron-sized particles, measurements of weak interactions between a freely diffusing single particle and a functionalized, e.g., bilayer-coated, surface are straightforward with total internal reflection microscopy (TIRM).26,27 Recent experiments show that such particles can be transiently trapped at specified separations from a solid interface in response to a shallow potential well (ΔU ∼ kBT).28 To test whether NPs with 51 nm in diameter gold cores could be similarly, transiently trapped in the vicinity of the lipid membrane, we analyzed the distribution of light scattered from thousands of individual NPs diffusing close to a lipid bilayer formed on the glass core of a waveguide chip in situations with and without binding, respectively (Figure 4a). This planar waveguide chip was designed to minimize background scattering in waveguideTIRM experiments by having a cladding material with refractive index matching that of water and an extremely smooth surface.29 As reference for the scattering intensity of diffusing NPs, the NPs functionalized with biotin were first sparsely bound to the streptavidin-modified lipid bilayer. Subsequently, identical NPs but without peripheral biotin were added, and snapshot images of the light scattered from both surface-bound and diffusing NPs were acquired and analyzed.

The scattering intensity, I0, of immobilized gold NPs vary with NP size in the Rayleigh fashion, I0 ∝ R6.30 If the size distribution of NPs is narrow, the size distribution of surfacebound NPs is expected to be approximately similar to that in bulk. Accordingly, the same normal distribution and variance, as measured for the core-size distribution with electron microscopy, was applied for the intensity distribution of all surfacebound NPs when plotted as 6 I0 (Figure 4b). Light scattered by diffusing NPs, I, is also attenuated in relation to their displacement z above the lipid bilayer due to the decreasing intensity of the incident light according to I = I0 exp(−z/dp), where I0 is the scattering intensity obtained at the interface and dp is the penetration depth of the evanescent light. The distribution of measured scattering intensities from an ensemble of diffusing NPs will, therefore, reflect both the NP 9977

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Figure 5. Influence of NP-membrane interaction potential on NP-binding rate constants. (a) Interaction potential as a function of the separation between the periphery of the PEG brush and the lipid bilayer calculated for core−shell NPs with core diameter 51 nm (red) and 18 nm (blue) for different ionic strengths. (b) Binding rate constants measured for core−shell NPs with core diameter 51 nm (red circles) and 18 nm (blue circles) having similar low ligand coverage under the influence of the different interaction potentials depicted in (a). The rate constants are given as a function of the encounter probability in accordance with eq 3, where r* ≡ 2(ρR)1/2, ρ = 2.5 nm, R = 19 nm for smaller NPs, and R = 35 nm for the larger NPs. Arrows label data points corresponding to binding at 110 mM ionic strength for small (blue) and large (red) NPs, respectively. (c) Binding rate constants measured for NPs with core diameter 51 nm (red circles) and 18 nm (blue circles) having different peripheral concentration of biotin ligands bound at similar binding conditions with respect to their interaction potential with the lipid membrane, corresponding to 22 mM and 15 mM ionic strength for the smaller and larger NPs, respectively. The average number of biotin molecules per NP is indicated within parentheses. The error bars represent the results from at least three experiments, and the broken line indicates a linear fit (weighted least-squares, R2 = 0.98) to the data obtained for binding of NPs with core diameter 51 nm.

size distribution, f(R) as well as the separation-dependent interaction potentials, U(z,R) of the individual, differently sized NPs. As derived in section 4 of the Supporting Information, the total number (per unit surface area) of diffusing NPs with scattering intensities to the power of 1/6 being smaller than a given value I1/6 can be calculated as N (I1/6) = c0

∞

∫0 ∫0

(I / C)1/6 exp(z /6d p)

distributions were calculated in accordance with relation (eq 5). For this calculation, well-known analytical expressions for the van der Waals interaction31 and the double-layer interaction32 were employed, whereas short-range hydrodynamic33 and steric contributions34,35 were fitted with a single exponentially decaying repulsive potential. This procedure confirmed that at 110 mM salt, NPs with 51 nm gold cores experienced an attractive interaction with the lipid membranecoated surface (Figure 4d), characterized by a well in the interaction potential with Umin ≈ − 2.5 kBT at z ∼ 1−2 nm, which essentially overlaps with the region where binding can occur in direct proximity of the bilayer (cf. Figure 3). Based on the parameters fitted for 51 nm NPs, an interaction potential for the smaller NPs, which are too small to be accurately detected on an individual level with the waveguide-TIRM, could be calculated, indicating a shallower well with Umin ≈ − 0.5 kBT, located at the same separation from the membrane interface as for the larger NPs. Binding Rate Is Tuned by the Particle−Membrane Interaction Potential. The above estimated difference in the depth of the interaction potential between large (51 nm) and small (18 nm) NPs correlates indeed quantitatively with the 1 order of magnitude increased association rate observed for the larger NPs. To further crosscheck the interaction potentials resulting from the light-scattering measurements with expression (eq 3), kon for NPs of both sizes displaying similar low surface coverage (∼5 × 10−3 nm−2) of biotin was measured at different DLVO conditions. In these experiments the ionic strength of the NP suspensions was chosen so that the interaction potential, U(z), experienced by the NP in the close vicinity of the lipid bilayer was varied in a narrow interval, ranging from weakly attractive at high ionic strength (as in the experiments above) to weakly repulsive at moderate ionic strengths. As shown in Figure 5a, U(z) in the contact zone adjacent to the lipid membrane then vary between kBT (at low ionic strength) to − kBT (at high ionic strength) for NPs with a diameter of 18 nm, whereas the corresponding variation is between 2 kBT and −3.5 kBT for NPs with a diameter of 51 nm. To explore how this dependence of U(z) on ionic strength in turn influences kon, in Figure 5b the latter parameter is plotted

f (R ) exp[− U (z , R )/kBT ]dRdz

(4)

where c0 is the NP concentration far from the interface, and C is the proportionality constant given by I0 = CR6. Thus, by solving relation (eq 4) for I1/6 being varied across an interval (here we choose the interval coinciding the intensity distribution measured for immobilized NPs shown in Figure 4b), the actual distribution of I1/6 observed for diffusing NPs is obtained from the derivate of N (I1/6) with respect to I1/6: F(I1/6) ∝

dN (I1/6) d(I1/6)

(5)

Taking advantage of that both the core−shell NPs and the lipid bilayer were slightly negatively charged (Supporting Information Table 1), experiments were performed in which the relative strength of the attractive van der Waals attraction and the repulsive double-layer interaction were varied. This was done by altering the ionic strength of the suspension upon scattering-based imaging of diffusing nonbinding, i.e., nonbiotinylated NPs, from near physiological salt conditions (110 mM), as used in the binding experiments above, to moderate salt conditions (11 mM). The main difference obtained by varying the experimental conditions in this way was a redistribution of intensities from many weakly scattering NPs at low ionic strength to a larger fraction of strongly scattering NPs at high ionic strength (Figure 4c). For a fixed NP-size distribution, this is consistent with an increased probability at high ionic strength of finding NPs close to the membrane interface where the light intensity is higher (Figure 4d and section 4 of the Supporting Information). To find plausible DLVO interaction potentials, U(z,R), for fitting the observed scattering distributions, theoretical 9978

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ACS Nano versus the probability of encounters between NP-grafted ligands and membrane receptors as obtained by using relation (eq 3), where the corresponding interaction potentials (Figure 5a) are taken into account. This analysis shows that kon for both NP sizes collapses onto a single curve (Figure 5b), thus confirming our hypothesis that the size-dependent NP-binding rates observed at physiological conditions are mainly caused by size-dependent colloidal interactions between the NPs and the lipid membrane. Further, at low ionic strength, at which NPs rather than displaying weakly attractive interactions (see operation at physiological conditions above), display weakly repulsive interaction, both the magnitude of kon and the dependence of kon on surface concentration of biotin were independent of NP size (Figure 5c). The fact that kon differs significantly for small and large NPs at high ionic strength when the Debye screening is strong (Figure 2c), but not for low ionic strength when double layer repulsion dominate (Figure 5c), further underlines that the high binding rate observed for large NPs at the former condition is an effect of net attraction between NP and lipid membrane and not caused by different electrostatic repulsion. Taken together, these experiments thus clearly demonstrate that the binding rate of targeted NPs is exclusively related to the surface concentarion of ligand only if the nonspecific attrative interaction beween NP and membrane is negligible, which is in many situations not necesserly the case. The potential importance of NP binding rate and its dependence on NP size for cellular uptake was identified previously;36−39 however the influence of weak colloidal interactions on the specific avidity of membrane targeted NPs has not been tested in experiments. We show that already the small attractive van der Waals potential of ∼ −2.5kBT present in the interaction between a lipid membrane and a PEG-coated gold NP with a diameter of 51 nm results in 1 order of magnitude higher binding rate compared to similar NPs with a diameter of 18 nm, for which the attractive potential is close to zero. From the analysis of single-NP light scattering data, and in analogy with previous observations made for micron-sized particles,28 we conclude that the attractive force between the NPs and the surface increases the residence times for the larger NPs in the vicinity of the interface. The probability to form a bond between ligands at the NP periphery and receptors at the lipid membrane interface thus increases with the number and duration of the encounters between the NP and the surface. Consequently, the avidity of targeted NPs can increase with NP size even without engaging multivalent bond formation. In fact, we observe that the colloidal interaction is most important for NPs with few ligands, since at high ionic strength conditions the dependence of kon on the surface concentration of ligands is weaker for larger NPs (Figure 2c). This observation can be related to a combination of factors such as NP rotation and heterogeneous distribution of the ligand on the NP surface, since the former will depend on the duration of the NP-surface encounters and the latter may increase with the surface concentration of ligands. 40 The influences of NP-size distribution and receptor depletion due to multivalent interactions (relating to the diffusivity of the membraneanchored streptavidin10) on the NP-binding kinetics were not explicitly taken into account in our model (Supporting Information section 3). One should note however that the sparsely modified NPs probed in this work are representative for NPs commonly employed in experiments and applications. For example, low surface concentration of active ligand (i.e., a

low ratio of binding to nonbinding surface area) is expected when ligands are randomly adsorbed or grafted to the NPs using nondirectional conjugation schemes like, e.g., carbodiimide coupling,41,42 when ligands comprise a minor part of a large inflexible protein, or are tethered via inflexible spacer molecules restricting the effective surface coverage of single ligands.21 Indeed, in several in vivo applications, NPs with submonolayer coverage of ligands have recently proven to increase the overall targeting efficiency.43 High surface concentration of ligands on a NP can, for example, cause local receptor depletion in the cell membrane,44 as also observed here for NPs with the highest surface concentration of biotin (Figure 2c). Notably, the here observed difference in binding rate for 18 and 51 nm NPs correlates quantitatively with the results from several studies where the cellular uptake of targeted gold NPs was shown to increase 10 times or somewhat less in response to increased NP size from approximately 15 to 50 nm in diameter.2−4 This difference remained also in the absence of functional endocytic machinery.45 To clarify the influence of different mechanisms that can lead to size dependence in NP− cell interaction, it is clear from this work that further studies need to discriminate kinetic effects from those related to NP transport across the cell membrane. Here we tracked and analyzed not only bound NPs but also unbound single NPs diffusing near the lipid membrane. These measurements were made possible by waveguide light-scattering microscopy, using an ultraflat membrane-functionalized surface that could resolve scattering from NPs as a function of distance from the membrane. Considering the low scattering intensity and high diffusivity of NPs smaller than 100 nm, the verification of kBTscale interactions between such small NPs and a surface has proven to be challenging and has, to our knowledge, been reported previously only for NPs entrapped between closely positioned surfaces46 or modulated light fields.47 The waveguide-based setup employed here offers, in addition to high sensitivity and a homogeneous illumination profile, also the possibility to apply surface modifications compatible with glass surfaces, where cell-membrane mimicking supported lipid bilayers is an important example.29 Our observations thus highlight that detailed insights regarding NP−cell interactions are facilitated by microscopy implementations capable to resolve the motion and binding or distribution of single NPs,48−50 with a next natural step being similar studies of native cells. Thus, our findings are expected to impact the design of NPs with optimal cell targeting. In particular this is valid for applications where high binding rate is necessary, e.g., if binding only can proceed during a short time or the concentration of NPs for any reason must be kept low. Based on our model, three size-dependent regimes can be pictured. For NPs with a few ligands both very small,15 due to their high ligand density and rotation, and larger NPs, due to colloidal attractions, may bind readily, whereas this is not necessarily true for NPs of intermediate size. The transition from the behavior of intermediate to large size will in this context depend on the material or combination of materials employed; for the gold NPs examined in this study, this transition correlates with the increase in size from 18 to 51 nm in diameter. The van der Waals interaction will in particular be strong for NPs with metal cores, which indeed has been the main model system used for cellular uptake studies.51 However, these long-range, weak colloidal forces will to a different extent act on all kinds of 9979

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dynamic diameters and zeta-potentials for the differently sized NPs at different buffer conditions were measured by dynamic light scattering using a Malvern Zeta Sizer, NanoZS instrument (Supporting Information Figure 3 and Table 1). Titration of the Number of Biotin Ligands Per Nanoparticle. The density of biotin on the different NPs was determined by cumulative titrations with biotin (5-fluorescein), here abbreviated B5F. The working principle of B5F is similar to that of biotin (4fluorescein).54 In a solution with a known concentration of streptavidin, the remaining unreacted biotin binding sites, after addition of the sample with unknown biotin content, can be determined from a titration plot of emitted fluorescence as a function of B5F concentration (Supporting Information Figure 5). To avoid interference between the localized surface plasmon resonance absorption of the NPs and the fluorescence of B5F, the NPs themselves were excluded from the titrand as detailed in section 1 of the Supporting Information. Briefly, this was done either by filtration of the titrand (employed for NPs with a few biotin ligands) or by ligand exchange of the biotinylated PEG-shell from the NP surface (employed for NPs with many biotin ligands) before titration. Formation of Supported Lipid Membranes. Supported lipid bilayers (SLBs) were formed on silicon dioxide-coated QCM-D sensor crystals and waveguide chips via spontaneous adsorption and rupture of small unilamellar vesicles. These vesicles were prepared from 1palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) and from mixture of POPC and 1 mol % 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine-N-(biotinyl) (POPC/DOPE-biotin), respectively. The lipids were dissolved in chloroform and dried under nitrogen and vacuum to form a thin film in a round-bottom flask. Lipid films were rehydrated in TRIS buffer (10 mM pH 7.4, 100 mM NaCl, 1 mM EDTA) and extruded through two stacked polycarbonate membranes with pore size 50 nm. For QCM-D measurements, SLBs were formed from the POPC/DOPE-biotin vesicle solutions diluted 1:40 or 1:400 with POPC vesicle solution. The SLB formation is recognized in QCM-D by a biphasic change of frequency and dissipation signals due to initial vesicle loading followed by vesicle rupture55 (Supporting Information Figure 6). For waveguide measurements, SLBs were formed from POPC/DOPE-biotin vesicle solutions diluted 1:40 with POPC vesicle solution. The SLB formation on waveguide chips was separately verified by fluorescence recovery after photobleaching experiments (Supporting Information Figure 10). Nanoparticle Binding Experiments. The uptake of NPs diluted to 1.6 nM (18 nm NPs) and 0.1 nM (51 nm NPs) in TRIS buffer by streptavidin-modified SLBs was measured under continuous flow conditions (200 μL min−1) using a Q-Sense E4 instrument. In the limit of low NP loading, the measured change in frequency (Δf) is proportional to the mass of the adsorbed NPs,56 however due to the viscoelastic nature of the NPs, direct conversion of Δf/Δt to NP binding rate based on estimated NP mass can be ambiguous.57 As detailed in section 2 of the Supporting Information, the absolute binding rates were thus determined by relating the binding response (Δf/Δt) for different NPs to that measured for globally diffusionlimited binding of the same NPs at the same conditions. The latter was obtained by measuring the uptake of the differently sized and functionalized NPs to sensor surfaces modified to become positively charged,58 and the corresponding binding rate was estimated from the Smoluchowski−Levich approximation.59 The surface concentration of streptavidin receptors was estimated from the frequency shift measured in QCM-D due to streptavidin binding, assuming that 1 Hz frequency shift corresponds to 2.4 × 1010 receptors cm−2.60 Calculation of the Particle−Membrane Interaction Potential. The separation-dependent interaction potential between core−shell NPs and the lipid membrane-coated surfaces was obtained in accordance with the extended DLVO model, where the balance between the van der Waals force, the electrostatic double layer force, and the shorter-ranged repulsive hydration/steric forces determines the total interaction energy. The calculations are detailed in section 5 of the Supporting Information.

targeted colloids. Based on our study and making use of DLVO-theory and Hamaker constants for common NP materials, it can be easily estimated whether nonspecific interactions will have a significant impact on NP targeting. For example, our findings should influence the design of liposome delivery systems, since a similar attraction corresponding to Umin ∼ −2.5kBT, as observed for 51 nm core−shell gold-PEG NPs, is expected between a planar lipid membrane and a hollow lipid vesicle of ∼100 nm in diameter (detailed in section 5 of the Supporting Information; our experiments with vesicles are in progress), a size similar to or even smaller than typically employed when lipid-based NPs are used as drugcontaining vehicles.

CONCLUSIONS In conclusion, we have demonstrated that the specific avidity of NPs targeted to membrane receptors can be strongly dependent on weak, colloidal interactions between the lipid membranes and NPs. For example, attractive van der Waals forces give rise to a NP size-dependent, nonhomogeneous distribution of NPs near the membrane. In particular, due to their larger van der Waals interaction, the residence time in the vicinity of the interface is longer for larger than for smaller NPs. Accordingly, the probability of bond formation between ligands at the NP periphery and receptors at the lipid membrane increases with NP size. The specific avidity of membranetargeted NPs is therefore size dependent also without the engagement of multivalent-bond formation. Our experiments and analysis show that already the weak energy minimum (a few kBT deep) present at close separation between gold NPs 50 nm in diameter and a lipid membrane increases their avidity by 1 order of magnitude compared to gold NPs 20 nm in diameter with a similar, low ligand coverage. The van der Waals attraction is relevant for NPs that are highly polarizable, including metal NPs and liposomes. These findings are therefore relevant both for the design of NPs with optimal cell targeting as well as for the understanding of “targeted” processes in a broader biological context. For example, studies of binding and cellular uptake of exosomes and viruses might require a stronger emphasis on long-range nonspecific, colloidal interactions to accurately predict binding avidity and therefore infectivity. Another example is the in vivo function of NPs surrounded by the protein corona. Thus, our findings provide both an additional tool for design of targeted NP systems and quantitative insight into how specific interactions in biological systems can be strongly modulated by nonspecific interaction. EXPERIMENTAL SECTION Gold Nanoparticle Synthesis and Characterization. Gold NPs with a diameter of 18 nm were prepared by citrate reduction of chloroauric acid (HAuCl4) with addition of tannic acid as an extra reductive agent.52 Larger gold NPs, 51 nm in diameter, were prepared by seed-mediated synthesis.53 NP-size distributions were measured with a Zeiss Ultra 55 FEG scanning electron microscope (Supporting Information Figure 1). Surface modification of NPs was done from mixtures of aqueous solutions of α-hydroxy-ω-mercapto-PEG, αcarboxy-ω-mercapto-PEG, and α-biotinyl-ω-mercapto-PEG (MW 5 kDa), where the fraction of α-carboxy-ω-mercapto-PEG was kept constant (50%), and the fractions of α-biotinyl-ω-mercapto-PEG and α-hydroxy-ω-mercapto-PEG were varied. Particles were purified from excess ω-mercapto-PEG by five sequential filtration steps using 300 kDa cut-off centrifuge filters. The grafting density of PEG was measured by thermogravimetric analysis employing a Mettler-Toledo TGA/DSC 1 instrument (Supporting Information Figure 2). Hydro9980

DOI: 10.1021/acsnano.6b04160 ACS Nano 2016, 10, 9974−9982

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ASSOCIATED CONTENT S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.6b04160. Detailed descriptions of the experimental procedures, particle characterization and mathematical derivations (PDF)

AUTHOR INFORMATION Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS The research leading to these results received funding from the Swedish Research Council under grants 2013-7421 (A.L.) and 2014-5557 (A.L., V.P.Z., F.H.), the Swedish Foundation for Strategic Research under grant no. RMA11-0104 (A.L., F.H.), the European Research Council under grant agreement no. 310034 (R.Z., E.R.), and the EMRP project HLT04 “BioSurf”, jointly funded by the EMRP-participating countries within EURAMET and the European Union under grant agreement no. 217257 (B.A.). REFERENCES (1) Mammen, M.; Choi, S. K.; Whitesides, G. M. Polyvalent Interactions in Biological Systems: Implications for Design and Use of Multivalent Ligands and Inhibitors. Angew. Chem., Int. Ed. 1998, 37, 2754−2794. (2) Chithrani, B. D.; Ghazani, A. A.; Chan, W. C. W. Determining the Size and Shape Dependence of Gold Nanoparticle Uptake into Mammalian Cells. Nano Lett. 2006, 6, 662−668. (3) Jiang, W.; Kim, B. Y. S.; Rutka, J. T.; Chan, W. C. W. Nanoparticle-Mediated Cellular Response Is Size-Dependent. Nat. Nanotechnol. 2008, 3, 145−150. (4) Sykes, E. A.; Chen, J.; Zheng, G.; Chan, W. C. W. Investigating the Impact of Nanoparticle Size on Active and Passive Tumor Targeting Efficiency. ACS Nano 2014, 8, 5696−5706. (5) Liu, X. S.; Huang, N.; Li, H.; Jin, Q.; Ji, J. Surface and Size Effects on Cell Interaction of Gold Nanoparticles with Both Phagocytic and Nonphagocytic Cells. Langmuir 2013, 29, 9138−9148. (6) Arnida; Malugin, A.; Ghandehari, H. Cellular Uptake and Toxicity of Gold Nanoparticles in Prostate Cancer Cells: A Comparative Study of Rods and Spheres. J. Appl. Toxicol. 2010, 30, 212−217. (7) Rejman, J.; Oberle, V.; Zuhorn, I. S.; Hoekstra, D. SizeDependent Internalization of Particles Via the Pathways of Clathrinand Caveolae-Mediated Endocytosis. Biochem. J. 2004, 377, 159−169. (8) Mironava, T.; Hadjiargyrou, M.; Simon, M.; Jurukovski, V.; Rafailovich, M. H. Gold Nanoparticles Cellular Toxicity and Recovery: Effect of Size, Concentration and Exposure Time. Nanotoxicology 2010, 4, 120−137. (9) Zhang, S. L.; Li, J.; Lykotrafitis, G.; Bao, G.; Suresh, S. SizeDependent Endocytosis of Nanoparticles. Adv. Mater. 2009, 21, 419− 424. (10) Gao, H. J.; Shi, W. D.; Freund, L. B. Mechanics of ReceptorMediated Endocytosis. Proc. Natl. Acad. Sci. U. S. A. 2005, 102, 9469− 9474. (11) Liu, J.; Weller, G. E. R.; Zern, B.; Ayyaswamy, P. S.; Eckmann, D. M.; Muzykantov, V. R.; Radhakrishnan, R. Computational Model for Nanocarrier Binding to Endothelium Validated Using in Vivo, in Vitro, and Atomic Force Microscopy Experiments. Proc. Natl. Acad. Sci. U. S. A. 2010, 107, 16530−16535. 9981

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