Strong dependence of the nano-bio interactions on core morphology and layer composition of ultrasmall nanostructures

Abstract

The interactions between nanoparticles (NPs) and proteins, cells, and tissues, broadly known as nano-bio interactions, depend on the NP size and shape and on the characteristics of the NP coating layer, such as density, thickness, and chemical makeup. The dependence of nano-membrane interactions on the design parameters of ultrasmall nanostructures is studied by computer simulations. Considered here are spheres, plates, rings, rods, tubes, and helices made up of either bare magnetite or passivated gold, interacting with charged or zwitterionic membranes. The analysis reveals a strong dependence on shape, size, and layer composition of various quantities that characterize the nano-bio behavior, including binding modes and affinities. This sensitivity can be exploited to design nanostructures that bind preferentially to membranes or that stabilize or disrupt membrane structural integrity. The method used here is general and not limited to the ultrasmall regime, so it can be adopted to study other nano-bio interactions systematically. The implications for the distribution of NPs in cells and tissues (biodistribution) and for passive and active transmembrane transport are discussed, both important processes in biomedicine.

I. INTRODUCTION

Understanding the behavior of nanoparticles (NPs) in biofluids and their interactions with proteins, cells, and tissues, broadly known as nano-bio interactions, is a prerequisite for the rational design of NPs in biomedical applications.^1,2 Core material and type, e.g., crystalline vs amorphous; shape, e.g., nanospheres (NSp’s) vs nanoplates (NPl’s); size, i.e., classical (∼10–60 nm across or larger) vs ultrasmall (<3 nm in at least one dimension); and surface characteristics, including chemical composition, coverage density, and layer thickness, can all be controlled, in varying degrees, during manufacturing and strongly determine their interactions with the environment and their potential utility. Variations in the core size affect a range of properties, including colloidal stability³ and excretion route;⁴ modest changes in surface chemistry can greatly influence protein-binding kinetics and affinities;⁵ changes in shape affect tumor accumulation,^6,7 biodistribution,⁸ and immune response;^8,9 and the core composition¹⁰ determines the chemicals that can be attached to the surface, as well as the intrinsic thermal, optical, magnetic, and electronic properties that make them valuable platforms for imaging, thermal ablation of tumors, and other industrial and technological applications (cf. Sec. IV). Establishing the optimal combination of design parameters for specific purposes is a major goal in bioengineering but a challenge due to numerous interrelated effects still poorly understood. Efforts are underway to control undesirable outcomes, such as retention in tissues, which may result in incomplete clearance from the body and lead to acute or chronic toxicity; or unintended organ uptake, leading to inadequate biodistribution in tissues and organs and inefficient accumulation in target cells.

The ability to control the behavior of NPs in biological media, such as membrane penetration, embedding, and transport is of interest in nanomedicine, from imaging to drug delivery. To this end, several experimental strategies have been devised, but available methods are usually inefficient, may damage the membrane integrity, or result in cytotoxicity.¹¹ Progress is being made to promote the entry of NPs into cells, e.g., by attaching amphiphilic molecules to ultrasmall AuNSp’s (a technique akin to protein transduction domains, or PTD),¹¹ but rational design remains a challenge. Likewise, the ability to control membrane selectivity is limited. This is an important consideration in the ultrasmall regime because NPs may bind directly to pristine areas of the membrane; by contrast, larger NPs, with their cargo of adsorbed proteins (soft and hard coronas), are likely to interact with patches of membranes containing bound or embedded proteins, so selectivity may be less important.

Therefore, two specific questions are addressed here, namely, whether the binding of NPs to membranes and the impact of NPs on membrane structural stability can be controlled through the particle design. The first one has implications for biodistribution; the second, for passive or active transport, among other processes.

The focus here is on ultrasmall nanostructures because they have unique features that make them potentially more attractive than their larger counterparts, both in their physicochemical behavior^3,12 and in the biological response to exposure.^13,14 Ultrasmall NPs are protein mimics,^15,16 with sizes comparable to those of an average biologically active protein (∼50 kDa), and interact with biomolecules as proteins do, through multiple binding modes, affinities, and kinetics. Lacking a well-defined protein corona,¹⁷ the nano-bio interactions of ultrasmall NPs can, in principle, be more subtly modulated: they can interact with a biological target directly, not mediated by layers of adsorbed proteins, the structure and dynamic behaviors of which are difficult to predict or control. Therefore, the binding specificity and selectivity of ultrasmall NPs can be fine-tuned though proper design. Having the capability to probe in silico, the effects of size, shape, surface chemistry, and other design variables can help achieve these goals. Computational studies of nano-bio interactions have traditionally been limited to nanospheres and to specific applications, although progress is being made toward the systematic design of NPs with dedicated software.¹⁸ Here, a method is proposed that combines a self-adaptive multiscaling algorithm (msSCP) for efficient simulations of crowded aqueous solutions¹⁹ with a practical yet robust modeling protocol for nanostructures of arbitrary designs. The method is applied to spheres, plates, rings, rods, tubes, and helices of different sizes made up of bare magnetite or gold passivated with l-glutathione (GSH) or p-mercaptobenzoic acid (MBA). The sensitivity of the nano-bio interactions with the design parameters is analyzed, which provides guidelines for reverse engineering nanostructures that interact with membranes in specific ways.

II. METHODS

Experimental studies of nano-bio interactions typically involve many NPs and proteins in states of moderate-to-high local condensation. These are the conditions that need to be replicated in a simulation to provide a molecular interpretation or make hard predictions. Because NPs can be highly charged, electrostatic forces can still operate far from their surfaces, especially in anisotropic or suboptimal conditions of hydration (e.g., during aggregation or clustering, or in proximity to membranes). These long-range effects are largely insensitive to the molecular details, so they can be modeled with low-resolution structures. By contrast, the forces that determine the nano-bio interactions depend more critically on the atomic details at the interfaces, and modest changes in surface chemistry can have profound effects on NP-protein interactions.⁵ These opposing, yet coexisting, demands motivated the development of a self-adaptive multiscaling algorithm that permits on-the-fly transitioning between molecular resolutions, speeding up computation while preserving the short- and long-range structural requirements.¹⁹ Special care is given to the treatment of the aqueous solution, as interfacial water is critical in nano-bio interactions.²⁰ In this method (msSCP), each molecule in a system of M molecules is assigned a set of M − 1 scaling factors λ, the values of which depend on the spatial configuration of the system. Each λ moves back and forth continuously between a minimum λ₁ (which defines the highest resolution, typically atomistic) and a maximum λ_P (lowest resolution), taking any of the intervening values through a self-guided process. The coarsening algorithm is reversible, prioritizes structural details at the protein surfaces over the protein cores, and preserves important features across scales, including mass and charge distributions, overall shape, and hydrodynamic radii. To study nano-bio interactions, the method assigns atomic resolution (λ₁) and single-particle resolution (λ_P) to all the components of the system except NPs, which are treated at fixed resolutions, as described below.

The NP core is represented by a flattened elliptical torus [Fig. 1(a)] from which different morphologies can be derived [Fig. 1(b)]. The torus surface is given by r = r_xi + r_yj + r_zk with r_x = x(1+δ₁us₁B/A), r_y = s₂(δ₁B/A + us₁), and r_z = δ₂s₃b/a, where s₁ = [A² + (B²/A² − 1)x²]^−1/2, s₂ = (A² − x²)^1/2, and s₃ = (a² − u²)^1/2, and δ₁ = ±1 and δ₂ = ±1 yield the four symmetrical domes, with parametric variables x = A cos(p) and u = a cos(q) defined in $p\in \left[0,\pi \right]$ and $q\in \left[0,\pi \right]$. The ellipsoidal line running along the axis of the tube (main axis) is defined by the points $x\mathit{î}+y\mathit{ĵ}$ such that x²/A² + y²/B² = 1, whereas the ellipsoidal line resulting from the intersection of the tube with a plane perpendicular to the main axis is defined by the points $u\widehat{\mathit{\rho }}+v\widehat{\mathbf{k}}$ such that u²/a² + v²/b² = 1; the axis ρ is on the (r_x, r_y)-plane but does not pass through the origin unless A = B. The core atoms occupy the volume enclosed by this surface, which is determined analytically from the normal unit vector at each point r. The cores are carved out of homogeneous crystals in the direction of choice, with parameters from Ref. 21. Considered here are spheres (NSp’s), plates (NPl’s), rings (NRi’s), rods (NRo’s), tubes (NTu’s), and helices (NHe’s), obtained with suitable combinations of A, B, a, and b; two additional parameters are needed for NHe’s [cf. Fig. 1(b)].

FIG. 1.

(a) Parameters of a flattened ellipsoidal torus that defines the outer surface of the nanostructure cores; continuous changes in the core morphology can be used as a practical approach for high-throughput screening of NPs. (b) Nanostructure core shapes used in this study: a nanosphere (NSp) of diameter d is obtained with A = ε, B = A, a = d/2, and b = a, where ε is a small positive number (in practice, ε = 10⁻³ length units); a nanoplate (NPl) of diameter d and thickness h, with A = B = ε, a = d/2 − A, and b = h/2; a nanorod (NRo) of length L and cross section d₁ × d₂, with A = L/2 − d₁/2, B = ε, a = d₁/2 − B, and b = d₂/2; a nanoring (NRi) of planar dimension L₁ × L₂ and tube cross sectisson d₁ × d₂, with A = L₁/2 − d₁/2, B = L₂/2−d₁/2, a = d₁/2, and b = d₂/2; a nanotube (NTu) of length L, inner diameter d, and wall thickness w, with A = B = d/2 + w/2, a = w/2, and b = L/2 (if A, B < 0, then A = B = ε by convention); a nanohelix (NHe) is formed from a circular ring (A = B) by adding to r_z a linear term in the form ±τl/2π, where the length of the arc along the main axis is l = Aθ, θ is the angle between axes ρ and r_x in the interval [0, 2πn], n is the number of turns, τ is the pitch, and the ± signs define the orientation of the helix. The dimensions (in nanometers) used in this study are (s and l refer to the smaller and larger structure; see Sec. IV for a discussion on experimental feasibility of high aspect ratio ultrasmall nanostructures): NRi: L₁ = L₂ = 2 (s) and 3 (l), d₁ = d₂ = 0.5; NSp: d = 2 (s) and 3 (l); NPl: d = 2 (s) and 3 (l), h = 0.5; NRo: L = 4 (s) and 6 (l), d₁ = d₂ = 1; NTu: L = 4 (s) and 6 (l), d = 0.5, and w = 0.5; and NHe: d = 2.5, w = h = 1, τ = 1.5, 2-turn (s) and 3-turn (l), right-handed (the shorter and longer 3-turn NHes are defined by τ = 1.3 and τ = 1.7). The charges in the Au atoms for the AuNP’s are zero; in magnetite, the average charge in O is −2, and those in the Fe atoms are +2.5 (octahedrally coordinated sites) and +3 (tetrahedral sites) units of charge. (c) left panel: atomistic model of a 2.5-nm diameter AuNSp coated with L-glutathione; middle: molecular surface of the atomistic model; right: molecular surface of the simplified model used in this study (see Sec. II); the model accounts for the space needed to accommodate the layer, so no coating is added in constrained space.

The NPs considered here are made up of bare magnetite or gold passivated with l-glutathione (GSH) or p-mercaptobenzoic acid (MBA). Although bare magnetite NPs are prone to oxidation and aggregation, they have been the focus of several experimental studies in biology and environmental science^22–24 and are thus considered first. In the absence of salts, this system enables the inherent effects of size and shape to be probed without the statistical complications introduced by the random distributions of surface charges or counterion atmosphere. Moreover, because of the large average charges on O and Fe, these NPs have features shared by NPs covered with zwitterionic or charged molecules, provided that counterions in the latter are viewed as part of their structures. Uncoated magnetite NPs can thus be used as model systems in simulations to probe general nano-bio behaviors prior to more demanding studies, as illustrated here for GSH- and MBA-coated AuNP’s. The behavior of ultrasmall gold NPs has been addressed in several previous studies.^3,5,25 In particular, GSH-AuNSp’s have certain advantages for in vivo applications, such as better renal clearance and tumor accumulation,^14,26 whereas MBA-AuNSp’s have been recently used to allosterically inhibit the activity of α-thrombin,²⁷ an enzyme that plays a central role in the blood coagulation cascade. A systematic study of the behavior of these nanostructures is then of interest as well.

The coating layers can be built one molecule at a time using simulated-annealing Monte Carlo (MC) sampling,³ resulting in equilibrated, structurally relaxed layers of atomic resolution. The NPs can thus be treated on equal footing as proteins in the msSCP method. An alternate, more practical approach suitable for systematic studies is used here to model different layer compositions, including hypothetical ones: the layer outer boundary is defined by a surface parallel to that of the core and separated from it by a distance δ (the layer thickness; δ has been estimated for both GSH and MBA from molecular dynamics (MD) simulations under ambient conditions^5,28). This surface is represented in the forcefield by a weak Lennard-Jones potential added to the core atoms with radii equal to the vdW radii plus δ. Functional groups are modeled as spherical particles with point charges q⁺ and q⁻ and radii σ⁺ and σ⁻ randomly distributed on the layer surface with coverage densities s⁺ and s⁻. Different coatings can thus be modeled with suitable combinations of q^±, σ ^±, s^±, and δ [cf. Fig. 1(c)]

Four single-phospholipid bilayers are considered: 1-palmitoyl-2-oleoyl-phosphatidic acid (POPA), -phosphatidylcholine (POPC), -phosphatidylglycerol (POPG), and -phosphatidylethanolamine (POPE). The initial packings of lipids were obtained from previous simulations,²⁹ replicated into square slabs with side lengths of 20 nm, immersed in a neutral solution of TIP3P water, and subjected to 10-ns MD simulations at 25 °C and 1 atm, using the CHARMM program³⁰ (all-atom force field; version c42b2) with cubic periodic boundary conditions and particle-mesh Ewald summations. Average membrane thickness and lipid packing agreed with previous reports.³¹ Snapshots at the end of the simulations were used in all the MC runs; due to the large number of lipids per layer (>400), these configurations are reasonable statistical ensembles for single-lipid membranes.

For each NP/membrane system, 50 independent temperature-annealing MC simulations were performed with the msSCP method and the CHARMM forcefield; the temperature was lowered in a 12-step logarithmic schedule, from 10³ °C to 25 °C, where conformations were collected and merged into a single ensemble for analysis. For each temperature, 2 × 10⁵ rigid-body trial moves of the NPs (one per simulation) were performed; rotations were not restricted and translations were limited to <3 nm; all the degrees of freedom were sampled with homogeneous a priori probabilities.

III. RESULTS

A. Magnetite nanostructures

The use of superparamagnetic iron oxide NPs is well established in molecular and cellular imaging.²⁴ They can be detected in living organisms at very low concentrations, providing a convenient way to track cell migration and trafficking. This makes them useful to study cancer progression, the dynamics of immune cells, and other fundamental processes relevant for diagnostics.²⁴ However, the ability to control biodistribution, tissue penetration, and subcellular localization is still problematic. These challenges motivated the analysis presented in this section.

The sensitivity of the nano-membrane interactions with the NP design is illustrated in Figs. 2–5, which show the binding modes, membrane penetration, and relative binding energies for a selected set (cf. complete data in the supplementary material). The binding modes (Fig. 2) are given in terms of the normalized probability distribution ρ of the engagement angle ϕ formed by the axes r_z of the torus and z normal to the membrane surface. This is the simplest characterization that might be accessed experimentally, e.g., by TEM under cryogenic conditions or through optical imaging, such as tip-enhanced Raman spectroscopy³² or related techniques.³³ The behavior of the larger NPl is qualitatively similar in the presence of the anionic and zwitterionic lipids, with a tendency to adopt a planar configuration (cf. Fig. 3); cationic lipids are not considered here, but they are expected to display distinct behaviors as well. By contrast, the binding modes of the smaller NPl’s are shifted toward a more tilted, even perpendicular configuration, depending on the membrane. In the presence of anionic lipids, the smaller NRi’s and NPl’s show similar behavior, but there is a sharp contrast in the modes of binding of the larger structures. When compared to the NPl, there is an increased tendency for the NRi to engage the zwitterionic membrane in an angle or in a near-perpendicular mode. The charged membranes select mainly tilted configurations of the smaller NRo but planar configurations of the larger NRo; neutral membranes select mainly planar configurations regardless of size. The fact that the larger NRo’s tend to lay flat, regardless of the membrane type, is not a direct consequence of their larger surface area (hence, a greater number of stabilizing electrostatic interactions) relative to the smaller NRo. The opposite behavior is indeed observed in NTu’s; for both types of membranes, the binding modes of the larger NTu are shifted toward a more perpendicular configuration when compared to the smaller NTu (Fig. 3). These perpendicular modes are stabilized by several favorable interactions along the NTu rim, which are not fully satisfied in the NRo. The trade-off of number and strength of favorable NP-lipid interactions determines the binding modes and their populations. The sensitivity observed in the ultrasmall regime is due to the rapid changes in the match/mismatch of favorable interactions as the size/shape of the nanostructures changes. NHe’s illustrate this point: for both types of membranes, the smaller structure tends to adopt a more perpendicular configuration relative to the larger one, which favors a planar mode. The smaller NHe’s are stabilized by many interactions along a sizable stretch of a single turn; the added turn in the larger NHe shifts the balance, as an increased number of favorable interactions can now develop along the shorter section in multiple turns. This implies that keeping the number of turns but changing the interturn distances (helix pitch) may lead to a mismatch of interactions that destabilizes the planar in favor of the perpendicular configuration. This is indeed observed for the longer NHe (Fig. 2, dashed line). It can be inferred as a corollary that changes in the density of charged groups on the surface of coated NPs could mimic these match/mismatch effects as well.

FIG. 2.

Characterization of the binding modes of nanostructures interacting with anionic (upper row) and zwitterionic (lower) phospholipid bilayers (only a representative set is shown; cf. supplementary material for the complete set); ρ(ϕ) is the normalized ($\int \rho d\varphi =1$) probability distribution and ϕ is the angle between the r_z axis of the torus [cf. Fig. 1(a)] and the axis z perpendicular to the membrane plane (inset); the scale of ρ is slightly different in each panel, hence not directly comparable (fully normalized sets in the supplementary material). A thin/thick line corresponds to the smaller/larger nanostructure of the two types in each panel; the distributions of the shorter/longer NHe are shown in dotted/dashed lines; statistical errors are negligible. Likewise, for GSH- (solid line) and MBA- (dashed) AuNP’s, the dimensions of the structures are specified in Fig. 1(b).

FIG. 3.

Representative binding-mode configurations of the Fe₃O₄ nanostructures (drawn to scale for comparison). Each structure is a representative member of a distinct conformational cluster of the ensemble at 25 °C. For the large NSp, at least two distinct submodes can be identified (1) and (2) which may have different effects in the perturbation or stabilization of the membrane.

FIG. 4.

Membrane penetration for a selected set of Fe₃O₄ nanostructures interacting with the four lipid bilayers considered in this study. N(z) is the number of atoms along a line normal to the membrane, for the NPs (solid; thick lines correspond to the larger structures), upper lipid layer (dashed), and atom P in the phosphate groups for reference (dotted; shifted downward for clarity); z = 0 corresponds to the average position of P in the initial membrane structure prior to the MD simulations; the three different N’s are scaled independently to fit in the same panel. The onset of the NP distributions determine the deepest penetration into the membrane, which is divided in the four regions indicated: high membrane-penetration power (black; at least 2 Å pass the phosphate group and interact with the glycerol backbone); moderate (dark gray); low (light gray); and least disruptive (white). A summary for all the Fe₃O₄ and GSH-coated Au NPs is show in the pixelated panel at the bottom; light/bold fonts in the NP name correspond to the smaller/larger structure of each type.

FIG. 5.

Relative NP-membrane binding energies for Fe₃O₄-NPs (representative sets). (a) ΔΔE_np→m (all the membranes against a single NP); (b) ΔΔE_m→np (all the NPs against a single membrane). A summary is shown in the pixelated panel (c) for Fe₃O₄ and GSH-coated Au NPs; the highest binding energies are shown in black, the second highest in dark gray, and the third in light gray; light/bold NP names correspond to the smaller/larger nanostructure. Statistical errors (not shown) are ∼2–5 kcal/mol for the zwitterionic membranes and ∼5–10 kcal/mol for the anionic membranes.

The potential to disrupt or stabilize a membrane can be estimated from the distribution N(z) of the core atoms along a line normal to the membrane surface. This quantity, or N(x, y), can be related to images obtained from cryo-EM or, ideally, as 3D reconstructions by electron tomography.³⁴ Figure 4 shows the distribution of atoms in the membrane (dashed), with the distribution of the phosphorus atom indicated for reference (dotted), and N(z) for NPls (solid). The smaller structure, adopting a more perpendicular configuration, tends to reach deeper into the membrane, past the phosphate and transiently interacting with the glycerol backbone. The larger structure, with a more planar configuration, barely touches the phosphate group. The widths of the distributions reflect these preferred modes. The analysis shows that a smaller NP of a given type not necessarily has a more penetrating power than its larger design; examples are NRi’s and NTu’s in the presence of anionic lipids. The degree of penetration depends on several factors, including the binding mode, the local curvature of the NP in contact with the membrane, and the size and chemical nature of the lipid head groups, which affect the local topography of the membrane, allowing certain areas to develop local crevices that can either accommodate and stabilize a NP or prevent deeper access. Penetrating power in the early stages of binding (the focus of this study) is thus a NP/membrane combined property (cf. Sec. IV).

The perturbations induced by a nanostructure need not be a frequent occurrence; a rare event during the earlier stages of binding may be enough to locally destabilize the membrane and initiate a cascade of more complex processes, such as embedding, membrane bending, or passive diffusion. The binding modes discussed here should be considered as the starting configurations in any MD simulations aimed to explore ensuing relaxation processes. Based on this notion, the penetrating power of the NPs is summarized in Fig. 4 (bottom panel), where the membrane/water interface is divided schematically into four regions. Least disruptive is the nanosphere; although the smaller nanoplate has the most penetrating potential, increasing its size turns it into one of the least disruptive structures; the larger NRi’s, NRo’s, and NTu’s all tend to have similar or higher penetration than their smaller counterparts.

Closer inspection of the NSp suggests that a more detailed characterization of binding modes may be necessary. The smaller nanosphere adopts random orientations, but the larger one displays two distinct submodes: in one [(1) in Fig. 3], a crystal plane is parallel to the surface, so the particle core gets closer to the membrane; in the other (2), the particle is stabilized by few head groups that interact with O and Fe atoms at a crystal corner, keeping the core further from the surface. These modes may have different effects on the membrane or show unique spectroscopic patterns, which could be used to probe the modes experimentally.

Figure 5 shows the relative binding energies calculated from the ensembles. The reason for an analysis based on relative rather than absolute binding energies is conceptual rather than practical (cf. Sec. IV). The binding energy ΔΔE_np→m of a NP for the membranes is calculated as ΔE = E_b − E_∞, where E_b = Z⁻¹∑_i E_i exp(−E_i/kT) ≈ ∑_n E_n/N_b and n runs over the N_b configurations; E_∞ is the energy in the fully dissociated state. If the highest binding energy of the NP among the four membranes is ΔE_max, then ΔΔE_np→m = ΔE − ΔE_max. Figure 5(a) illustrates the behavior of NSp’s and NRo’s when exposed to the four membranes, with the former selecting POPG and the latter POPA. The summary shown in Fig. 5(c) indicates that, when exposed simultaneously to all the membranes, a magnetite NP preferentially selects anionic lipids, mostly POPA, although increasing the size of a nanosphere or a nanohelix makes them more attractive to POPG. Statistics of close contacts show that this propensity is related to the easier access of Fe to the phosphate groups and to more efficient interactions of O and Fe with the hydroxy and glycerol head groups rather than to the membrane charge (the NPs are strictly neutral by design). This contrasts with the zwitterionic membranes: POPC is not selected by any of the particles because the choline groups interact poorly with magnetite and are bulky, which hinders access to the phosphates. To target POPC, a more heterogeneous and less dense distribution of surface charges is necessary, as shown below for GSH- and MBA-AuNP’s. Finally, all NPs select POPE over POPC because the ethanolamine head groups interact directly with the core atoms and allow deeper membrane penetration.

The relative binding energies ΔΔE_m→np of a membrane for the NPs are calculated analogously. This quantity indicates which of the several NPs in a mixed solution would be selected by a given membrane. Figure 5(b) illustrates the behavior of POPG and POPE. The summary in Fig. 5(c) indicates that, when exposed simultaneously to all the structures, NHes are preferred over any other morphologies, regardless of lipid type; if these structures are removed, others will follow, with NRo’s and NPl’s preferred next, depending on the membrane. Among the weakest binders are NSp’s. Although the larger structure of a type tends to bind more strongly, this is not always the case because the structural details of the binding modes and their relative populations play a major role in the overall affinity of a membrane. Beyond the ultrasmall regime, however, as the binding modes of a given type become less differentiated, the binding energies are likely to be more correlated with size.

Estimates of the overall k_on and k_off rates of the NP-membrane binding mechanism, and of the associated residence times of the NPs on the membrane surface, are important characterizations of all nano-bio interactions,⁵ with implications for the design of nanopharmaceuticals. However, accurate calculation of the association/dissociation energy barriers would require extensive biased simulations. Umbrella sampling has been used to estimate the potentials of mean force for NP-NP²⁸ and NP-protein⁵ associations and can be used to calculate the kinetic barriers for NP-membrane interactions along a reaction coordinate normal to the membrane plane. Although the multiscale method used here is well suited for such demanding computations, the study of kinetics is beyond the scope of the present study.

B. Gold nanostructures

The analysis here is the same as before, so only the most salient results are discussed (cf. complete sets in the supplementary material); these are summarized in Figs. 2, 4, and 5; nanohelices were not considered. In the presence of an anionic membrane, the binding modes of the smaller NPl, regardless of coating, are qualitatively similar to those of the smaller Fe₃O₄-NPl, showing in all cases a tendency to adopt a more perpendicular configuration (Fig. 2); the larger structures, on the other hand, show variations in distributions that contrast with those of the larger Fe₃O₄-NPl. Almost the opposite trend is seen in the presence of zwitterionic membranes; the binding modes of the small NPl show important qualitative differences among the three NP types, but the behaviors of the larger structures are similar. Other contrasting behaviors involve NRos in the presence of anionic membranes; the modes of MBA-AuNRo are similar to those of Fe₃O₄-NRo but the size dependence is reversed in GSH-AuNRo. Least sensitive to size, coating, and lipid type are nanotubes, although their distributions differ from those of magnetite.

For the coated NPs, perturbations of a membrane in the early stages of binding are caused by the surface charges and the bound counterions rather than by the metallic core. When compared to Fe₃O₄-NP’s, both GSH- and MBA-AuNP’s show less variability in membrane penetration, although both tend to reach the phosphate groups regardless of shape or size. The exception is the larger GSH-AuNSp on POPA and POPC (Fig. 4 and supplementary material).

The binding energies show important differences with respect to magnetite. Zwitterionic membranes are now preferred by several GSH-coated structures [Fig. 5(c)], including POPC, which can now be targeted by small nanorods, and have become second in preference by several designs. Likewise, POPE can now be selected preferentially by larger plates or smaller rings. Also noteworthy is that POPA is no longer overwhelmingly preferred, ranking second to POPG. Unique features can also be seen for MBA-AuNP’s (cf. supplementary material). Another apparent difference is the preference of membranes for GSH-AuNP’s [Fig. 5(c)]; anionic membranes tend to bind the larger NSp, while zwitterionic membranes select the larger NTu; like for Fe₃O₄-NPs, the larger structure of a type would be preferred by a membrane if both were present in the solution.

IV. DISCUSSION

A clearer understanding of the molecular mechanisms of nano-bio interactions may pave the way for the rational design of nanostructures as viable agents in diagnostics and therapeutics. Having the capability to probe in silico the effects of a NP design on specific nano-bio behaviors may help this process along. The systematic study of nano-membrane interactions reported here illustrates this point, as the results may have implications for biodistribution, membrane fission or fusion, or transmembrane transport, among others processes. All the nanostructures considered here belong to the ultrasmall size domain. Fine-tune manufacturing and shape characterization of such NPs are still technically challenging,³⁵ so some of the nanostructures may be only of theoretical interest at present. However, the NP morphology need not be limited to free-standing all-crystal cores, especially if the NP is hollow (NHe) or has a high aspect ratio (NRo) or both (NRi). Indeed, rapid advances in chemical synthesis and nanofabrication^36,37 may eventually produce stable complex shapes through chemical linkage of stable simpler building blocks, whereas carbon nanotubes³⁸ or other molecular nanostructures³⁹ in the nanometer and subnanometer length scales may conceivably be used to guide growth or help stabilization. The results in this paper show that efforts in these directions are at any rate justified. The importance of controlling the NP size and shape is well known in other emerging technologies, including selective optical filters and bio-sensors, where the optical properties of gold NPs depend strongly on their shape anisotropy;⁴⁰ data storage, where the limited efficiency of magnetic NPs at room temperature can be enhanced with anisotropic shapes;⁴¹ and in catalysis, where the shape of the catalyst particles plays often an important role.⁴² Advances are also being made in manufacturing polyelemental cores,¹⁰ which may help control the plasmonic and catalytic properties of NPs, and may potentially be used to create heterogeneous coating layers. In vivo studies have highlighted the importance of the NP morphology in biomedicine;^6–8,43 and the results reported here show that the control of shape or size in the ultrasmall regime is critical to manipulate the nano-bio behavior.

Unlike traditional NPs, which enter the cell through several endocytosis mechanisms, smaller NPs have the potential to do so through passive diffusion (unless they aggregate, in which case active transport is necessary). It was shown here that the ability to stabilize or destabilize the membrane can be controlled through the NP design. It can be argued, although not demonstrated in this study, that perturbation of the membrane structure in the early stages of binding can facilitate embedding or diffusion, e.g., by lowering the kinetic barrier of ensuing dynamic processes, whereas membrane stabilization may hinder it. Such processes involve a hierarchy of relaxation times, and only the first stage has been discussed here. This is still an important achievement because these modes are optimal starting points for any subsequent dynamic studies, which would be difficult to conduct otherwise.

The ripples observed in the binding-mode distributions of some of the nanostructures in Fig. 2 suggest varying degrees of nonspecific NP/membrane binding. Understanding the stabilizing forces behind a particular peak may suggest strategies to select specifically the associated mode over all the other modes through proper design. The selected mode may have unique properties, including membrane-affinity and membrane-disruptive potentials, that may be more desirable than other modes in particular applications.

Generally, nanospheres are shown to be poor disruptors of the membrane structure, so more complex structures are needed. Ultrasmall NPs can also increase the permeability of membranes to allow proteins and other biomolecules to enter the cell. Techniques such as electroporation are typically used to achieve this goal, generally in vitro but also for therapeutic purposes;⁴⁴ this study suggests that the process may be facilitated (or hampered) by properly designed ultrasmall NPs.

Plasma membranes in living cells are typically composed of a mixture of lipids, so a single-phospholipid membrane is a simplified environment; in addition, accumulating evidence suggests a mosaic-like structure,^45,46 which may also include local curvatures in the nanometer length-scale.^47,48 This structural complexity only broadens the range of possibilities in terms of chemical groups and topographic features that determine the NP binding modes. Synthetic layers or artificial cell membranes⁴⁹ add to the variability of scenarios in which the computational method employed here can be used to help design NPs and NP/membrane systems. Cell membranes also contain bound and integral proteins that compete with the lipid bilayers for binding to the NPs. The multiscale method does not discriminate between a lipid molecule and a protein and is thus a practical approach to the study of these more realistic systems.

The computational method used here combines a self-adaptive multiscaling algorithm¹⁹ (msSCP) with a prescription to model nanostructures with arbitrary design parameters. The development was motivated by the need to explain the behavior of NPs in the blood serum, as measured by continuous photon-correlation spectroscopy;⁵⁰ to understand the aggregative behavior of NPs in biofluids, as measured with analytical ultracentrifugation;^3,28 and to explain changes in the NP-protein binding kinetics upon modest changes in surface chemistry, as inferred from surface plasmon resonance data.⁵ The msSCP method is general and not restricted to the ultrasmall regime. It is well suited for simulations of aqueous solutions containing NPs and/or proteins at high concentrations or local crowding, a common situation in most experiments. The basis of the forcefield is the atomistic SCP model of solvation,^51–53 which was developed for proteins. Therefore, it also contains the basic elements to describe the interactions of ultrasmall nanostructures as protein mimics: dielectric screening of electrostatic forces by water, effects of water-structure forces at interfaces, and modulation of vdW forces by water dispersion. The SCP model is intended to represent the effects of water only; ions, cosolutes, and osmolytes are all treated in atomic detail, on equal footing as proteins, nanoparticles, and any other biomolecules. This makes efficient MC sampling conceptually challenging because when proteins or NPs are moved, ions in their hydration shells need to move in concert to have any chance of acceptance; on the other hand, such a representation is expected to be a more accurate treatment than a continuum approximation in the nanometer length scale.⁵⁴ For highly-charged ultrasmall NPs, even this approach is incomplete, as shown in a recent study of the effects of ions on ultrasmall GSH-AuNP pair interactions.²⁸ The qualitative behavior of the solvent forces is similar to those acting on proteins, which justifies the use of the SCP model, with one exception: the net effects of the vdW forces exerted by ions on the NPs. When two NPs are far apart, the pressure exerted by ions on the NP surfaces is the same in all directions. When they approach one another, the behavior of the liquid in the interparticle space changes, affecting the rate/strength of collisions of ions on the NP inner hemispheres. This results in an ion pressure imbalance, not compensated by water, which induces interparticle attraction. The effect resembles osmotic pressure, with a NP playing the role of an impermeable membrane separating two aqueous solutions. Similar forces are expected between ultrasmall NPs and membranes. These effects are mediated by changes in the structure and dynamics of water in the interparticle space, which have not yet been represented in the SCP model; therefore, an analysis based on relative rather than absolute binding energies reduces the systematic errors.

SUPPLEMENTARY MATERIAL

See supplementary material for the complete sets of binding mode distributions, membrane penetration, and relative binding energies of the magnetite and gold nanostructures.