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Nanoindentation of Isometric Viruses on Deterministically Corrugated Substrates M. Hernando-Pérez,† C. Zeng,† L. Delalande,† I.B. Tsvetkova,† A. Bousquet,‡ M. Tayachi-Pigeonnat,‡ R. Temam,‡ and B. Dragnea*,† †

Department of Chemistry and ‡Department of Mathematics, Indiana University, Bloomington, Indiana 47405, United States S Supporting Information *

ABSTRACT: It has been just over 100 years since inventor Joseph Coyle perfected the egg cartona package format that has known very little changes since its first appearance (Dhillon, S. B. C. Inventor Created Better Way to Carry Eggs. In The Globe and Mail Vancouver, 2013). In this article, we extend Coyle’s old idea to the study of mechanical properties of viruses. Virus stiffness, strength, and breaking force obtained by force spectroscopy atomic force microscopy (AFM) provide the knowledge required for designing nanocontainers for applications in biotechnology and medicine, and for understanding the fundamentals of virus−host interaction such as virus translocation from one cellular compartment to another. In previous studies, virus particles adsorbed on flat surfaces from a physiological buffer were subjected to directional deformation by a known force exerted via a microscopic probe. The affinity between the virus shell and surface is required to be strong enough to anchor particles on the substrate while they are indented or imaged, yet sufficiently weak to preserve the native structure and interactions prior deformation. The specific question addressed here is whether an experimental scheme characterized by increased contact area and stable mechanical equilibrium under directional compression would provide a more reliable characterization than the traditional flat substrate approach.

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INTRODUCTION

Moreover, instances of virus−membrane interaction leading to changes in virion stability are known to occur, e.g., at the endosomal binding step of virions from the alphavirus family.11,12 Another example of strong interaction possibly requiring remodeling of the virion structure are translocation events by the tread milling mechanism of plant viruses through plasmodesmata,13,14 and DNA viruses crossing into the nucleus through the nuclear pore complex.15 A method naturally adapted to the measurement of virus mechanical properties in interaction with a substrate, and thus to addressing this dilemma, is atomic force microscopy (AFM) nanoindentation.16,17 In this method, the virus particle must adhere to the surface with sufficient force to allow compression by the AFM tip without desorption from, or slippage on the substrate. While it is recognized that the latter could adversely affect readings of the force required to compress the virus particle by a given amount, to the best of our knowledge there have been no attempts at controlling surface morphology in ways that would minimize the potentially adverse effects on the measurement of elastic constants of lateral slippage or rolling. Moreover, in all simulations to date, the contact between the virus and a rigid surface (AFM tip or substrate) is modeled as a rough frictional contact.18−20 Tangential slippage or rolling is disallowed. To

The very first step of a viral infection−virion translocation through the cell membrane involves interactions and transformations which can be adequately described using the language of classical mechanics.2 This is because viruses are composed of hundreds to thousands of macromolecules and some of their properties must have collective character. Thus, to understand the virus cycle, and in particular the general features of how viruses interact with interfaces, it is of fundamental interest to complement traditional molecular biology approaches by borrowing concepts from mechanics of materials. This could be useful as well in the rational design of nanocontainers for therapeutic delivery applications.3 In the broadest sense, the nature of the virus−cell surface interaction includes both physical and chemical factors. Substrate morphology and substrate mechanics are examples of physical factors. While numerous studies of virus mechanics have focused on the relationship between structural and chemical states of viruses or virus capsids and their mechanical properties,4−8 it remains unclear whether external factors, e.g., multivalent vs monovalent binding to cellular interfaces, elicit a specific mechanical response from the virus, which may relate to biological function. Some models posit that mechanical deformation during virus binding to the cell surface is a negligible factor in the overall sequence of processes leading to virus entry,9 others suggest that virus deformation resulted from binding to the surface is, at least in some specific cases, an important part of viral entry strategy.10 © 2015 American Chemical Society

Received: August 27, 2015 Revised: November 17, 2015 Published: December 16, 2015 340

DOI: 10.1021/acs.jpcb.5b08362 J. Phys. Chem. B 2016, 120, 340−347

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Figure 1. Schematic of virus adsorption site geometries: Adsorption of a particle on top of a bead (A) is characterized by stable equilibrium in only one direction (normal). Adsorption in a bridge position (B) offers stable equilibrium in two directions, but unstable equilibrium in the third one. Adsorption in a 3-fold position (C) provides stable equilibrium in three directions. Adsorption on a flat surface corresponds to stable equilibrium in one direction (normal to substrate) and neutral equilibrium in any direction perpendicular to it.

Figure 2. An egg carton for viruses. (a) Adsorption of BMV particles on a 100 nm diameter polystyrene bead grid. (b−c) Narrow scan images have enough resolution to discriminate 5 nm wide morphological features on viral particle surface at each of the adsorption sites. Scale bar = 40 nm.

reconstituted from nucleic acid and coat proteins into fully functional virions. It possesses a capsid of ∼28 nm diameter, composed of 180 identical proteins arranged quasi-equivalently in a T = 3 structure. The BMV genome is tripartite and consists of four single-stranded RNA (ssRNA) molecules. RNA1 and RNA2 are each found separately in virions, while RNA3 and RNA4 are copackaged together. Therefore, the wild type (wt) virus consists of three types of particles and differences in the interactions between the protein capsid and the encapsulated genome are expected.23,24 These differences have a putative biological role and could, in principle, be measured by AFM indentation.24 Discriminating between different RNAs encapsulated in morphologically similar virions is an example of application that would greatly benefit from a reduction of sources of heterogeneous broadening, e.g., cargo type, and environment.

the best of our knowledge, this assumption has not been through specific experiments. Here we are investigating the effect on the nanoindentation measurement of a substrate to which viruses adsorb in a nonplanar geometry corresponding to stable equilibrium at compression (Figure 1). This corrugated substrate offers in principle a higher contact area for the adsorbed virus. The question is: How does substrate morphology influence the measurement of mechanical parameters such as the elastic constant and the yield force in terms of their mean absolute values and their statistical spread? Answering it is important because, in comparison with flat substrates, which afford a smaller contact area, corrugated substrates could further immobilize virus particles against slippage or rolling during indentation, potentially providing a tightened control over instrumental error sources. Moreover, being able to vary the geometry of mechanical interaction would enable further experimental tests of analysis of virus mechanical properties in terms of normal mode decomposition, a useful theoretical strategy that can unify different types of mechanical stress experiments including hydrostatic and osmotic pressure and AFM nanoindentation.21 As a case study, the elastic constant and the yield force were measured for particles of Brome Mosaic Virus (BMV) physisorbed on a raft of close-packed 100 nm diameter polystyrene (PS) beads (Figure 2) (also, see Supporting Information, Figure S1). The bead grid has three-dimensional cusps where viruses can adsorb, thus the analogy with an eggcarton. BMV was chosen because it has been a model for 70 years for simple icosahedral positive-sense single-stranded RNA viruses. These are the most abundant viruses on Earth.22 Their hosts include members of all domains of life, including bacteria, animals, and plants. Moreover, BMV can be in vitro

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MATERIALS AND METHODS Hexagonally Close-Packed Pattern Substrate. A drop of suspension containing monodisperse polystyrene (PS) spherical colloids (Polybead Microspheres 0.1 μM, Polysciences, Inc., Warrington, PA, USA) was deposited on a flat substrate of highly ordered pyrolytic graphite (HOPG). Upon drying in a vacuum chamber for 90 min, a hexagonal-closepacked (hcp) lattice crystal is formed. As the solvent (MiliQ-water) evaporates, capillary forces draw the nanospheres together and crystallize on a hexagonally close-packed pattern on the substrate in the order of microns. As in all natural crystals, nanospheres in a hexagonal lattice include a variety of defects that arise from sphere dispersity, vacancies, site randomness, and polycrystalline domains25,26 (Supporting Information, Figure S1). 341

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Figure 3. Particle adsorption on an hcp bead grid. (a) Color-coded schematic representation of adsorption sites: red = on top, black = 2-fold or bridge, blue = 3-fold. (b) Graphic of relative percentage of adsorption sites, assuming equivalent surface affinities. (c) Graphic of relative percentage of adsorption sites found in the experiments. (d) Experimental site frequency normalized to geometric frequency.

AFM Imaging and Characterization. Experimental measurements on wt BMV and empty capsids were made using a commercial Cypher AFM instrument operating at room temperature (Asylum Research, Santa Barbara, CA, USA), and using soft silicon nitride microcantilevers (BioLeverMini, Olympus, Tokio, Japan) with a tip radius of 9 nm, nominal spring constant of 0.05−0.1 N/m and Q = 1.8−2, in liquid, with a resonant frequency of ω = 35 kHz that were excited at an amplitude Afree ∼ 1.2 nm (A/Aratio = 0.85−0.90). Samples were imaged in tapping mode AFM. The AFM probe was directly driven near its first resonant frequency of its flexural mode and then engaged to the sample. The cantilever spring constant and quality factor of the first flexural mode was calibrated by using the thermal noise method in liquid.27 Excitation frequency was chosen from the peak of the tuning curve, where the phase lag became 90°. A droplet containing a suspension of wt BMV virions (or empty capsids) was deposited on surface (HOPG, flat PS, or hcp PS beads) and incubated for 10 min before scanning. Then a scan area of 500 nm x 500 nm was imaged to corroborate the particle adsorption. For the nanoindentation experiments a high resolution image (70 nm × 70 nm, 128 points) of the virus is recorded in the DM-AFM in order to check the integrity of the structure and locate the center of the shell. Then, the AFM tip is moved on the top of the particle and a force−distance curve with trigger force set around 0.8−1 nN, and a loading rate of 150 nm/s was acquired.28 During the first stages of the indentation, the viral particles show linear deformation which provided the spring constant of the virus kv.29,30 The force value at the first sharp decay after linear behavior was selected as the yield force.6,28 After each nanoindentation assay, a new image is recorded to check the particle irreversible deformation. Quantification of the instrumental error in the measurement of elastic constants were achieved by repeatedly taking force− displacement curves (force vs z-piezo extension) at loading rate of 200 nm/s on individual viral particles and the polystyrene

nano spheres. From the measurement of lever deflection when the tip deforms the particle the effective stiffness (keff) of the system cantilever-particle can be obtained. This system, additionally, can be considered as two springs model30,31 which assumes that cantilever and particle act as two spring in series. Knowing the spring constant of the cantilever (kL), the spring constant of the sample (kp) can be obtained from the force−displacement curves, eqs 1 and 2:

1 1 1 = + keff kp kL keff =

kL 1 + kL / k p

(1)

(2)

In the limit of nondeformable particles kp ≫ kL, the effective elastic constant, keff measured corresponds to the cantilever. Topography images and force vs indentation curves were rendered and processed in WSxM32 and IGOR Pro 6.2 (WaveMetrics, Lake Oswego, OR) software for analysis and data presentation. BMV Purification. Purification of the particles was carried out as described in previous work.23 Briefly, BMV was expressed in Nicotiana benthamiana via an Agrobacteriummediated gene delivery system. Seven days after infection, the leaves were homogenized in virus buffer [250 mM NaOAc, 10 mM MgCl2 (pH 4.5)] and then centrifuged at 5000 rpm for 25 min using an Eppendorf F-35−6−30 rotor. The supernatant was then layered on a 10% sucrose cushion (virus buffer) and centrifuged at 26 000 rpm for 3 h using a Beckman SW 32 rotor. The pellets were resuspended in 38.5% CsCl (w/v, virus buffer) and centrifuged at 45 000 rpm for 24 h on a Beckman 65 TY rotor. The white band was collected and dialyzed against SAMA [50 mM Na(OAc), 8 mM Mg(OAc)2 (pH 4.6)] buffer for 24 h with three changes and was stored at −80 °C until use. Empty Capsid Reassembly. Purified virus was dialyzed against disassembly buffer [0.5 M CaCl2 (pH 7.4)] with for 48 342

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Figure 4. Single indentation assays. AFM images of BMV adsorbed on the hcp bead grid, before (left column) and after fracture (right column) induced by nanoindentation. Sites: (a) on top (red color). (b) bridge (gray color), and (c) 3-fold. Scale bar = 15 nm.

a sphere in the Langbein sense: The 3-fold possesses the largest contact area, followed by bridge, and on top. From a purely geometric point of view of the frequency of each type of site within the hcp lattice, and assuming that virions would have same affinity for each of the sites, the highest frequency of adsorption would be expected on the bridge site (16.6% on top, 50% on bridge, and 33.3% on 3fold), Figure 3b. In contrast, the experimental result indicated that the dominant factor in the relative frequency of adsorption events is the contact area provided by a site rather than its relative frequency in the lattice (15.5% on top, 34.5% on bridge, and 50% on 3-fold) as is shown in Figure 3c. Normalizing the experimental frequency of a site to its geometric, lattice frequency allows a direct comparison of adsorption site affinity (Figure 3d). The 3-fold site is clearly dominating. The chemical nature of surface affinity is not clear, but about a third of the BMV outer surface is covered by nonpolar residue patches. Hydrophobic interactions may occur between these residues and the PS bead surface, which is also nonpolar. PS particles in this work are stabilized in aqueous solution by slight anionic charge from sulfate ester. Therefore, an electrostatic interaction is expected to occur between the PS surface and the cationic residues on the BMV surface, as well. Altogether, these interfacial interactions are responsible for holding the particle on the surface while scanning. Interestingly, even on a flat PS surface, the strength of interfacial forces exerted upon contact is comparable with that of interactions that stabilize the virus particle, as suggested by the data presented in Supporting Information, Figure S2. Here,

h with one change of buffer to precipitate RNA. Solution was centrifuged for 45 min at 40 000 rpm using a Beckman 70 Ti rotor. The supernatant containing the dissociated proteins was dialyzed against 10 mM Tris (pH 7.4) and then TKM [0.01 M Tris base, 1 M KCl, and 5 mM MgCl2 (pH 7.5)]. Protein concentration and purity from RNA was determined by UV− vis spectrometry. Protein dimers were reassembled into empty capsids by dialysis against empty capsid reassembly buffer [50 mM NaOAc, 5 mM MgCl2, 1 M KCl (pH 4.7)] for 48 h with one change of buffer.

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RESULTS AND DISCUSSION Virus Adsorption on Surface. To create a corrugated substrate with a larger contact surface area than the traditional flat substrates, a bottom-up approach was followed by which a hexagonal close packed (hcp) lattice of 100 nm diameter polystyrene (PS) nanospheres was deposited on highly oriented pyrolithic graphite (HOPG) via solvent evaporation26 (Materials and Methods, M&M). A solution of BMV particles was then incubated with the substrate. BMV particles readily adsorbed on the PS grid as observed by liquid-cell dynamic mode AFM (Figure 2). Adsorbed virus particles were stable enough to be imaged at a lateral spatial resolution sufficient to resolve individual coat protein oligomers. BMV particles were localized at sites that can be broadly classified as corresponding to on top, bridge, and 3-fold positions with respect to the underlying PS bead lattice (Figure 3a). These sites are different in their specific contact areas with 343

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Figure 5. Box-and-whisker plots representation of spring constant and yield force for wt BMV and BMV empty capsids. (a) Elastic constants on different adsorption sites and flat PS surface for wt BMV. (b) Yield force of viruses on different adsorption sites and flat PS surface for wt BMV. (c) A comparison of elastic constant for full and empty BMV capsids. (d) Comparison of yield force measurements for wt BMV and empty capsids.

sites than for the top site (Figure 5). The median spring constant was similar for all different sites (Figure 5a), comparable with flat PS surface (kPS = 0.30 ± 0.18 N/m) and close to values previously reported on flat substrates.23,24 However, the median yield force value was significantly lower for the 3-fold site than for the other two types of sites, Figure 5b. On top adsorption sites are characterized by a stiffness distribution ∼15% broader than that for bridge or 3-fold sites. We posit that the difference is likely due to the reduced contact area of the on top site, unstable equilibrium, and lateral slippage liability. Note that distribution breadths are similar for bridge and 3-fold adsorption sites despite the fact that they have different contact areas. This suggests that other factors responsible for distribution breath are also at work. These other possibilities include: anisotropic structural stiffness, statistical fluctuations in the deformation process, and cargo variation from particle to particle, which is a characteristic of BMV. Moreover, interactions between genomic RNAs and protein capsids in BMV are thought to differ in the three types of particles.24 To quantify the latter possibility, we have characterized empty capsid adsorbed on hcp polystyrene spheres (Supporting Information, Figure S4) and compared the spring constants and yield forces with those from native BMV particles localized on 3-fold and bridge positions (Figure 5c and d). The on-top site was not included here because it had the broadest width distribution. Instead, we focused on the two narrowest distribution sites. Empty particles have lower median spring constants and yield forces than wt BMV, consistent with previously published work on a similar virus.33 However, the difference in standard deviations (SD) for wt and empty particles was negligible, Table 1. We deduce that heterogeneous broadening due to lateral motion was effectively canceled in

an ensemble of BMV particles was imaged after adsorption on a flat, spin-coated PS surface, Figure S2a. The histogram of heights suggests particles is squatting upon adsorption under the influence of surface adhesion forces (Figure S2b). In contrast with earlier experiments performed on a different system,16 the spring constant, which is derived from small indentation measurements, remained the same regardless the amount of surface induced deformation, Figure S2c. These experiments suggest that strong interfacial interactions favor adsorption sites characterized by large contact areas, but these interactions do not affect elastic moduli, at least for small deformations. Response under Compression. Next, we have studied the mechanical response of wt BMV adsorbed on hcp lattice sites by performing indentations large enough to induce irreversible disruption of shells. Two mechanical characteristics were measured as a function of adsorption site: the spring constant and the yield force (see Supporting Information, Figure S3). Note that, if adhesion forces were neglected, these three main adsorption geometries would correspond to three types of equilibria: unstable (on top), saddle point (bridge), and stable (3-fold). Figure 4 shows typical force vs indentation curves at maximum forces exceeding the fracture threshold (>600 pN) and AFM micrographs before and after fracture of the shell. The spring constant/stiffness of each particle was determined from the slope of the linear part of the curve (see Figure S3)29,30 resulting in ktop = 0.22 ± 0.30 N/m (34 particles), kbridge = 0.27 ± 0.18 N/m (34 particles), and in k3‑fold = 0.21 ± 0.20 N/m (23 particles) (median ± SD) for on top, bridge, and 3-fold localized particles, respectively. For both the spring constant and the yield force, the two quartiles closest to the median are grouped ∼30% more tigtly for the bridge and 3-fold 344

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The Journal of Physical Chemistry B Table 1. Stiffness and Yield Forcea position bridge full 3-fold full bridge empty 3-fold empty

k (N/m) 0.27 0.21 0.22 0.15

± ± ± ±

0.18 0.20 0.18 0.20

yield force (nN) 0.70 0.58 0.51 0.47

± ± ± ±

0.25 0.23 0.60 0.40

a

Summary of stiffness and yield force of BMV adsorbed on different sites (median ± SD) obtained from 57 wt BMV viral particles, on bridged (35) and in 3-fold (23) localization, and 67 empty capsid, on bridged (34) and in 3-fold (33) localization, respectively.

both bridge and 3-fold adsorption geometries and a factor other than heterogeneity in RNA content must be now dominant in generating broadening, of a possibly homogeneous nature. To explore this possibility, we have measured repeatedly the spring constant of a single virus immobilized on a surface. In this case, in conditions of negligible thermal drift, pressure is exerted every time on the same area of the virus and the virus does not change orientation. Therefore, contributions from structural anisotropy are minimal. As a control, force− displacement curves were sequentially acquired from PS nanospheres (see M&M). The results show that, for BMV particles adsorbed on a HOPG, the SD from the mean is ∼20% of the mean value (Supporting Information Figure S5a and Table S1). In contrast, on nanospheres, which are hardly deformable, the SD is ten times lower ∼2% (Figure S5b and Table S1). This value corresponds to the instrumentation broadening and is an order of magnitude lower than the broadening from a single virus particle. Thus, either during nanoindentation the pressure exerted on the virus particle was not always in the same spot on the virus surface, or a relatively small number of molecules are participating in the virus deformation, which leads to stochastic fluctuations in stiffness. The first scenario is less likely, since the sequence of curves is collected at a speed that minimizes possibility of thermal drift and poking on different virus areas each time. However, further experiments will be necessary in order to pinpoint the exact cause of statistical stiffness fluctuations on single virus particles. Numerical Simulations. It is interesting to note that median spring constant and yield force values were the lowest when measured on 3-fold sites. To understand why, we have performed qualitative numerical simulations using continuum elasticity theory on a shell adsorbed at a 3-fold site and indented along the adsorption geometry symmetry axis, and we have compared the force−displacement curve with that of the shell places on a flat surface, Figure 6a. The force displacement curve on a cusp site shows a more nonlinear character, with the particle starting stiff and becoming softer as the deformation increases. This is why the average spring constant difference between sites is small, but the yield force, a variable describing large deformations, drops a significant 50% for the 3-fold adsorption sites. This result can be understood in terms of a wedge effect that increases the effective crushing force on the particle, as the particle squeezes in the cusp, Figure 6b. Thus, for strong interactions (and large deformations), the adsorption geometry is likely to play an important role in the mechanical response of the virus. It is worth noting that another explanation for loss in stability at the 3-fold site could be that the tertiary structure of protein complexes adsorbed to surfaces could be affected which also could destabilize the protein shell. However, we rule out this possibility because on-top stability is

Figure 6. Numerical simulation: (a) Comparison of two-dimensional numerical simulations of indentation of a shell absorbed at a cusp site and flat surface. (b) Two dimensional schematic of forces acting on a BMV particle adsorbed in a cusp between spheres. At constant indentation force, the normal force on the shell increases as the shell gets squeezed in the cusp.

clearly lower than that on a flat surface (which has greater contact area), Figure 5b. Note that the model was two-dimensional, for simplicity, hence the unrealistically low forces required for deformation, but the qualitative trends are expected to persist when passing to a full three-dimensional description.

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CONCLUSION AFM indentation experiments on a small icosahedral virus adsorbed on a deterministically nonplanar substrate suggest that an increased contact area leads to ∼30% narrower stiffness distributions in the best-case scenario. In these conditions, elastic constants measured by AFM indentation are similar regardless the geometry of adsorption site. By contrast, yield force is a function of adsorption site geometry. The dominant factor responsible for broadening in the measured mechanical properties remains unclear. Our work shows that it is not due to lateral slippage, which was suppressed via a corrugated substrate. Broadening could rather have a homogeneous nature. The ensemble of proteins making a virion is small statistically 345

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The Journal of Physical Chemistry B speaking. Large fluctuations in global properties such as the spring constant are expected. More specifically, deformation may be the result of partially random, relative molecular displacements under compression force. The way each particle yields under compression is stochastic, possibly mediated by thermally activated defects since protein−protein interactions are weak. That means that, even if particles start as structurally identical, under deformation they will behave differently, hence a homogeneous broadening effect.

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(10) Bao, G.; Bao, X. R. Shedding Light on the Dynamics of Endocytosis and Viral Budding. Proc. Natl. Acad. Sci. U. S. A. 2005, 102, 9997−9998. (11) Zhang, X.; Sheng, J.; Austin, S. K.; Hoornweg, T. E.; Smit, J. M.; Kuhn, R. J.; Diamond, M. S.; Rossmann, M. G. Structure of Acidic pH Dengue Virus Showing the Fusogenic Glycoprotein Trimers. J. Virol. 2015, 89, 743−750. (12) Zeng, X.; Mukhopadhyay, S.; Brooks, C. L. Residue-level Resolution of Alphavirus Envelope Protein Interactions in PhDependent Fusion. Proc. Natl. Acad. Sci. U. S. A. 2015, 112, 2034− 2039. (13) Niehl, A.; Heinlein, M. Cellular Pathways for Viral Transport through Plasmodesmata. Protoplasma 2011, 248, 75−99. (14) Heinlein, M. Plasmodesmata: Channels for Viruses on the Move. In plasmodesmata; Heinlein, M., Ed.; Springer: New York, 2015; Vol. 1217; 25−52. (15) Nonnenmacher, M.; Weber, T. Intracellular Transport of Recombinant Adeno-associated Virus Vectors. Gene Ther. 2012, 19, 649−658. (16) Knez, M.; Sumser, M. P.; Bittner, A. M.; Wege, C.; Jeske, H.; Hoffmann, D. M.; Kuhnke, K.; Kern, K. Binding the Tobacco Mosaic Virus to Inorganic Surfaces. Langmuir 2004, 20, 441−447. (17) Roos, W. H.; Bruinsma, R.; Wuite, G. J. L. Physical Virology. Nat. Phys. 2010, 6, 733−743. (18) Gibbons, M. M.; Klug, W. S. Mechanical Modeling of Viral Capsids. J. Mater. Sci. 2007, 42, 8995−9004. (19) Roos, W. H.; Gibbons, M. M.; Arkhipov, A.; Uetrecht, C.; Watts, N. R.; Wingfield, P. T.; Steven, A. C.; Heck, A. J. R.; Schulten, K.; Klug, W. S.; et al. Squeezing Protein Shells: How Continuum Elastic Models, Molecular Dynamics Simulations, and Experiments Coalesce at the Nanoscale. Biophys. J. 2010, 99, 1175−1181. (20) May, E. R.; Brooks, C. L. Determination of Viral Capsid Elastic Properties from Equilibrium Thermal Fluctuations. Phys. Rev. Lett. 2011, 106, 188101. (21) May, E. R.; Aggarwal, A.; Klug, W. S.; Brooks, C. L. Viral Capsid Equilibrium Dynamics Reveals Nonuniform Elastic Properties. Biophys. J. 2011, 100, L59−L61. (22) Flint, S. J.; Enquist, L. W.; Racaniello, V. R.; Skalka, A. M. Principles of Virology, 3rd ed.; ASM Press, 2009. (23) Ni, P.; Wang, Z.; Ma, X.; Das, N. C.; Sokol, P.; Chiu, W.; Dragnea, B.; Hagan, M.; Kao, C. C. An Examination of the Electrostatic Interactions between the N-Terminal Tail of the Brome Mosaic Virus Coat Protein and Encapsidated RNAs. J. Mol. Biol. 2012, 419, 284−300. (24) Vaughan, R.; Tragesser, B.; Ni, P.; Ma, X.; Dragnea, B.; Kao, C. C. The Tripartite Virions of the Brome Mosaic Virus Have Distinct Physical Properties That Affect the Timing of the Infection Process. J. Virol. 2014, 88, 6483−6491. (25) Grzelczak, M.; Vermant, J.; Furst, E. M.; Liz-Marzan, L. M. Directed Self-assembly of Nanoparticles. ACS Nano 2010, 4, 3591− 3605. (26) Colson, P.; Henrist, C.; Cloots, R. Nanosphere Lithography: A Powerful Method for the Controlled Manufacturing of Nanomaterials. J. Nanomater. 2013, 2013, 948510. (27) Sader, J. E.; Chon, J. W. M.; Mulvaney, P. Calibration of Rectangular Atomic Force Microscope Cantilevers. Rev. Sci. Instrum. 1999, 70, 3967−3969. (28) Snijder, J.; Ivanovska, I.; Baclayon, M.; Roos, W. H.; Wuite, G. J. L. Probing the Impact of Loading Rate on the Mechanical Properties of Viral Nanoparticles. Micron 2012, 43, 1343−1350. (29) Landau, L. D.; Lifshizt, E. Theory of Elasticity, 3rd ed.; Pergamon: London. 1986. (30) Ivanovska, I. L.; de Pablo, P. J.; Ibarra, B.; Sgalari, G.; MacKintosh, F. C.; Carrascosa, J. L.; Schmidt, C. F.; Wuite, G. J. L. Bacteriophage Capsids: Tough Nanoshells with Complex Elastic Properties. Proc. Natl. Acad. Sci. U. S. A. 2004, 101, 7600−7605. (31) Schaap, I. A. T.; Carrasco, C.; de Pablo, P. J.; MacKintosh, F. C.; Schmidt, C. F. Elastic Response, Buckling, and Instability of

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.5b08362. AFM images of hexagonal closed packed of PS 100 nm diameter beads, mechanical characterization of BMV adsorbed on spin-coated PS surface, mechanical characterization of empty capsid BMV adsorbed on HOPG and hcp of PS beads, and stiffness values BMV adsorbed on HOPG (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +1 (812) 856-0087. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been supported primarily by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under award DE-SC0010507 (sample preparation and characterization, and atomic force microscopy studies) and by Indiana University (numerical simulations).

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REFERENCES

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