Nanoindentation of Isometric Viruses on Deterministically Corrugated Substrates

1Nanoindentation of Isometric Viruses on Deterministically 2Corrugated Substrates 3M. Hernando-Pe rez, † C. Zeng, † L. Delalande, † I.B. Tsvetkova, † A. Bousquet, ‡ M. Tayachi-Pigeonnat, ‡ 4R. Temam, ‡ and B. Dragnea* ,† 5 † Department of Chemistry and ‡ Department of Mathematics, Indiana University, Bloomington, Indiana 47405, United States 6* SSupporting Information 7ABSTRACT: It has been just over 100 years since inventor Joseph Coyle perfected the egg 8cartona package format that has known very little changes since its first appearance (Dhillon, 9S. B. C. Inventor Created Better Way to Carry Eggs. In The Globe and Mail Vancouver, 2013). In 10 this article, we extend Coyle’s old idea to the study of mechanical properties of viruses. Virus 11 stiffness, strength, and breaking force obtained by force spectroscopy atomic force microscopy 12 (AFM) provide the knowledge required for designing nanocontainers for applications in 13 biotechnology and medicine, and for understanding the fundamentals of virus−host interaction 14 such as virus translocation from one cellular compartment to another. In previous studies, virus 15 particles adsorbed on flat surfaces from a physiological buffer were subjected to directional 16 deformation by a known force exerted via a microscopic probe. The affinity between the virus 17 shell and surface is required to be strong enough to anchor particles on the substrate while they 18 are indented or imaged, yet sufficiently weak to preserve the native structure and interactions prior deformation. The specific 19 question addressed here is whether an experimental scheme characterized by increased contact area and stable mechanical 20 equilibrium under directional compression would provide a more reliable characterization than the traditional flat substrate 21 approach. 22 ■INTRODUCTION 23 The very first step of a viral infection−virion translocation 24 through the cell membrane involves interactions and trans25 formations which can be adequately described using the 26 language of classical mechanics. 2 This is because viruses are 27 composed of hundreds to thousands of macromolecules and 28 some of their properties must have collective character. Thus, 29 to understand the virus cycle, and in particular the general 30 features of how viruses interact with interfaces, it is of 31 fundamental interest to complement traditional molecular 32 biology approaches by borrowing concepts from mechanics of 33 materials. This could be useful as well in the rational design of 34 nanocontainers for therapeutic delivery applications. 3 35 In the broadest sense, the nature of the virus−cell surface 36 interaction includes both physical and chemical factors. 37 Substrate morphology and substrate mechanics are examples 38 of physical factors. While numerous studies of virus mechanics 39 have focused on the relationship between structural and 40 chemical states of viruses or virus capsids and their mechanical 41 properties, 4−8 it remains unclear whether external factors, e.g., 42 multivalent vs monovalent binding to cellular interfaces, elicit a 43 specific mechanical response from the virus, which may relate 44 to biological function. Some models posit that mechanical 45 deformation during virus binding to the cell surface is a 46 negligible factor in the overall sequence of processes leading to 47 virus entry, 9 others suggest that virus deformation resulted from 48 binding to the surface is, at least in some specific cases, an 49 important part of viral entry strategy. 10 50 Moreover, instances of virus−membrane interaction leading 51 to changes in virion stability are known to occur, e.g., at the 52 endosomal binding step of virions from the alphavirus 53 family. 11,12 Another example of strong interaction possibly 54 requiring remodeling of the virion structure are translocation 55 events by the tread milling mechanism of plant viruses through 56 plasmodesmata, 13,14 and DNA viruses crossing into the nucleus 57through the nuclear pore complex. 15 58 A method naturally adapted to the measurement of virus 59 mechanical properties in interaction with a substrate, and thus 60 to addressing this dilemma, is atomic force microscopy (AFM) 61nanoindentation. 16,17 62 In this method, the virus particle must adhere to the surface 63 with sufficient force to allow compression by the AFM tip 64 without desorption from, or slippage on the substrate. While it 65 is recognized that the latter could adversely affect readings of 66 the force required to compress the virus particle by a given 67 amount, to the best of our knowledge there have been no 68 attempts at controlling surface morphology in ways that would 69 minimize the potentially adverse effects on the measurement of 70 elastic constants of lateral slippage or rolling. Moreover, in all 71 simulations to date, the contact between the virus and a rigid 72 surface (AFM tip or substrate) is modeled as a rough frictional 73contact. 18−20 Tangential slippage or rolling is disallowed. To Received: August 27, 2015 Revised: November 17, 2015 Article pubs.acs.org/JPCB © XXXX American Chemical Society ADOI: 10.1021/acs.jpcb.5b08362 J. Phys. Chem. B XXXX, XXX, XXX−XXX amc00 |ACSJCA |JCA10.0.1465/W Unicode |research.3f (R3.6.i11:4432 |2.0 alpha 39) 2015/07/15 14:30:00 |PROD-JCA1 |rq_4436975 |12/23/2015 11:18:04 |8|JCA-DEFAULT 74 the best of our knowledge, this assumption has not been 75 through specific experiments. 76 Here we are investigating the effect on the nanoindentation 77 measurement of a substrate to which viruses adsorb in a 78 nonplanar geometry corresponding to stable equilibrium at f1 79 compression (Figure 1). This corrugated substrate offers in 80 principle a higher contact area for the adsorbed virus. The 81 question is: How does substrate morphology influence the 82 measurement of mechanical parameters such as the elastic 83 constant and the yield force in terms of their mean absolute 84 values and their statistical spread? Answering it is important 85 because, in comparison with flat substrates, which afford a 86 smaller contact area, corrugated substrates could further 87 immobilize virus particles against slippage or rolling during 88 indentation, potentially providing a tightened control over 89 instrumental error sources. 90 Moreover, being able to vary the geometry of mechanical 91 interaction would enable further experimental tests of analysis 92 of virus mechanical properties in terms of normal mode 93 decomposition, a useful theoretical strategy that can unify 94 different types of mechanical stress experiments including 95 hydrostatic and osmotic pressure and AFM nanoindentation. 21 96 As a case study, the elastic constant and the yield force were 97 measured for particles of Brome Mosaic Virus (BMV) 98 physisorbed on a raft of close-packed 100 nm diameter f2 99 polystyrene (PS) beads (Figure 2) (also, see Supporting 100 Information, Figure S1). The bead grid has three-dimensional 101 cusps where viruses can adsorb, thus the analogy with an egg102 carton. BMV was chosen because it has been a model for 70 103 years for simple icosahedral positive-sense single-stranded RNA 104 viruses. These are the most abundant viruses on Earth. 22 Their 105 hosts include members of all domains of life, including bacteria, 106 animals, and plants. Moreover, BMV can be in vitro 107 reconstituted from nucleic acid and coat proteins into fully 108 functional virions. It possesses a capsid of ∼28 nm diameter, 109 composed of 180 identical proteins arranged quasi-equivalently 110 in a T= 3 structure. The BMV genome is tripartite and consists 111 of four single-stranded RNA (ssRNA) molecules. RNA1 and 112 RNA2 are each found separately in virions, while RNA3 and 113 RNA4 are copackaged together. Therefore, the wild type (wt) 114 virus consists of three types of particles and differences in the 115 interactions between the protein capsid and the encapsulated 116 genome are expected. 23,24 These differences have a putative 117 biological role and could, in principle, be measured by AFM 118 indentation. 24 Discriminating between different RNAs encapsu119 lated in morphologically similar virions is an example of 120 application that would greatly benefit from a reduction of 121 sources of heterogeneous broadening, e.g., cargo type, and 122environment. 123 ■MATERIALS AND METHODS 124 Hexagonally Close-Packed Pattern Substrate. A drop 125 of suspension containing monodisperse polystyrene (PS) 126 spherical colloids (Polybead Microspheres 0.1 μM, Poly127 sciences, Inc., Warrington, PA, USA) was deposited on a flat 128 substrate of highly ordered pyrolytic graphite (HOPG). Upon 129 drying in a vacuum chamber for 90 min, a hexagonal-close130packed (hcp) lattice crystal is formed. 131 As the solvent (MiliQ-water) evaporates, capillary forces 132 draw the nanospheres together and crystallize on a hexagonally 133 close-packed pattern on the substrate in the order of microns. 134 As in all natural crystals, nanospheres in a hexagonal lattice 135 include a variety of defects that arise from sphere dispersity, 136 vacancies, site randomness, and polycrystalline domains 25,26 137(Supporting Information Figure S1). 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. The Journal of Physical Chemistry B Article DOI: 10.1021/acs.jpcb.5b08362 J. Phys. Chem. B XXXX, XXX, XXX−XXX B 138 AFM Imaging and Characterization. Experimental 139 measurements on wt BMV and empty capsids were made 140 using a commercial Cypher AFM instrument operating at room 141 temperature (Asylum Research, Santa Barbara, CA, USA), and 142 using soft silicon nitride microcantilevers (BioLeverMini, 143 Olympus, Tokio, Japan) with a tip radius of 9 nm, nominal 144 spring constant of 0.05 0.1 N/m and Q= 1.8−2, in liquid, with 145 a resonant frequency of ω= 35 kHz that were excited at an 146 amplitude Afree ∼1.2 nm (A/Aratio = 0.85−0.90). Samples were 147 imaged in tapping mode AFM. The AFM probe was directly 148 driven near its first resonant frequency of its flexural mode and 149 then engaged to the sample. The cantilever spring constant and 150 quality factor of the first flexural mode was calibrated by using 151 the thermal noise method in liquid. 27 Excitation frequency was 152 chosen from the peak of the tuning curve, where the phase lag 153 became 90°. 154 A droplet containing a suspension of wt BMV virions (or 155 empty capsids) was deposited on surface (HOPG, flat PS, or 156 hcp PS beads) and incubated for 10 min before scanning. Then 157 a scan area of 500 nm x 500 nm was imaged to corroborate the 158 particle adsorption. For the nanoindentation experiments a 159 high resolution image (70 nm ×70 nm, 128 points) of the virus 160 is recorded in the DM-AFM in order to check the integrity of 161 the structure and locate the center of the shell. Then, the AFM 162 tip is moved on the top of the particle and a force−distance 163 curve with trigger force set around 0.8−1 nN, and a loading 164 rate of 150 nm/s was acquired. 28 During the first stages of the 165 indentation, the viral particles show linear deformation which 166 provided the spring constant of the virus kv. 29,30 The force value 167 at the first sharp decay after linear behavior was selected as the 168 yield force. 6,28 After each nanoindentation assay, a new image is 169 recorded to check the particle irreversible deformation. 170 Quantification of the instrumental error in the measurement 171 of elastic constants were achieved by repeatedly taking force− 172 displacement curves (force vs z-piezo extension) at loading rate 173 of 200 nm/s on individual viral particles and the polystyrene 174nano spheres. From the measurement of lever deflection when 175the tip deforms the particle the effective stiffness (keff) of the 176system cantilever-particle can be obtained. This system, 177additionally, can be considered as two springs model 30,31 178which assumes that cantilever and particle act as two spring in 179series. Knowing the spring constant of the cantilever (kL), the 180spring constant of the sample (kp) can be obtained from the 181force−displacement curves, eqs 1 and 2: =+ kkk 111 eff p L 182 (1) = + kk kk1/ eff L Lp 183 (2) 184In the limit of nondeformable particles kp≫kL, the effective 185elastic constant measured corresponds to the cantilever. 186Topography images and force vs indentation curves were 187rendered and processed in WSxM 32 and IGOR Pro 6.2 188(WaveMetrics, Lake Oswego, OR) software for analysis and 189data presentation. 190BMV Purification. Purification of the particles was carried 191out as described in previous work. 23 Briefly, BMV was 192expressed in Nicotiana benthamiana via an Agrobacterium193mediated gene delivery system. Seven days after infection, the 194leaves were homogenized in virus buffer [250 mM NaOAc, 10 195mM MgCl2(pH 4.5)] and then centrifuged at 5000 rpm for 25 196min using an Eppendorf F-35−6−30 rotor. The supernatant 197was then layered on a 10% sucrose cushion (virus buffer) and 198centrifuged at 26 000 rpm for 3 h using a Beckman SW 32 199rotor. The pellets were resuspended in 38.5% CsCl (w/v, virus 200buffer) and centrifuged at 45 000 rpm for 24 h on a Beckman 20165 TY rotor. The white band was collected and dialyzed against 202SAMA [50 mM Na(OAc), 8 mM Mg(OAc)2(pH 4.6)] buffer 203for 24 h with three changes and was stored at −80 °C until use. 204Empty Capsid Reassembly. Purified virus was dialyzed 205against disassembly buffer [0.5 M CaCl2(pH 7.4)] with for 48 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. The Journal of Physical Chemistry B Article DOI: 10.1021/acs.jpcb.5b08362 J. Phys. Chem. B XXXX, XXX, XXX−XXX C we provide a new figure. 206 h with one change of buffer to precipitate RNA. Solution was 207 centrifuged for 45 min at 40 000 rpm using a Beckman 70 Ti 208 rotor. The supernatant containing the dissociated proteins was 209 dialyzed against 10 mM Tris (pH 7.4) and then TKM [0.01 M 210 Tris base, 1 M KCl, and 0.005 M MgCl2, pH 7.5]. Protein 211 concentration and purity from RNA was determined by UV− 212 vis spectrometry. Protein dimers were reassembled into empty 213 capsids by dialysis against empty capsid reassembly buffer [50 214 mM NaOAc, 5 mM MgCl2, 1 M KCl (pH 4.7)] for 48 h with 215 one change of buffer. 216 ■RESULTS AND DISCUSSION 217 Virus Adsorption on Surface. To create a corrugated 218 substrate with a larger contact surface area than the traditional 219 flat substrates, a bottom-up approach was followed by which a 220 hexagonal close packed (hcp) lattice of 100 nm diameter 221 polystyrene (PS) nanospheres was deposited on highly oriented 222 pyrolithic graphite (HOPG) via solvent evaporation 26 (Materi223 als and Methods, M&M). A solution of BMV particles was then 224 incubated with the substrate. BMV particles readily adsorbed 225 on the PS grid as observed by liquid-cell dynamic mode AFM 226 (Figure 2). Adsorbed virus particles were stable enough to be 227 imaged at a lateral spatial resolution sufficient to resolve 228 individual coat protein oligomers. 229 BMV particles were localized at sites that can be broadly 230 classified as corresponding to on top, bridge, and 3-fold f3 231 positions with respect to the underlying PS bead lattice (Figure f3 232 3a). These sites are different in their specific contact areas with 233 a sphere in the Langbein sense: The 3-fold possesses the largest 234contact area, followed by bridge, and on top. 235 From a purely geometric point of view of the frequency of 236each type of site within the hcp lattice, and assuming that 237 virions would have same affinity for each of the sites, the 238 highest frequency of adsorption would be expected on the 239bridge site (16.6% on top, 50% on bridge, and 33.3% on 3240 fold), Figure 3b. In contrast, the experimental result indicated 241 that the dominant factor in the relative frequency of adsorption 242events is the contact area provided by a site rather than its 243 relative frequency in the lattice (15.5% on top, 34.5% on bridge, 244 and 50% on 3-fold) as is shown in Figure 3c. Normalizing the 245experimental frequency of a site to its geometric, lattice 246 frequency allows a direct comparison of adsorption site affinity 247(Figure 3d). The 3-fold site is clearly dominating. 248 The chemical nature of surface affinity is not clear, but about 249 a third of the BMV outer surface is covered by nonpolar residue 250patches. Hydrophobic interactions may occur between these 251 residues and the PS bead surface, which is also nonpolar. PS 252 particles in this work are stabilized in aqueous solution by slight 253anionic charge from sulfate ester. Therefore, an electrostatic 254 interaction is expected to occur between the PS surface and the 255 cationic residues on the BMV surface, as well. Altogether, these 256interfacial interactions are responsible for holding the particle 257on the surface while scanning. 258Interestingly, even on a flat PS surface, the strength of 259 interfacial forces exerted upon contact is comparable with that 260 of interactions that stabilize the virus particle, as suggested by 261the data presented in Supporting Information, Figure S2. Here, 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. The Journal of Physical Chemistry B Article DOI: 10.1021/acs.jpcb.5b08362 J. Phys. Chem. B XXXX, XXX, XXX−XXX D 262 an ensemble of BMV particles was imaged after adsorption on a 263 flat, spin-coated PS surface, Figure S2a. The histogram of 264 heights suggests particles is squatting upon adsorption under 265 the influence of surface adhesion forces (Figure S2b). In 266 contrast with earlier experiments performed on a different 267 system, 16 the spring constant, which is derived from small 268 indentation measurements, remained the same regardless the 269 amount of surface induced deformation, Figure S2c. These 270 experiments suggest that strong interfacial interactions favor 271 adsorption sites characterized by large contact areas, but these 272 interactions do not affect elastic moduli, at least for small 273 deformations. 274 Response under Compression. Next, we have studied the 275 mechanical response of wt BMV adsorbed on hcp lattice sites 276 by performing indentations large enough to induce irreversible 277 disruption of shells. Two mechanical characteristics were 278 measured as a function of adsorption site: the spring constant 279 and the yield force (see Supporting Information, Figure S3). 280 Note that, if adhesion forces were neglected, these three main 281 adsorption geometries would correspond to three types of 282 equilibria: unstable (on top), saddle point (bridge), and stable 283 (3-fold). f4 284 Figure 4 shows typical force vs indentation curves at 285 maximum forces exceeding the fracture threshold (>600 pN) 286 and AFM micrographs before and after fracture of the shell. 287 The spring constant/stiffness of each particle was determined 288 from the slope of the linear part of the curve (see Figure 289 S3) 29,30 resulting in ktop = 0.22 ±0.30 N/m (34 particles), 290 kbridge = 0.27 ±0.18 N/m (34 particles), and in k3‑fold = 0.21 ± 291 0.20 N/m (23 particles) (median ±SD) for on top, bridge, and 292 3-fold localized particles, respectively. For both the spring 293 constant and the yield force, the two quartiles closest to the f5 294 median are grouped ∼30% more tigtly for the bridge and 3-fold 295 f5 sites than for the top site (Figure 5). The median spring 296 constant was similar for all different sites (Figure 5a), 297 comparable with flat PS surface (kPS = 0.30 ±0.18 N/m) 298 and close to values previously reported on flat substrates. 23,24 299 However, the median yield force value was significantly lower 300 for the 3-fold site than for the other two types of sites, Figure 301 5b. On top adsorption sites are characterized by a stiffness 302 distribution ∼15% broader than that for bridge or 3-fold sites. 303 We posit that the difference is likely due to the reduced contact 304 area of the on top site, unstable equilibrium, and lateral slippage 305 liability. Note that distribution breadths are similar for bridge 306 and 3-fold adsorption sites despite the fact that they have 307 different contact areas. This suggests that other factors 308 responsible for distribution breath are also at work. These 309 other possibilities include: anisotropic structural stiffness, 310 statistical fluctuations in the deformation process, and cargo 311 variation from particle to particle, which is a characteristic of 312BMV. 313 Moreover, interactions between genomic RNAs and protein 314 capsids in BMV are thought to differ in the three types of 315 particles. 24 To quantify the latter possibility, we have 316 characterized empty capsid adsorbed on hcp polystyrene 317 spheres (Supporting Information, Figure S4) and compared 318 the spring constants and yield forces with those from native 319 BMV particles localized on 3-fold and bridge positions (Figure 320 5c and d). The on-top site was not included here because it had 321 the broadest width distribution. Instead, we focused on the two 322 narrowest distribution sites. Empty particles have lower median 323 spring constants and yield forces than wt BMV, consistent with 324 previously published work on a similar virus. 33 However, the 325 difference in standard deviations (SD) for wt and empty 326 t1 particles was negligible, Table 1. We deduce that heterogeneous 327broadening due to lateral motion was effectively canceled in 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. (b) Yield force of viruses on different adsorption sites and flat PS surface. (c) A comparison of elastic constant for full and empty BMV capsids. (d) Comparison of yield force measurements for wt BMV and empty capsids. The Journal of Physical Chemistry B Article DOI: 10.1021/acs.jpcb.5b08362 J. Phys. Chem. B XXXX, XXX, XXX−XXX E 328 both bridge and 3-fold adsorption geometries and a factor other 329 than heterogeneity in RNA content must be now dominant in 330 generating broadening, of a possibly homogeneous nature. 331 To explore this possibility, we have measured repeatedly the 332 spring constant of a single virus immobilized on a surface. In 333 this case, in conditions of negligible thermal drift, pressure is 334 exerted every time on the same area of the virus and the virus 335 does not change orientation. Therefore, contributions from 336 structural anisotropy are minimal. As a control, force− 337 displacement curves were sequentially acquired from PS 338 nanospheres (see M&M). The results show that, for BMV 339 particles adsorbed on a HOPG, the SD from the mean is ∼20% 340 of the mean value (Supporting Information Figure S5a and 341 Table S1). In contrast, on nanospheres, which are hardly 342 deformable, the SD is ten times lower ∼2% (Figure S5b and 343 Table S1). This value corresponds to the instrumentation 344 broadening and is an order of magnitude lower than the 345 broadening from a single virus particle. Thus, either during 346 nanoindentation the pressure exerted on the virus particle was 347 not always in the same spot on the virus surface, or a relatively 348 small number of molecules are participating in the virus 349 deformation, which leads to stochastic fluctuations in stiffness. 350 The first scenario is less likely, since the sequence of curves is 351 collected at a speed that minimizes possibility of thermal drift 352 and poking on different virus areas each time. However, further 353 experiments will be necessary in order to pinpoint the exact 354 cause of statistical stiffness fluctuations on single virus particles. 355 Numerical Simulations. It is interesting to note that 356 median spring constant and yield force values were the lowest 357 when measured on 3-fold sites. To understand why, we have 358 performed qualitative numerical simulations using continuum 359 elasticity theory on a shell adsorbed at a 3-fold site and 360 indented along the adsorption geometry symmetry axis, and we 361 have compared the force−displacement curve with that of the f6 362 shell places on a flat surface, Figure 6a. The force displacement 363 curve on a cusp site shows a more nonlinear character, with the 364 particle starting stiffand becoming softer as the deformation 365 increases. This is why the average spring constant difference 366 between sites is small, but the yield force, a variable describing 367 large deformations, drops a significant 50% for the 3-fold 368 adsorption sites. This result can be understood in terms of a 369 wedge effect that increases the effective crushing force on the 370 particle, as the particle squeezes in the cusp, Figure 6b. Thus, 371 for strong interactions (and large deformations), the adsorption 372 geometry is likely to play an important role in the mechanical 373 response of the virus. It is worth noting that another 374 explanation for loss in stability at the 3-fold site could be that 375 the tertiary structure of protein complexes adsorbed to surfaces 376 could be affected which also could destabilize the protein shell. 377 However, we rule out this possibility because on-top stability is 378clearly lower than that on a flat surface (which has greater 379contact area), Figure 5b. 380Note that the model was two-dimensional, for simplicity, 381hence the unrealistically low forces required for deformation, 382but the qualitative trends are expected to persist when passing 383to a full three-dimensional description. 384 ■CONCLUSION 385AFM indentation experiments on a small icosahedral virus 386adsorbed on a deterministically nonplanar substrate suggest 387that an increased contact area leads to ∼30% narrower stiffness 388distributions in the best-case scenario. In these conditions, 389elastic constants measured by AFM indentation are similar 390regardless the geometry of adsorption site. By contrast, yield 391force is a function of adsorption site geometry. The dominant 392factor responsible for broadening in the measured mechanical 393properties remains unclear. Our work shows that it is not due 394to lateral slippage, which was suppressed via a corrugated 395substrate. Broadening could rather have a homogeneous nature. 396The ensemble of proteins making a virion is small statistically Table 1. Stiffness and Yield Force a position K(N/m) yield force (nN) bridge full 0.27 ±0.18 0.70 ±0.25 3-fold full 0.21 ±0.20 0.58 ±0.23 bridge empty 0.22 ±0.18 0.51 ±0.60 3-fold empty 0.15 ±0.20 0.47 ±0.40 a Summary of stiffness and yield force of BMV adsorbed on different surfaces (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. 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. The Journal of Physical Chemistry B Article DOI: 10.1021/acs.jpcb.5b08362 J. Phys. Chem. B XXXX, XXX, XXX−XXX F 397 speaking. Large fluctuations in global properties such as the 398 spring constant are expected. More specifically, deformation 399 may be the result of partially random, relative molecular 400 displacements under compression force. The way each particle 401 yields under compression is stochastic, possibly mediated by 402 thermally activated defects since protein−protein interactions 403 are weak. That means that, even if particles start as structurally 404 identical, under deformation they will behave differently, hence 405 a homogeneous broadening effect. 406 ■ASSOCIATED CONTENT 407 * SSupporting Information 408 The Supporting Information is available free of charge on the 409 ACS Publications website at DOI: 10.1021/acs.jpcb.5b08362. 410 AFM images of hexagonal closed packed of PS 100 nm 411 diameter beads, mechanical characterization of BMV 412 adsorbed on spin-coated PS surface, mechanical 413 characterization of empty capsid BMV adsorbed on 414 HOPG and hcp of PS beads, and stiffness values BMV 415 adsorbed on HOPG (PDF) 416 ■AUTHOR INFORMATION 417 Corresponding Author 418 *E-mail: [email protected]. Phone: +1 (812) 856-0087. 419 Notes 420 The authors declare no competing financial interest. 421 ■ACKNOWLEDGMENTS 422 This work has been supported primarily by the U.S. 423 Department of Energy, Office of Science, Basic Energy 424 Sciences, under award DE-SC0010507 (sample preparation 425 and characterization, and atomic force microscopy studies) and 426 by Indiana University (numerical simulations). 427 ■REFERENCES (1)428 Dhillon, S. B. C. Inventor Created Better Way to Carry Eggs. In 429 The Globe and Mail Vancouver, 2013. (2) 430 de Pablo, P. J.; Mateu, M. G. Mechanical Properties of Viruses. 431 Subcell. Biochem. 2013,68, 519−551. (3) 432 Bruckman, M. A.; VanMeter, A.; Steinmetz, N. F. Nano433 manufacturing of Tobacco Mosaic Virus-Based Spherical Biomaterials 434 Using a Continuous Flow Method. ACS Biomater. Sci. Eng. 2015,1, 435 13−18. (4) 436 Castellanos, M.; Pe rez, R.; Carrasco, C.; Hernando-Pe rez, M.; 437 Gomez-Herrero, J.; de Pablo, P. J.; Mateu, M. G. 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