Steric and Electrostatic Complementarity in the ... - ACS Publications

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Steric and Electrostatic Complementarity in the Assembly of Two-Dimensional Virus Arrays Chin Li Cheung,*,†, Alexander I. Rubinstein,‡ Erik J. Peterson,†,^ Anju Chatterji,§ Renat F. Sabirianov,‡ Wai-Ning Mei,‡ Tianwei Lin,§,# John E. Johnson,§ and James J. DeYoreo†,& Lawrence Livermore National Laboratory, Livermore, California 94550, ‡Department of Physics, University of Nebraska at Omaha, Omaha, Nebraska 68182, and §Department of Molecular Biology, The Scripps Research Institute, La Jolla, California 92037. Present address: Department of Chemistry, University of Nebraska at Lincoln, Lincoln, NE 68588. ^Present address: Department of Psychology, Colorado State University, Fort Collins, CO 80523. #Present address: School of Life Sciences, Xiamen University, China. &Present address: Lawrence Berkeley National Laboratory, Berkeley, CA 94720. )

†

Received August 20, 2009 A highly ordered assembly of biological molecules provides a powerful means to study the organizational principles of objects at the nanoscale. Two-dimensional cowpea mosaic virus arrays were assembled in an ordered manner on mica using osmotic depletion effects and a drop-and-dry method. The packing of the virus array was controlled systematically from rhombic packing to hexagonal packing by modulating the concentrations of poly(ethylene glycol) surfactant in the virus solutions. The orientation and packing symmetry of the virus arrays were found to be tuned by the concentrations of surfactants in the sample solutions. A phenomenological model for the present system is proposed to explain the assembly array morphology under the influence of the surfactant. Steric and electrostatic complementarity of neighboring virus capsids is found to be the key factors in controlling the symmetry of packing.

Introduction Assembling biological materials is an active research area due to their potential in medical and biotechnological applications. Two- (2D) and three-dimensional (3D) ordered artificial structures have been recently created using bionanoparticles as elemental building blocks. In particular, the assembly of DNA,1-3 proteins,4 bacteria phages,5,6 and viruses7-9 were recently reported. The assembly reflects the geometrical peculiarity of these building blocks and physicochemical features of biomolecular recognition associated with noncovalent (van der Waals, hydrophobic, and electrostatic) interactions between subunits. Particularly, the self-assembly of bionanoparticles is a promising means to organize materials from the nano- to macroscale.10 This phenomenon has been exploited in natural biological systems, for examples, in the formation of micrometer-long microtubules inside cells or spherical virus capsids from a few different types of protein building blocks.11-13 Artificial building blocks containing *Corresponding author: e-mail [email protected]; Tel (402) 472-5172; Fax (402) 472-9402. (1) Zhang, C.; Su, M.; He, Y.; Zhao, X.; Fang, P.-a.; Ribbe, A. E.; Jiang, W.; Mao, C. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 10665. (2) Schaeferling, M.; Schiller, S.; Paul, H.; Kruschina, M.; Pavlickova, P.; Meerkamp, M.; Giammasi, C.; Kambhampati, D. Electrophoresis 2002, 23, 3097. (3) Hagan, M. F.; Chandler, D. Biophys. J. 2006, 91, 42. (4) Adachi, E.; Nagayama, K. Adv. Biophys. 1997, 34, 81. (5) Chattopadhyay, S.; Puls, R. W. Environ. Sci. Technol. 1999, 33, 3609. (6) Rong, J.; Lee, L. A.; Li, K.; Harp, B.; Mello, C. M.; Niu, Z.; Wang, Q. Chem. Commun. 2008, 5185. (7) Steinmetz, N. F.; Evans, D. J. Org. Biomol. Chem. 2007, 5, 2891. (8) Klem, M. T.; Willits, D.; Young, M.; Douglas, T. J. Am. Chem. Soc. 2003, 125, 10806. (9) Li, T.; Ye, B.; Niu, Z.; Thompson, P.; Seifert, S.; Lee, B.; Wang, Q. Chem. Mater. 2009, 21, 1046. (10) Boncheva, M.; Whitesides, G. M. MRS Bull. 2005, 30, 736. (11) Herzog, W.; Weber, K. Proc. Natl. Acad. Sci. U.S.A. 1977, 74, 1860. (12) Steven, A. C.; Trus, B. L.; Booy, F. P.; Cheng, N.; Zlotnick, A.; Caston, J. R.; Conway, J. F. FASEB J. 1997, 11, 733. (13) Sleytr, U. B.; Messner, P.; Pum, D.; Sara, M. Angew. Chem., Int. Ed. 1999, 38, 1034.

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interaction sites with complicated surface topology such as engineered DNA strands and hydrophilic-hydrophobic organic components have also been designed to explore the self-assembly principles for materials organization and fabrication.14-16 Selforganization of materials due to phase changes in systems of coblock polymer17 and spatial confinement effect provide other routes to generating ordered 2D and 3D structures with order on the length scale of micrometers.18,19 Assembly from simple building blocks is one of the most fundamental approaches to fabricate 3D hierarchical complex structures and naturally enable templated organization.20 Ordered arrays of colloids, nanocrystals, and nanowires have been fabricated through various means ranging from Langmuir trough assembly,21 template-induced order on substrates,19 the phage display method,22 capillary forces and depletion forces,23 addition of polymer to induce phase changes,9,24-27 and through spatial confinement effects.18,19 Monodispersity of the building blocks in (14) Aldaye, F. A.; Palmer, A. L.; Sleiman, H. F. Science 2008, 321, 1795. (15) Barauskas, J.; Johnsson, M.; Tiberg, F. Nano Lett. 2005, 5, 1615. (16) Yan, H.; Park, S. H.; Finkelstein, G.; Reif, J. H.; LaBean, T. H. Science 2003, 301, 1882. (17) Kawakatsu, T. Statistical Physics of Polymers; Springer: Berlin, 2004. (18) Yang, P.; Rizvi, A. H.; Messer, B.; Chmelka, B. F.; Whitesides, G. M.; Stucky, G. D. Adv. Mater. 2001, 13, 427. (19) Thomas, A.; Schierhorn, M.; Wu, Y.; Stucky, G. D. J. Mater. Chem. 2007, 17, 4558. (20) Falkner, J. C.; Turner, M. E.; Bosworth, J. K.; Trentler, T. J.; Johnson, J. E.; Lin, T.; Colvin, V. L. J. Am. Chem. Soc. 2005, 127, 5274. (21) Tao, A. R.; Huang, J.; Yang, P. Acc. Chem. Res. 2008, 41, 1662. (22) Lee, S.-W.; Mao, C.; Flynn, C. E.; Belcher, A. M. Science 2002, 296, 892. (23) Murray, C. B.; Kagan, C. R.; Bawendi, M. G. Annu. Rev. Mater. Sci. 2000, 30, 545. (24) Polavarapu, L.; Xu, Q.-H. Langmuir 2008, 24, 10608. (25) Yoo, P. J.; Nam, K. T.; Qi, J.; Lee, S. K.; Park, J.; Belcher, A. M.; Hammond, P. T. Nat. Mater. 2006, 3, 234. (26) Ramos, L.; Lubensky, T. C.; Dan, N.; Nelson, P.; Weitz, D. A. Science 1999, 286, 2325. (27) Lin, Y.; B€oker, A.; He, J.; Sill, K.; Xiang, H.; Abetz, C.; Li, X.; Wang, J.; Emrick, T.; Long, S.; Wang, Q.; Balazs, A.; Russell, T. P. Nature 2005, 434, 55.

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terms of shapes and sizes was found to be crucial in influencing the order of the arrays.28 Viruses are particularly interesting bioscaffold building blocks because they combine the chemical functionality of the virus coat proteins with atomically precise shape and size. Cowpea mosaic virus (CPMV), which is a plant virus from the Comovirus family that contains the genetic material (RNA) enclosed in a protein capsid,29 is comprised of 60 identical copies of asymmetric units forming an icosahedral sphere with 20 equivalent triangular faces and a diameter of 28 nm (Figure 1).29 Each asymmetric unit has two protein subunits: (i) S subunit contains A domain; (ii) L subunit contains B and C domains. The unique distribution of the icosahedra asymmetric units in the CPMV capsid gives rises to the formation of pentamers and hexamers of the capsid. Each pentamer is composed of five A domains, whereas each hexamer is composed of three B and three C domains. CPMV has been regarded as an addressable nanobuilding block, which displays different active chemical groups on the capsid exterior and its inner surface. A wide variety of selective chemistry such as bioconjugation techniques have been developed to permit efficient attachment of a range of molecules, polymers, and proteins on the surface of CPMV.7 Recently, the CPMV virions were immobilized using bifunctional linkers, followed by decoration of the viral particles with quantum dots.30 Despite numerous studies of CPMV in solutions, the studies of its assembly on solid substrates are few. Monolayers, bilayers, and multilayers of CPMV were obtained on solid substrates using molecular recognition of streptavidin by biotinylated virions.31 Recent studies have also illustrated other assembly strategies such as the layer-by-layer assembly of CPMV32 and dip pen nanolithography as a means to direct ordered assembly.33,34 One of the alternative approaches was previously employed35 to assemble 1D and 2D arrays of CPMV to bind specifically and reversibly on nanoscale chemical templates. Virus arrays have also been demonstrated as scaffolds for the directed growth of inorganic materials in the design of integrated mechanical, optical, and electronic devices.36-38 However, rapid progress in the applications of these materials in nanoelectronic and nanobiotechnological devices is limited by difficulties in programming distinct structural size of each building block and fine geometric control of a large-area array assembly. Therefore, a systematic study of virus array assembly mechanisms is necessary to reveal key factors that control their long-range order. Furthermore, it is critical to achieve control over the orientation of individual virus particles if they are to be exploited as scaffolds to create high-density nanoelectronic components. (28) Claridge, S. A.; Castleman, A. W. J.; Khanna, S. N.; Murray, C. B.; Sen, A.; Weiss, P. A. ACS Nano 2009, 3, 244. (29) Lin, T.; Chen, Z.; Usha, R.; Stauffacher, C. V.; Dai, J.-B.; Schmidt, T.; Johnson, J. E. Virology 1999, 265, 20. (30) Medintz, I. L.; Sapsford, K. E.; Konnert, J. H.; Chatterji, A.; Lin, T.; Johnson, J. E.; Mattoussi, H. Langmuir 2005, 21, 5501. (31) Steinmetz, N. F.; Calder, G.; Lomonossoff, G. P.; Evans, D. J. Langmuir 2006, 22, 10032. (32) Lin, Y.; Su, Z.; Niu, Z.; Li, S.; Kaur, G.; Lee, L. A.; Wang, Q. Acta Biomater. 2008, 4, 838. (33) Smith, J. C.; Lee, K. B.; Wang, Q.; Finn, M. G.; Johnson, J. E.; Mrksich, M.; Mirkin, C. A. Nano Lett. 2003, 3, 883. (34) Salaita, K.; Wang, Y.; Mirkin, C. A. Nat. Nanotechnol. 2007, 2, 145. (35) Cheung, C. L.; Chung, S. W.; Chatterji, A.; Lin, T.; Johnson, J. E.; Hok, S.; Perkins, J.; De Yoreo, J. J. J. Am. Chem. Soc. 2006, 128, 10801. (36) Peelle, B. R.; Krauland, E. M.; Wittrup, K. D.; Belcher, A. M. Langmuir 2005, 21, 6929. (37) Nam, K. T.; Kim, D. W.; Yoo, P. J.; Chiang, C. Y.; Meethong, N.; Hammond, P. T.; Chang, Y. M.; Belcher, A. M. Science 2006, 312, 885. (38) Blum, A. S.; Soto, C. M.; Wilson, C. D.; Brower, T. L.; Pollack, S. K.; Schull, T. L.; Chatterji, A.; Lin, T.; Johnson, J. E.; Amsinck, C.; Franzon, P.; Shashidhar, R.; Ratna, B. R. Small 2005, 1, 702.

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Figure 1. Molecular architecture of a cowpea mosaic virus (CPMV) viral capsid and its icosahedral asymmetric unit. Both the unit and the whole capsid are represented using the van der Waals spheres for each atom. (a) Structure of the CPMV protein capsid. The capsid is comprised of symmetrically arranged pentamer (orange) and hexamer (purple and green color). Each pentamer is assembled by five A domains, while a hexamer is by three B domains and three C domains of the icosahedral asymmetric unit. (b) Structure of the icosahedral asymmetric unit. This unit consists of two assembled protein subunits: the S subunit which contains domain A (orange) and the L subunit which contains domains B (purple) and C (green).

In this present work, we investigate the 2D assembly of ordered CPMV arrays on mica surfaces induced by the evaporation of electrolyte solution (drop-and-dry method) containing nonionic surfactant poly(ethylene glycol) and propose explanations for observed array symmetries. Atomic force microscopy was used to directly image the assembled structure and obtain real-space confirmation of the 2D structural order. We demonstrate that CPMV on the mica surfaces can be assembled into different 2D periodic lattices of different packing symmetries, from rhombic to hexagonal, depending on the surfactant concentrations. Analysis of the obtained data suggests that these packing configurations satisfy the electrostatic and geometric complementarity of neighboring virus capsids and are governed by the capillary forces arising in the system and the polymer-induced depletion attractive interactions between the capsids.

Experimental Section The formation of 2D virus layers on mica surfaces was explored by the slow evaporation of a constant volume of virus solution completely spread over circular diameter mica disks (1.2 cm in diameter, Ted-Pella, Inc., Redding, CA) under a control environment. Wild type cowpea mosaic virus (CPMV) was produced as described in several works.29,39 The virus stock solution was stored at 4 C in 0.1 M potassium phosphate buffer (SigmaAldrich, Milwaukee, WI) at neutral pH = 7 (referred to as pH 7). To modulate the intervirus interactions, nonionic surfactant 6 kDa poly(ethylene glycol) (PEG, Sigma-Aldrich, Milwaukee, WI) was added to the virus droplet solutions. Typically, the virus sample solution was prepared by diluting the stock solution with the appropriate amount of PEG solution (in the range of final concentrations: 0, 0.0002, 0.001, and 0.04 wt %) and filtered deionized water to yield solutions with 0.5 mg/mL virus concentration and 2 mM potassium phosphate buffer. After the preparation of a sample virus solution, 30 μL of this solution was deposited and spread evenly onto freshly cleaved mica disks. The wetted disks were then put in a covered 2 in. diameter Petri dish and let dry overnight at room temperature. The humidity of the laboratory ranged between 45% and 60%. Since the acidic amino acid residues dominate on the exterior of the CPMV protein capsid when compared with basic ones,29 CPMV is expected have (39) Wang, Q.; Lin, T.; Tang, L.; Johnson, J. E.; Finn, M. G. Angew. Chem., Int. Ed. 2002, 41, 459.

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a net negative charge at pH 7. This argument is also supported by the experimentally determined isoelectric point (pI) of the CPMV (about 5-7).40,41 Thus, the negatively charged silicate surface of mica and virions are expected to electrostatically repel each other. Although nonspecific adsorption of virions onto the mica substrate can still be observed due to the counterion condensation effects present in the electrolyte,42 the rotational and translational mobility of virus on mica surface should not be restricted substantially because the PEG used in the solution is well-known to minimize the nonspecific adsorption of biomolecules.43 Poly-Llysine-coated mica disks, which are positively charged at neutral pH, are often used to immobilize negatively charged biological molecules such as DNA. To examine the effect of positive surface charges on the mobility of virion and its importance in the virion assembly, control experiments were also performed with poly-Llysine (Ted-Pella, Inc., Redding, CA) coated mica disks so as to increase virion immobilization (see section SI1 and Figure S1, Supporting Information). The resulting morphology of the virus layer was then examined by optical microscopy and atomic force microscopy (AFM, multimode atomic force microscope with Nanoscope IIIa controller, Veeco Metrology, Santa Barbara, CA) in tapping mode with silicon probes (force modulation probes, Nanosensors Gmb, Germany). The resulting AFM height images were plane-fitted, “flattened”, and analyzed with the Nanoscope software provided by the AFM manufacturer. 2D fast Fourier transform (FFT) analysis was performed on the resulting virus array images to yield the packing periodicity for different packing morphology obtained with virus solutions of different compositions. Because of the tip deconvolution effect, the accuracy of the AFM measurement is estimated to be (2 nm. To elucidate the distribution of the charged amino acid residues at the protein capsid, the 3D structure of the icosahedral asymmetric unit of the CPMV as well as the whole protein capsid was analyzed by the Sybyl software (Tripos, Inc., St. Louis, MO) and DS Visualizer software (Accelrys, Inc., San Diego, CA). The coordinates of the icosahedral unit structure were obtained from the Protein Data Bank (PDB ID: 1NY7),29 and the whole capsid structure was reconstituted using the VIPERdb.44

Results and Discussion CPMV films prepared by the described drop-and-dry method on mica surfaces were found to yield mostly 2D single-layer array structures. The order of these CPMV films after the drying process was investigated by examining the orientation of each virion and the resulting packing arrangement of these virions by AFM. The icosahedral symmetry of the virion capsid with its characteristic protrusions (Figure 1a) provides easy visual identification of its particular orientation on the substrate surface. Typically, high-resolution AFM topographical image of a CPMV film reveals arrays of triangle structures (Figure 2a). Each triangular structure of about 30 nm in width can be interpreted to be the three capsid protrusions of a single virion. Since this is the top face of a virion, the AFM data indicate that icosahedral viral capsids were predominantly oriented with their 3-fold symmetric triangular face “sitting” on the mica surface during the end of the sample drying process. Both the virions and mica in the considered experimental system are negatively charged at pH 7.40,41 Negative electrostatic repulsions are expected between (40) Siler, D. J.; Babcock, J.; Bruening, G. Virology 1976, 71, 560. (41) Nichols, M. E. K.; Stanislaus, T.; Keshavarz-Moore, E.; Young, H. A. J. Biotechnol. 2002, 92, 229. (42) Harding, J. H.; Duffy, D. M.; Sushko, M. L.; Rodger, P. M.; Quigley, D.; Elliott, J. A. Chem. Rev. 2008, 108, 4823. (43) Kingshott, P.; Griesser, H. J. Curr. Opin. Solid State Chem. 1999, 4, 403. (44) Shepherd, C. M.; Borelli, I. A.; Lander, G.; Natarajan, P.; Siddavanahalli, V.; Bajaj, C.; Johnson, J. E.; Brooks, C. L.; Reddy, V. S. Nucleic Acids Res. 2006, 34, D386.

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Figure 2. (left panel) Atomic force microscopy (AFM) images of CPMV virion assembly obtained by the drop-and-dry method from virion sample solutions containing different concentrations of 6 kDa poly(ethylene glycol) (PEG): (a) 0, (c) 0.0002, and (e) 0.001 wt %. (right panel) Parts b, d, and f show the 2D fast Fourier transforms (FFT) of the AFM images corresponding to parts a, c, and e, respectively. The periodicities along the rhombic symmetry axes of the virion assemblies are indicated in each transformed image.

the mica and the virions. The virions are expected to freely rotate and translate on the mica surface until the virion film dried out in the preparation process. Since the freshly cleaved mica is atomically flat, a “tripod” formed by the three adjacent corner protrusions of a capsid gives the most stable configuration of an icosahedral particle on the flat mica surface. Probably, such configuration results in an increase in virion-substrate interaction without any counteracting penalty. The arrangement of the 2D CPMV arrays was found to vary from rhombic to hexagonal closed packed order by increasing the PEG concentration in the virus drop solution in the film preparation (Figure 2). The relative orientation of the triangle structures and their arrangement formed by the virions represented in the AFM topographical data indirectly portray the order and arrangement of these virion films. First, when the virion solution contains no PEG, the virions in the resulting film forms islands of rhombic packed ordered arrays (Figure 2a). Several single-layer virion domains (regions of compact ordered virion arrays with characteristic symmetry) with rhombic packing were found in the center of the mica substrates. 2D fast Fourier Langmuir 2010, 26(5), 3498–3505

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transform of AFM images indicates that this domain contains virions with periods (R) of 28.7 and 30.3 nm along the two axes defined by the rhombic lattice. The first R period implies that the virions were closely packed in one of the rhombic lattice direction, but not in the other direction. Structural defects are present in our films such as “vacancy” (with missing virions) and “stacking faults” (seen as lines of virions with different orientations of upright and inverted “triangles”) (Figure 2). Addition of 6 kDa PEG to the initial viral solution droplets decreases the intervirus distances and changes the packing geometry of the CPMV array films. When the virus droplet solution contains 0.0002 wt % PEG, after the drop-and-dry process, the resulting CPMV array also adopts a rhombic order. However, the packing of the arrays becomes closer with the two smaller R periods to be 27.0 and 29.1 nm from the FFT image analysis, when compared to case without PEG (Figure 2c,d). More drastic changes in the virions packing were found in samples prepared with 0.001 wt % PEG in the initial droplet. First, instead of the rhombic packing order, slightly distorted hexagonal closed packed virion arrarys were obtained (Figure 2e,f). Second, besides the packing morphology, the FFT image of the resulting array indicates that these virions are much more tightly packed than the ones with lower or zero PEG concentration in the virial solution. The R periods for the three major directions of this virion array are 27.6, 25.3, and 25.4 nm, which are smaller than the typical diameter of a CPMV virus (28 nm). Occasionally, because of the large PEG concentration, double-layered arrays of similar packing are found. Upon an increase in the PEG concentration to 0.04 wt % in the initial virus solution, we still observe some hexagonal closed pack domains of virions, but the detailed features of the capsids cannot be revealed by AFM due to an overcoating of PEG on the samples (data not shown). The observed different CPMV array geometries formed with virus solution of different PEG 6 kDa concentrations can be explained by further detailed structural analysis of the CPMV capsid, its surface topology, and peculiarities of the intercapsid interactions during the drying process during film preparation. In our experiments, the electrolyte solution layer with the CPMV particles is sandwiched between the hydrophilic dielectric (mica) surface and a gaseous phase (air). The layer contains solvated CPMV virus particles (at a given concentration) with different concentrations of the polymer surfactant (PEG). Aggregation of the virus particles (2D arrays) is achieved by the attractive depletion force from the evaporation process. The ordering, quality, structural arrangement, and stability of 2D virus arrays depend largely on the effective balance between attractive and repulsive interparticle interactions in the system. It is reasonable to suggest that when the thickness of the solution layer is larger than the colloidal particle size (28 nm for a CPMV particle in our case), the interactions between particles during their diffusion collisions (due to Brownian motion) are governed by electrostatic, U(r)El, and short-range van der Waals force interactions, U(r)vdW.45,46 The PEG molecules are responsible for an additional entropic effect: polymer-induced depletion (attractive) interactions between virus particles.45-48 Since the size of the colloidal (virus) particle in electrolyte solution is much greater than the PEG polymer size (the radius of gyration Rg ∼ 2 (45) Israelachvili, J. Intermolecular and Surface Forces; Academic Press: San Diego, 1985. (46) Wentzel, N.; Pagan, D. L.; Gunton, J. D. J. Chem. Phys. 2007, 127, 165105. (47) Kulkarni, A. M.; Chatterjee, A. P.; Schweizer, K. S.; Zukoski, C. F. J. Chem. Phys. 2000, 113, 9863. (48) Kozer, N.; Kuttner, Y. Y.; Haran, G.; Schreiber, G. Biophys. J. 2007, 92, 2139.

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nm26,46), one can describe these interactions by the AsakuraOosawa potential: U(r)AO.46,47 In this description, the polymer can be considered as hard spheres which do not adsorb on the colloidal particles.47,48 During the evaporation process, the thickness of the solution layer on the mica is becoming less than the virus particle size. In this case, long-range lateral forces of capillary attraction (or attractive capillary immersion forces, UCIF(r)) are developed,45,49,50 mainly due to the deformation of the liquid surface, which is supposed to be flat in the absence of particles. The larger the interfacial deformation created by the particles during evaporation, the stronger is the capillary interaction between them. The virions in the solution layer can be considered in the simplest manner as rigid spherelike particles interacting with each other and with the mica surface. Thus, by using the four different interaction forces described, the pairwise effective force potential, U(r), between two virus particles can be obtained as U(r) = UCIF(r) + U(r)El + U(r)vdW + U(r)AO. The first and last term of the potential describe the major driving forces for the compression of the virions into the observed 2D ordered arrays on mica in our work. In the case of the arising depletion interactions, when 6 0, a compressive effect between viral capsids should be U(r)AO ¼ significantly larger than the case when the depletion interactions are lacking and U(r)AO = 0. These two different conditions are the major factors for the two distinct virion packing schemes in the presence and absence of PEG surfactant. Charge Mapping of the Virus Capsid. To understand the nature of the two different CPMV packing arrays in the experiment, we analyze the distribution of the ionogenic groups of the titrating amino acid residues on the protein capsid in solutions at pH 7 to reveal influence of interviral electrostatic interactions. To simplify this analysis, we focus on the distribution of the charged ionogenic groups of the residues (Asp/Glu and Arg/Lys/His) within the icosahedral asymmetric unit of the CPMV capsid. This distribution is illustrated in Figure 3a, where the unit is oriented in the same manner as in the original crystallographic work (see Figure 3c in Lin et al.29). Figure 3b shows the electrostatic potential mapped on the solvent-accessible surface of the icosahedral unit oriented similarly as in Figure 3a. Simple estimations indicate that the S protein subunit (or A domain) of the unit of interest has dominant negative charges equal to -4e, which is the total effective charge of the 17 negatively (Glu/Asp) and 13 positively (Arg/Lys/His) charged residues located at this subunit. The L protein subunit (composed of B and C domains) has a positive effective charge equal to +2e, which is the total effective charge of the 34 negatively and 36 positively charged residues distributed on this subunit. Our analysis also shows that at the outside interface between the L and S subunits there is a region with high density of positively charged residues (Figure 3a) which corresponds to two areas of the positive electrostatic potentials (Figure 3b). These positively charged residues in the region were found to be mostly concentrated in the L subunit and related to Arg in positions 97, 143, 145, 147, 170, 195, 243, 315, and 367 as well as His66 and Lys in positions 99 and 352. For the S subunit these residues were the Arg61, Arg170, and Lys66. The average distance (Ædaaæ) between CR atoms of the two amino acid residues at the apex of the A domain (Lys82 and Ala84) and the corresponding charged residues in the above boundary region is found to be about 5 nm. This distance between the apex of negatively charged protrusions and positively charged patches (49) Kralchevsky, P. A.; Nagayama, K. Langmuir 1994, 10, 23. (50) Kralchevsky, P. A.; Denkov, N. D. Curr. Opin. Colloid Interface Sci. 2001, 6, 383.

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Figure 3. Schematic representation of charged amino acid residues and corresponding electrostatic potential mapped on the solvent-accessible surface on the icosahedral asymmetric unit. (a) Distribution of the negatively (Asp/Glu) and positively (Arg/ Lys/His) charged amino acid residues at pH 7 are displayed by the red and blue colors, respectively. The arrows indicate the surface region at the outside interface between L and S subunits that contains a dominant number of positively charged residues. (b) Distribution of the effective electrostatic potential (in arbitrary units) mapped on the solvent-accessible surface of the unit.

can be considered as an averaged characteristic length scale of main charge modulation on the surface of a viral capsid. Hence, at the distances much larger than this characteristic length, the virion can be considered as a uniformly charged spherical particle. The surface topology (protrusions and valleys) and heterogeneous surface charge distribution of the capsid should be taken into account at distances smaller than this characteristic length. It should be noted that around neutral pH the imidazole ring of His residues can be rather sensitive to the shift of the pH into the basic region and thereby could be found also in deprotonated state. In this case, the effective charge of the subunits could be changed to -6e for S subunit and to -3e for L subunit. Thus, if other titratable residues do not change their charge state under the possible moderate pH shift, the positively charged region of the outside interface between L and S subunits is not expected to change significantly. The unique distribution of the icosahedra asymmetric units of the CPMV capsid forms the symmetrical pentamers and hexamers (Figure 1). As revealed in the crystallographic work,29 the pentamers (orange regions) correspond to the capsid protrusions, whereas the hexamers (purple and green regions) correspond to the capsid valleys. Hence, as it follows from our analysis, the CPMV capsid has symmetrically arranged regions (pentamers and hexamers) that carry effectively negative and/or positive charges. At the interface between them, there are five discrete, evenly distributed patches that present identical positive charges. Each of the patches includes charges at the interface between C and A domains of the one icosahedral unit and the charges in B domain at its interface with A domain of the adjoining unit (Figures 1 and 3). Phenomenological Model of the Virus Packing. General explanations of the possible phenomenological scenarios that resulted in the two different packing types of the CPMV particles can be deduced by considering the steric and electrostatic complementarity39 between adjacent virions and also the osmotic depletion forces appearing in the sample drying process. The 2D arrays of the CPMV particles were formed by evaporation of the sample solution layer until the particles came in contact on the flat, hydrophilic mica surface. In this process, the long-range capillary attractive interaction between the particles plays the major role.49,50 This interaction can be much greater than the thermal energy (kT) for particles of nanometer size.50 The capillary attraction develops between capsids after the tops of these particles protrude at the surface of the solution layer. The deformation of the solution surface in the considered system is 3502 DOI: 10.1021/la903114s

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due to the highly wetting properties of the hydrophilic capsid surface. This hydrophilicity is associated with the large number of the charged and polar amino acid residues located on the capsid surface which can easily form hydrogen bonds with water molecules of the solution. The capsids in the monolayer touch the mica surface with the apexes of the three capsid protrusions. The capillary condensation of solution on the corresponding valley surface (between the protrusions adjacent to the mica surface) also facilitates the adhesion of capsids to the mica.45 Thus, some restricted translational and rotational diffusion mobility of the capsids on the mica surface can be achieved. The described interparticle capillary interactions provide a compressive effect between capsids in spite of the electrostatic repulsive interactions that arise between capsids with identical charges. In the beginning of the virion assembly process, when the distance, D, between two particle surfaces is much larger than the length scale, Ædaaæ, the capsid icosahedral geometry and its charge distribution peculiarities can be neglected. In this case, the capsids can be approximated as identical spheres. Upon the evaporation of the virial solution, the compression between capsids increases and D becomes about or less than Ædaaæ. Under this condition, the geometrical and charge distribution properties of the capsid become the major factors governing the inter-virion interactions. Because of the evaporation, the electrolyte concentration increase significantly in comparison with the initial buffer concentration. As a result, the Debye length, LD, in the electrolyte solution (effect of the mobile ions)23 significantly decreases. For example, if the electrolyte concentration increases by 1 order of magnitude from the initial buffer concentration (∼1 mM) to ∼1  10-2 M, the length LD at room temperature changes from a value of ∼7 nm to about 1 nm or less. In this case, electrostatic interactions between charges on the surfaces of the two close and adjacent capsids are strongly screened at all distances exceeding the corresponding LD. Furthermore, since the Debye-H€uckel screening23 is proportional to exp(-r/LD) and the thickness of the protein capsid is within a range of 2-3 nm,24 the influence of the charges located at the viral RNA inside of the capsid on the electrostatic potential outside capsid can be neglected. Therefore, it is reasonable to suggest that electrostatic potential at any point of the solution at the capsid-solution interface is determined mainly by charged and polar residues of the capsid of the closest encirclement. Thus, under enough compression of the capsid ensembles on mica, the optimal 2D packing of these ensembles would lead to energetically favorable orientations of the capsids. In this scenario, the capsid protrusions (the pentamer regions), which carry effective negative charges, are brought close together and oriented face-to-face to the patches of the capsids, which have effective positive charge and are located at the edges of the valleys (the hexamers regions) (Figures 1, 3, and 4). This configuration simultaneously provides the best geometric fit between the surfaces of two adjacent virions and an increase in their superficial contact area. Such favorable steric configuration provides maximum contribution from van der Waals interactions between two touching virions. To investigate the effect of geometric factors on localized electrostatic interactions, we performed crude estimation of the electrostatic interaction energy (Ue) between these adjacent virons using a 2D projection model of the two neighboring viral capsids in the assembly layer on mica (Figure 4a,b). The model approximates the cross section of a virion as a slighted distorted hexagonal with point charges at the corresponding locations. For the estimation of Ue, we applied Coulomb’s law modified by Debye-H€uckel exponential screening between point charges to mimic the characteristic charged regions (residing on Langmuir 2010, 26(5), 3498–3505

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Figure 4. Schematic representation of the steric and electrostatic complementarity of two neighboring CPMV capsids. Each capsid is represented by a hexagon which depicts the 2D projection of the capsid when viewed along one of its 3-fold axes. (a) Two neighboring capsids represented by two hexagons with negatively charged protrusions (peach) and positively charged patches (blue). The magnitudes of the charges were deduced from the numbers of ionogenic groups (amino acid residues) contained in the protrusions and patches of the CPMV crystal structure. The transverse shift of the position of the symmetry axes through the center of the projected image (dotted line) with respect to each other is shown as d. The double-ended arrows indicate the complementary (favorable) electrostatic interactions. (b) Plot of estimated relative electrostatic interaction energy (Ue) for pairwise neighboring virus capsids laid on their 3-fold faces on mica as a function of transversal displacement d. The first minimum is at around 5 nm, and the second minimum is at around 9 nm.

the protrusions and the patches) on the capsid surface without consideration of the electrostatic boundary conditions (see Figure S3, Supporting Information). This approximation is sufficient for qualitative discussion of the energy landscape. The neighboring virions are expected to prefer arrangement with opposite charges of nearest capsids closest to each other. We estimated Ue landscape for the relative arrangement of neighboring virions by “shifting” (sliding) pairwise viral capsids along their contact plane. Figure 4 shows the dependence of Ue as a function of the magnitude of the “shift”, d, between two capsids from the common symmetry axis. The two minima indicated by arrows on this curve correspond to the two electrostatically complementary positions of neighboring virions where negatively charged protrusions are located at the closest distance to the positively charged patches (for details of calculations see section SI2, Supporting Information). Consequently, we postulate that detailed electrostatic complementarity of charge distribution patterns on the viral capsids would guide the subtle assembly of virions. It should be noted that even if the effective charge of the “valleys” on the viral capsids is negative (as we described above in the case of the deprotonated His residues), a “lateral” electrostatic repulsion between the protrusion of one capsid and both the protrusion and neighboring valley of the other capsid would facilitate favorable orientation between the protrusion and positively charged patch. If the effective charge of the valley is positive, the favorable orientation would be preserved. Thus, the rhombic arrangement of the 2D packing of the CPMV capsids observed in the present work (Figure 2a,c) can be achieved by geometrical and electrostatic complementarity (Figures 5 and 6) between the capsid protrusions and valleys. In the final stage of evaporation, the translational and rotational diffusional motion of the capsids provides the final stabilization of the above packing Langmuir 2010, 26(5), 3498–3505

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Figure 5. Periodic CPMV virus arrays and the corresponding postulated electrostatic complementarity explanations. (a) AFM image and (b) rhombic model for the virus array formed from virus solutions without PEG surfactant. The angle between two principal axes of the array lattice explained as a result of electrostatic and geometry complementarity is shown as R ∼ 20. It increases the rhombic angle, θrhombic, to ∼80 from 60, the corresponding value of a hexagonal closed packed array. The lengths of the two basis vectors, a and b, are approximately equal in length (a ≈ b ≈ 28.5 nm). (c) AFM image of the virus array from virion solution with 0.001 wt % PEG surfactant and (d) the corresponding hexagonal packing model. Exerts show the location of negatively charged protrusions and positively charged patches satisfying the electrostatic and steric complementarity.

by simultaneous reduction of the solution thickness on the mica and sedimentation of the capsids on the surface. Since only His (out of all titratable amino acid residues) may change its sidechain charge in a wide range of pH (4-8), the 2D assembly should be insensitive to the pH shift. When the polymer surfactant (PEG) was added to the solution, the assembly of the 2D capsid arrays resulted in different packing symmetry. The addition of the PEG leads to effective depletion (attractive) interaction between the capsid particles with the strength governed by the polymer concentration through the polymer solution osmotic pressure.45-48,51 Consequently, possible phenomenological scenarios for the intercapsid interaction energy landscape may also have changed. First, the compressive effect between the CPMV capsids can be dramatically reinforced by the depletion attractive forces because the PEG concentration in the electrolyte layer should increase due to the evaporation of the solution. Simple estimation of the entropic attraction effect induced by the PEG osmotic pressure can be achieved by applying the Asakura-Oosawa attractive potential U(r)AO46,47 when the corresponding intervirion distance r is much smaller than R + Rg, where R is the radius of the virus particle (∼14 nm) and Rg is the radius of gyration of the utilized PEG polymer (6 kDa). Using the known model parameters, the Rg of this polymer is estimated to (51) Barrat, J.-L.; Hansen, J.-P. Basic Concepts for Simple and Complex Liquids; Cambridge University Press: Cambridge, 2003.

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Figure 6. Stacking fault observed in an AFM image of a CPMV array produced by the drop-and-dry method without surfactants. (a) AFM image of the stacking fault shows the adjacent virions having reversed orientation with respect to each other. The corners of the capsids are labeled with white dots to indicate the two different orientations of the virions shown in the image. (b) Virus array model using the hexagonal representation of the 2D projection of a virion. Negatively charged protrusions (peach) and positively charged patches (blue) are shown on the hexagon models to show a possible stable electrostatic packing scenario. The electrostatic complementarity is still satisfied with only one contact along the side with the faulted neighbor. This gives rise to two basis vectors of unequal length (a = 28.5 nm and b = 29.7 nm).

be ∼2 nm.46,26 Our evaluation shows that the value of (-1)U(r)AO potential in the virus solution increases from 0.17 kT to 7 kT as the polymer concentration increases from 0.001% (∼1.7  10-6 M) to 0.04% (∼6.7  10-5 M). Thus, even under relatively low polymer concentrations (∼0.04%), the U(r)AO attractive potential is rather strong. The value of this potential is comparable to the high attractive electrostatic interaction energy of two model protein molecules that are in the transition state before their final complex is formed.52-54 As the electrolyte concentration further increases during evaporation, the attractive potential, (-1)U(r)AO, increases as well and may be significantly larger than 7 kT. As a consequence of the evaporation of viral solutions, the PEG-induced attraction effect is accompanied by reduction of the inter-virion particle distance, which leads to additional strong compressive effects among the viral capsids. This effect can significantly compensate for all relevant nonfavorable electrostatic interactions between capsids and produce their closest packing (Figure 2e,f and Figure 5c). This packing is associated with the favorable orientation of the capsids considered above without PEG with the clockwise shift of neighboring capsid protrusions toward the other capsid valley (see Figure 5d). With the virus capsids under such orientations, the hexagonally packed arrangement of the capsids in the 2D arrays is achieved. Under such circumstances, the capillary condensation of solution at the capsid-capsid contact sites (the valley between the two protrusions) probably traps some PEG polymer and water molecules. In fact, these condensation regions fasten (“cement”) the hexagonal packing of the capsids by the attractive van der (52) Rubinstein, A.; Sherman, S. Biopolymers 2007, 87, 149. (53) Vijayakumar, M.; Wong, K.-Y.; Schreiber, G.; Fersht, A. R.; Szabo, A.; Zhou, H.-X. J. Mol. Biol. 1998, 278, 1015. (54) Alsallaq, R.; Zhou, H.-X. Proteins 2008, 71, 320.

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Waals forces. The final stabilization of the packing on the mica surface is achieved by the sedimentation described previously. Furthermore, the hexagonal symmetry revealed in our experiments for the 2D arrays is consistent with the same symmetry of the unit cell revealed for the 3D crystal packing of CPMV virus and described in the original crystallographic work.29 The observed CPMV capsid packing in the considered system yields either rhombic or hexagonal periodic lattices. The latter can be considered as a specific case of rhombic lattice with the 60 angle between two symmetry axes. The rhombic lattice is formed because electrostatic interactions favor the arrangement consisting of regions with pairing of opposite charges on two neighboring virus. The negatively charged protrusions of the viral capsid tend to be close to the positively charged patches on the adjacent capsid. Thus, because of the electrostatic and steric complementarity, the relative orientation of neighboring viruses should have the shift of its protrusions of ∼5 nm (as discussed above and shown in section SI3 of the Supporting Information). As shown in Figure 5a, this rearrangement gives rise to voids in the rhombic packing. This increases the angle between the two basis vectors (a and b in Figures 5a,b) of periodic lattice from 60 in the case of the closest packing hexagonal structure to a total angle of about 80. Figures 5c,d illustrates the scenario of hexagonal packing which satisfies the electrostatic complementarity. Under high PEG concentrations (or strong compression), negatively charged protrusions (vertexes) of neighboring hexagonal virion in 2D projections are shifted toward the positive patches in a clockwise manner. This packing preserves the 60 angle between the two basis vectors. At the same time, the length of basis vectors is shorter than the case of low PEG concentration as shown in Figures 5a,b. The average distance between surfaces of neighboring virions estimated from the image and FFT data is only about 0.5-0.6 nm, which is much smaller than the 3-4 nm in rhombic lattices obtained under low concentration of PEG. The Fourier analysis of the periodic lattices of virus assembly shows that the lengths of the basis vectors, a and b, are reduced with an increase in the surfactant concentration. Using experimentally obtained packing data shown in Figure 5, we estimate the average shift of the vertices of virus protrusions toward positively charged patch. The obtained values for different concentrations of PEG are presented in Table S1 of the Supporting Information. The estimated distance between the protrusion vertex and the positive patch of the single virion matches well with the predicted packing shift d (∼5-6 nm). The Fourier transformed images of the virus arrays frequently indicate two slightly different periodicity scales along same symmetry directions (basis vectors a and b in real space). The major reason for this observation can be attributed to the presence of stacking faults in the lattice. A common structure of the stacking fault can be explained using the electrostatic and steric complementarity arguments (Figure 6). In most of these cases, neighboring virions can have the same orientation as confirmed by AFM images showing the triangles formed by three protrusions on the top capsid faces. These triangles have the same spatial arrangement in short distances. However, the orientation of virions in two neighboring rows can be reversed, i.e., triangles of the top face flipped upside down. This changes the relative elevation of positive patches with respect to protrusions from the neighboring virions and increases the shift of neighboring virions along the side to satisfy the new steric and electrostatic complementarity conditions. The estimated ratio of two basis vectors, a/b, from FFT analysis is about 1.04. The stacking fault of the structure shown in the inset of Figure 6b increases this ratio a/b to 1.08. Langmuir 2010, 26(5), 3498–3505

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Similarity between Viral Capsids Self-Assembly and Protein-Protein Association. Our results are well-correlated within the modern view of the protein-protein complex formation under physiological conditions. Favorable electrostatic forces acting between interacting proteins considered together with their steric complementarity as well as the depletion forces increase the association rate of protein-protein complexes.47,48,51-53,55-58 In particular, in vivo, the association of proteins occurs in crowded environments, namely inside the cell or in the extracellular matrix. In these environments, besides proteins of interest, many other macromolecules of various sizes and different chemical compositions are also present. Synthetic polymers such as PEG are commonly used as a means to simulate the molecular “crowding” inside a cell.47,48 Under this simulated condition, PEG can affect the interactions between protein structures through induced depletion attraction.48,58 Our experimental procedure to regulate the interactions between supramolecular structures (i.e., viral capsids) for generating the 2D virus arrays mimics the effect of increasing the concentration of PEG in protein solutions. In a virus solution containing dilute or moderate concentration of PEG, the osmotic forces induced by the PEG promote attraction between viral capsids. Such a scenario mimics the case of protein-protein association in PEG solution. Kozer et al. reported that repulsive depletion interactions were observed in concentrated protein-polymer solutions (ref 48 and references therein). In the present work, virus films formed with virus solutions containing excessive concentration of PEG (0.04 wt % or more) would result in the diminishing of the 2D ordering with the films due to the codeposition of PEG (Figure S5). We attribute this observed destructive effect to the same reason discussed for the protein-protein association in the concentrated PEG solutions.48,58 Thus, our investigation of the interaction between viral protein capsids during the array assembly process could potentially be applied to model the physicochemical nature of protein-protein association.

Conclusion Experimental studies of cowpea mosaic virus assembly on mica surfaces by the drop-and-dry method revealed two distinct 2D periodic rhombic and hexagonal packing structures controlled by (55) (56) 106. (57) (58)

McCoy, A. J.; Epa, V. C.; Colman, P. M. J. Mol. Biol. 1997, 268, 570. Grabb, H. A.; Jackson, R. M.; Sternberg, M. J. E. J. Mol. Biol. 1997, 272, Heifetz, A.; Katchalski-Katzir, E.; Eisenstein, M. Protein Sci. 2002, 11, 571. Phillip, Y.; Sherman, E.; Haran, G.; Schreiber, G. Biophys. J. 2009, 97, 875.

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the concentrations of polymer surfactant additive (PEG 6 kDa). We explain the symmetry of the 2D packing by considering the features of the charged amino acid residue distribution on the virus capsid surface and its unique capsid geometry. Our data suggest that the obtained characteristic packing types satisfy the electrostatic and geometric complementarity of neighboring virus capsids. They are also governed by the capillary forces arising in the system and the polymer-induced depletion attractive interactions between the capsids. The hexagonal symmetry of the 2D arrays is consistent with the same symmetry of the unit cell revealed by 3D crystal packing of CPMV and described in the original crystallographic work.29 Our results also imply that the formation of the ordered 2D capsid arrays on mica can be explained without taking into account the virus interior genetic content such as RNA. Our study also suggests that the steric and electrostatic complementarity principles can be applied to assemble other biological building blocks and design the symmetry of these arrays. Our findings are significant not only for applications in the governing of supramolecular assembly but also for formulating models to evaluate mechanisms of protein-protein association. In addition, the striking correlation of our results for the interacting ordered viral capsid arrays and the formation of proteinprotein complexes under physiological conditions enhances our insights into mechanisms for the interaction of the latter. Thus, our results can in principle be applied to many potential systems of biological macromolecules. Acknowledgment. Part of this work was performed under the auspices of the U.S. Department of Energy by the University of California, Lawrence Livermore National Laboratory, under Contract W-7405-Eng-48. C.L.C., A.R., R.F.S., and W.N.M. thank the University of Nebraska at Lincoln and Nebraska Research Initiative for partial financial support. T.L. and J.E.J. acknowledge the support of Office of Naval Research (N0001400-1-0671). J.D.Y. acknowledges U.S. Department of Energy (DOE), Office of Basic Energy Science (BES), Division of Materials Science and Engineering for support of this research Supporting Information Available: AFM data of control experiment, estimation of electrostatic interactions between two CPMV virions, and calculation of the transversal shift of neighboring virions. This material is available free of charge via the Internet at http://pubs.acs.org.

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