Deciphering the Kinetic Mechanism of Spontaneous Self-Assembly of Icosahedral Capsids Hung D. Nguyen, Vijay S. Reddy, and Charles L. Brooks III* Department of Molecular Biology, TPC6, 10550 North Torrey Pines Road, La Jolla, California 92037 Received October 18, 2006; Revised Manuscript Received November 21, 2006 ABSTRACT Self-assembly of viral proteins into icosahedral capsids is an interesting yet poorly understood phenomenon of which elucidation may aid the exploration of beneficial applications of capsids in materials science and medicine. Using molecular dynamics simulations of coarse-grained models for capsid proteins, we show that the competition between the formation of full capsids and nonidealized structures is strongly dependent upon the protein concentration and temperature, occurring kinetically as a cascade of elementary reactions in which free monomers are added to the growing oligomers on a downhill free-energy landscape. However, the insertion of the final subunits is the rate-limiting, energetically unfavorable step in viral capsid assembly. A phase diagram has been constructed to show the regions where capsids or nonidealized structures are stable at each concentration and temperature. We anticipate that our findings will provide guidance in identifying suitable conditions required for in vitro viral capsid assembly experiments. Introduction. For about half of the known virus families, the protein coat that protects the viral genome, in the form of DNA or RNA, is a “spherical” or icosahedral capsid. 1,2 These capsids are composed of multiples of 60 copies of individual proteins that must assemble correctly, rapidly, and spontaneously on a biological time scale in order to propagate an infection in vivo. 3 Elucidating the means by which viral capsid self-assembly occurs may have potential in assisting the development of novel approaches to interfere with the assembly process and ultimately viral infections. In addition, gaining insights into the capsid self-assembly process may also aid our exploitation of beneficial applications of viral capsids in medicine and materials science. In medicine, empty capsids without the viral genome can be used as a vaccine to prevent cancers; for example, exposure to empty capsids of the human papilloma virus produces antibodies in the body priming an effective immune response in case of subsequent exposure to the infectious virus that causes cervical cancer. 4,5 Also, capsids may be used as carriers in drug delivery because of their ability to specifically target tumor cells; for example, canine parvovirus capsids gain entry into human cells by binding transferrin receptors, which are produced by a variety of tumor cells. 6 In materials science, because of their highly symmetrical monodisperse architectures, viral capsids are versatile nanoscale materials that can be used as templates in catalysis and nanostructure synthesis. 7 While progress toward understanding the molecular-level mechanisms driving capsid formation has been made through theoretical studies, 8-15 structural analysis, 16,17 and in vitro experiments on the self-assembly of empty capsids using only purified capsids proteins, 11,18,19 relevant atomic-resolution computer simulation studies have been impossible due to the large system sizes required and the long timescales involved although initial attempts are emerging. 20 As a consequence, to-date most simulation studies of capsid formation have been limited to simplified models 21,22 that obscure the geometric nature of the capsid subunits. Because of the importance geometrical factors appear to play, quasi- symmetry and the structural organization of viral capsids is well described by the organization of geometrical shapes into a closed icosahedral structure, 2 these models have not made strong connections to existing experiments on capsid as- sembly. One inspiring study that did strive to capture the geometrical nature of this problem is by Rapaport et al., 23,24 who performed the first exploratory molecular dynamics simulations on capsid self-assembly of a polyhedral structure from trapezoidal units. However, they enforced many nonphysical assembly rules ensuring that only full capsids would be formed; therefore, their simulations fail to capture the spontaneous self-assembly process and its dependency on the environment. In this study, we have extended these initial ideas to develop two geometric models that capture geometric and energetic details without any specific built- in self-assembly rules such as a nucleation step; these models * Corresponding author. Phone: 858/784-8035. FAX: 858/784-8688. E-mail: brooks@scripps.edu. NANO LETTERS 2007 Vol. 7, No. 2 338-344 10.1021/nl062449h CCC: $37.00 © 2007 American Chemical Society Published on Web 01/09/2007