1
|
Villanueva Valencia JR, Tsimtsirakis E, Krueger S, Evilevitch A. Temperature-induced DNA density transition in phage λ capsid revealed with contrast-matching SANS. Proc Natl Acad Sci U S A 2023; 120:e2220518120. [PMID: 37903276 PMCID: PMC10636372 DOI: 10.1073/pnas.2220518120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2022] [Accepted: 09/25/2023] [Indexed: 11/01/2023] Open
Abstract
Structural details of a genome packaged in a viral capsid are essential for understanding how the structural arrangement of a viral genome in a capsid controls its release dynamics during infection, which critically affects viral replication. We previously found a temperature-induced, solid-like to fluid-like mechanical transition of packaged λ-genome that leads to rapid DNA ejection. However, an understanding of the structural origin of this transition was lacking. Here, we use small-angle neutron scattering (SANS) to reveal the scattering form factor of dsDNA packaged in phage λ capsid by contrast matching the scattering signal from the viral capsid with deuterated buffer. We used small-angle X-ray scattering and cryoelectron microscopy reconstructions to determine the initial structural input parameters for intracapsid DNA, which allows accurate modeling of our SANS data. As result, we show a temperature-dependent density transition of intracapsid DNA occurring between two coexisting phases-a hexagonally ordered high-density DNA phase in the capsid periphery and a low-density, less-ordered DNA phase in the core. As the temperature is increased from 20 °C to 40 °C, we found that the core-DNA phase undergoes a density and volume transition close to the physiological temperature of infection (~37 °C). The transition yields a lower energy state of DNA in the capsid core due to lower density and reduced packing defects. This increases DNA mobility, which is required to initiate rapid genome ejection from the virus capsid into a host cell, causing infection. These data reconcile our earlier findings of mechanical DNA transition in phage.
Collapse
Affiliation(s)
| | - Efthymios Tsimtsirakis
- Department of Experimental Medical Science and NanoLund, Lund University, Lund22184, Sweden
| | - Susan Krueger
- Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD20899-6102
| | - Alex Evilevitch
- Department of Experimental Medical Science and NanoLund, Lund University, Lund22184, Sweden
| |
Collapse
|
2
|
Fizari M, Keller N, Jardine PJ, Smith DE. Role of DNA-DNA sliding friction and nonequilibrium dynamics in viral genome ejection and packaging. Nucleic Acids Res 2023; 51:8060-8069. [PMID: 37449417 PMCID: PMC10450192 DOI: 10.1093/nar/gkad582] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2023] [Revised: 06/17/2023] [Accepted: 06/27/2023] [Indexed: 07/18/2023] Open
Abstract
Many viruses eject their DNA via a nanochannel in the viral shell, driven by internal forces arising from the high-density genome packing. The speed of DNA exit is controlled by friction forces that limit the molecular mobility, but the nature of this friction is unknown. We introduce a method to probe the mobility of the tightly confined DNA by measuring DNA exit from phage phi29 capsids with optical tweezers. We measure extremely low initial exit velocity, a regime of exponentially increasing velocity, stochastic pausing that dominates the kinetics and large dynamic heterogeneity. Measurements with variable applied force provide evidence that the initial velocity is controlled by DNA-DNA sliding friction, consistent with a Frenkel-Kontorova model for nanoscale friction. We confirm several aspects of the ejection dynamics predicted by theoretical models. Features of the pausing suggest that it is connected to the phenomenon of 'clogging' in soft matter systems. Our results provide evidence that DNA-DNA friction and clogging control the DNA exit dynamics, but that this friction does not significantly affect DNA packaging.
Collapse
Affiliation(s)
- Mounir Fizari
- Department of Physics, University of California, San Diego, La Jolla, CA 92093, USA
| | - Nicholas Keller
- Department of Physics, University of California, San Diego, La Jolla, CA 92093, USA
| | - Paul J Jardine
- Department of Diagnostic and Biological Sciences and Institute for Molecular Virology, University of Minnesota, Minneapolis, MN 55455, USA
| | - Douglas E Smith
- Department of Physics, University of California, San Diego, La Jolla, CA 92093, USA
| |
Collapse
|
3
|
Bong S, Park CB, Cho SG, Bae J, Hapsari N, Jin X, Heo S, Lee JE, Hashiya K, Bando T, Sugiyama H, Jung KH, Sung B, Jo K. AT-specific DNA visualization revisits the directionality of bacteriophage λ DNA ejection. Nucleic Acids Res 2023; 51:5634-5646. [PMID: 37158237 PMCID: PMC10287942 DOI: 10.1093/nar/gkad340] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2022] [Revised: 03/14/2023] [Accepted: 04/21/2023] [Indexed: 05/10/2023] Open
Abstract
In this study, we specifically visualized DNA molecules at their AT base pairs after in vitro phage ejection. Our AT-specific visualization revealed that either end of the DNA molecule could be ejected first with a nearly 50% probability. This observation challenges the generally accepted theory of Last In First Out (LIFO), which states that the end of the phage λ DNA that enters the capsid last during phage packaging is the first to be ejected, and that both ends of the DNA are unable to move within the extremely condensed phage capsid. To support our observations, we conducted computer simulations that revealed that both ends of the DNA molecule are randomized, resulting in the observed near 50% probability. Additionally, we found that the length of the ejected DNA by LIFO was consistently longer than that by First In First Out (FIFO) during in vitro phage ejection. Our simulations attributed this difference in length to the stiffness difference of the remaining DNA within the phage capsid. In conclusion, this study demonstrates that a DNA molecule within an extremely dense phage capsid exhibits a degree of mobility, allowing it to switch ends during ejection.
Collapse
Affiliation(s)
- Serang Bong
- Department of Chemistry, Sogang University, Seoul 04107, Korea
| | - Chung Bin Park
- Department of Chemistry, Sogang University, Seoul 04107, Korea
| | - Shin-Gyu Cho
- Department of Life Science, Sogang University, Seoul 04107, Korea
| | - Jaeyoung Bae
- Department of Chemistry, Sogang University, Seoul 04107, Korea
| | - Natalia Diyah Hapsari
- Department of Chemistry, Sogang University, Seoul 04107, Korea
- Chemistry Education Program, Department of Mathematics and Science Education, Sanata Dharma University, Yogyakarta 55282, Indonesia
| | - Xuelin Jin
- Department of Chemistry, Sogang University, Seoul 04107, Korea
- College of Agriculture, Yanbian University, Yanji133000, China
| | - Sujung Heo
- Department of Chemistry, Sogang University, Seoul 04107, Korea
| | - Ji-eun Lee
- Department of Life Science, Sogang University, Seoul 04107, Korea
| | - Kaori Hashiya
- Department of Chemistry, Graduate School of Science, Kyoto University, Sakyo-Ku, Kyoto606-8502, Japan
| | - Toshikazu Bando
- Department of Chemistry, Graduate School of Science, Kyoto University, Sakyo-Ku, Kyoto606-8502, Japan
| | - Hiroshi Sugiyama
- Department of Chemistry, Graduate School of Science, Kyoto University, Sakyo-Ku, Kyoto606-8502, Japan
| | - Kwang-Hwan Jung
- Department of Life Science, Sogang University, Seoul 04107, Korea
| | - Bong June Sung
- Department of Chemistry, Sogang University, Seoul 04107, Korea
| | - Kyubong Jo
- Department of Chemistry, Sogang University, Seoul 04107, Korea
| |
Collapse
|
4
|
Fizari M, Keller N, Jardine PJ, Smith DE. Role of DNA-DNA sliding friction and non-equilibrium dynamics in viral genome ejection and packaging. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.04.03.535472. [PMID: 37066220 PMCID: PMC10104077 DOI: 10.1101/2023.04.03.535472] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/19/2023]
Abstract
Many viruses eject their DNA via a nanochannel in the viral shell, driven by internal forces arising from the high-density genome packing. The speed of DNA exit is controlled by friction forces that limit the molecular mobility, but the nature of this friction is unknown. We introduce a method to probe the mobility of the tightly confined DNA by measuring DNA exit from phage phi29 capsids with optical tweezers. We measure extremely low initial exit velocity, a regime of exponentially increasing velocity, stochastic pausing that dominates the kinetics, and large dynamic heterogeneity. Measurements with variable applied force provide evidence that the initial velocity is controlled by DNA-DNA sliding friction, consistent with a Frenkel-Kontorova model for nanoscale friction. We confirm several aspects of the ejection dynamics predicted by theoretical models. Features of the pausing suggest it is connected to the phenomenon of "clogging" in soft-matter systems. Our results provide evidence that DNA-DNA friction and clogging control the DNA exit dynamics, but that this friction does not significantly affect DNA packaging.
Collapse
|
5
|
Barberi L, Livolant F, Leforestier A, Lenz M. Local structure of DNA toroids reveals curvature-dependent intermolecular forces. Nucleic Acids Res 2021; 49:3709-3718. [PMID: 33784405 PMCID: PMC8053110 DOI: 10.1093/nar/gkab197] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2020] [Revised: 02/17/2021] [Accepted: 03/12/2021] [Indexed: 01/15/2023] Open
Abstract
In viruses and cells, DNA is closely packed and tightly curved thanks to polyvalent cations inducing an effective attraction between its negatively charged filaments. Our understanding of this effective attraction remains very incomplete, partly because experimental data is limited to bulk measurements on large samples of mostly uncurved DNA helices. Here we use cryo electron microscopy to shed light on the interaction between highly curved helices. We find that the spacing between DNA helices in spermine-induced DNA toroidal condensates depends on their location within the torus, consistent with a mathematical model based on the competition between electrostatic interactions and the bending rigidity of DNA. We use our model to infer the characteristics of the interaction potential, and find that its equilibrium spacing strongly depends on the curvature of the filaments. In addition, the interaction is much softer than previously reported in bulk samples using different salt conditions. Beyond viruses and cells, our characterization of the interactions governing DNA-based dense structures could help develop robust designs in DNA nanotechnologies.
Collapse
Affiliation(s)
- Luca Barberi
- Université Paris-Saclay, CNRS, LPTMS, 91405, Orsay, France
| | | | | | - Martin Lenz
- Université Paris-Saclay, CNRS, LPTMS, 91405, Orsay, France.,PMMH, CNRS, ESPCI Paris, PSL University, Sorbonne Université, Université de Paris, F-75005 Paris, France
| |
Collapse
|
6
|
Bores C, Woodson M, Morais MC, Pettitt BM. Effects of Model Shape, Volume, and Softness of the Capsid for DNA Packaging of phi29. J Phys Chem B 2020; 124:10337-10344. [PMID: 33151690 PMCID: PMC7903877 DOI: 10.1021/acs.jpcb.0c07478] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Double-stranded DNA is under extreme confinement when packed in phage phi29 with osmotic pressures approaching 60 atm and densities near liquid crystalline. The shape of the capsid determined from experiment is elongated. We consider the effects of the capsid shape and volume on the DNA distribution. We propose simple models for the capsid of phage phi29 to capture volume, shape, and wall flexibility, leading to an accurate DNA density profile. The effect of the packaging motor twisting the DNA on the resulting density distribution has been explored. We find packing motor induced twisting leads to a greater numbers of defects formed. The emergence of defects such as bubbles or large roll angles along the DNA shows a sequence dependence, and the resulting flexibility leads to an inhomogeneous distribution of defects occurring more often at TpA steps and AT-rich regions. In conjunction with capsid elongation, this has effects on the global DNA packing structures.
Collapse
Affiliation(s)
- Cecilia Bores
- University of Texas Medical Branch, 301 University Boulevard, Galveston, Texas 77555, United States
| | - Michael Woodson
- University of Texas Medical Branch, 301 University Boulevard, Galveston, Texas 77555, United States
| | - Marc C Morais
- University of Texas Medical Branch, 301 University Boulevard, Galveston, Texas 77555, United States
| | - B Montgomery Pettitt
- University of Texas Medical Branch, 301 University Boulevard, Galveston, Texas 77555, United States
| |
Collapse
|
7
|
Bores C, Pettitt BM. Structure and the role of filling rate on model dsDNA packed in a phage capsid. Phys Rev E 2020; 101:012406. [PMID: 32069548 DOI: 10.1103/physreve.101.012406] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2019] [Indexed: 06/10/2023]
Abstract
The conformation of DNA inside bacteriophages is of paramount importance for understanding packaging and ejection mechanisms. Models describing the structure of the confined macromolecule have depicted highly ordered conformations, such as spooled or toroidal arrangements that focus on reproducing experimental results obtained by averaging over thousands of configurations. However, it has been seen that more disordered states, including DNA kinking and the presence of domains with different DNA orientation can also accurately reproduce many of the structural experiments. In this work we have compared the results obtained through different simulated filling rates. We find a rate dependence for the resulting constrained states showing different anisotropic configurations. We present a quantitative analysis of the density distribution and the DNA orientation across the capsid showing excellent agreement with structural experiments. Second, we have analyzed the correlations within the capsid, finding evidence of the presence of domains characterized by aligned segments of DNA characterized by the structure factor. Finally, we have measured the number and distribution of DNA defects such as the emergence of bubbles and kinks as function of the filling rate. We find the slower the rate the fewer kink defects that appear and they would be unlikely at experimental filling rates with our model parameters. DNA domains of various orientation get larger with slower rates.
Collapse
Affiliation(s)
- Cecilia Bores
- Department of Biochemistry and Molecular Biology, University of Texas Medical Branch at Galveston Tx, 77555, USA
| | - B Montgomery Pettitt
- Department of Biochemistry and Molecular Biology, University of Texas Medical Branch at Galveston Tx, 77555, USA
| |
Collapse
|
8
|
Kwon S, Lee S, Cho HW, Kim J, Kim JS, Sung BJ. The breakdown of the local thermal equilibrium approximation for a polymer chain during packaging. J Chem Phys 2019; 150:204901. [PMID: 31153198 DOI: 10.1063/1.5093946] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The conformational relaxation of a polymer chain often slows down in various biological and engineering processes. The polymer, then, may stay in nonequilibrium states throughout the process such that one may not invoke the local thermal equilibrium (LTE) approximation, which has been usually employed to describe the kinetics of various processes. In this work, motivated by recent single-molecule experiments on DNA packaging into a viral capsid, we investigate how the nonequilibrium conformations and the LTE approximation would affect the packaging of a polymer chain into small confinement. We employ a simple but generic coarse-grained model and Langevin dynamics simulations to investigate the packaging kinetics. The polymer segments (both inside and outside the confinement) stay away from equilibrium under strong external force. We devise a simulation scheme to invoke the LTE approximation during packaging and find that the relaxation of nonequilibrium conformations plays a critical role in regulating the packaging rate.
Collapse
Affiliation(s)
- Seulki Kwon
- Department of Chemistry, Sogang University, Seoul 04107, South Korea
| | - Seulgi Lee
- Department of Chemistry, Sogang University, Seoul 04107, South Korea
| | - Hyun Woo Cho
- Department of Chemistry, Sogang University, Seoul 04107, South Korea
| | - Jeongmin Kim
- Department of Chemistry, Sogang University, Seoul 04107, South Korea
| | - Jun Soo Kim
- Department of Chemistry and Nano Science, Ewha Womans University, Seoul 03760, South Korea
| | - Bong June Sung
- Department of Chemistry, Sogang University, Seoul 04107, South Korea
| |
Collapse
|
9
|
Zhang CY, Zhang NH. Influence of Microscopic Interactions on the Flexible Mechanical Properties of Viral DNA. Biophys J 2018; 115:763-772. [PMID: 30119833 DOI: 10.1016/j.bpj.2018.07.023] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2017] [Revised: 07/09/2018] [Accepted: 07/23/2018] [Indexed: 10/28/2022] Open
Abstract
During the packaging and ejection of viral DNA, its mechanical properties play an essential role in viral infection. Some of these mechanical properties originate from different microscopic interactions of the encapsulated DNA in the capsid. Based on an updated mesoscopic model of the interaction potential by Parsegian et al., an alternative continuum elastic model of the free energy of the confined DNA in the capsid is developed in this work. With this model, we not only quantitatively identify the respective contributions from hydration repulsion, electrostatic repulsion, entropy and elastic bending but also predict the ionic effect of viral DNA's mechanical properties during the packaging and ejection. The relevant predictions are quantitively or qualitatively consistent with the existing experimental results. Furthermore, the nonmonotonous or monotonous changes in the respective contributions of microscopic interactions to the ejection force and free energy at different ejection stages are revealed systematically. Among these, the nonmonotonicity in the entropic contribution implies a transition of viral DNA structure from order to disorder during the ejection.
Collapse
Affiliation(s)
- Cheng-Yin Zhang
- Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, China
| | - Neng-Hui Zhang
- Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, China; Department of Mechanics, College of Sciences, Shanghai University, Shanghai, China.
| |
Collapse
|
10
|
Evilevitch A. The mobility of packaged phage genome controls ejection dynamics. eLife 2018; 7:37345. [PMID: 30178745 PMCID: PMC6122950 DOI: 10.7554/elife.37345] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2018] [Accepted: 07/29/2018] [Indexed: 12/31/2022] Open
Abstract
The cell decision between lytic and lysogenic infection is strongly influenced by dynamics of DNA injection into a cell from a phage population, as phages compete for limited resources and progeny. However, what controls the timing of viral DNA ejection events was not understood. This in vitro study reveals that DNA ejection dynamics for phages can be synchronized (occurring within seconds) or desynchronized (displaying minutes-long delays in initiation) based on mobility of encapsidated DNA, which in turn is regulated by environmental factors, such as temperature and extra-cellular ionic conditions. This mechano-regulation of ejection dynamics is suggested to influence viral replication where the cell’s decision between lytic and latent infection is associated with synchronized or desynchronized delayed ejection events from phage population adsorbed to a cell. Our findings are of significant importance for understanding regulatory mechanisms of latency in phage and Herpesviruses, where encapsidated DNA undergoes a similar mechanical transition. Viruses are tiny ‘parasites’ that smuggle their genetic material inside a cell and then hijack its resources for their own benefit. A viral infection can either be lytic or latent. In a lytic cycle, viruses make their host produce many copies of themselves, ultimately killing the cell. In contrast, during a latent infection, the viruses go ‘dormant’: for instance, some of them can insert their genetic material into the DNA of their host, which then gets passed on as the cell divides. Certain viruses are capable of both lytic and latent infections. One example is the lambda phage, which targets Escherichia coli bacteria. In the first stage of infection, the genetic material ‘shoots out’ of the virus and gets injected inside the bacterium. The dynamics of the ejection process determine the type of infection that will follow. If multiple phages release their genomes quickly and within seconds of each other into the same cell, the bacterium tends to incorporate the viral DNA into its own genome, leading to a latent cycle. If the infections take place more slowly and not all at the same time, the cell is more likely to go through a lytic phase. However, the mechanism behind the different injection behaviors is still unknown; in particular, it is unclear which factors control the specificities of the ejection process in the first place. Here, Alex Evilevitch demonstrates that the mechanical state of the phage DNA just before ejection dictates how the genetic material will then be injected in the bacteria. The experiments measured the stiffness of the DNA and the amount of heat given off during infection. Like fluid toothpaste, if the DNA is more liquid and flexible, it gets ejected quickly and simultaneously from several phages. Then, the genetic information of these viruses can be incorporated in the genome of the bacteria. On the other hand, if the DNA is more solid, it is likely to ‘stick’ and take time before it can be squeezed out: the injections become unsynchronised, which leads to a lytic phase. Evilevitch then shows that the environment can influence the properties of the phages’ genome. A little more heat, or certain chemicals, can make the DNA more fluid inside the viruses, and change the way it can be injected inside the bacteria. Many viruses that cause diseases in humans – from cold sores to glandular fever – can switch between the lytic and latent cycles. For the first time, these results show that the mechanical properties of the DNA inside a virus influence the ‘decision’ between the two types of infection. This knowledge could help us prevent infections from becoming lytic and ultimately allow us to control the spread of disease.
Collapse
Affiliation(s)
- Alex Evilevitch
- Department of Pathobiology, Division of Microbiology and Immunology, College of Veterinary Medicine, University of Illinois at Urbana-Champaign, Champaign, United States.,Department of Experimental Medical Sciences, Virus Biophysics Group, Lund University, Lund, Sweden
| |
Collapse
|
11
|
Keller N, Berndsen ZT, Jardine PJ, Smith DE. Experimental comparison of forces resisting viral DNA packaging and driving DNA ejection. Phys Rev E 2017; 95:052408. [PMID: 28618627 DOI: 10.1103/physreve.95.052408] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2017] [Indexed: 11/07/2022]
Abstract
We compare forces resisting DNA packaging and forces driving DNA ejection in bacteriophage phi29 with theoretical predictions. Ejection of DNA from prohead-motor complexes is triggered by heating complexes after in vitro packaging and force is inferred from the suppression of ejection by applied osmotic pressure. Ejection force from 0% to 80% filling is found to be in quantitative agreement with predictions of a continuum mechanics model that assumes a repulsive DNA-DNA interaction potential based on DNA condensation studies and predicts an inverse-spool conformation. Force resisting DNA packaging from ∼80% to 100% filling inferred from optical tweezers studies is also consistent with the predictions of this model. The striking agreement with these two different measurements suggests that the overall energetics of DNA packaging is well described by the model. However, since electron microscopy studies of phi29 do not reveal a spool conformation, our findings suggest that the spool model overestimates the role of bending rigidity and underestimates the role of intrastrand repulsion. Below ∼80% filling the inferred forces resisting packaging are unexpectedly lower than the inferred ejection forces, suggesting that in this filling range the forces are less accurately determined or strongly temperature dependent.
Collapse
Affiliation(s)
- Nicholas Keller
- Department of Physics, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA
| | - Zachary T Berndsen
- Department of Physics, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA.,Department of Chemistry and Biochemistry, University of California, San Diego, California 92093, USA
| | - Paul J Jardine
- Department of Diagnostic and Biological Sciences and Institute for Molecular Virology, University of Minnesota, 515 Delaware Street SE, Minneapolis, Minnesota 55455, USA
| | - Douglas E Smith
- Department of Physics, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA
| |
Collapse
|