# The Missing Tailed Phages: Prediction of Small Capsid Candidates

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{*}

## Abstract

**:**

## 1. Introduction

_{i}(h,k) = α

_{i}T

_{0}(h,k), where h and k are the steps in the hexagonal sublattice joining two consecutive vertices in the icosahedral capsid. T

_{0}is the classic T-number associated with the hexagonal lattice and is given by the equation T

_{0}(h,k) = h

^{2}+ hk + k

^{2}. The subindex i takes the values h, t, s, and r, associated, respectively, with the hexagonal, trihexagonal, snub hexagonal, and rhombitrihexagonal icosahedral lattices. The number of major capsid proteins in a capsid is 60T

_{0}(h,k). The hexagonal lattice case only contains major capsid proteins, that is, T

_{h}(h,k) = T

_{0}(h,k), with α

_{h}= 1. If the size of the major capsid protein is conserved across lattices, the other three lattices must include minor capsid proteins occupying the secondary polygons (triangles and squares). This increases the surface of the capsid by a factor α

_{t}= 4/3 ≈ 1.33 (trihexagonal), α

_{s}= 7/3 ≈ 2.33 (snub hexagonal), and α

_{r}= 4/3 + 2/$\sqrt{3}$ ≈ 2.49 (rhombitrihexagonal). When combining all lattices, the first four elements of the generalized T-number are T = 1, 1.33, 2.33, and 2.49, containing 60 major capsid proteins each. The fifth element of the series is T = 3 and contains 180 major capsid proteins. Tailed phages have been observed to form capsids adopting the hexagonal and trihexagonal lattices [19,20], but no tailed phages have been observed to form T ≤ 3 capsids (Figure 1). The smallest characterized tailed phage structure corresponds to the Bacillus phage phi29, which adopts an elongated structure with icosahedral T = 3 caps and a Q = 5 body [12,21,22], and Streptococcus phage C1, which adopts a T = 4 icosahedral capsid [10,23].

## 2. Materials and Methods

## 3. Results

#### 3.1. Structural Properties of Characterized Tailed Phage Capsids

^{4}to 8.22 × 10

^{5}nm

^{3}range). The largest genome (280 kbp) was about 16 times larger than the smallest one (17 kbp). The average genome packing density within the capsid was approximately 0.5 bp/nm

^{3}, ranging from 0.34 to 0.62 bp/nm

^{3}. The values for the interior and exterior capsid surface areas spanned 8.5-fold (5.08 × 10

^{3}–4.32 × 10

^{4}nm

^{2}) and 8-fold (6.55 × 10

^{3}–5.19 × 10

^{4}nm

^{2}) respectively, with the exterior capsid surface area being 15% to 43% larger than the interior area. The average surface area for each major capsid protein in the interior and exterior parts of the capsid was approximately 23 nm

^{2}(19 to 26 nm

^{2}) and 30 nm

^{2}(24 to 35 nm

^{2}) per major capsid protein, respectively. The genome density (rho = −0.16, p-value = 0.47) and major capsid exterior surface area (rho = 0.38, p-value = 0.082) were the only variables that did not display a significant correlation with capsid size (see Supplementary Table S1).

#### 3.2. Tailed Phage Capsids: Statistical Models and Predictions

^{2}= 0.985, n = 7) of the variance (Figure 3a). The pre-factor was $\mathrm{log}{a}_{G}=0.37\pm 0.10$ (S.E.) with ${a}_{G}$ in kbp units. The allometric exponent was ${b}_{G}=1.47\pm 0.09$. The coefficient of variation (CV = S.E./mean) for the intercept was 27%, significantly larger than the CV associated with the power exponent, 6.1%. Similarly, the allometric model for the average capsid diameter, D, as a function of the architecture index, T, explained 98.6% (R

^{2}= 0.986, n = 7) of the variance (Figure 3b). The pre-factor was $\mathrm{log}{a}_{D}=1.38\pm 0.34$ (S.E.) with ${a}_{D}$ in nm units and coefficient of variation (CV) of 25%. The allometric exponent was ${b}_{D}=0.52\pm 0.03$ with a CV of 5.8%. The qualitative diagnostic of the residuals was similar for both models, consistent with the standard assumptions associated with the statistics of the linear regression analysis (Supplementary Figures S1 and S2). The residuals were scattered around zero with a near-normal distribution and a standardized range on the order of ±1 with relatively homoscedastic variance and relatively low leverage.

^{3}between the genome length and capsid diameter. The T-number, by definition, is proportional to the capsid surface, and the units are implicitly related to the major capsid protein surface [19,65]. The exposed surface of the major capsid protein obtained in the structural analysis was constant. Since the capsid surface of a quasi-spherical shell depends on the square of the diameter, this leads to the scaling T ~ D

^{2}relating to the T-number and the capsid diameter. The scaling relationships derived led to the allometric relationships G ~ T

^{3/2}and D ~ T

^{1/2}. The theoretical exponent for the genome length versus capsid architecture relationship was ${b}_{G}^{th}=3/2=1.5$, which was within the empirical range obtained in the statistical model, ${b}_{G}=1.47\pm 0.09$ (Figure 3a). The theoretical exponent for the capsid diameter versus capsid architecture yielded ${b}_{D}^{th}=1/2=0.5$, which was also within the empirical range obtained in the statistical model ${b}_{D}=0.52\pm 0.03$ (Figure 3b). The agreement between the statistical model and the theoretical allometric exponents provides confidence in using the statistical model to predict the properties of capsids for T-number architectures outside the range used to train the statistical model.

#### 3.3. Putative Small-Tailed Phage Candidates

#### 3.3.1. Predictions from Isolated Tailed Phages

#### 3.3.2. Predictions from Metagenome-Assembled Tailed Phages

#### 3.3.3. Small-Tailed Phage Capsid Candidates

## 4. Discussion

^{3}. This leads to a genome length scaling with the volume of the capsid. Since the T-number is proportional to the surface of the capsid and the exposed surface of the capsid protein is conserved, this led to a scaling of 3/2 (statistically, $1.47\pm 0.09$) relating the genome length and the capsid architecture expressed in terms of the T-number. The genome length can be determined experimentally through molecular biology methods while the T-number can be obtained from high-resolution microscopy methods. The derived relationship between the genome length and T-number thus provided a direct approach to estimate the capsid architectures from the abundant molecular biology data. It also reduced the uncertainty of incorporating intermediate relationships, for example, with the capsid volume. The application of such relationship to isolated and assembled tailed phage genomes provided a method to predict the existence of missing small-tailed phage capsids.

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Cobián Güemes, A.G.; Youle, M.; Cantú, V.A.; Felts, B.; Nulton, J.; Rohwer, F. Viruses as winners in the game of life. Annu. Rev. Virol.
**2016**, 3, 197–214. [Google Scholar] [CrossRef] [PubMed] - Wommack, K.E.; Colwell, R.R. Virioplankton: Viruses in aquatic ecosystems. Microbiol. Mol. Biol. Rev.
**2000**, 64, 69–114. [Google Scholar] [CrossRef] [PubMed][Green Version] - Danovaro, R.; Corinaldesi, C.; Dell’Anno, A.; Fuhrman, J.A.; Middelburg, J.J.; Noble, R.T.; Suttle, C.A. Marine viruses and global climate change. FEMS Microbiol. Rev.
**2011**, 35, 993–1034. [Google Scholar] [CrossRef] [PubMed] - Knowles, B.; Silveira, C.B.; Bailey, B.A.; Barott, K.; Cantu, V.A.; Cobián-Güemes, A.G.; Coutinho, F.H.; Dinsdale, E.A.; Felts, B.; Furby, K.A.; et al. Lytic to temperate switching of viral communities. Nature
**2016**, 531, 466–470. [Google Scholar] [CrossRef] - Luque, A.; Silveira, C. Quantification of lysogeny caused by phage coinfections in microbial communities from biophysical principles. mSystems
**2020**, 5, e00353-20. [Google Scholar] [CrossRef] - Silveira, C.B.; Coutinho, F.H.; Cavalcanti, G.S.; Benler, S.; Doane, M.P.; Dinsdale, E.A.; Edwards, R.A.; Francini-Filho, R.B.; Thompson, C.C.; Luque, A.; et al. Genomic and ecological attributes of marine bacteriophages encoding bacterial virulence genes. BMC Genomics
**2020**, 21, 126. [Google Scholar] [CrossRef] - Paez-Espino, D.; Eloe-Fadrosh, E.A.; Pavlopoulos, G.A.; Thomas, A.D.; Huntemann, M.; Mikhailova, N.; Rubin, E.; Ivanova, N.N.; Kyrpides, N.C. Uncovering Earth’s virome. Nature
**2016**, 5636, 425–430. [Google Scholar] [CrossRef] - Hua, J.; Huet, A.; Lopez, C.A.; Toropova, K.; Pope, W.H.; Duda, R.L.; Hendrix, R.W.; Conway, J.F. Capsids and genomes of jumbo-sized bacteriophages reveal the evolutionary reach of the HK97 fold. MBio
**2017**, 8. [Google Scholar] [CrossRef][Green Version] - Briani, F.; Dehò, G.; Forti, F.; Ghisotti, D. The plasmid status of satellite bacteriophage P4. Plasmid
**2001**, 45, 1–17. [Google Scholar] [CrossRef] - Suhanovsky, M.M.; Teschke, C.M. Nature’s favorite building block: Deciphering folding and capsid assembly of proteins with the HK97-fold. Virology
**2015**, 479–480, 487–497. [Google Scholar] [CrossRef][Green Version] - Ackermann, H.W. 5500 Phages examined in the electron microscope. Arch. Virol.
**2007**, 152, 227–243. [Google Scholar] [CrossRef] [PubMed] - Luque, A.; Reguera, D. The structure of elongated viral capsids. Biophys. J.
**2010**, 98, 2993–3003. [Google Scholar] [CrossRef][Green Version] - Luque, A.; Zandi, R.; Reguera, D. Optimal architectures of elongated viruses. Proc. Natl. Acad. Sci. USA
**2010**, 107, 5323–5328. [Google Scholar] [CrossRef] [PubMed][Green Version] - Krupovic, M.; Koonin, E. V Multiple origins of viral capsid proteins from cellular ancestors. Proc. Natl. Acad. Sci. USA
**2017**, 114, E2401–E2410. [Google Scholar] [CrossRef][Green Version] - Ho, P.T.; Montiel-Garcia, D.J.; Wong, J.J.; Carrillo-Tripp, M.; Brooks III, C.L.; Johnson, J.E.; Reddy, V.S. VIPERdb: A Tool for Virus Research. Annu. Rev. Virol.
**2018**, 5, 477–488. [Google Scholar] [CrossRef] [PubMed] - Sutter, M.; Boehringer, D.; Gutmann, S.; Günther, S.; Prangishvili, D.; Loessner, M.J.; Stetter, K.O.; Weber-Ban, E.; Ban, N. Structural basis of enzyme encapsulation into a bacterial nanocompartment. Nat. Struct. Mol. Biol.
**2008**, 15, 939–947. [Google Scholar] [CrossRef] [PubMed] - Giessen, T.W.; Orlando, B.J.; Verdegaal, A.A.; Chambers, M.G.; Gardener, J.; Bell, D.C.; Birrane, G.; Liao, M.; Silver, P.A. Large protein organelles form a new iron sequestration system with high storage capacity. Elife
**2019**, 8, e46070. [Google Scholar] [CrossRef] [PubMed] - Caspar, D.L.; Klug, A. Physical principles in the construction of regular viruses. Cold Spring Harb. Symp. Quant. Biol.
**1962**, 27, 1–24. [Google Scholar] [CrossRef] - Twarock, R.; Luque, A. Structural puzzles in virology solved with an overarching icosahedral design principle. Nat. Commun.
**2019**, 10, 4414. [Google Scholar] [CrossRef][Green Version] - Podgorski, J.; Calabrese, J.; Alexandrescu, L.; Jacobs-Sera, D.; Pope, W.; Hatfull, G.; White, S. Structures of three actinobacteriophage capsids: Roles of symmetry and accessory proteins. Viruses
**2020**, 12, 294. [Google Scholar] [CrossRef][Green Version] - Tao, Y.; Olson, N.H.; Xu, W.; Anderson, D.L.; Rossmann, M.G.; Baker, T.S. Assembly of a tailed bacterial virus and its genome release studied in three dimensions. Cell
**1998**, 95, 431–437. [Google Scholar] [CrossRef][Green Version] - Choi, K.H.; Morais, M.C.; Anderson, D.L.; Rossmann, M.G. Determinants of bacteriophage phi29 head morphology. Structure
**2006**, 14, 1723–1727. [Google Scholar] [CrossRef] [PubMed][Green Version] - Aksyuk, A.; Bowman, V.D.; Kaufmann, B.; Fields, C.; Klose, T.; Holdaway, H.; Fischetti, V.; Rossmann, M.G. Structural investigations of a Podoviridae streptococcus phage C1, implications for the mechanism of viral entry. Proc. Natl. Acad. Sci. USA
**2012**, 109, 14001–14006. [Google Scholar] [CrossRef] [PubMed][Green Version] - Zandi, R.; Reguera, D.; Bruinsma, R.F.; Gelbart, W.M.; Rudnick, J. Origin of icosahedral symmetry in viruses. Proc. Natl. Acad. Sci. USA
**2004**, 101, 15556–15560. [Google Scholar] [CrossRef] [PubMed][Green Version] - Luque, A.; Reguera, D.; Morozov, A.; Rudnick, J.; Bruinsma, R. Physics of shell assembly: Line tension, hole implosion, and closure catastrophe. J. Chem. Phys.
**2012**, 136, 184507. [Google Scholar] [CrossRef] [PubMed] - Hagan, M.F. Modeling viral capsid assembly. Adv. Chem. Phys.
**2014**, 155, 1. [Google Scholar] [CrossRef][Green Version] - Aznar, M.; Reguera, D. Physical ingredients controlling stability and structural selection of empty viral capsids. J. Phys. Chem. B
**2016**, 120, 6147–6159. [Google Scholar] [CrossRef] - Rice, G.; Tang, L.; Stedman, K.; Roberto, F.; Spuhler, J.; Gillitzer, E.; Johnson, J.E.; Douglas, T.; Young, M. The structure of a thermophilic archaeal virus shows a double-stranded DNA viral capsid type that spans all domains of life. Proc. Natl. Acad. Sci. USA
**2004**, 101, 7716–7720. [Google Scholar] [CrossRef][Green Version] - Koonin, E.V.; Dolja, V.V.; Krupovic, M.; Varsani, A.; Wolf, Y.I.; Yutin, N.; Zerbini, F.M.; Kuhn, J.H. Global organization and proposed megataxonomy of the virus world. Microbiol. Mol. Biol. Rev.
**2020**, 84. [Google Scholar] [CrossRef] - Krupovic, M.; Dolja, V.V.; Koonin, E.V. The LUCA and its complex virome. Nat. Rev. Microbiol.
**2020**, 18, 661–670. [Google Scholar] [CrossRef] - Doore, S.M.; Fane, B.A. The microviridae: Diversity, assembly, and experimental evolution. Virology
**2016**, 491, 45–55. [Google Scholar] [CrossRef] - Creasy, A.; Rosario, K.; Leigh, B.A.; Dishaw, L.J.; Breitbart, M. Unprecedented diversity of ssDNA phages from the family Microviridae detected within the gut of a protochordate model organism (Ciona robusta). Viruses
**2018**, 10, 404. [Google Scholar] [CrossRef] [PubMed][Green Version] - Mavrich, T.N.; Hatfull, G.F. Evolution of Superinfection Immunity in Cluster A Mycobacteriophages. Am. Soc. Microbiol.
**2019**, 10. [Google Scholar] [CrossRef] [PubMed][Green Version] - Wiegand, T.; Karambelkar, S.; Bondy-Denomy, J.; Wiedenheft, B. Structures and Strategies of Anti-CRISPR-Mediated Immune Suppression. Annu. Rev. Microbiol.
**2020**, 74, E5122–E5128. [Google Scholar] [CrossRef] [PubMed] - Breitbart, M.; Thompson, L.R.; Suttle, C.A.; Sullivan, M.B. Exploring the vast diversity of marine viruses. Oceanography
**2007**, 20, 135–139. [Google Scholar] [CrossRef] - Edwards, K.F.; Steward, G.F.; Schvarcz, C.A. Making sense of virus size and the tradeoffs shaping viral fitness. Ecol. Lett.
**2020**. [Google Scholar] [CrossRef] - Liu, X.; Zhang, Q.; Murata, K.; Baker, M.L.; Sullivan, M.B.; Fu, C.; Dougherty, M.T.; Schmid, M.F.; Osburne, M.S.; Chisholm, S.W.; et al. Structural changes in a marine podovirus associated with release of its genome into Prochlorococcus. Nat. Struct. Mol. Biol.
**2010**, 17, 830–836. [Google Scholar] [CrossRef][Green Version] - Bebeacua, C.; Lai, L.; Vegge, C.S.; Brøndsted, L.; van Heel, M.; Veesler, D.; Cambillau, C. Visualizing a complete Siphoviridae member by single-particle electron microscopy: The structure of lactococcal phage TP901-1. J. Virol.
**2013**, 87, 1061–1068. [Google Scholar] [CrossRef][Green Version] - Parent, K.N.; Tang, J.; Cardone, G.; Gilcrease, E.B.; Janssen, M.E.; Olson, N.H.; Casjens, S.R.; Baker, T.S. Three-dimensional reconstructions of the bacteriophage CUS-3 virion reveal a conserved coat protein I-domain but a distinct tailspike receptor-binding domain. Virology
**2014**, 464, 55–66. [Google Scholar] [CrossRef][Green Version] - Spilman, M.S.; Dearborn, A.D.; Chang, J.R.; Damle, P.K.; Christie, G.E.; Dokland, T. A conformational switch involved in maturation of Staphylococcus aureus bacteriophage 80α capsids. J. Mol. Biol.
**2011**, 405, 863–876. [Google Scholar] [CrossRef][Green Version] - Effantin, G.; Figueroa-Bossi, N.; Schoehn, G.; Bossi, L.; Conway, J.F. The tripartite capsid gene of Salmonella phage Gifsy-2 yields a capsid assembly pathway engaging features from HK97 and λ. Virology
**2010**, 402, 355–365. [Google Scholar] [CrossRef] [PubMed][Green Version] - Shen, P.S.; Domek, M.J.; Sanz-García, E.; Makaju, A.; Taylor, R.M.; Hoggan, R.; Culumber, M.D.; Oberg, C.J.; Breakwell, D.P.; Prince, J.T. Sequence and structural characterization of great salt lake bacteriophage CW02, a member of the T7-like supergroup. J. Virol.
**2012**, 86, 7907–7917. [Google Scholar] [CrossRef] [PubMed][Green Version] - Dai, W.; Hodes, A.; Hui, W.H.; Gingery, M.; Miller, J.F.; Zhou, Z.H. Three-dimensional structure of tropism-switching Bordetella bacteriophage. Proc. Natl. Acad. Sci. USA
**2010**, 107, 4347–4352. [Google Scholar] [CrossRef] [PubMed][Green Version] - White, H.E.; Sherman, M.B.; Brasilès, S.; Jacquet, E.; Seavers, P.; Tavares, P.; Orlova, E. V Capsid Structure and Its Stability at the Late Stages of Bacteriophage SPP1 Assembly. J. Virol.
**2012**, 86, 6768–6777. [Google Scholar] [CrossRef][Green Version] - Grose, J.H.; Belnap, D.M.; Jensen, J.D.; Mathis, A.D.; Prince, J.T.; Merrill, B.D.; Burnett, S.H.; Breakwell, D.P. The Genomes, Proteomes, and Structures of Three Novel Phages That Infect the Bacillus cereus Group and Carry Putative Virulence Factors. J. Virol.
**2014**, 88, 11846–11860. [Google Scholar] [CrossRef][Green Version] - Lander, G.C.; Baudoux, A.; Azam, F.; Potter, C.S.; Carragher, B.; Johnson, J.E. Article Capsomer Dynamics and Stabilization in the T = 12 Marine Bacteriophage SIO-2 and Its Procapsid Studied by CryoEM. Struct. Des.
**2012**, 20, 498–503. [Google Scholar] [CrossRef][Green Version] - Vernhes, E.; Renouard, M.; Gilquin, B.; Cuniasse, P.; Durand, D.; England, P.; Hoos, S.; Huet, A.; Conway, J.F.; Glukhov, A. High affinity anchoring of the decoration protein pb10 onto the bacteriophage T5 capsid. Sci. Rep.
**2017**, 7, 41662. [Google Scholar] [CrossRef] - Lander, G.C.; Tang, L.; Casjens, S.R.; Gilcrease, E.B.; Prevelige, P.; Poliakov, A.; Potter, C.S.; Carragher, B.; Johnson, J.E. The structure of an infectious P22 virion shows the signal for headful DNA packaging. Science
**2006**, 312, 1791–1795. [Google Scholar] [CrossRef][Green Version] - Stroupe, M.E.; Brewer, T.E.; Sousa, D.R.; Jones, K.M. The structure of Sinorhizobium meliloti phage ΦM12, which has a novel T= 19l triangulation number and is the founder of a new group of T4-superfamily phages. Virology
**2014**, 450, 205–212. [Google Scholar] [CrossRef][Green Version] - Effantin, G.; Hamasaki, R.; Kawasaki, T.; Bacia, M.; Moriscot, C.; Weissenhorn, W.; Yamada, T.; Schoehn, G. Cryo-electron microscopy three-dimensional structure of the jumbo phage ΦRSL1 infecting the phytopathogen Ralstonia solanacearum. Structure
**2013**, 21, 298–305. [Google Scholar] [CrossRef][Green Version] - Fokine, A.; Kostyuchenko, V.; Efimov, A.V.; Kurochkina, L.P.; Sykilinda, N.N.; Robben, J.; Volckaert, G.; Hoenger, A.; Chipman, P.R.; Battisti, A.J.; et al. A three-dimensional cryo-electron microscopy structure of the bacteriophage φKZ head. J. Mol. Biol.
**2005**, 352, 117–124. [Google Scholar] [CrossRef] [PubMed] - Pietilä, M.; Laurinmäki, P.; Russell, D.A.; Ching-Chung, K.; Jacobs-Sera, D.; Hendrix, R.W.; Bamford, D.H.; Butcher, S.J. Structure of the archaeal head-tailed virus HSTV-1 completes the HK97 fold story. Proc. Natl. Acad. Sci. USA
**2013**, 110, 10604–10609. [Google Scholar] [CrossRef] [PubMed][Green Version] - Guo, F.; Liu, Z.; Fang, P.-A.; Zhang, Q.; Wright, E.T.; Wu, W.; Zhang, C.; Vago, F.; Ren, Y.; Jakana, J. Capsid expansion mechanism of bacteriophage T7 revealed by multistate atomic models derived from cryo-EM reconstructions. Proc. Natl. Acad. Sci. USA
**2014**, 111, E4606–E4614. [Google Scholar] [CrossRef] [PubMed][Green Version] - Parent, K.N.; Gilcrease, E.B.; Casjens, S.R.; Baker, T.S. Structural evolution of the P22-like phages: Comparison of Sf6 and P22 procapsid and virion architectures. Virology
**2012**, 427, 177–188. [Google Scholar] [CrossRef][Green Version] - Baker, M.L.; Hryc, C.F.; Zhang, Q.; Wu, W.; Jakana, J.; Haase-Pettingell, C.; Afonine, P.V.; Adams, P.D.; King, J.; Jiang, W.; et al. Validated near-atomic resolution structure of bacteriophage epsilon15 derived from cryo-EM and modeling. Proc. Natl. Acad. Sci. USA
**2013**, 110, 12301–12306. [Google Scholar] [CrossRef][Green Version] - Gipson, P.; Baker, M.L.; Raytcheva, D.; Haase-Pettingell, C.; Piret, J.; King, J.A.; Chiu, W. Protruding knob-like proteins violate local symmetries in an icosahedral marine virus. Nat. Commun.
**2014**, 5, 4278. [Google Scholar] [CrossRef][Green Version] - Leiman, P.G.; Battisti, A.J.; Bowman, V.D.; Stummeyer, K.; Mühlenhoff, M.; Gerardy-Schahn, R.; Scholl, D.; Molineux, I.J. The structures of bacteriophages K1E and K1-5 explain processive degradation of polysaccharide capsules and evolution of new host specificities. J. Mol. Biol.
**2007**, 371, 836–849. [Google Scholar] [CrossRef] - Lander, G.C.; Evilevitch, A.; Jeembaeva, M.; Potter, C.S.; Carragher, B.; Johnson, J.E. Bacteriophage lambda stabilization by auxiliary protein gpD: Timing, location, and mechanism of attachment determined by cryo-EM. Structure
**2008**, 16, 1399–1406. [Google Scholar] [CrossRef][Green Version] - Pettersen, E.F.; Goddard, T.D.; Huang, C.C.; Couch, G.S.; Greenblatt, D.M.; Meng, E.C.; Ferrin, T.E. UCSF Chimera—A visualization system for exploratory research and analysis. J. Comput. Chem.
**2004**, 25, 1605–1612. [Google Scholar] [CrossRef][Green Version] - Kutner, M.H.; Neter, J.; Nachtsheim, C.J.; Li, W. Applied Linear Statistical Models, 5th ed.; McGraw-Hill Education: New York, NY, USA, 2004. [Google Scholar]
- James, G.; Witten, D.; Hastie, T.; Tibshirani, R. An Introduction to Statistical Learning, 7th ed.; Springer: New York, NY, USA, 2017. [Google Scholar]
- R Core Team. R: A Language and Environment for Statistical Computing; R Foundation for Statistical Computing: Vienna, Austria, 2018. [Google Scholar]
- O’Leary, N.A.; Wright, M.W.; Brister, J.R.; Ciufo, S.; Haddad, D.; McVeigh, R.; Rajput, B.; Robbertse, B.; Smith-White, B.; Ako-Adjei, D. Reference sequence (RefSeq) database at NCBI: Current status, taxonomic expansion, and functional annotation. Nucleic Acids Res.
**2016**, 44, D733–D745. [Google Scholar] [CrossRef][Green Version] - Benler, S.; Yutin, N.; Antipov, D.; Raykov, M.; Shmakov, S.A.; Gussow, A.B.; Pevzner, P.A.; Koonin, E. V Thousands of previously unknown phages discovered in whole-community human gut metagenomes. bioRxiv
**2020**. [Google Scholar] [CrossRef] - Aznar, M.; Luque, A.; Reguera, D. Relevance of capsid structure in the buckling and maturation of spherical viruses. Phys. Biol.
**2012**, 9, 036003. [Google Scholar] [CrossRef] [PubMed] - Dearborn, A.D.; Laurinmaki, P.; Chandramouli, P.; Rodenburg, C.M.; Wang, S.; Butcher, S.J.; Dokland, T. Structure and size determination of bacteriophage P2 and P4 procapsids: Function of size responsiveness mutations. J. Struct. Biol.
**2012**, 178, 215–224. [Google Scholar] [CrossRef] [PubMed][Green Version] - McNair, K.; Zhou, C.; Dinsdale, E.A.; Souza, B.; Edwards, R.A. PHANOTATE: A novel approach to gene identification in phage genomes. Bioinformatics
**2019**, 35, 4537–4542. [Google Scholar] [CrossRef][Green Version] - Dutilh, B.E.; Cassman, N.; McNair, K.; Sanchez, S.E.; Silva, G.G.Z.; Boling, L.; Barr, J.J.; Speth, D.R.; Seguritan, V.; Aziz, R.K. A highly abundant bacteriophage discovered in the unknown sequences of human faecal metagenomes. Nat. Commun.
**2014**, 5, 1–11. [Google Scholar] [CrossRef][Green Version] - Edwards, R.A.; Vega, A.A.; Norman, H.M.; Ohaeri, M.; Levi, K.; Dinsdale, E.A.; Cinek, O.; Aziz, R.K.; McNair, K.; Barr, J.J. Global phylogeography and ancient evolution of the widespread human gut virus crAssphage. Nat. Microbiol.
**2019**, 4, 1727–1736. [Google Scholar] [CrossRef][Green Version] - Shkoporov, A.N.; Khokhlova, E.V.; Fitzgerald, C.B.; Stockdale, S.R.; Draper, L.A.; Ross, R.P.; Hill, C. ΦCrAss001 represents the most abundant bacteriophage family in the human gut and infects Bacteroides intestinalis. Nat. Commun.
**2018**, 9, 1–8. [Google Scholar] [CrossRef][Green Version] - Guerin, E.; Shkoporov, A.; Stockdale, S.R.; Clooney, A.G.; Ryan, F.J.; Sutton, T.D.S.; Draper, L.A.; Gonzalez-Tortuero, E.; Ross, R.P.; Hill, C. Biology and taxonomy of crAss-like bacteriophages, the most abundant virus in the human gut. Cell Host Microbe
**2018**, 24, 653–664. [Google Scholar] [CrossRef][Green Version] - Yutin, N.; Makarova, K.S.; Gussow, A.B.; Krupovic, M.; Segall, A.; Edwards, R.A.; Koonin, E. V Discovery of an expansive bacteriophage family that includes the most abundant viruses from the human gut. Nat. Microbiol.
**2018**, 3, 38–46. [Google Scholar] [CrossRef] - Sivanandam, V.; Mathews, D.; Garmann, R.; Erdemci-Tandogan, G.; Zandi, R.; Rao, A.L.N. Functional analysis of the N-terminal basic motif of a eukaryotic satellite RNA virus capsid protein in replication and packaging. Sci. Rep.
**2016**, 6, 26328. [Google Scholar] [CrossRef][Green Version] - Beren, C.; Cui, Y.; Chakravarty, A.; Yang, X.; Rao, A.L.N.; Knobler, C.M.; Zhou, Z.H.; Gelbart, W.M. Genome organization and interaction with capsid protein in a multipartite RNA virus. Proc. Natl. Acad. Sci. USA
**2020**, 117, 10673–10680. [Google Scholar] [CrossRef] [PubMed] - Carrillo-Tripp, M.; Shepherd, C.M.; Borelli, I.A.; Venkataraman, S.; Lander, G.; Natarajan, P.; Johnson, J.E.; Brooks III, C.L.; Reddy, V.S. VIPERdb2: An enhanced and web API enabled relational database for structural virology. Nucleic Acids Res.
**2008**, 37, D436–D442. [Google Scholar] [CrossRef] - Hulo, C.; De Castro, E.; Masson, P.; Bougueleret, L.; Bairoch, A.; Xenarios, I.; Le Mercier, P. ViralZone: A knowledge resource to understand virus diversity. Nucleic Acids Res.
**2011**, 39, D576–D582. [Google Scholar] [CrossRef][Green Version] - Daufresne, M.; Lengfellner, K.; Som-mer, U. Global warming benefits the small in aquatic ecosystems, 12788-12793. Proc. Natl. Acad. Sci. USA
**2009**, 106, 21. [Google Scholar] [CrossRef][Green Version] - Morán, X.A.G.; López-Urrutia, Á.; Calvo-Díaz, A.; Li, W.K.W. Increasing importance of small phytoplankton in a warmer ocean. Glob. Chang. Biol.
**2010**, 16, 1137–1144. [Google Scholar] [CrossRef] - Nifong, R.L.; Gillooly, J.F. Temperature effects on virion volume and genome length in dsDNA viruses. Biol. Lett.
**2016**, 12, 20160023. [Google Scholar] [CrossRef] [PubMed][Green Version] - Schooley, R.T.; Biswas, B.; Gill, J.J.; Hernandez-Morales, A.; Lancaster, J.; Lessor, L.; Barr, J.J.; Reed, S.L.; Rohwer, F.; Benler, S. Development and use of personalized bacteriophage-based therapeutic cocktails to treat a patient with a disseminated resistant Acinetobacter baumannii infection. Antimicrob. Agents Chemother.
**2017**, 61. [Google Scholar] [CrossRef][Green Version] - Hatfull, G.F. Actinobacteriophages: Genomics, Dynamics, and Applications. Annu. Rev. Virol.
**2020**, 7, 37–61. [Google Scholar] [CrossRef]

**Figure 1.**HK97-fold protein compartments. The left side of the figure focuses on encapsulins, nanocompartments responsible for chemical storage and biochemical reactions in bacteria and archaea. The right side of the figure focuses on viruses and gene transfer agents. The viruses belong to the realm of Duplodnaviria. Tailed phages in the phylum Uroviricota and class Cauviricetes are the most diverse and abundant representatives of this group.

**Figure 2.**Icosahedral lattices for T(2,1) = 7 capsids. The label on the top displays the name of the lattice. The blue arrows and blue dots display the h and k steps in the hexagonal lattice, h = 2 and k = 1 in this case. The generalized T

_{h}, T

_{t}, T

_{s}, and T

_{r}numbers are obtained from the classic T-number multiplied by the lattice factor associated with the minor polygons (triangles and squares) of each lattice: h (hexagonal), t (trihexagonal), s (snub hexagonal), and r (rhombitrihexagonal).

**Figure 3.**Tailed phage statistical models. Genome length (

**a**) and capsid diameter (

**b**) plotted as a function of capsid architecture for the studied tailed phage structures (black circles) and the predicted small-tailed phage structures (blue diamonds). (

**a**,

**b**) The solid blue lines and grey areas correspond, respectively, to the mean values and 95% confidence interval predicted from the statistical model. The mean values and standard errors of the fitted parameters, as well as the coefficient of determination (R

^{2}), are displayed.

**Figure 4.**Predicted small-tailed phage capsids. The sequence of three-dimensional (3D) capsid icosahedral models generated with the new hkcage tool in ChimeraX and available in https://github.com/luquelab/hkcage.git. The information below each structure corresponds to the T-number architecture, (h,k) steps, lattice (h: hexagonal, t: trihexagonal, s: snub hexagonal, and r: rhombitrihexagonal), the average predicted genome length (95% confidence interval), and the average predicted capsid diameter (95% confidence interval).

**Figure 5.**Predicted architectures among tailed phage isolates. (

**a**) Genome length distribution for tailed phage isolates obtained from the NCBI Reference Sequence Database. (

**b**) Frequency (percentage) of predicted T-number architectures from the genome lengths of isolated tailed phages. The grey area highlights the absence of T < 3 architectures. (

**c**,

**d**) Genome length distribution and predicted T-number architectures for putative gut tailed phages. (

**a**–

**d**) The arrows indicate the significant peaks of the genome length distribution and the associated T-number architectures. (

**b**,

**d**) The parenthesis indicates the number of predicted T ≤ 4 phage capsid architectures.

**Figure 6.**Predicted small-tailed phages. (

**a**) List of isolated tailed phages predicted to adopt a T = 3 capsid architecture. The panel displays the phage name, genome length, host, and hosts’ phylogenetic tree. (

**b**) List of putative gut tailed phage genomes predicted to adopt T ≤ 3 capsid architectures. The list displays the contig name and genome length in parenthesis. (

**c**) Genome map of the smallest genome encoding a major capsid protein (MCP). The scale is 1 kbp. The genes are grouped by function: packaging (red), replication (orange), structural (green), and hypothetical (yellow).

**Table 1.**Summary of measured structural properties. * The sphere factor ranged from 0 (polyhedral) to 1 (spherical).

^{†}Maximum (icosahedral) diameter determined from the vertex (5-fold) to vertex (5-fold).

Property | Range | Property | Range |
---|---|---|---|

Capsids analyzed | 23 | Genome size | 17–280 kbp |

T-number | 4–27 | Genome density | 0.34–0.62 bp/nm^{3} |

Interior sphericity * | 0.25–0.75 | Interior surface | 5.08 × 10^{3}–4.32 × 10^{4} nm^{2} |

Exterior sphericity * | 0.14–0.55 | MCP interior area | 19–26 nm^{2} |

Capsid diameter ^{†} | 49–143 nm | Exterior surface | 6.55 × 10^{3}–5.19 × 10^{4} nm^{2} |

Capsid thickness | 3–8 nm | MCP exterior area | 24–35 nm^{2} |

Interior volume | 3.36 × 10^{4}–8.22 × 10^{5} nm^{3} | MCP ratio (%) | 15–43% |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Luque, A.; Benler, S.; Lee, D.Y.; Brown, C.; White, S.
The Missing Tailed Phages: Prediction of Small Capsid Candidates. *Microorganisms* **2020**, *8*, 1944.
https://doi.org/10.3390/microorganisms8121944

**AMA Style**

Luque A, Benler S, Lee DY, Brown C, White S.
The Missing Tailed Phages: Prediction of Small Capsid Candidates. *Microorganisms*. 2020; 8(12):1944.
https://doi.org/10.3390/microorganisms8121944

**Chicago/Turabian Style**

Luque, Antoni, Sean Benler, Diana Y. Lee, Colin Brown, and Simon White.
2020. "The Missing Tailed Phages: Prediction of Small Capsid Candidates" *Microorganisms* 8, no. 12: 1944.
https://doi.org/10.3390/microorganisms8121944