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Publications

2019

R. Twarock & P.G. Stockley (2019) RNA-Mediated Virus Assembly: Mechanisms and Consequences for Viral Evolution and Therapy, Ann. Rev. Biophys. 48, 495-514.

G. Indelicato, P. Cermelli & R. Twarock (2019) A Coarse-grained model of the expansion of the human rhinovirus 2 capsid reveals insights into genome release, J. R. Soc. Interface 16, 20190044.

R. Twarock (2019) Geometry as a Weapon in the Fight Against Viruses, to appear in Mathematics Today.

R. Twarock & A. Luque (2019) Structural puzzles in virology solved with an overarching icosahedral design principle, to appear in Nature Comms.

2018

R. Twarock, R.J. Bingham, E.C. Dykeman & P.G. Stockley (2018) A modelling paradigm for RNA virus assembly, Curr. Opin. Virol. 30, 1.

R. Twarock, G. Leonov & P.G. Stockley (2018) Hamiltonian Path Analysis of Viral Genomes, Nature Comms. 9, 2021.

K. Al Shaikhahmed, G. Leonov, P.-Y. Sung, R.J. Bingham, R. Twarock, P. Roy (2018) Dynamic network approach for the modelling of genomic sub-complexes in multi-segmented viruses, Nucl. Acids Res. 46, 12087-12098.

2017

G. Indelicato, P. Burkhard & R. Twarock (2017) Classification of self-assembling protein nanoparticle architectures for applications in vaccine design, R. Soc. Open Sci. 4(4):161092.

S. Shakeel, E.C. Dykeman, S.J. White, A. Ora, J.J.B. Cockburn, S.J. Butcher, P.G. Stockley & R. Twarock (2017) Genomic RNA folding mediates assembly of human parechovirus, Nature Comms. 8, 5.

N. Patel, E. Wroblewski, G. Leonov, S.E.V. Phillips, R. Tuma, R. Twarock & P.G. Stockley (2017) Rewriting Nature’s assembly manual for a ssRNA virus, PNAS 114(46), 12255-12260.

R.J. Bingham, E.C. Dykeman, P.G. Stockley & R. Twarock (2017) RNA Virus Evolution via a Quasispecies-Based Model Reveals a Drug Target with a High Barrier to Resistance, Viruses 9, 347.

S.J. White, N. Patel, R.F. Thompson, R. Bingham, E.U. Weiß, A. Zlotnick, E.C. Dykeman, R. Tuma, R. Twarock, N.A. Ranson & P.G. Stockley (2017) The HBV RNA pre-genome encodes specific motifs that mediate interactions with the viral core protein that promotes nucleocapsid assembly, Nature Microbiol. 2, 17098.

L. Poudel, R. Twarock, N. Steinmetz, R. Podgornik & W.-Y. Ching (2017) Impact of Hydrogen Bonding in Binding Site Between Capsid Protein and MS2 Bacteriophage ssRNA, J. Phys. Chem. B 121(26):6321-6330.

J. Geraets, J. Baldwin, R. Twarock & Y. Hancock (2017) A proposed simulation method for directed self-assembly of nanographene, J. Phys. Condens. Matter 29(35): 355901.

2016

Rolfsson Ó, Middleton S, Manfield IW, White SJ, Fan B, Vaughan R, Ranson NA, Dykeman E, Twarock R, Ford J, Cheng Kao C & Stockley PG. (2016) Direct Evidence for Packaging Signal-Mediated Assembly of Bacteriophage MS2, J. Mol. Biol. 428, 431-48.

P.G. Stockley, S. White, E.C. Dykeman, I. Manfield, O. Rolfsson, N. Patel, R. Bingham, A. Barker, E. Wroblewski, R. Chandler-Bostock, E. Weiß, N. Ranson, R. Tuma & R. Twarock (2016) MS2 Genomic RNA Encodes an Assembly Instruction Manual for Its Capsid, Bacteriophage 6, e115766.

G. Indelicato, N. Wahome, P. Ringler, S. A. Müller, M.-P. Nieh, P. Burkhard & R. Twarock (2016) Principles Governing the Self-Assembly of Coiled-Coil Protein Nanoparticles, Biophys. J. 110, 646-60 - cover article

H. Stewart, R.J. Bingham, S. J. White, E. C. Dykeman, k, C. Zothner, A. K. Tuplin, P. G. Stockley, R. Twarock & M. Harris (2016) Identification of novel RNA secondary structures within the hepatitis C virus genome reveals a cooperative involvement in genome packaging, Sci. Rep. 6, 22952.

2015

J.A. Geraets, E.C. Dykeman, P.G. Stockley, N.A. Ranson & R. Twarock (2015) Asymmetric genome organization in an RNA virus revealed via graph-theoretical analysis of tomographic data, PLoS Comp. Biol. 11(3):e1004146.

R. Twarock, M. Valiunas & E. Zappa (2015) Orbits of crystallographic embedding of non-crystallographic groups and applications to virology, Acta Cryst. A 71, 569-82.

N. Patel, E.C. Dykeman, R.H.A. Coutts, G. Lomonossoff, D.J. Rowlands, S.E.V. Phillips, N.A. Ranson, R. Twarock, R. Tuma & P.G. Stockley (2015) Revealing the density of encoded functions in a viral RNA, PNAS 112, 2227-2232.

D. G. Salthouse, G. Indelicato, P. Cermelli, T. Keef & R. Twarock (2015) Approximation of virus structure by icosahedral tilings, Acta Cryst. A 71, 410-422.

2014

P-P. Dechant, J. Wardman, T. Keef & R. Twarock, Viruses and fullerenes - symmetry as a common thread? Acta Cryst. A 70:162-7 (2014) - cover article; [Article has been featured in Nature Physics (“Know your onion”, Vol 10, p. 244, April 2014).]

E.C. Dykeman, P.G. Stockley & R. Twarock (2014) Solving a Levinthal’s Paradox for Virus Assembly suggests a novel anti-viral therapy, PNAS 111, 5361-5366.

E. Zappa, E.C. Dykeman & R. Twarock (2014) On the subgroup structure of the hyperoctahedral group in six dimensions, Acta Cryst. A 70, 417-428.

2013

G. Polles, G. Indelicato, R. Potestio, P. Cermelli, R. Twarock & C. Micheletti, Mechanical and assembly units of viral capsids identified via quasi-rigid domain decomposition, PLOS Comp. Biol. 9:e1003331 (2013) - cover article. [Special recommendation by the Faculty of 1000 (F1000Prime).]

P-P. Dechant, C. Bœhm & R. Twarock, Affine extensions of non-crystallographic Coxeter groups induced by projection, J. Math. Phys. 54, 093508 (2013) - cover article

P. Cermelli, G. Indelicato & R. Twarock (2013) Nonicosahedral pathways for capsid expansion, Phys. Rev. E 88, 032710. 

T. Keef, J.P. Wardman, N.A. Ranson, P.G. Stockley & R. Twarock (2013) Structural constraints on the three-dimensional geometry of simple viruses: case studies of a new predictive tool, Acta Cryst. A 69, 140-50 - received special mention in the newsletter of the International Union of Crystallography

P.G. Stockley, N.A. Ranson & R. Twarock (2013) A new paradigm for the roles of the genome in ssRNA viruses, Future Virol. 8, 531-543.

E.C. Dykeman, P.G. Stockley & R. Twarock (2013) Packaging signals in two single-stranded RNA viruses imply a conserved assembly mechanism and geometry of the packaged genome, J. Mol. Biol. 425, 3235-49.

E.C. Dykeman, P.G. Stockley & R. Twarock (2013) Building a viral capsid in the presence of genomic RNA, Phys. Rev. E 87, 022717.

P.G. Stockley, R. Twarock, S.E. Bakker, A.M. Barker, A. Borodavka, E.C. Dykeman, R.J. Ford, A.R. Pearson, S.E. Phillips, N.A. Ranson & R. Tuma (2013) Packaging signals in single-stranded RNA viruses: nature’s alternative to a purely electrostatic assembly mechanism. J. Biol. Phys. 39, 277-87.

2012

K.M. Elsawy, R. Twarock, C.S. Verma & L.S. Caves (2012) Peptide inhibitors of viral assembly: a novel route to broad-spectrum antivirals, J. Chem. Inf. Model 52:770-6.

G. Indelicato, T. Keef, P. Cermelli, D.G. Salthouse, R. Twarock & G. Zanzotto (2012) Structural transitions in quasicrystals induced by higher dimensional lattice transitions, Proc. R. Soc. A 468: 1452-1471.

G. Indelicato, P. Cermelli, D.G. Salthouse, S. Racca, G. Zanzotto & R. Twarock (2012) A crystallographic approach to structural transitions in icosahedral viruses, J. Math. Biol. 64,745-73.

P.-P. Dechant, C. Bœhm & R. Twarock (2012) Novel Kac-Moody-type affine extensions of non-crystallographic Coxeter groups, J. Phys. A 45(28), 285202.

2011

D.H. Bunka, S.W. Lane, C.L. Lane, E.C. Dykeman, R.J. Ford, A.M. Barker, R. Twarock, S.E. Phillips & P.G. Stockley (2011) Degenerate RNA packaging signals in the genome of Satellite Tobacco Necrosis Virus: implications for the assembly of a T=1 capsid, J. Mol. Biol. 413, 51-65.

K.M. ElSawy, L.S. Caves & R. Twarock (2011) On the origin of order in the genome organization of ssRNA viruses. Biophys. J. 101, 774-80.

E.C. Dykeman, N.E. Grayson, K. Toropova, N.A. Ranson, P.G. Stockley & R. Twarock (2011) Simple rules for efficient assembly predict the layout of a packaged viral RNA, J. Mol. Biol. 408, 399-407 - also received special mention by Global Medical Discovery

2010

E.C. Dykeman & R. Twarock (2010) All-atom normal-mode analysis reveals an RNA-induced allostery in a bacteriophage coat protein, Phys. Rev. E 81, 031908.

K.M. Elsawy, L.S. Caves & R. Twarock (2010) The impact of viral RNA on the association rates of capsid protein assembly: bacteriophage MS2 as a case study, J. Mol. Biol. 400, 935-47.

V.L. Morton, E.C. Dykeman, N.J. Stonehouse, A.E. Ashcroft, R. Twarock & P.G. Stockley (2010) The impact of viral RNA on assembly pathway selection, J. Mol. Biol. 401, 298-308.

R. Twarock & T. Keef (2010) Viruses and geometry – where symmetry meets function, Microbiology Today 37: 24-27.

E.C. Dykeman, P.G. Stockley & R. Twarock (2010) Dynamic allostery controls coat protein conformer switching during MS2 phage assembly, J. Mol. Biol. 395, 916-23.  

2009

N.E. Grayson, A. Taormina & R. Twarock (2009) RNA and DNA Cages with Icosahedral Symmetry, J. Theor. Comp. Sci. 410, 1440.

N. Jonoska, A. Taormina & R. Twarock (2009) DNA cages with icosahedral symmetry in bionanotechnology in: Algorithmic Bioprocesses, Natural Computing Series, Springer Verlag, 141-158.

T. Keef & R. Twarock (2009) Affine extensions of the icosahedral group with applications to the three-dimensional organisation of simple viruses, J. Math. Biol. 59, 287-313.

2008

K.M. ElSawy, A. Taormina, R. Twarock & L. Vaughan (2008) Dynamical Implications of Viral Tiling Theory, J. Theor. Biol. 252, 357-369.

T. Keef & R. Twarock (2008) New insights into viral architecture via affine extended symmetry groups, Comp. Math. Meth. Med. 9, 221-229.

K. M. ElSawy, L. S.D. Caves & R. Twarock (2008) Polyomaviridae assembly polymorphism from an energy landscape perspective, Comp. Math. Meth. Med. 9, 245-256.

N. Jonoska & R. Twarock (2008) Blueprints for Dodecahedral DNA Cages, J. Phys. A 41, 304043-304057.

T. Keef, R. Twarock & K.M. Elsawy (2008) Blueprints for viral capsids in the family of polyomaviridae, J. Theor. Biol. 253, 808-16.

K. Toropova, G. Basnak, R. Twarock, P.G. Stockley & N.A. Ranson (2008) The three-dimensional structure of genomic RNA in bacteriophage MS2: implications for assembly, J. Mol. Biol. 375, 824-36.

2006

R. Twarock (2006) A Mathematical Physicist's Approach to the Structure and Assembly of Viruses, Phil. Trans. A 365, 3357-3374.

T. Keef, C. Micheletti & R. Twarock (2006) Master equation approach to the assembly of viral capsids, J. Theor. Biol. 242, 713-21.

R. Twarock & R. Hendrix (2006) Crosslinking in Viral Capsids via Tiling Theory, J. Theor. Biol. 240, 419-424.

T. Keef, A. Taormina & R. Twarock (2006) Classification of capped tubular viral particles in the family of Papovaviridae, J. Phys.: Condens. Matter 18, S375-S387.

D. Fairlie, R. Twarock & C. Zachos (2006) Lie algebras associated with one-dimensional aperiodic point sets, J. Phys. A 39, 1367-1374.

2005

R. Twarock (2005) Mathematical models for tubular structures in the family of Papovaviridae, Bull. Math. Biol. 67, 973-987.

T. Keef, A. Taormina & R. Twarock (2005) Assembly Models for Papovaviridae based on Tiling Theory, Phys. Biol. 2, 175-188.

R. Twarock (2005) The architecture of viral capsids based on tiling theory, J. Theor. Med. 6, 87-90.

2004

R. Twarock (2004) Mathematical Models for Tubular Malformations during Virus Assembly of Papovaviridae, WSEAS Trans. Biol. Biomed. 1, 243-248.

R. Twarock (2004) The Protein Stoichiometry of Viral Capsids via Tiling Theory, WSEAS Trans. Biol. Biomed. 1, 68-72.

R. Twarock (2004) A tiling approach to virus capsid assembly explaining a structural puzzle in virology, J. Theor. Biol. 226, 477-482.

2003

V. Mazorchuk & R. Twarock (2003) Virasoro-type algebras associated with a Penrose tiling, J. Phys. A 36, 4091-4111.

E. Pelantova & R. Twarock (2003) Tiles in Quasicrystals with Cubic Irrationality, J. Phys. A 36, 4363-4373.

R. Twarock (2003) Quadratic algebras in traffic flow models, Rep. Math. Phys. 51, 381-389.

2002

J. Patera & R. Twarock (2002) Affine extensions of noncrystallographic Coxeter groups and quasicrystals, J. Phys. A 35, 1551-1574.

R. Twarock (2002) New group structures for carbon onions and carbon nanotubes via affine extensions of noncrystallographic Coxeter groups, Phys. Lett. A 300, 437-444.

V.K. Dobrev, H.-D. Doebner & R. Twarock (2002) Quantum mechanics with difference operators, Rep. Math. Phys. 50, 409.

P. Pyatov & R. Twarock (2002) Construction of diffusion algebras, J. Math. Phys. 43, 3268-3279.

R. Twarock (2002) Recurrence times in dynamical systems via a quasicrystal approach, Phys. Part. Nucl. 33, 114-117.

2001 

R. Twarock (2001) An affine extension of non-crystallographic Coxeter groups with applications in the theory of quasicrystals and integrable systems, Czech. J. Phys. 51, 400-408.

2000

R. Twarock (2000) An Exactly Solvable Calogero Model for a Non-Integral Laced Group, Phys. Lett. A 275, 169-172.

R. Twarock (2000) A Calogero-Sutherland Model Based on the Aperiodic Virasoro Algebra, Int. J. Mod. Phys. A 15, 4179-4189.

R. Twarock (2000) Special Lie algebras for quasicrystals, J. Mat. Sci. Eng. A 294-296, 434-437.

R. Twarock (2000) Aperiodic Virasoro Algebra, J. Math. Phys. 41, 5088-5106.

1999

J. Patera & R. Twarock (1999) Quasicrystal Lie algebras and their generalizations, Phys. Rep. 315, 241-256.

R. Twarock (1999) A q-Schrödinger Equation Based on a Hopf q-Deformation of the Witt Algebra, J. Phys. A: Math. Gen. 32, 4971-4981.

J.-P. Antoine, L. Jacques & R. Twarock (1999) Investigation of a Quasiperiodic Tiling with Fivefold Symmetry Via Wavelet Analysis, Phys. Lett. A 261, 265-274.

1998

J. Patera, E. Pelantova & R. Twarock (1998) Quasicrystal Lie algebras, Phys. Lett. A 246, 209-213.

R. Twarock (1998) q-Borel quantization on S1 and Tn, Phys. Atomic Nucl. 61(11), 1842-1846.

1997

V. Dobrev, H.-D. Doebner & R. Twarock (1997) A Discrete, Nonlinear q-Schrödinger Equation Via Borel Quantization and q-Deformation of the Witt Algebra, J. Phys. A: Math. Gen. 30, 6841-6859.

P. Stovicek & R. Twarock (1997) Representations of Uh (su(N)) derived from Quantum Flag Manifolds, J. Math. Phys. 38, 1161-1182.

Proceedings

C. Schulte & R. Twarock (1995) The Rigged Hilbert Space Formulation of Quantum Mechanics and its Implications for Irreversibility, in: Nonlinear, Deformed and Irreversible Quantum Systems (eds. H.-D. Doebner, V. Dobrev, and P. Nattermann), pp. 53-70, World Scientific.

R. Twarock (1996) A discrete quantum kinematics based on q-derivatives, in: Symmetry Methods in Physics (eds. A. Sissakian and G. Pogosyan), pp. 583-587, Publ. Dept. JINR, Dubna.

R. Twarock (1997) q-Quantum Mechanics on S1, in: Symmetries in Science IX (eds. B. Gruber and M. Ramek), pp. 331-344, Plenum Publ., New York.

R. Twarock (1997) Derivation of a q-Schrödinger Equation on S1 via q-Deformation of the Kinematical Algebra Cinfty(S1) semidirect Vect(S1), in: q-Group 21 (eds. V. Dobrev and H.-D. Doebner), pp. 158-164, Heron Press, Sofia.

R. Twarock (1998) q-Derivatives, Quantization Methods and q-Algebras, in: AIP Conference Proceedings 453 (ed. J. Rembielinski), pp. 146-154, Am. Inst. of Phys., Woodbury, New York.

R. Twarock (1998) q-Quantum mechanics on Tn, in: Symmetries in Science X (eds. B. Gruber and M. Ramek), pp. 435-441, Plenum Publ., New York.

R. Twarock (1999) Oscillator Representations for the Aperiodic Virasoro Algebra and its Planar Generalization, in: Lie Theory and its Applications in Physics III (eds. H.-D. Doebner, V. Dobrev, and J. Hilgert), pp. 110-123, World Scientific.

R. Twarock (1999) Breaking Virasoro Symmetry, in: Quantum Theory and Symmetries (eds. H.-D. Doebner, V. Dobrev, J.-D. Hennig, and W. Lücke), pp. 530-534, World Scientific, Singapore.

R. Twarock (2002) Representations for selected types of Diffusion algebras, in: Proceedings of Quantum Theory and Symmetries, (eds. E. Kapuscik and A. Horzela) pp. 615-620, World Scientific.

R. Twarock (2002) A New Virasoro Type Symmetry and its Application in Quantum Physics, in: Proceedings of Sixth Wigner Symposium (eds. M. Arik), pp. 425-432, Bogazici Univ. Press, Istanbul.

R. Twarock (2003) Quadratic algebras in simple exclusion models,
in: Group-24: Physical and Mathematical Aspects of Symmetries, Conference Series Number 173 (eds. J.-P. Gazeau, R. Kerner, J.-P. Antoine, S. Metens and J.-Y. Thibon), pp. 703-706, Institute of Physics Publishing, Bristol and Philadelphia.

V. Mazorchuk & R. Twarock (2004) Virasoro-type algebras associated with higher-rank aperiodic point sets, in: Proceedings of the Third International Symposium on Quantum Theory and Symmetries, University of Cincinnati, USA (10-14 September 2003), eds. P.C. Argyres, T.J. Hodges, F. Mansouri, J.J. Scanio, P. Suranyi, L.C.R. Wijewardhana (University of Cincinnati, USA).

R. Twarock (2005) Mathematical Virology: A mathematical physicist's approach to the protein stoichiometry and bonding structure of viral capsids, in: Proceedings of IX. International Conference on Symmetry Methods in Physics, eds. G.S. Pogosyan, L.E. Vicent, K.B. Wolf, IOP Conference Series 185, pp. 113 – 120.

R. Twarock (2006) Structural description of viral particles based on affine extensions of non-crystallographic Coxeter groups, in: Quantum Theory and Symmetries IV, ed. V.K. Dobrev, Heron Press, Sofia, pp. 829-838.

N. Jonoska, A. Taormina & R. Twarock (2009) DNA cages with icosahedral symmetry in bionanotechnology, in: Algorithmic Bioprocesses, eds. A. Condon, D. Harel, J. N. Kok, A. Salomaa, and E. Winfree Editors, Natural Computing Series, Springer Verlag, p. 141-158.

P. Cermelli, G. Indelicato & R. Twarock (2014) The role of symmetry in conformational changes of viral capsids: a mathematical approach, Discrete and Topological Models in Molecular Biology, Eds. Jonoska, Saito, Natural Computing book series, Springer, 217-240.

Patents

“Anti-viral Therapy” (4363P/US and 4363P/EP)
“Viral Packaging Signals” (GB1618094.5)
“Virus-Like Particles” (GB1708709)
“Methods of treating HBV” (U.S. Patent Application No. 62/685,145 filed June 14, 2018) – joint patent filing with the NIH in Washington

Book

Stockley, P. G. & Twarock, R. (Eds.) Emerging Topics in Physical Virology, Imperial College Press, London, 2010 (ISBN:978-1-84816-464-2)

Special Journal Issues

“Mathematical Virology”, Journal for Theoretical Medicine (2005, Vol. 6, with Peter G. Stockley)
“Mathematical Virology”, Journal of Computational and Mathematical Methods in Medicine                                              (2008, Vol. 9, with Peter G. Stockley)
“The physics of virus assembly”, Journal of Physical Biology (2010, Vol.7, with Peter G. Stockley)
Special issue on “Medicine and Biology” for Mathematics Today (2019, with Ellen Brooks-Pollocks)