Skip to main content
SpringerLink
Log in

Modeling Autonomous Supramolecular Assembly

  • Chapter
  • First Online:
Discrete and Topological Models in Molecular Biology

Part of the book series: Natural Computing Series ((NCS))

Abstract

Supramolecular assembly is often a remarkably robust, rapid and spontaneous process, starting from a small number of monomeric types. Although the process occurs widely in nature and is increasingly important in healthcare and engineering, it is poorly understood. Icosahedral viral shell assembly is one such outstanding example. We sketch the experimental roadblocks that necessitate mathematical and computational modeling of assembly, and list the types of experimental data available for model validation, thereby defining the models’ input and output, and framing the scope of model predictions. We isolate the various factors, specifically configurational and combinatorial entropy that influence spontaneous supramolecular assembly, pinpointing the modeling challenges and motivating the use of multiscale models. We then survey existing modeling paradigms for the modeling different scales, emphasizing the newest models and paradigms developed by the author’s group, geared towards not only predicting, but also intuitively explaining, analyzing and engineering assembly processes. The models leverage geometric and algebraic characteristics unique to molecular assembly (as opposed to folding), and permit provable performance guarantees together with some level of forward and backward analysis as well as a desired level of precision and refinability of prediction.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. M. Agbandje-McKenna, A.L. Llamas-Saiz, F. Wang, P. Tattersall, M.G. Rossmann, Functional implications of the structure of the murine parvovirus, minute virus of mice. Structure 6, 1369–1381 (1998)

    Article  Google Scholar 

  2. I. Andricioaei, M. Karplus, On the calculation of entropy from covariance matrices of the atomic fluctuations. J. Chem. Phys. 115(14), 6289 (2001)

    Google Scholar 

  3. B. Berger, P.W. Shor, On the mathematics of virus shell assembly (1994)

    Google Scholar 

  4. B. Berger, P.W. Shor, Local rules switching mechanism for viral shell geometry. Technical report, MIT-LCS-TM-527, 1995

    Google Scholar 

  5. B. Berger, P. Shor, J. King, D. Muir, R. Schwartz, L. Tucker-Kellogg, Local rule-based theory of virus shell assembly. Proc. Natl. Acad. Sci. U.S.A. 91, 7732–7736 (1994)

    Article  MATH  Google Scholar 

  6. M. Bóna, M. Sitharam, The influence of symmetry on the probability of assembly pathways for icosahedral viral shells. Comput. Math. Methods Med. Special Issue on Mathematical Virology 9(3–4), 295–302 (Hindawi Publishing Corporation, New York, 2008). Stockley and Twarock (Ed.)

    Google Scholar 

  7. M. Bóna, M. Sitharam, A. Vince, Enumeration of viral capsid assembly pathways: tree orbits under permutation group action. Bull. Math. Biol. 73(4), 726–753 (2011). DOI:10.1007/s11538-010-9606-4

    Article  MATH  MathSciNet  Google Scholar 

  8. G.S. Chirikjian, Chapter four – modeling loop entropy, in Computer Methods, Part C, ed. by M.L. Johnson, L. Brand. Volume 487 of Methods in Enzymology (Academic, San Diego, 2011), pp. 99–132

    Google Scholar 

  9. U. Chittamuru, Sampling configuration space of partial 2-trees in 3D. Master’s thesis, University of Florida, 2011

    Google Scholar 

  10. M. Dyer, A. Frieze, R. Kannan, A random polynomial-time algorithm for approximating the volume of convex bodies. J. ACM 38, 1–17 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  11. D. Gfeller, D. Morton, D. Lachapelle, P. De Los Rios, G. Caldarelli, F. Rao, Uncovering the topology of configuration space networks. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 76(2 Pt 2), 026113 (2007)

    Article  Google Scholar 

  12. M.S. Head, J.A. Given, M.K. Gilson, Mining minima, direct computation of conformational free energy. J. Phys. Chem. A 101(8), 1609–1618 (1997)

    Article  Google Scholar 

  13. U. Hensen, O.F Lange, H. GrubmĂĽller, Estimating absolute configurational entropies of macromolecules: the minimally coupled subspace approach. PLoS ONE 5(2), 8 (2010)

    Google Scholar 

  14. V. Hnizdo, E. Darian, A. Fedorowicz, E. Demchuk, S. Li, H. Singh, Nearest-neighbor nonparametric method for estimating the configurational entropy of complex molecules. J. Comput. Chem. 28(3), 655–668 (2007)

    Article  Google Scholar 

  15. V. Hnizdo, J. Tan, B.J. Killian, M.K. Gilson, Efficient calculation of configurational entropy from molecular simulations by combining the mutual-information expansion and nearest-neighbor methods. J. Comput. Chem. 29(10), 1605–1614 (2008)

    Article  Google Scholar 

  16. W. Im, M. Feig, C.L. Brooks, An implicit membrane generalized Born theory for the study of structure, stability, and interactions of membrane proteins. Biophys. J. 85(5), 2900–2918 (2003)

    Article  Google Scholar 

  17. J.E. Johnson, J.A. Speir, Quasi-equivalent viruses: a paradigm for protein assemblies. J. Mol. Biol. 269, 665–675 (1997)

    Article  Google Scholar 

  18. M. Karplus, J.N. Kushick, Method for estimating the configurational entropy of macromolecules. Macromolecules 14(2), 325–332 (1981)

    Article  Google Scholar 

  19. B.J. Killian, J. Yundenfreund Kravitz, M.K. Gilson, Extraction of configurational entropy from molecular simulations via an expansion approximation. J. Chem. Phys. 127(2), 024107 (2007)

    Google Scholar 

  20. B.M. King, N.W. Silver, B. Tidor, Efficient calculation of molecular configurational entropies using an information theoretic approximation. J. Phys. Chem. B 116, 2891–2904 (2012)

    Article  Google Scholar 

  21. T.-C. Kuo, On Thom-Whitney stratification theory. Math. Ann. 234, 97–107 (1978). doi:10.1007/BF01420960.

    Article  MATH  MathSciNet  Google Scholar 

  22. Z. Lai, J. Su, W. Chen, C. Wang, Uncovering the properties of energy-weighted conformation space networks with a hydrophobic-hydrophilic model. Int. J. Mol. Sci. 10(4), 1808–1823 (2009)

    Article  Google Scholar 

  23. T. Lazaridis, Effective energy function for proteins in lipid membranes. Proteins 52(2), 176–192 (2003)

    Article  Google Scholar 

  24. T. Lazaridis, M. Karplus, Effective energy function for proteins in solution. Proteins 35(2), 133–152 (1999)

    Article  Google Scholar 

  25. C.J. Marzec, L.A. Day, Pattern formation in icosahedral virus capsids: the papova viruses and nudaurelia capensis β virus. Biophys. J. 65, 2559–2577 (1993)

    Article  Google Scholar 

  26. A. Ozkan, M. Sitharam, EASAL: efficient atlasing and search of assembly landscapes, in Proceedings of BiCoB, New Orleans, 2011

    Google Scholar 

  27. E. Padron, V. Bowman, N. Kaludov, L. Govindasamy, H. Levy, P. Nick, R. McKenna, N. Muzyczka, J.A. Chiorini, T.S. Baker, M. Agbandje-McKenna, Structure of adeno-associated virus type 4. J. Virol. 79, 5047–5058 (2005)

    Article  Google Scholar 

  28. E. Padron, R. McKenna, N. Muzyczka, N. Kaludov, J.A. Chiorini, M. Agbandje-McKenna, Structurally mapping the diverse phenotype of adeno associatedvirus serotype 4. J. Virol. 80, 11556–11570 (2006)

    Article  Google Scholar 

  29. J. Peters, J. Fan, M. Sitharam, Y. Zhou, Elimination in generically rigid 3D geometric constraint systems, in Proceedings of Algebraic Geometry and Geometric Modeling, Nice, 27–29 Sept 2004 (Springer, 2005), pp. 1–16

    Google Scholar 

  30. D. Prada-Gracia, J. GĂłmez-Garde\(\mathrm{\tilde{n}}\) es, P. Echenique, F. Falo, Exploring the free energy landscape: from dynamics to networks and back. PLoS Comput. Biol. 5(6), e1000415 (2009)

    Google Scholar 

  31. D. Rapaport, J. Johnson, J. Skolnick, Supramolecular self-assembly: molecular dynamics modeling of polyhedral shell formation. Comput. Phys. Commun. 121, 231–255 (1998)

    Google Scholar 

  32. V.S. Reddy, H.A. Giesing, R.T. Morton, A. Kumar, C.B. Post, C.L. Brooks, J.E. Johnson, Energetics of quasiequivalence: computational analysis of protein-protein interactions in icosahedral viruses. Biophys. J. 74, 546–558 (1998)

    Article  Google Scholar 

  33. R. Schwartz, P.E. Prevelige, B. Berger, Local rules modeling of nucleation-limited virus capsid assembly. Technical report, MIT-LCS-TM-584, 1998

    Google Scholar 

  34. R. Schwartz, P.W. Shor, P.E. Prevelige, B. Berger, Local rules simulation of the kinetics of virus capsid self-assembly. Biophys. J. 75, 2626–2636 (1998)

    Article  Google Scholar 

  35. M. Sitharam, M. Agbandje-McKenna, Sampling virus assembly pathway: avoiding dynamics. J. Comput. Biol. 13(6), 1232–1265 (2006)

    Article  MathSciNet  Google Scholar 

  36. M. Sitharam, M. BĂłna, Combinatorial enumeration of macromolecular assembly pathways, in Proceedings of the International Conferecnce on Bioinformatics and Applications (World Scientific, Fort Lauderdale, 2004)

    Google Scholar 

  37. M. Sitharam, H. Gao, Characterizing graphs with convex Cayley configuration spaces. Discret. Comput. Geom. 43, 594–625 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  38. G. Varadhan, Y.J. Kim, S. Krishnan, D. Manocha, Topology preserving approximation of free configuration space, in ICRA 2006. Proceedings 2006 IEEE International Conference, 3041–3048 (2006)

    Google Scholar 

  39. P. Wu, W. Xiao, T. Conlon, J. Hughes, M. Agbandje-McKenna, T. Ferkol, T. Flotte, N. Muzyczka, Mutational analysis of the adeno-associated virus type 2 (AAV2) capsid gene and construction of AAV2 vectors with altered tropism. J. Virol. 74(18), 8635–8647 (2000)

    Article  Google Scholar 

  40. R. Wu, A. Ozkan, A. Bennett, M. Agbandje-McKenna, M. Sitharam, Robustness measure for AAV2 is correctly predicted by configuration space atlasing using EASAL, in Proceedings of ACM Bioinformatics and Comptutational Biology, Orlando, 2012

    Google Scholar 

  41. Y. Yao, J. Sun, X. Huang, G.R. Bowman, G. Singh, M. Lesnick, L.J. Guibas, V.S Pande, G. Carlsson, Topological methods for exploring low-density states in biomolecular folding pathways. J. Chem. Phys. 130(14), 144115 (2009)

    Google Scholar 

  42. H.-X. Zhou, M.K Gilson, Theory of free energy and entropy in noncovalent binding. Chem. Rev. 109(9), 4092–4107 (2009)

    Google Scholar 

  43. A. Zlotnick, To build a virus capsid: an equilibrium model of the self assembly of polyhedral protein complexes. J. Mol. Biol. 241, 59–67 (1994)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer and Information Sciences and Engineering, University of Florida, 32611-6120, Gainesville, FL, USA

    Meera Sitharam

Authors
  1. Meera Sitharam
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Meera Sitharam .

Editor information

Editors and Affiliations

  1. Dept. Mathematics & Statistics, University of South Florida, Tampa, Florida, USA

    Nataša Jonoska

  2. Dept. Mathematics & Statistics, University of South Florida, Tampa, Florida, USA

    Masahico Saito

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Sitharam, M. (2014). Modeling Autonomous Supramolecular Assembly. In: Jonoska, N., Saito, M. (eds) Discrete and Topological Models in Molecular Biology. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40193-0_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-40193-0_9

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40192-3

  • Online ISBN: 978-3-642-40193-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation