, Volume 1, Issue 4, pp 153–161 | Cite as

Reoccurring Patterns in Hierarchical Protein Materials and Music: The Power of Analogies

  • Tristan Giesa
  • David I. Spivak
  • Markus J. BuehlerEmail author


Complex hierarchical structures composed of simple nanoscale building blocks form the basis of most biological materials. Here, we demonstrate how analogies between seemingly different fields enable the understanding of general principles by which functional properties in hierarchical systems emerge, similar to an analogy learning process. Specifically, natural hierarchical materials like spider silk exhibit properties comparable to classical music in terms of their hierarchical structure and function. As a comparative tool, here, we apply hierarchical ontology logs that follow a rigorous mathematical formulation based on category theory to provide an insightful system representation by expressing knowledge in a conceptual map. We explain the process of analogy creation, draw connections at several levels of hierarchy, and identify similar patterns that govern the structure of the hierarchical systems silk and music and discuss the impact of the derived analogy for nanotechnology.


Hierarchical materials Nanostructure Category theory Music Composition Analogy Pattern Natural materials Biomaterials 



We acknowledge support from AFOSR and DOD-PECASE (funded by ONR grant # N00014-10-1-0562). Additional support was received from the German National Academic Foundation (Studienstiftung des deutsches Volkes) and ONR grant # N00014-10-1-0841.


  1. 1.
    Gentner, D., Holyoak, K. J., Kokinov, B. N. (2001). The analogical mind: perspectives from cognitive science (Vol. xii, p. 541). Cambridge: MIT Press.Google Scholar
  2. 2.
    Bransford, J., National Research Council (U.S.), Committee on Developments in the Science of Learning., National Research Council (U.S.), & Committee on Learning Research and Educational Practice. (2000). How people learn: brain, mind, experience, and school (Vol. x, p. 374). Washington: National Academy Press.Google Scholar
  3. 3.
    Oppenheimer, R. (1956). Analogy in science. American Psychologist, 11, 127–135.CrossRefGoogle Scholar
  4. 4.
    Vosniadou, S., & Ortony, A. (1989). Similarity and analogical reasoning (Vol. xiv, p. 592). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  5. 5.
    Taylor, P. C., Fraser, B. J., Fisher, D. L. (1997). Monitoring constructivist classroom learning environments. International Journal of Educational Research, 27, 293–302.CrossRefGoogle Scholar
  6. 6.
    Tsai, C.-C. (1999). Overcoming junior high school students’ misconceptions about microscopic views of phase change: a study of an analogy activity. Journal of Science Education and Technology, 8, 83–91.CrossRefGoogle Scholar
  7. 7.
    Stavy, R. (1991). Using analogy to overcome misconceptions about conservation of matter. Journal of Research in Science Teaching, 28, 305–313.CrossRefGoogle Scholar
  8. 8.
    Novick, L. R., & Holyoak, K. J. (1991). Mathematical problem-solving by analogy. Journal of Experimental Psychology: Learning, Memory, and Cognition, 17, 398–415.CrossRefGoogle Scholar
  9. 9.
    Kaniel, S., Harpaz-Itay, Y., Ben-Amram, E. (2006). Analogy construction versus analogy solution, and their influence on transfer. Learning and Instruction, 16, 583–591.CrossRefGoogle Scholar
  10. 10.
    Spivak, D. I., & Kent, R. E. (2011). Ologs: a categorical framework for knowledge representation. PLoS ONE, e24274. doi: 10.1371/journal.pone.0024274.
  11. 11.
    Eilenberg, S., & Maclane, S. (1945). General theory of natural equivalences. Transactions of the American Mathematical Society, 58, 231–294.MathSciNetzbMATHGoogle Scholar
  12. 12.
    Ellis, N. C., Larsen-Freeman, D., Research Club in Language Learning (Ann Arbor Mich.). (2009). Language as a complex adaptive system (Vol. viii, p. 275). Chichester: Wiley.Google Scholar
  13. 13.
    Croft, W. (2010). Pragmatic functions, semantic classes, and lexical categories. Linguistics, 48, 787–796.CrossRefGoogle Scholar
  14. 14.
    Croft, W. (2003). Typology and universals (Vol. xxv, p. 341). Cambridge: Cambridge University Press.Google Scholar
  15. 15.
    Sica, G. (2006). What is category theory? (p. 290). Monza: Polimetrica.Google Scholar
  16. 16.
    Awodey, S. (2010). Category theory. London: Oxford University Press.zbMATHGoogle Scholar
  17. 17.
    Cranford, S. W., & Buehler, M. J. (2010). Materiomics: biological protein materials, from nano to macro. Nanotechnology, Science and Applications, 3, 127–148.Google Scholar
  18. 18.
    Spivak, D. I., Giesa, T., Wood, E., Buehler, M. J. (2011). Category theoretic analysis of hierarchical protein materials and social networks. PLoS One, 6, e23911.CrossRefGoogle Scholar
  19. 19.
    Csermely, P. (2008). Creative elements: network-based predictions of active centres in proteins and cellular and social networks. Trends in Biochemical Sciences, 33, 569–576.CrossRefGoogle Scholar
  20. 20.
    Pugno, N. M. (2007). A statistical analogy between collapse of solids and death of living organisms: proposal for a ‘law of life’. Medical Hypotheses, 69, 441–447.CrossRefGoogle Scholar
  21. 21.
    Gimona, M. (2006). Protein linguistics—a grammar for modular protein assembly? Nature Reviews Molecular Cell Biology, 7, 68–73.CrossRefGoogle Scholar
  22. 22.
    Ji, S. C. (1997). Isomorphism between cell and human languages: molecular biological, bioinformatic and linguistic implications. Biosystems, 44, 17–39.CrossRefGoogle Scholar
  23. 23.
    Chomsky, N. (2002). Syntactic structures (Vol. xviii, p. 117). Berlin: Mouton de Gruyter.CrossRefGoogle Scholar
  24. 24.
    Nijholt, A. (1979). From left-regular to Greibach normal form grammars. Information Processing Letters, 9, 51–55.MathSciNetzbMATHCrossRefGoogle Scholar
  25. 25.
    Deline, G., Lin, F., Wen, D., Gagevic, D., Kinshuk, A. (2007). Ontology-driven development of intelligent educational systems. 2007 Ieee Pacific Rim Conference on Communications, Computers and Signal Processing, Vols. 1 and 2: 34–37.Google Scholar
  26. 26.
    Halle, M. (2002). From memory to speech and back: papers on phonetics and phonology, 1954–2002 (Vol. vi, p. 261). Berlin: Mouton de Gruyter.Google Scholar
  27. 27.
    International Phonetic Association. (1999). Handbook of the International Phonetic Association: a guide to the use of the International Phonetic Alphabet (Vol. viii, p. 204). Cambridge: Cambridge University Press.Google Scholar
  28. 28.
    Clements, G. N. (1985). The geometry of phonological features. Phonology, 2, 225–252.CrossRefGoogle Scholar
  29. 29.
    Abramson, A. S. (1977). Laryngeal timing in consonant distinctions. Phonetica, 34, 295–303.CrossRefGoogle Scholar
  30. 30.
    Jessen, M., & Ringen, C. (2002). Laryngeal features in German. Phonology, 19, 189–218.CrossRefGoogle Scholar
  31. 31.
    Espinosa, H. D., & Bao, G. (Eds.). (2012). Nano and cell mechanics. New York: Wiley.Google Scholar
  32. 32.
    Moorer, J. A. (1977). Signal-processing aspects of computer music—survey. Proceedings of the IEEE, 65, 1108–1137.CrossRefGoogle Scholar
  33. 33.
    Cutting, J. E., & Rosner, B. S. (1974). Categories and boundaries in speech and music. Perception & Psychophysics, 16, 564–570.CrossRefGoogle Scholar
  34. 34.
    Buehler, M. J., & Yung, Y. C. (2009). Deformation and failure of protein materials in physiologically extreme conditions and disease. Nature Materials, 8, 175–188.CrossRefGoogle Scholar
  35. 35.
    Frishman, D., & Argos, P. (1995). Knowledge-based protein secondary structure assignment. Proteins-Structure Function and Genetics, 23, 566–579.CrossRefGoogle Scholar
  36. 36.
    Sun, Z. R., & Hua, S. J. (2001). A novel method of protein secondary structure prediction with high segment overlap measure: support vector machine approach. Journal of Molecular Biology, 308, 397–407.CrossRefGoogle Scholar
  37. 37.
    Nova, A., Keten, S., Pugno, N. M., Redaelli, A., Buehler, M. J. (2010). Molecular and nanostructural mechanisms of deformation, strength and toughness of spider silk fibrils. Nano Letters, 10, 2626–2634.CrossRefGoogle Scholar
  38. 38.
    Keten, S., & Buehler, M. J. (2010). Nanostructure and molecular mechanics of spider dragline silk protein assemblies. Journal of the Royal Society, Interface, 7, 1709–1721.CrossRefGoogle Scholar
  39. 39.
    Keten, S., & Buehler, M. J. (2010). Atomistic model of the spider silk nanostructure. Applied Physics Letters, 96, 153701.CrossRefGoogle Scholar
  40. 40.
    Keten, S., & Buehler, M. J. (2008). Asymptotic strength limit of hydrogen-bond assemblies in proteins at vanishing pulling rates. Physical Review Letters, 100(19), 198301.CrossRefGoogle Scholar
  41. 41.
    Keten, S., & Buehler, M. J. (2008). Geometric confinement governs the rupture strength of H-bond assemblies at a critical length scale. Nano Letters, 8, 743–748.CrossRefGoogle Scholar
  42. 42.
    Keten, S., Xu, Z., Ihle, B., Buehler, M. J. (2010). Nanoconfinement controls stiffness, strength and mechanical toughness of beta-sheet crystals in silk. Nature Materials, 9, 359–367.CrossRefGoogle Scholar
  43. 43.
    Erickson, R. (1975). Sound structure in music (Vol. ix, p. 205). Berkeley: University of California Press.Google Scholar
  44. 44.
    Bharucha, J., & Krumhansl, C. L. (1983). The representation of harmonic structure in music—hierarchies of stability as a function of context. Cognition, 13, 63–102.CrossRefGoogle Scholar
  45. 45.
    Shell, A., & Ellis, D. P. (2003). Chord segmentation and recognition using EM-trained hidden Markov models, pp. 185–191.Google Scholar
  46. 46.
    Pardo, B., & Birmingham, W. P. (2002). Algorithms for chordal analysis. Computer Music Journal, 26, 27–49.CrossRefGoogle Scholar
  47. 47.
    Pardo, B., & Birmingham, W. P. (2001). The chordal analysis of tonal music.Google Scholar
  48. 48.
    Deutsch, D. (1969). Music recognition. Psychological Review, 76, 300.CrossRefGoogle Scholar
  49. 49.
    Jensen, K. (2007). Multiple scale music segmentation using rhythm, timbre, and harmony. Eurasip Journal on Advances in Signal Processing.Google Scholar
  50. 50.
    Randel, D. M. (2003). The Harvard dictionary of music (Vol. xxvii, p. 978). Cambridge: Belknap Press of Harvard University Press.Google Scholar
  51. 51.
    Krumhansl, C. L., & Shepard, R. N. (1979). Quantification of the hierarchy of tonal functions within a diatonic context. Journal of Experimental Psychology. Human Perception and Performance, 5, 579–594.CrossRefGoogle Scholar
  52. 52.
    Izar, P., Ferreira, R. G., Sato, T. (2006). Describing the organization of dominance relationships by dominance-directed tree method. American Journal of Primatology, 68, 189–207.CrossRefGoogle Scholar
  53. 53.
    Tymoczko, D. (2011). A geometry of music: harmony and counterpoint in the extended common practice (Vol. xviii, p. 450). New York: Oxford University Press.zbMATHGoogle Scholar
  54. 54.
    Maddage, N. C., Xu, C., Kankanhalli, M. S., Shao X. (2004). Content-based music structure analysis with applications to music semantics understanding. pp. 112–119.Google Scholar
  55. 55.
    Schafer, T., & Sedlmeier, P. (2009). From the functions of music to music preference. Psychology of Music, 37, 279–300.CrossRefGoogle Scholar
  56. 56.
    Sloboda, J. A. (1991). Music structure and emotional response: some empirical findings. Psychology of Music, 19, 110–120.CrossRefGoogle Scholar
  57. 57.
    Hartmann, W. M. (1997). Signals, sound, and sensation (Vol. xvii, p. 647). Woodbury: American Institute of Physics.Google Scholar
  58. 58.
    Giesa, T., Arslan, M., Pugno, N., Buehler, M. J. (2011). Nano- confinement of spider silk fibrils begets superior strength, extensibility and toughness. Nano Letters. doi: 10.1021/nl203108t.
  59. 59.
    Rohrmeier, M. (2007). A generative grammar approach to diatonic harmonic structure. In: Anagnostopoulou Georgaki K, editor. Proceedings of the 4th Sound and Music Computing Conference. pp. 97–100.Google Scholar
  60. 60.
    Bigand, E., Parncutt, R., Lerdahl, F. (1996). Perception of musical tension in short chord sequences: the influence of harmonic function, sensory dissonance, horizontal motion, and musical training. Perception & Psychophysics, 58, 125–141.CrossRefGoogle Scholar
  61. 61.
    Cranford, S. W., Tarakanova, A., Pugno N, Buehler M. J. (2011). Nonlinear behaviour of spider silk begets web robustness from the molecules up. In submission.Google Scholar
  62. 62.
    Rohrmeier, M. (2011). Towards a generative syntax of tonal harmony. Journal of Mathematics and Music, 5, 35–53.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Tristan Giesa
    • 1
    • 2
  • David I. Spivak
    • 3
  • Markus J. Buehler
    • 1
    • 4
    Email author
  1. 1.Laboratory for Atomistic and Molecular Mechanics, Department of Civil and Environmental EngineeringMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Department of Mechanical EngineeringRWTH Aachen UniversityAachenGermany
  3. 3.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA
  4. 4.Center for Computational EngineeringMassachusetts Institute of TechnologyCambridgeUSA

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