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Formal Models of the Calyx of Held

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Algorithmic Bioprocesses

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Abstract

We survey some recent work on the behavior of the calyx of Held synapse. The analysis considered are based on formal and quantitative models aimed at capturing emerging properties about signal transmission and plasticity phenomena. While surveying work about a specific and real-scale biological system, we distinguish between deterministic and stochastic approaches. We elaborate on the fact that in some cases, as in the calyx, the latter ones seem to be more adequate. The stochastic models, which we have developed, are based on a computational interpretation of biological systems. We illustrate the advantages of this approach in terms of expressiveness.

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References

  1. Arbib MA (ed) (1995) The handbook of brain theory and neural networks. MIT Press, Cambridge

    Google Scholar 

  2. Ascoli GA (ed) (2002) Computational neuroanatomy. Humana, Totowa

    Google Scholar 

  3. Atwood HL, Karunanithi S (2002) Diversification of synaptic strength: presynaptic elements. Nat Rev 3:497–516

    Google Scholar 

  4. Bollmann JH, Sakmann B (2005) Control of synaptic strength and timing by the release-site Ca2+ signal. Nat Neurosci 8:426–434

    Google Scholar 

  5. Bracciali A, Brunelli M, Cataldo E, Degano P (2007) Expressive models for synaptic plasticity. In: Calder M, Gilmore P (eds) Computational methods in system biology (CMSB’07). LNBI, Springer, Edinburgh, pp 152–167

    Chapter  Google Scholar 

  6. Bracciali A, Brunelli M, Cataldo E, Degano P (2008) Stochastic models for the in silico simulation of synaptic processes. BMC Bioinform 9(4):S7

    Article  Google Scholar 

  7. Bracciali A, Brunelli M, Cataldo E, Degano P (2008) Synapses as stochastic concurrent systems. Theor Comput Sci 408(1):66–82

    Article  MATH  MathSciNet  Google Scholar 

  8. Calder M, Gilmore S, Hillston J (2006) Modelling the influence of RKIP on the ERK signalling pathway using the stochastic process algebra pepa. Trans Comput Syst Biol VII 4230:1–23

    Article  MathSciNet  Google Scholar 

  9. Cardelli L (2004) Brane calculi-interactions of biological membranes. In: Vincent V, Schachter V (eds) Proceedings of computational methods in systems biology. LNCS, vol 3082. Springer, Paris, pp 257–280

    Google Scholar 

  10. Cardelli L (2008) On process rate semantics. Theor Comput Sci 391(3):190–215

    Article  MATH  MathSciNet  Google Scholar 

  11. Cassman M, Arkin A, Doyle F, Katagiri F, Lauffenburger D, Stokes C (2007) System biology—international research and development. Springer, The Netherlands

    Google Scholar 

  12. Clements JD (1996) Transmitter timecourse in the synaptic cleft: its role in central synaptic function. Trends Neurosci 19:163–171

    Article  Google Scholar 

  13. Cooper LN, Intrator N, Blais BS, Shouval HZ (2004) Theory of cortical platicity. World Scientific, New Jersey

    Google Scholar 

  14. Dayan P, Abbot LF (2001) Theoretical neuroscience—computational and mathematical modeling of neural systems. MIT Press, Cambridge

    Google Scholar 

  15. De Schutter E (2000) Computational neuroscience: more math is needed to understand the human brain. In: Engquist B, Schmid W (eds) Mathematics unlimited—2001 and beyond, 1st edn. Springer, Berlin, pp 381–391

    Google Scholar 

  16. Destexhe A, Mainen ZF, Sejnowski TJ (1998) Kinetic models of synaptic transmission. In: Koch C, Segev I (eds) Methods in neuronal modeling. MIT Press, Cambridge, pp 1–25

    Google Scholar 

  17. Destexhe A, Mainen ZF, Sejnowski TJ (1994) Synthesis of models for excitable membrane, synaptic transmission and neuromodulation using a common kinetic formulation. J Comput Neurosci 1:195–231

    Article  Google Scholar 

  18. Ermentrout B (2002) Simulating, analyzing, and animating dynamical systems. SIAM, Philadelphia

    MATH  Google Scholar 

  19. Fall CP, Marland ES, Wagner JM, Tyson JJ (eds) (2005) Computational cell biology. Springer, New York

    Google Scholar 

  20. Felmy F, Neher E, Schneggenburger R (2003) Probing the intracellular calcium sensitivity of transmitter release during synaptic facilitation. Neuron 37:801–811

    Article  Google Scholar 

  21. Gardiner CW (2001) Handbook of stochastic methods—for physics, chemistry and the natural science. Springer, Berlin

    Google Scholar 

  22. Ghijsen WEJM, Leenders AGM (2005) Differential signaling in presynaptic neurotransmitter release. Cell Mol Life Sci 62:937–954

    Article  Google Scholar 

  23. Gillespie DT (1977) Exact stochastic simulation of coupled chemical reactions. J Phys Chem 81:2340–2361

    Article  Google Scholar 

  24. Gillespie DT, Petzold LR (2006) Numerical simulation for biochemical kinetics. In: Szallasi Z, Stelling J, Perival V (eds) System modeling in cellular biology, 1st edn. MIT Press, Cambridge, pp 331–354

    Google Scholar 

  25. Graham BP, Wong AYC, Forsythe ID (2001) A computational model of synaptic transmission at the calyx of Held. Neurocomputing 38(40):37–42

    Article  Google Scholar 

  26. Graham BP, Wong AYC, Forsythe ID (2004) A multi-component model of depression at the calyx of Held. Neurocomputing 58(60):449–554

    Article  Google Scholar 

  27. Hennig MH, Postlethwaite M, Forsythe ID, Graham BP (2007) A biophysical model of short-term plasticity at the calyx of Held. Neurocomputing 70:1626–1629

    Article  Google Scholar 

  28. Hertz J, Krogh A, Palmer RG (1991) Introduction to the theory of neural computation. Westview, Santa Fe

    Google Scholar 

  29. Hillston J (1996) A compositional approach to performance modeling. Cambridge University Press, Cambridge

    Google Scholar 

  30. Holmes WR (2005) Calcium signaling in dendritic spines. In: Reeke GN, Poznanski RR, Lindsay KA, Rosenberg JR, Sporns O (eds) Modeling in the neuroscience—from biological systems to neuromimetic robotics, 2nd edn. CRC Press, New York, pp 25–60

    Google Scholar 

  31. Hosoi N, Sakaba T, Neher E (2007) Quantitative analysis of calcium-dependent vesicle recruitment and its functional role at the calyx of Held synapse. J Neurosci 27:14286–14298

    Article  Google Scholar 

  32. Izhikevich EM (2006) Dynamical system in neuroscience: the geometry of excitability and bursting. MIT Press, Cambridge

    Google Scholar 

  33. Van Kampen NG (1992) Stochastic processes in physics and in chemistry. Elsevier, Amsterdam

    Google Scholar 

  34. Kierzek AM (2002) Stocks: stochastic kinetic simulations of biochemical system with gillespie algorithm. Bioinformatics 18:470–481

    Article  Google Scholar 

  35. Kitano H (2002) Systems biology: a brief overview. Theor Comput Sci 295(5560):1662–1664

    Google Scholar 

  36. Koch C (1999) Biophysics of computation—information processing in single neuron. Oxford University Press, New York

    Google Scholar 

  37. Koch C, Segev I (eds) (1998) Methods in neuronal modeling. MIT Press, Cambridge

    Google Scholar 

  38. Lecca P, Priami C, Quaglia P, Rossi B, Laudanna C, Costantin G (2004) A stochastic process algebra approach to simulation of autoreactive lymphocyte recruitment. SIMULATION: Trans Soc Model Simul Int 80(4):273–288

    Article  Google Scholar 

  39. Lou X, Scheuss V, Schneggenburger R (2005) Allosteric modulation of the presynaptic Ca2+ sensor for vesicle fusion. Nature 435:497–501

    Article  Google Scholar 

  40. Lytton WW (2002) From computer to brain—foundations of computational neuroscience. Springer, New York

    Google Scholar 

  41. Mathias J, Ewald R, Uhrmacher AM (2008) A spatial extension to the π calculus. Electron Notes Theor Comput Sci 194(3):133–148

    Article  Google Scholar 

  42. Milner R (1999) Communicating and mobile systems: the π-calculus. Cambridge University Press, Cambridge

    Google Scholar 

  43. Mitra PP, Bokil H (2008) Observed brain dynamics. Oxford University Press, Oxford

    Google Scholar 

  44. Nagasaki M, Onami S, Miyano S, Kitano H (1999) Bio-calculus: its concept and molecular interaction. Genome Inform 10:133–143

    Google Scholar 

  45. Neher E (2006) A comparison between exocytic control mechanisms in adrenal chromaffin cells and a glutamatergic synapse. Eur J Physiol 453:261–268

    Article  Google Scholar 

  46. Neher E (2007) Short-term plasticity turns plastic. Focus on synaptic transmission at the calyx of Held under in vivo-like activity levels. J Neurophysiol 98:577–578

    Article  Google Scholar 

  47. Nicholls JG, Martin AR, Wallace BG, Fuchs PA (2001) From neuron to brain. Sinauer Associates, Sunderland

    Google Scholar 

  48. Phillips A, Cardelli L (2007) Efficient, correct simulation of biological processes in the stochastic pi-calculus. In: Calder M, Gilmore S (eds) Proceedings of computational methods in systems biology. LNCS, vol 4695. Springer, Edinburgh, pp 184–199

    Chapter  Google Scholar 

  49. Priami C (1995) Stochastic π-calculus. Comput J 36(6):578–589

    Article  Google Scholar 

  50. Priami C, Regev A, Shapiro E, Silvermann W (2004) Application of a stochastic name-passing calculus to representation and simulation of molecular processes. Theor Comput Sci 325(1):141–167

    Article  Google Scholar 

  51. Regev A, Panina E, Silverman W, Cardelli L, Shapiro E (2004) Bioambients: an abstraction for biological compartements. Theor Comput Sci 325(1):141–167

    Article  MATH  MathSciNet  Google Scholar 

  52. Regev A, Shapiro E (2002) Cellular abstractions: cells as computation. Nature 419:343

    Article  Google Scholar 

  53. Rieke F, Warland D, von Steveninck RR, Bialek W (1997) Spikes—exploring the neural codes. MIT Press, Cambridge

    Google Scholar 

  54. Sakaba T, Stein A, Jahn R, Neher E (2005) Distinct kinetic changes in neurotransmitter release after snare protein cleavage. Science 309:491–494

    Article  Google Scholar 

  55. Savtchenko LP, Rusakov DA (2007) The optimal height of the synaptic cleft. Proc Natl Acad Sci 104:1823–1828

    Article  Google Scholar 

  56. Schneggenburger R, Forsythe ID (2006) The calxy of Held. Cell Tissue Res 326:311–337

    Article  Google Scholar 

  57. Schneggenburger R, Neher E (2000) Intracellular calcium dependence of transmitter release rates at a fast central synapse. Nature 46:889–893

    Article  Google Scholar 

  58. Schneggenburger R, Neher E (2005) Presynaptic calcium and control of vesicle fusion. Curr Opin Neurobiol 15:266–274

    Article  Google Scholar 

  59. Schneggenburger R, Sakaba T, Neher E (2002) Vescicle pools and short-term synaptic depression: lessons from a large synapse. Trends Neurosci 25:206–212

    Article  Google Scholar 

  60. De Schutter E (ed) (2001) Computational neuroscience—realistic modeling for experimentalist. CRC Press, Boca Raton

    Google Scholar 

  61. Segel LA (1987) Modeling dynamic phenomena in molecular and cellular biology. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  62. Smith GD (2005) Modeling the stochastic gating of ion channels. In: Fall CP, Marland ES, Wagner JM, Tyson JJ (eds) Computational cell biology, 2nd edn. Springer, New York, pp 285–319

    Google Scholar 

  63. Smolen PD, Baxter DA, Byrne JH (2004) Mathematical modeling and analysis of intracellular signaling pathways. In: Byrne JH, Roberts JL (eds) From molecules to networks—an introduction to cellular and molecular neuroscience. Elsevier/Academic Press, Amsterdam, pp 391–429

    Google Scholar 

  64. Sorensen JB (2004) Formation, stabilization and fusion of the readily releasable pool of secretory vescicles. Eur J Neurosci 448:347–362

    Google Scholar 

  65. Sudhof TC (2004) The synaptic vesicle cycle. Annu Rev Neurosci 27:509–547

    Article  Google Scholar 

  66. Ullah M, Wolkenhauer O (2007) Family tree of Markov models in Systems Biology. IET Syst Biol 1:247–254

    Article  Google Scholar 

  67. Voit EO (2000) Computational analysis of biochemical systems—a practical guide for biochemists and molecular biologists. Cambridge University Press, Cambridge

    Google Scholar 

  68. Weis S, Schneggenburger R, Neher E (1999) Properties of a model of Ca2+-dependent vesicle pool dynamics and short term synaptic depression. Biophys J 77:2418–2429

    Article  Google Scholar 

  69. Wilkinson DJ (2006) Stochastic modeling for System Biology. Chapman and Hall/CRC Press, London

    Google Scholar 

  70. Wolfel M, Lou X, Schneggenburger R (2007) A mechanism intrinsic to the vesicle fusion machinery determines fast and slow transmitter release at a large cns synapse. J Neurosci 27:3198–3210

    Article  Google Scholar 

  71. Wolkenhauer O (2009) System Biology—dynamic pathway modeling (to appear)

    Google Scholar 

  72. Wolkenhauer O, Ullah M, Kolch W, Cho K-H (2004) Modeling and simulation of intracellular dynamics: choosing an appropriate framework. IEEE Trans Nanobiosci 3:200–207

    Article  Google Scholar 

  73. Wong AYC, Graham BP, Billups B, Forsythe ID (2003) Distinguishing between presynaptic and postsynaptic mechanisms of short-term depression during action potentials trains. J Neurosci 23:4868–4877

    Google Scholar 

  74. Xu-Friedman MA, Regehr WG (2004) Structural contribution to short-term synaptic plasticity. Physiol Rev 84:69–85

    Article  Google Scholar 

  75. Zucker RS, Kullmann DM, Schwartz TL (2004) Release of neurotransmitters. In: Byrne JH, Roberts JL (eds) From molecules to networks—an introduction to cellular and molecular neuroscience. Elsevier/Academic Press, San Diego, pp 197–244

    Google Scholar 

  76. Zucker RS, Regehr WG (2002) Short-term synaptic plasticity. Annu Rev Physiol 64:355–405

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Università di Pisa, Pisa, Italy

    Andrea Bracciali & Pierpaolo Degano

  2. Dipartimento di Biologia, Università di Pisa, Pisa, Italy

    Marcello Brunelli & Enrico Cataldo

Authors
  1. Andrea Bracciali
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  2. Marcello Brunelli
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  3. Enrico Cataldo
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  4. Pierpaolo Degano
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Corresponding author

Correspondence to Andrea Bracciali .

Editor information

Editors and Affiliations

  1. Dept. Computer Science, University of British Columbia, Main Mall 201-2366, Vancouver, V6T 1Z4, Canada

    Anne Condon

  2. Dept. Applied Mathematics, Weizmann Institute of Science, Rehovot, 76100, Israel

    David Harel

  3. Leiden Inst. Advanced Computer Science, Leiden University, Niels Bohrweg 1, Leiden, 2333 CA, Netherlands

    Joost N. Kok

  4. Turku Centre for Computer Science, Lemminkaisenkatu 14 A, Turku, 20520, Finland

    Arto Salomaa

  5. Computer Science, Computation,, California Inst. of Technology, Pasadena, 91125, U.S.A.

    Erik Winfree

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Bracciali, A., Brunelli, M., Cataldo, E., Degano, P. (2009). Formal Models of the Calyx of Held . In: Condon, A., Harel, D., Kok, J., Salomaa, A., Winfree, E. (eds) Algorithmic Bioprocesses. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88869-7_18

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  • DOI: https://doi.org/10.1007/978-3-540-88869-7_18

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