Pharmacopsychiatry 2010; 43: S42-S49
DOI: 10.1055/s-0030-1249025
Original Paper

© Georg Thieme Verlag KG Stuttgart · New York

The Evolution of Synapse Models – from Numbers to Networks to Spaces

B. Dulam-Banawa1 , A. Marin-Sanguino2 , E. Mendoza3 , 4
  • 1Institute of Mathematics, University of the Philippines Diliman, Quezon City, Philippines
  • 2Department of Membrane Biochemistry, Max Planck Institute of Biochemistry, Martinstried, Germany
  • 3Faculty of Physics and Center for NanoScience, Ludwig-Maximilians-University, Munich, Germany
  • 4Department of Computer Science, University of the Philippines Diliman, Quezon City, Philippines
Further Information

Publication History

Publication Date:
17 May 2010 (online)

Abstract

We review the evolution of synapse models over the last sixty-five years in terms of the changing paradigms: initially, the synapse was modelled only as part of a neuronal system, both as a number (weight of an edge in a connectionist network) and as a channel in a conductance-based model. With the availability of more structural and kinetic data, it came to be seen as a full-fledged biochemical network, accompanied by a shift from the previous “top-down” approach to a more “bottom-up” network reconstruction. Most recently, the synapse is seen as a geometric 3-dimensional space with various processes driving the dynamics. A particular focus is placed on models of the dopamine synapse and their connections to schizophrenia. The advances of detailed modelling on the synaptic level have highlighted the challenges of integrating the various functional levels, which are tightly coupled with processes on different scales in time and space. On the other hand, this effort will contribute to bridging the currently perceived gap between computational neuroscience and (computational) systems biology.

References

  • 1 Abbott LF, Kepler TB. Model neurons: From Hodgkin-Huxley to Hopfield.. In: Garrido L, ed. Statistical Mechanics of Neural Networks. 1990: 5-18
  • 2 Abbott LF, Regehr WG. Synaptic computation 2004.  Nature. 2004;  431 (7010) 796-803
  • 3 Braver TS, Barch DM, Cohen JD. Cognition and control in schizophrenia: a computational model of dopamine and prefrontal function.  Biological Psychiatry. 1999;  46 (3) 312-328
  • 4 Broderick G, Ruaini M, Chan E. et al . A life-like virtual cell membrane using discrete automata.  In Silico Biol. 2005;  5 (2) 163-178
  • 5 Burrage K, Hancock JF, Leier A. et al . Modelling and simulation techniques for membrane biology.  Briefings in Bioinformatics. 2007;  8 (4) 234-244
  • 6 Canavier CC, Landry RS. An increase in AMPA and a decrease in SK conductance increase burst firing by different mechanisms in a model of a dopamine neuron in vivo.  J Neurophysiol. 2006;  96 (5) 2549-2563
  • 7 Chapeau-Blondeau F, Chambet N. Synapse models for neural networks: from ion channel kinetics to multiplicative coefficients.  Neural Computation. 1995;  7 (4) 713-734
  • 8 Chou I, Voit EO. Recent developments in parameter estimation and structure identification of biochemical and genomic systems.  Math Biosci. 2009;  219 (2) 57-83
  • 9 De Schutter E. Why are computational neuroscience and systems biology so different?.  PLoS Comp Bio. 2008;  4 (5) e10000078
  • 10 Deco G, Rolls ET. Attention, short-term memory, and action selection: a unifying theory.  Prog Neurobiol. 2005;  76 (4) 236-256
  • 11 Destexhe A, Mainen ZF, Sejnowski T. An efficient method for computing synaptic conductances based on a kinetic model of receptor binding.  Neural Computation. 1994;  6 (1) 14-18
  • 12 Destexhe A, Mainen ZF, Sejnowski TJ. Synthesis of models for excitable membranes, synaptic transmission and neuromodulation using a common kinetic formalism.  Journal of Computational Neuroscience. 1994;  1 (3) 195-230
  • 13 Emes RD, Pocklington AJ, Anderson CN. et al . Evolutionary expansion and anatomical specialization of synapse proteome complexity.  Nat Neurosci. 2008;  11 (7) 799-806
  • 14 Fernandez E, Schiappa R, Girault JA. et al . DARPP-32 is a robust integrator of dopamine and glutamate signals.  PLoS Comput Biol. 2006;  2 (12) e176
  • 15 FitzHugh R. Impulses and physiological states in theoretical models of nerve membrane.  Biophysical Journal. 1961;  1 (6) 445
  • 16 Garris PA, Wightman RM. Different kinetics govern dopaminergic transmission in the amygdala, prefrontal cortex, and striatum: an in vivo voltammetric study.  J Neurosci. 1994;  14 (1) 442-450
  • 17 Hatzikirou H, Breier G, Deutsch A. Cellular automaton models for tumor invasion.. Encyclopedia of complexity and complex systems: Springer; 2008
  • 18 Hebb DO. The organization of behavior: a neuropsychological theory.  Wiley. 1949; 
  • 19 Hodgkin AL, Huxley A. A quantitative description of membrane current and its application to conduction and excitation in nerve.  The Journal of physiology. 1952;  117 (4) 500-544
  • 20 Hoffman R, Dobscha S. Cortical pruning and the development of schizophrenia: a computer model.  Schizophr Bull. 1989;  15 (3) 477-490
  • 21 Hopfield J. Neural networks and physical systems with emergent collective computational abilities.  PNAS. 1982;  79 (8) 2554-2558
  • 22 Hopfield J, Tank D. Computing with neural circuits: a model.  Science. 1986;  233 (4764) 625-633
  • 23 Izhikevich EM, Edelman GM. Large-scale model of mammalian thalamocortical systems simple model of spiking neurons.  PNAS. 2008;  105 (9) 3593-3598
  • 24 Izhikevich EM, Gally JA, Edelman GM. Spike-timing dynamics of neuronal groups.  Cereb Cortex. 2004;  14 (8) 933-944
  • 25 Jamshidi N, Palsson BO. Formulating genome-scale kinetic models in the post-genome era.  Mol Syst Biol. 2008;  4 171
  • 26 Justice JB, Nicolaysen LC, Michael AC. Modeling the dopaminergic nerve terminal.  J Neurosci Methods. 1988;  22 (3) 239-252
  • 27 Kawagoe KT, Garris PA, Wiedemann DJ. et al . Regulation of transient dopamine concentration gradients in the microenvironment surrounding nerve terminals in the rat striatum.  Neuroscience. 1992;  51 (1) 55-64
  • 28 Keener J, Sneyd J. Mathematical Physiology. New York : Springer-Verlag; 1998
  • 29 Le Novere N. The long journey of a systems biology of neuronal function.  BMC Systems Biology. 2007;  I 28
  • 30 Lindskog M. Modelling of DARPP-32 regulation to understand intracellular signaling in psychiatric disease.  Pharmacopsychiatry. 2008;  41 (S 01) S99-S104
  • 31 Lindskog M, Kim M, Wikström M. et al . Transient calcium and dopamine increase PKA activity and DARPP-32 phosphorylation.  PLoS Comput Biol. 2006;  2 (9) e119
  • 32 Loh M, Rolls ET, Deco G. A dynamical systems hypothesis of schizophrenia.  PLoS Comput Biol. 2007;  3 (11) e228
  • 33 Marin-Sanguino A, Mendoza ER. Hybrid modeling in computational neuropsychiatry.  Pharmacopsychiatry. 2008;  41 (S1) S85-S89
  • 34 McCulloch WS, Pitts W. A logical calculus of the ideas immanent in nervous activity.  Bull of Mathbiol. 1943;  5 (4) 115-133
  • 35 Montague PR, Hyman SE, Cohen JD. Computational roles for dopamine in behavioral control.  Nature. 2004;  431 (7010) 760-767
  • 36 Nagumo, Arimoto S, Yoshizawa S. An Active Pulse Transmission Line Simulating Nerve Axon.  Proceedings of the IRE. 1962;  50 (10) 2061-2070
  • 37 Nicolaysen LC, Justice JB. Effects of cocaine on release and uptake of dopamine in vivo: differentiation by mathematical modeling.  Pharmacol Biochem Behav. 1988;  31 (2) 327-335
  • 38 O'Reilly RC. Biologically based computational models of high-level cognition.  Science. 2006;  314 (5796) 91-94
  • 39 Petrov V, Nikolova E, Wolkenhauer O. Reduction of nonlinear dynamic systems with an application to signal transduction pathways.  Systems Biology. 2005;  1 (1) 2-9
  • 40 Pocklington AJ, Armstrong JD, Grant SG. Organization of brain complexity--synapse proteome form and function.  Brief Funct Genomic Proteomic. 2006;  5 (1) 66-73
  • 41 Pocklington AJ, Cumiskey M, Armstrong JD. et al . The proteomes of neurotransmitter receptor complexes form modular networks with distributed functionality underlying plasticity and behavior.  Mol Syst Biol. 2006;  2 0023
  • 42 Qi Z, Miller GW, Voit EO. Computational Systems Analysis of Dopamine Metabolism.  PLoS ONE. 2008;  3 (6) e2444
  • 43 Reid AG. A critical analysis of an attractor network model of schihzophrenia.  CNS '96: Proceedings of the annual conference on Computational neuroscience: trends in research. 1997;  3 463-470
  • 44 Rosenblatt F. The perceptron: A probabilistic model for information storage and organization in the brain.  Psychological Review. 1958;  65 (6) 386-408
  • 45 Song S, Miller KD, Abbott L. Competitive hebbian learning through spike-timing-dependent synaptic plasticity.  Nature Neuroscience. 2000;  3 (9) 919-926
  • 46 Stiles JR, Bartol TM, Salpeter MM. et al .New insights from reconstruction and monte carlo simulations with MCELL.. In “Synapses”.. In: Cowan M, Südhof TC, Stevens CF, eds. The Johns Hopkins University Press; 2001
  • 47 Takahashi K, Arjunan SNV, Tomita M. Space in systems biology of signaling pathways – towards intracellular molecular crowding in silico.  FEBS Letters. 2005;  579 (8) 1783-1788
  • 48 Vera J, Curto R, Cascante M. et al . Detection of potential enzyme targets by metabolic modelling and optimization: application to a simple enzymopathy.  Bioinformatics. 2007;  23 (17) 2281-2289
  • 49 Voit EO, Qi Z, Miller GW. Steps of modeling complex biological systems.  Pharmacopsychiatry. 2008;  41 (S 01) S78-S84
  • 50 Wightman RM, Amatore C, Engstrom RC. et al . Real-time characterization of dopamine overflow and uptake in the rat striatum.  Neuroscience. 1988;  25 (2) 513-523
  • 51 Young D, Stark J, Kirschner D. Systems biology of persistent infection: tuberculosis as a case study.  Nature Review Microbiology. 2008;  6 (7) 520-528

Correspondence

Dr. E. Mendoza

Faculty of Physics and Center for NanoScience

Ludwig-Maximilians-University

Geschwister-Scholl-Platz 1

80539 Munich

Germany

Phone: +49/1735729934

Email: mendoza@lmu.de