Biological Cybernetics

, Volume 70, Issue 3, pp 267–273 | Cite as

Synaptic integration of NMDA and non-NMDA receptors in large neuronal network models solved by means of differential equations

  • C. Bernard
  • Y. C. Ge
  • E. Stockley
  • J. B. Willis
  • H. V. Wheal


Alpha functions are commonly used to describe different receptor channel kinetics (non-NMDA, GABAA and GABAB). In this paper we show that they may be represented as solutions to simple ordinary differential equations. This alternative method is compared with the commonly used direct summation of the alpha function conductances in a high-level neuronal circuit model. A parametric study shows that the differential equation method greatly speeds up the previous summation method. The forward Euler method used to solve this differential equation is shown to be accurate for this type of simulation. The modelling of NMDA receptor channel kinetics is also discussed.


NMDA NMDA Receptor Neuronal Network Circuit Model Equation Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Ascher P, Nowak L (1988) The role of divalent cations in the N-methyl-d-aspartate responses of mouse central neurons in culture. J Physiol 399:247–267Google Scholar
  2. Ge Y, Bernard C, Willis J, Wheal H (1992) Transputer modelling of epileptiform activity in the CA1 region of the hippocampus. Am Soc Neurosci 18:1242Google Scholar
  3. Holmes WR, Levy WB (1990) Insights into associative LTP from computational models of NMDA receptor-mediated calcium influx and intracellular calcium concentration changes. J Neurophys 63:1148–1168Google Scholar
  4. Jack JJB, Noble D, Tsien RW (1975, 1983) Electric current flow in excitable cells, 1st and 2nd edns. Oxford University Press, OxfordGoogle Scholar
  5. Johnson JW, Ascher P (1990) Voltage-dependent block by intracellular Mg2+ of N-methyl-d-aspartate activated channels. Biophys J 57:1085–1090Google Scholar
  6. Lester RA, Jahr CE (1992) NMDA channel behaviour depends on agonist affinity. J Neurosci 12:635–643Google Scholar
  7. MacGregor RJ (1987) Neural and brain modeling. Academic Press, New YorkGoogle Scholar
  8. Rall W (1967) Distinguishing theoretical synaptic potentials computed for different soma-dendritic distributions of synaptic inputs. J Neurophys 30:1138–1168Google Scholar
  9. Ropert N, Miles R, Korn H (1990) Characteristics of miniature inhibitory postsynaptic currents in CA1 pyramidal neurones of rat hippocampus. J Physiol (Lond) 428:707–722Google Scholar
  10. Segev I, Fleshman W, Miller JP, Bunow B (1985) Modelling the electrical behaviour of anatomically complex neurons using a network analysis program: passive membrane. Biol Cybern 53:27–40Google Scholar
  11. Stern P, Edwards FA, Sakmann B (1992) Fast and slow components of unitary EPSCs on stellate cells elicited by focal stimulation in slices of rat visual cortex. J Physiol (Lond) 449:247–278Google Scholar
  12. Stevens CF (1966) Neurophysiology: a primer. Wiley, New YorkGoogle Scholar
  13. Traub RD, Miles R (1991) Neuronal networks of the hippocampus. Cambridge University Press, Cambridge, UKGoogle Scholar
  14. Traub RD, Wong RKS, Miles R, Michelson H (1991) A model of a CA3 hippocampal pyramidal neuron incorporating voltage-clamp data on intrinsic conductances. J Neurophys 66:635–650Google Scholar
  15. Tuckwell HC (1988) Introduction to theoretical neurobiology. Cambridge University Press, Cambridge, UKGoogle Scholar
  16. Wheal HV, Simpson L, Phelps S, Stockley E (1991) Excitatory amino acid receptor subtypes and their roles in epileptiform synaptic potentials in the hippocampus. In: Wheal HV, Thomson AM (eds) Excitatory amino acids and synaptic transmission. Academic Press, London, pp 239–264Google Scholar
  17. Williams SH, Johnston D (1991) Kinetic properties of two anatomically distinct excitatory synapses in hippocampal CA3 pyramidal neurons. J Neurophys 66:1010–1020Google Scholar
  18. Willis J, Ge Y, Wheal H (1992) Simulation of epileptiform activity in the hippocampus using transputers. J Neurosci MethodsGoogle Scholar
  19. Wilson M, Bower J (1989) The simulation of large-scale neural networks. In: Koch C, Segev I (eds) Methods in neural modeling. MIT Press, pp 291–334Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • C. Bernard
    • 1
  • Y. C. Ge
    • 1
  • E. Stockley
    • 1
  • J. B. Willis
    • 2
  • H. V. Wheal
    • 1
  1. 1.Department of Physiology and PharmacologySouthampton UniversitySouthamptonUK
  2. 2.Department of MathematicsSouthampton UniversitySouthamptonUK

Personalised recommendations