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A Simple Mathematical Model of Second-Messenger Mediated Slow Excitatory Postsynaptic Potentials

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Abstract

We have developed a novel and simple mathematical model of a slow excitatory postsynaptic potential (EPSP) based on an abstraction of the processes of activation, inactivation, and summation of a cAMP, protein kinase A (PKA)-dependent second-messenger cascade. The model describes the activation of receptors, G-proteins, and production of cAMP as the first stage and uses first-order, non-rate-limited kinetics. The second stage corresponds to the release of active, PKA catalytic subunit and can use first- or higher-order kinetics. The third stage represents simple phosphorylation of ion channels and is limited by the number of channels available. The decay of each stage is based on first-order, mass-action kinetics. These equations and some variations were solved numerically and values of the parameters were determined by fitting to a variety of experimental data from myenteric neurons of the guinea-pig ileum. The model produced a slow EPSP with a nonlinear stimulus-response relationship that resulted from the underlying kinetics of the signaling cascade. This system of equations is suitable for incorporation into a large-scale computer simulation, and the methodology should be generalizable to other pathways.

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References

  • Acton SF (1970) Numerical Methods That Work. Harper & Row, New York.

    Google Scholar 

  • Akasu T, Tokimasa T (1989) Potassium currents in submucous neurones of guinea-pig caecum and their synaptic modification. J. Physiol. 416:571–588.

    PubMed  Google Scholar 

  • Baidan LV, Fertel RH, Wood JD (1992) Effects of brain-gut related peptides on cAMP levels in myenteric ganglia of guinea-pig small intestine. Eur. J. Pharmacol. 225:21–27.

    PubMed  Google Scholar 

  • Bennett MR, Gibson WG (1995) On the contribution of quantal secretion from close-contact and loose-contact varicosities to the synaptic potentials in the vas deferens. Phil. Trans. Royal Soc. Lond. 347:187–204.

    Google Scholar 

  • Bertrand PP, Galligan JJ (1994) Contribution of chloride conductance increase to slow EPSC and tachykinin current in guinea-pig myenteric neurones. J. Physiol. 481:47–60.

    PubMed  Google Scholar 

  • Bertrand PP, Galligan JJ (1995) Signal-transduction pathways causing slow synaptic excitation in guinea pig myenteric AH neurons. Am. J. Physiol. 269:G710-G720.

    PubMed  Google Scholar 

  • Bornstein JC, Furness JB, Kelly HF, Bywater RA, Neild TO, Bertrand PP (1997) Computer simulation of the enteric neural circuits mediating an ascending reflex: Roles of fast and slow excitatory outputs of sensory neurons. J. Autonomic Nervous Sys. 64:143–157.

    Google Scholar 

  • Builder SE, Beavo JA, Krebs, EG (1980) Stoichiometry of cAMP and 1,N6-etheno-cAMP binding to protein kinase. J. Biol. Chem. 255:2350–2354.

    PubMed  Google Scholar 

  • Buxbaum JD, Dudai Y (1989) A quantitative model for the kinetics of cAMP-dependent protein kinase (Type II) activity. J. Biol. Chem. 264:9344–9351.

    PubMed  Google Scholar 

  • Carman CV, Benovic JL (1998) G-protein-coupled receptors: Turnons and turn-offs. Current Opinions in Neurobiol. 8:335–344.

    Google Scholar 

  • Clapham DE, Neer EJ (1997)G protein αγ subunits. Ann. Rev. Pharmacol. and Toxicol. 37:167–203.

    Google Scholar 

  • Clerc N, Furness JB, Kunze WAA, Thomas EA and Bertrand PP (1999) Long-term effects of synaptic activation at low frequency on excitability of myenteric AH neurons. Neurosci. 90:277–278.

    Google Scholar 

  • Destexhe A, Mainen ZF, Sejnowski TJ (1994) Synthesis of models for excitable membranes, synaptic transmission and neuromodulation using a common kinetic formalism. J. Comput. Neurosci. 1:195–230.

    PubMed  Google Scholar 

  • Destexshe A, Sejnowski TJ (1995) G protein activation kinetics and spillover of gamma-aminobutyric acid may account for differences between inhibitory responses in the hippocampus and thalamus. Proc. Natl. Acad. Sci. (USA) 92:9515–9519.

    Google Scholar 

  • Furness JB, Costa M (1987) The Enteric Nervous System. Churchill Livingston, Edinburgh.

    Google Scholar 

  • Galligan JJ, Tokimasa T, North RA (1987) Effects of three mammalian tachykinins on single enteric neurons. Neurosci. Letters 82:167–171.

    Google Scholar 

  • Gray PC, Scott JD, Catterall WA (1998) Regulation of ion channels by cAMP-dependent protein kinase and A-kinase anchoring protein. Current Opinion in Neurobiol. 8:330–334.

    Google Scholar 

  • Hempel CM, Vincent P, Adams SR, Tsien RY, Selverston AI (1996) Spatio-temporal dynamics of cyclic AMP signals in an intact neural circuit. Nature 384:166–169.

    PubMed  Google Scholar 

  • Hille B (1992) Ionic Channels of Excitable Membranes (2nd ed.) Sinauer Associates, Sunderland, MA.

    Google Scholar 

  • Johnson PJ, Bornstein JC, Burcher E (1998) Roles of neuronal NK1 and NK3 receptors in synaptic transmission during motility reflexes in the guinea-pig ileum. Br. J. Pharmacol. 124 (7):1375–1384.

    PubMed  Google Scholar 

  • Katayama Y, North RA (1978) Does substance P mediate slow synaptic excitation within the myenteric plexus? Nature 274:387–388.

    PubMed  Google Scholar 

  • Kunze WAA, Furness JB, Bornstein JC (1993) Simultaneous intracellular recordings from enteric neurons reveal that myenteric AH neurons transmit via slow excitatory postsynaptic potentials. Neurosci. 55:685–694.

    Google Scholar 

  • Kunze WAA, Bertrand PP, Furness JB, Bornstein JC (1997) Influence of the mucosa on the excitability of myenteric neurons. Neurosci. 76:619–634.

    Google Scholar 

  • Kunze WAA, Furness JB (1999). The enteric nervous system and regulation of intestinal motility. Ann. Rev. Physiol. 61:117–124.

    Google Scholar 

  • Lamb TD (1996) Gain and kinetics of activation in the G-protein cascade of phototransduction. Proc. Nat. Acad. Sci. 93:556–570.

    Google Scholar 

  • Lamb TD, Pugh EN (1992) A quantitative account of the activation steps involved in phototransduction in amphibian photoreceptors. J. Physiol. 449:719–758.

    PubMed  Google Scholar 

  • Morita K, Katayama K (1992) Substance P inhibits activation of calcium-dependent potassium conductances in guinea-pig myenteric neurones. J. Physiol. 447:293–308.

    PubMed  Google Scholar 

  • Morita K, North RA (1985) Significance of slow synaptic potentials for transmission of excitation in guinea-pig myenteric plexus. Neurosci. 14:661–672.

    Google Scholar 

  • Nauroschat J, an der Heiden U (1997) A theoretical approach to Gprotein modulation of cellular responsiveness. Math. Biol. 35:609–627.

    Google Scholar 

  • Nemeth PR, Palmer JM, Wood JD, Zafirov DH (1986) Effects of forskolin on electrical behaviour of myenteric neurones in guineapig small intestine. J. Physiol. 376:439–450.

    PubMed  Google Scholar 

  • Pan H, Wang HY, Friedman E, Gershon MD (1997) Mediation by protein kinases C and A of Go-linked slow responses of enteric neurons to 5-HT. J. Neurosci. 17:1011–1024

    PubMed  Google Scholar 

  • Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical Recipes in C: The Art of Scientific Computing (2nd ed.). Cambridge University Press, Cambridge.

    Google Scholar 

  • Ross EM (1989) Signal sorting and amplification through G protein-coupled receptors. Neuron 3:141–152.

    PubMed  Google Scholar 

  • Southwell BR, Woodman HL, Murphy R, Royal SJ, Furness JB (1996) Characterisation of substance P-induced endocytosis of NK1 receptors on enteric neurons. Histochem. and Cell Biol. 106:563–571.

    Google Scholar 

  • Taylor SS (1989) cAMP-dependent protein kinase: Model for an enzyme family. J. Biol. Chem. 264:8443–8446.

    PubMed  Google Scholar 

  • Thomas EA, Bertrand PP, Bornstein JC (1999) Genesis and role of coordinated firing in a feed forward network: A model study of the enteric nervous system. Neurosci. 93:1525--.

    Google Scholar 

  • Torre V, Ashmore JF, Lamb TD, Menini A (1995) Transduction and adaptation in sensory receptor cells. J. Neurosci. 15:7757–7768.

    PubMed  Google Scholar 

  • Vergara C, Latorre R, Marrion NV, Adelman JP (1998) Calcium-activated potassium channels. Current Opinions in Neurobiol. 8(3):321–329.

    Google Scholar 

  • Wood JD (1994) Physiology of the enteric nervous system. In: Johnson LR, ed. Physiology of the Gastrointestinal Tract. Raven Press, New York. pp. 423–482.

    Google Scholar 

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Authors and Affiliations

  1. Department of Physiology and Department of Anatomy and Cell Biology, University of Melbourne, Parkville, 3052, Australia

    P.P. Bertrand

  2. Department of Physiology and Department of Anatomy and Cell Biology, University of Melbourne, Parkville, 3052, Australia

    E.A. Thomas, W.A.A. Kunze & J.C. Bornstein

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  1. P.P. Bertrand
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  2. E.A. Thomas
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  3. W.A.A. Kunze
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  4. J.C. Bornstein
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Bertrand, P., Thomas, E., Kunze, W. et al. A Simple Mathematical Model of Second-Messenger Mediated Slow Excitatory Postsynaptic Potentials. J Comput Neurosci 8, 127–142 (2000). https://doi.org/10.1023/A:1008969115017

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