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An electro-diffusion model for computing membrane potentials and ionic concentrations in branching dendrites, spines and axons

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Abstract

The Nernst-Planck equation for electrodiffusion was applied to axons, dendrites and spines. For thick processes (1 μm) the results of computer simulation agreed accurately with the cable model for passive conduction and for propagating action potentials. For thin processes (0.1 μm) and spines, however, the cable model may fail during transient events such as synaptic potentials. First, ionic concentrations can rapidly change in small compartments, altering ionic equilibrium potentials and the driving forces for movement of ions across the membrane. Second, longitudinal diffusion may dominate over electrical forces when ionic concentration gradients become large. We compare predictions of the cable model and the electro-diffusion model for excitatory postsynaptic potentials on spines and show that there are significant discrepancies for large conductance changes. The electro-diffusion model also predicts that inhibition on small structures such as spines and thin processes is ineffective. We suggest a modified cable model that gives better agreement with the electro-diffusion model.

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References

  • Brandon JG, Coss RG (1982) Rapid dendritic spine stem shortening during one-trial learning: the honeybee's first orientation flight. Brain Res 252:51–61

    Google Scholar 

  • Cooley JW, Dodge FA (1966) Digital computer solutions for excitation and propagation of the nerve impulse. Biophys J 6:583–599

    Google Scholar 

  • Coss RG, Globus A (1978) Spine stems on tectal interneurons in jewelfish are shortened by social stimulation. Science 200:787–789

    Google Scholar 

  • Coss RG, Perkel DH (1985) The function of dendritic spines. Behav Neur Biol 44:151–185

    Google Scholar 

  • Coss RG, Brandon JG, Globus A (1980) Changes of morphology of dendritic spines on honeybee calycal interneurons associated with cumulative nursing and foraging experiences. Brain Res 192:49–59

    Google Scholar 

  • Fogelson AL, Zucker RS (1985) Presynaptic calcium diffusion from various arrays of single channels. Biophys J 48:1003–1017

    Google Scholar 

  • Frankenhaeuser B, Huxley AF (1964) The action potential in the myelinated nerve fiber ofXenopus laevis computed on the basis of voltage clamp data. J Gen Physiol 171:302–315

    Google Scholar 

  • Gamble E, Koch C (1987) The dynamics of free calcium in dendritic spines in response to repetitive synaptic input. Science 236:1311–1315

    Google Scholar 

  • Goldman DE (1943) Potential, impedance and rectification in membranes. J Gen Physiol 27:37–60

    Google Scholar 

  • Hille B (1984) Ionic channels of excitable membranes. Sinauer, Sunderland, Mass

    Google Scholar 

  • Hodgkin AL, Huxley AF (1952) Currents carried by sodium and potassium ions through the membrane of the giant axon ofLoligo. J Physiol 116:449–472

    Google Scholar 

  • Jack JJB, Noble D, Tsien RW (1975) Electrical current flow in excitable cells. Oxford University Press, Oxford

    Google Scholar 

  • Koch C, Poggio T (1983) A theoretical analysis of electrical properties of spines. Proc R Soc London B 218:455–477

    Google Scholar 

  • Koch C, Poggio T, Torre V (1983) Nonlinear interaction in a dendritic tree: location, timing, and role in information processing. Proc Natl Acad Sci USA 80:2799–2802

    Google Scholar 

  • Malenka RC, Kauer JA, Zucker RS, Nicoll RA (1988) Postsynaptic calcium is sufficient for potentiation of hippocampal synaptic transmission. Science 242:81–84

    Google Scholar 

  • Mascagni MA (1989) Numerical methods for neuronal modeling. In: Koch C, Segev I (eds) Methods in neuronal modeling. MIT Press, Cambridge

    Google Scholar 

  • Perkel DH, Perkel DJ (1985) Dendritic spines: role of active membrane modulating synaptic efficacy. Brain Res 325:331–335

    Google Scholar 

  • Qian N, Sejnowski TJ (1988) Electro-diffusion model of electrical conduction in neuronal processes. In: Woody CW, Alkon DL, McGaugh JL (eds) Cellular mechanisms of conditioning and behavioral plasticity. Plenum Press, New York

    Google Scholar 

  • Qian N, Sejnowski TJ (1989) Inhibition on spines and thin dendrites may be ineffective because of ionic concentration changes. Soc Neurosci (abstr) 15

  • Rall W (1967) Distinguishing theoretical synaptic potentials computed for different soma-dendritic distribution of synaptic input. J Neurophysiol 30:1136–1168

    Google Scholar 

  • Rall W (1977) Core conductor theory and cable properties of neurons. In: Kandel ER (ed) Handbook of physiology: the nervous system. American Physiological Society, Bethesda, Md, pp 39–97

    Google Scholar 

  • Rall W (1978) Dendritic spines and synaptic potency. In: Poeter R (ed) Studies in neurophysiology. Cambridge University Press, Cambridge

    Google Scholar 

  • Rall W, Segev I (1987) Functional possibilities for synapses on dendrites and dendritic spines. In: Edelman GM, Gall WF, Cowan WM (eds) New insights into synaptic function. Wiley, New York

    Google Scholar 

  • Rausch G, Scheich H (1982) Dendritic spine loss and enlargement during maturation of the speech control system in mynah bird (Gracula religiosa). Neurosci Lett 29:129–133

    Google Scholar 

  • Segev I, Rall W (1988) Computational study of an excitable dendritic spine. J Neurophysiol 60:499–523

    Google Scholar 

  • Shepherd GM, Brayton RK, Miller JP, Segev I, Rinzel J, Rall W (1985) Signal enhancement in distal cortical dendrites by means of interactions between active dendritic spines. Proc Natl Acad Sci USA 82:2192–2195

    Google Scholar 

  • Simon SM, Llinas RR (1985) Compartmentalization of the submembrane calcium activity during calcium influx and its significance in transmitter release. Biophys J 48:485–498

    Google Scholar 

  • Stockbridge N, Moore JW (1984) Dynamics of intracellular calcium and its possible relationship to phasic transmitter release and facilitation at the frog neuromuscular junction. J Neurosci 4:803–811

    Google Scholar 

  • Wathey J, Lytton W, Jester J, Sejnowski T (1989) Simulations of synaptic potentials using realistic models of hippocampal pyramidal neurons. Soc Neurosci (abstr) 15

  • Weer PD, Rakowski RF (1984) Current generated by backwardrunning electrogenic Na+ pump in squid giant axons. Nature 309:450–452

    Google Scholar 

  • Yamada WM, Koch C, Adams PR (1989) Multiple channels and calcium dynamics. In: Koch C, Segev I (eds) Methods in neuronal modeling. MIT Press, Cambridge

    Google Scholar 

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Qian, N., Sejnowski, T.J. An electro-diffusion model for computing membrane potentials and ionic concentrations in branching dendrites, spines and axons. Biol. Cybern. 62, 1–15 (1989). https://doi.org/10.1007/BF00217656

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  • DOI: https://doi.org/10.1007/BF00217656

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