Journal of Computational Neuroscience

, Volume 6, Issue 1, pp 5–26 | Cite as

Signals in Stochastically Generated Neurons

  • James L. Winslow
  • Stephan F. Jou
  • Sabrina Wang
  • J. Martin Wojtowicz
Article

Abstract

To incorporate variation of neuron shape in neural models, we developed a method of generating a population of realistically shaped neurons. Parameters that characterize a neuron include soma diameters, distances to branch points, fiber diameters, and overall dendritic tree shape and size. Experimentally measured distributions provide a means of treating these morphological parameters as stochastic variables in an algorithm for production of neurons. Stochastically generated neurons shapes were used in a model of hippocampal dentate gyrus granule cells. A large part of the variation of whole neuron input resistance RN is due to variation in shape. Membrane resistivity Rm computed from RN varies accordingly. Statistics of responses to synaptic activation were computed for different dendritic shapes. Magnitude of response variation depended on synapse location, measurement site, and attribute of response.

stochastic neurons dendrites synapse location hippocampus membrane resistivity 

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References

  1. Andersen P, Silfvenius H, Sunberg SH, Sveen O (1980) A comparison of distal and proximal dendritic synapses on CA1 pyramids in guinea pig hippocampal slices in vitro. J. Physiol. (Lond.) 307:273–299.Google Scholar
  2. Bekkers JM, Stevens CF (1996) Cable properties of cultured hippocampal neurons determined from sucrose-evoked miniature EPSCs. J. Neurophysiol. 75:1250–1255.Google Scholar
  3. Benz R, Frölich P, Länuger P, Montal M(1975) Electrical capacity of black lipid film of lipid bilayers made from monolayers. Biochem. Biophys. Acta 394:323–334.Google Scholar
  4. Borst A, Haag J (1996) The intrinsic electrophysiological characteristics of fly lobula plate tangential cells: I. Passive membrane properties. J. Comput. Neurosci. 3:313–336.Google Scholar
  5. Claiborne BJ, Amaral DG, Cowan WM (1990) Quantitative, threedimensional analysis of granule cell dendrites in the rat dentate gyrus. J. Comp. Neurol. 302:206–219.Google Scholar
  6. Cook EP, Johnston D (1997) Active dendrites reduce locationdependent variability of synaptic input trains. J. Neurophysiol. 78:2116–2128.Google Scholar
  7. Cotman C, Taylor D, Lynch G (1973) Ultrastructural changes in synapses in the dentate gyrus of the rat during development. Brain Res. 63:205–213.Google Scholar
  8. Cowan J (1972) Stochastic models of neuroelectric activity. In: SA Rice, KF Freed, JC Light, eds. Statistical Mechanics: New Concepts, New Problems, New Applications. Proc. 6-th IUPAP Conf. Statistical Mechanics. University of Chicago Press, Chicago, IL. pp. 109–127.Google Scholar
  9. Cowan WM, Stanfield BB, Kishi K (1980) The development of the dentate gyrus. Current Topics in Develop. Biol. 15:103–157.Google Scholar
  10. Crain B, Cotman C, Taylor D, Lynch G (1973) Aquantitative electron microscopic study of synaptogenesis in the dentate gyrus of the rat. Brain Res. 63:195–204.Google Scholar
  11. de Schutter ED, Bower JM (1994a) An active membrane model of the cerebellar purkinje cell. I: Simulation of current clamps in slice. J. Neurophysiol. 71(1):375–400.Google Scholar
  12. de Schutter E, Bower JM (1994b) An active membrane model of the cerebellar purkinje cell. II: Simulation of synaptic responses. J. Neurophysiol. 71(1):401–419.Google Scholar
  13. Desmond NL, Levy WB (1984) Dendritic caliber and the threetwo power relationship of dentate granule cells. J. Comp. Neurol. 227:589–596.Google Scholar
  14. Desmond NL, Levy WB (1985) Granule cell dendritic spine density in the rat hippocampus varies with spine shape and location. Neurosci. Letters 54:219–224.Google Scholar
  15. Fettiplace R, Andrews DM, Haydon DA (1971) The thickness, composition and structure of some lipid bilayers and natural membranes. J. Membr. Biol. 5:277–296.Google Scholar
  16. Hama K, Arii T, Kosaka T (1989) Three-dimensional morphometrical study of dendritic spines of the granule cell in the rat dentate gyrus with hvem stereo images. J. Electron Microscopy Technique 12:80–87.Google Scholar
  17. Harris KM, Stevens JK (1989) Dendritic spines of CA1 pyramidal cells in the rat hippocampus: Serial electron microscopy with reference to their biophysical characteristics. J. Neurosci. 9:2982–2997.Google Scholar
  18. Hayat MA (1981) Principles and Techniques of Electron Microscopy: Biological Applications (2nd ed.), University Park Press, Baltimore, MD.Google Scholar
  19. Haydon DA, Requena J, Urban BW (1980) Some effect of aliphatic hydrocarbons on the electrical capacity and ionic currents of the squid giant axon membrane. J. Physiol. (Lond.) 309:229–245.Google Scholar
  20. Hines M (1984) Efficient computation of branched nerve equations. Int. J. Biomed. Comput. 15:69–76.Google Scholar
  21. Hines M (1989) A program for simulation of nerve equations with branching geometries. J. Physiol. (Lond.) 117:500–544.Google Scholar
  22. Holmes WR (1989) The role of dendritic diameters in maximizing the effectiveness of synaptic inputs. Brain Res. 478:127–137.Google Scholar
  23. Holmes WR, Levy WB (1990) Insights into associative long-term potentiation from computational models of NMDA receptormediated calcium influx and intracellular calcium concentration changes. J. Neurophysiol. 63:1148–1168.Google Scholar
  24. Holmes WR, Rall WR (1992) Electrotonic models of neuronal dendrites and single neuron computation. In T McKenna, J Davis, SF Zornetzer, eds. Single Neuron Computation. Academic Press, New York. pp. 7–25.Google Scholar
  25. Iansek R, Redman SJ (1973) The amplitude, time course and charge of unitary excitatory post-synaptic potentials evoked in spinal motoneurone dendrites. J. Physiol. 234:665–688.Google Scholar
  26. Jack JJB, Miller S, Porter R, Redman SJ (1971) The time course of minimal excitatory post-synaptic potentials evoked in spinal motoneurons by group Ia afferent fibres. J. Physiol. 215:321–352.Google Scholar
  27. Jack JJB, Noble D, Tsien RW (1975) Electric Current Flow in Excitable Cells. Clarendon Press, Oxford.Google Scholar
  28. Johnston D, Wu SM-S (1995) Foundations of Cellular Neurophysiology. MIT Press, Cambridge.Google Scholar
  29. Jonas P, Major G, Sakmann B (1993) Quantal components of unitary EPSCs at the mossy fibre synapse on CA3 pyramidal cells of rat hippocampus. J. Physiol. 472:615–663.Google Scholar
  30. Jou SF, Winslow JL, Wang S, Wojtowicz JM (1995) Families of generated hippocampal dentate granule shapes used to determine effects of location on synaptic response. Society for Neurosci. Abstr. 21:584.Google Scholar
  31. Koch C, Zador A (1993) The function of dendritic spines: Devices subserving biochemical rather than electrical compartmentalization. J. Neurosci. 13:413–422.Google Scholar
  32. Liu G, Tsien R (1995) Properties of synaptic transmission at single hippocampal synaptic boutons. Nature 375:404–408.Google Scholar
  33. Major G (1992) The physiology, morphology and modelling of cortical pyramidal neurones. Ph.D. thesis, Oxford University.Google Scholar
  34. Major G, Larkman AU, Jonas P, Sakmann B, Jack JJB (1994) Detailed passive cable models of whole-cell recorded CA3 pyramidal neurons in rat hippocampal slices. J. Neurosci. 14(8):4613–4638.Google Scholar
  35. Manor Y, Rinzel J, Segev I, Yarom Y (1997) Low-amplitude oscillations in the inferior olive: A model based on electrical coupling of neurons with heterogeneous channel densities. J. Neurophysiol. 77(5):2736–52.Google Scholar
  36. Nitzan R, Segev I, Yarom Y (1990) Voltage behavior along the irregular dendritic structure of morphologically and physiologically characterized vagal motoneurons in the guinea pig. J. Neurophysiol. 63(2):333–346.Google Scholar
  37. Pettit DL, Wang SSH, Gee KR, Augustine GJ (1997) Chemical twophoton uncaging: A novel approach to mapping glutamate receptors. Neuron 19:465–471.Google Scholar
  38. Pierce JP, Mendell LM (1993) Quantitative ultrastructure of Ia boutons in the ventral horn: Scaling and positional relationships. J. Neurosci. 13:4748–4763.Google Scholar
  39. Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical Recipes in C. Press Syndicate of the University of Cambridge, New York.Google Scholar
  40. Rall W (1957) Membrane time constant of motoneurons. Science 126:454.Google Scholar
  41. Rall W (1959) Branching dendritic trees and motoneuron membrane resistivity. Exper. Neurol. 1:491–527.Google Scholar
  42. Rall W (1964) Theoretical significance of dendritic trees for neuronal input-output relations. In: RF Reiss, ed. Neural Theory and Modeling. Stanford University Press, Palo Alto, CA. pp. 73–97.Google Scholar
  43. Rall W (1989) Cable theory for dendritic neurons. In: C Koch, I Segev, eds. Methods in Neuronal Modeling: From Synapses to Networks. MIT Press, Cambridge, MA. pp. 9–62.Google Scholar
  44. Rall W, Burke RE, Holmes WR, Jack, JJB, Redman SJ, Segev I (1992) Matching dendritic neuron models to experimental data. Physiol. Rev. 72(4) (Suppl.):S159–S186.Google Scholar
  45. Rall W, Rinzel J (1973) Branch input resistance and steady attenuation for input to one branch of a dendritic neuron model. Biophys. J. 13:648–688.Google Scholar
  46. Rapp M, Segev I, Yarom Y (1994) Physiology, morphology and detailed passive models of guinea-pig cerebellar purkinje cells. J. Physiol. 474(1):101–118.Google Scholar
  47. Segev I, Fleshman JW, Burke RE (1989) Compartmental models of complex neurons. In: C Koch, I Segev, eds. Methods in Neuronal Modeling: From Synapses to Networks. MIT Press, Cambridge, MA. pp. 63–96.Google Scholar
  48. Segev I, Rapp M, Manor Y, Yarom Y (1992) Analog and digital processing in single nerve cells: Dendritic integration and axonal propagation. In: T McKenna, J Davis, SF Zornetzer, eds. Single Neuron Computation. Academic Press, New York. pp. 173–198.Google Scholar
  49. Shelton DP (1985) Membrane resistivity estimated by means of a passive computer model. Neurosci. 14:111–131.Google Scholar
  50. Spruston N, Jaffe DB, Johnston D (1994) Dendritic attenuation of synaptic potentials and currents: The role of passive membrane properties. TINS 17(4):161–166.Google Scholar
  51. Spruston N, Jaffe DB, Williams SH, Johnston D (1993) Voltageand space-clamp errors associated with the measurement of electrotonically remote synaptic events. J. Neurophysiol. 70(2):781–802.Google Scholar
  52. Staley KJ, Otis TS, Mody I (1992) Membrane properties of dentate gyrus granule cells: Comparison of sharp microelectrode and whole-cell recordings. J. Neurophysiol. 67:1346–1358.Google Scholar
  53. Stratford KA, Mason A, Larkman A, Major G, Jack JJB (1989) The modelling of pyramidal neurons in the visual cortex. In: R Durbin, C Miall, G Mitchison, eds. The Computing Neurons. Addison-Wesley, Reading, MA. pp. 296–321.Google Scholar
  54. Stricker C, Field AC, Redman SJ (1996) Statistical analysis of amplitude fluctuations in EPSCs evoked in rat CA1 pyramidal neurones in vitro. J. Physiol. (Lond.) 490.2:419–441.Google Scholar
  55. Stuart GJ, Sakmann B (1994) Active propagation of somatic action potentials into neocortical pyramidal cell dendrites. Nature 367:69–72.Google Scholar
  56. Takashima S (1976) Membrane capacity of squid giant axon during hyper-and depolarisations. J. Membr. Biol. 27:21–39.Google Scholar
  57. Takashima S, Schwan HP (1974) Passive electrical properties of squid axon membrane. J. Membr. Biol. 17:51–68.Google Scholar
  58. Thurbon D, Field A, Redman S (1994) Electrotonic profiles of interneurons in stratum pyramidale of the CA1 region of rat hippocampus. J. Neurophysiol. 71(5):1948–1958.Google Scholar
  59. Traub R, Miles R (1991) Neuronal Networks of the Hippocampus. Cambridge University Press, Cambridge.Google Scholar
  60. Wang S, Wojtowicz JM (1997) Effect of GABA B receptors on synaptic interactions in dentate gyrus granule neurons of the rat. Neurosci. 79(1):117–127.Google Scholar
  61. Wang S, Wojtowicz JM, Atwood HL (1996) Synaptic recruitment during long-term potentiation at synapses of the medial perforant pathway in the dentate gyrus of the rat brain. Synapse 22:78–86.Google Scholar
  62. Wilson MA, Bower JM (1989) The simulation of large-scale neural networks. In: C Koch, I Segev, eds. Methods in Neural Modeling: From Synapses to Networks. MIT Press, Cambridge, MA. pp. 291–333.Google Scholar
  63. Winslow JL (1990) Analysis and numerical solution of the dendrite equation with synapses applied to cochlear neurons. Prog. Neurobiol. 34:91–105.Google Scholar
  64. Winslow JL (1994) Manual for WIN: A convenient video digitizing of NTSC, RS-170 or PAL video format. Physiology Department, University of Toronto, Toronto, Canada.Google Scholar
  65. Winslow JL (1995) Tree: A neuron tree tracing program. Physiology Department, University of Toronto, Toronto, Canada. lGoogle Scholar
  66. Winslow JL, Bjerknes M, Cheng H (1987) Three-dimensional reconstruction of biological objects using a graphics engine. Computers and Biomed. Res. 20:583–602.Google Scholar
  67. Witter MP (1993) Organization of the entorhinal-hippocampal system: Areviewof current anatomical data. Hippocampus 3 (special issue), 33–44.Google Scholar
  68. Zhang L, Valiante TA, Carlen PL (1993) Contribution of the lowthreshold T-type calcium current in generating the post-spike depolarizing afterpotential in dentate granule neurons of immature rats. J. Neurophysiol. 70(1):223–231.Google Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • James L. Winslow
    • 1
  • Stephan F. Jou
    • 1
  • Sabrina Wang
    • 2
  • J. Martin Wojtowicz
    • 2
  1. 1.Physiology Department and Institute of Biomedical EngineeringUniversity of TorontoToronto
  2. 2.Physiology DepartmentUniversity of TorontoToronto

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