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Democratization in a passive dendritic tree : an analytical investigation

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Timofeeva, Yulia, Cox, S. J., Coombes, Stephen and Josić, Krešimir. (2008) Democratization in a passive dendritic tree : an analytical investigation. Journal of Computational Neuroscience, Vol.25 (No.2). pp. 228-244. ISSN 0929-5313

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Official URL: http://dx.doi.org/10.1007/s10827-008-0075-9

Abstract

One way to achieve amplification of distal synaptic inputs on a dendritic tree is to scale the amplitude and/or duration of the synaptic conductance with its distance from the soma. This is an example of what is often referred to as “dendritic democracy”. Although well studied experimentally, to date this phenomenon has not been thoroughly explored from a mathematical perspective. In this paper we adopt a passive model of a dendritic tree with distributed excitatory synaptic conductances and analyze a number of key measures of democracy. In particular, via moment methods we derive laws for the transport, from synapse to soma, of strength, characteristic time, and dispersion. These laws lead immediately to synaptic scalings that overcome attenuation with distance. We follow this with a Neumann approximation of Green’s representation that readily produces the synaptic scaling that democratizes the peak somatic voltage response. Results are obtained for both idealized geometries and for the more realistic geometry of a rat CA1 pyramidal cell. For each measure of democratization we produce and contrast the synaptic scaling associated with treating the synapse as either a conductance change or a current injection. We find that our respective scalings agree up to a critical distance from the soma and we reveal how this critical distance decreases with decreasing branch radius.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions:	Faculty of Science > Computer Science
Library of Congress Subject Headings (LCSH):	Dendritic trees
Journal or Publication Title:	Journal of Computational Neuroscience
Publisher:	Springer New York LLC
ISSN:	0929-5313
Date:	6 February 2008
Volume:	Vol.25
Number:	No.2
Page Range:	pp. 228-244
Identification Number:	10.1007/s10827-008-0075-9
Status:	Peer Reviewed
Access rights to Published version:	Open Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC), National Science Foundation (U.S.) (NSF), Norman Hackerman Advanced Research Program (NHARP)
Grant number:	GR/R76219 (EPSRC), DMS-0604429 (NSF)
References:	[1] L F Abbott, E Fahri, and S Gutmann, The path integral for dendritic trees, Biological Cybernetics 66 (1991), 49–60. [2] H. Agmon-Snir, A novel theoretical approach to the analysis of dendritic transients, Biophysical Journal 69 (1995), no. 5, 1633–1656. [3] P Andersen, H Silfvenius, S H Sundberg, and O Sveen, A comparison of distal and proximal dendritic synapses on CA1 pyramids in guinea-pig hippocampal slices in vitro, Journal of Physiology 307 (1980), 273–299. [4] B K Andrasfalvy and J C Magee, Distance-dependent increase in AMPA receptor number in the dendrites of adult hippocampal ca1 pyramidal neurons, Journal of Neuroscience 21 (2001), 9151–9159. [5] P.C. Bressloff and S. Coombes, Physics of the extended neuron, International Journal of Modern Physics B 11 (1997), 2343–2392. [6] W. Burke, Spontaneous potentials in slow muscle fibres of the frog., J Physiol 135 (1957), no. 3, 511–21. [7] N T Carnevale and M L Hines, The NEURON book, Cambridge University Press, 2006. [8] S Coombes, Y Timofeeva, C-M Svensson, G J Lord, K Josi´c, S J Cox, and C M Colbert, Branching dendrites with resonant membrane: a “sum-over-trips” approach, Biological Cybernetics 97 (2007), 137–149. [9] H Cuntz, A Borst, and I Segev, Optimization principles of dendritic structure, Theoretical Biology and Medical Modelling 4 (2007). [10] E De Schutter and JMBower, Simulated responses of cerebellar Purkinje cells are independent of the dendritic location of granule cell synaptic inputs, Proceedings of the National Academy of Sciences USA 91 (1994), 4736–4740. [11] P. Fatt and B. Katz, An analysis of the end-plate potential recorded with an intracellular electrode., J Physiol 115 (1951), no. 3, 320–70. [12] N.L. Golding, T.J. Mickus, Y. Katz, W.L. Kath, and N. Spruston, Fac- tors mediating powerful voltage attenuation along CA1 pyramidal neuron dendrites, The Journal of Physiology 568 (2005), no. 1, 69–82. [13] Michael H¨ausser, Synaptic function: Dendritic democracy, Current Biology 11 (2001), R10–R12. [14] R Iansek and S J Redman, The amplitude, time course and charge of unitary excitatory post-synaptic potentials evoked in spinal motoneurone dendrites, Journal of Physiology 234 (1973), 665–688. [15] J J Jack, S J Redman, and K Wong, The components of synaptic poten- tials evoked in cat spinal motoneurones by impulses in single group Ia afferents, Journal of Physiology 321 (1981), 65–96. [16] J.J.B. Jack, D. Noble, and R.W. Tsien, Electric Current Flow in Ex- citable Cells, Oxfor University Press, Oxford, UK, 1975. [17] C. Koch, Biophysics of Computation: Information Processing in Single Neurons, Oxford University Press, 1999. [18] M London and I Segev, Synaptic scaling in vitro and in vivo, Nature Neuroscience 4 (2001), 853–854. [19] J C Magee, Dendritic integration of excitatory synaptic input, Nature Reviews Neuroscience 1 (2000), 181–190. [20] J.C. Magee and E.P. Cook, Somatic EPSP amplitude is independent of synapse location in hippocampal pyramidal neurons, Nature Neuroscience 3 (2000), 895–903. [21] M Migliore, M Ferrante, and G A Ascoli, Signal propagation in oblique dendrites of CA1 pyramidal cells, Journal of Neurophysiology 94 (2005), 4145–4155. [22] D.A. Nicholson, R. Trana, Y. Katz, W.L. Kath, N. Spruston, and Y. Geinisman, Distance-Dependent Differences in Synapse Number and AMPA Receptor Expression in Hippocampal CA1 Pyramidal Neurons, Neuron 50 (2006), no. 3, 431–442. [23] Daniel A Nicholson, Rachel Trana, Yael Katz, William L Kath, Nelson Spruston, and Yuri Geinisman, Distance-dependent differences in synapse number and AMPA receptor expression in hippocampal CA1 pyramidal neurons, Neuron 50 (2006), no. 3, 431–442. [24] W Rall, Theoretical significance of dendritic trees for neuronal input- output relations, Neural Theory and Modeling, Stanford University Press, 1964. [25] W Rall and H Agmon-Snir, Cable theory for dendritic neurons, Methods in Neuronal Modeling, 2nd ed., MIT Press, Cambridge, MA, 1998, pp. 27–92. [26] C C Rumsey and L F Abbott, Equalization of synaptic efficacy by activity- and timing-dependent synaptic plasticity, Journal of Neurophysiology 91 (2004), 2273–2280. [27] Clifton C Rumsey and L F Abbott, Synaptic democracy in active den- drites, Journal of Neurophysiology 96 (2006), no. 5, 2307–2318. [28] Y Timofeeva, G J Lord, and S Coombes, Dendritic cable with active spines: a modeling study in the spike-diffuse spike framework, Neurocomputing 69 (2006), 1058–1061. [29] Y Timofeeva, G J Lord, and S Coombes, Spatio-temporal filtering prop- erties of a dendritic cable with active spines, Journal of Computational Neuroscience 21 (2006), 293–306. [30] H C Tuckwell, Introduction to theoretical neurobiology: Linear cable the- ory and dendritic structure, Cambridge Studies In Mathematical Biology, vol. I, Cambridge University Press, 1988. [31] H C Tuckwell, Introduction to theoretical neurobiology: Nonlinear and stochastic theories, Cambridge Studies In Mathematical Biology, vol. II, Cambridge University Press, 1988
URI:	http://wrap.warwick.ac.uk/id/eprint/355