Abstract
Geometry and membrane properties of the dendrites crucially determine input–output relations in neurons. Unlike geometry often available in detail from computer reconstruction, the membrane resistivity is fragmentarily known if at all. Moreover, it varies during ongoing activity. In this study we address the question: what is the impact of the variation in membrane resistivity on the transfer properties of dendrites? Following a standard approach of the control system theory, we derive and explore the sensitivity functions complementary to the transfer functions of the passive dendrites with arbitrary geometrical parameters (length and diameter) and boundary conditions. We use the location-dependent somatopetal current transfer ratio (the reciprocal of the somatofugal voltage) as the transfer function, and its membrane resistivity derivatives, as the sensitivity functions. In the dendrites, at every path distance from the origin, the sensitivity function in a common form relates the transfer function, membrane resistivity, characteristic input conductance of semi-infinite cable and directional somatofugal input conductances at the given internal site and origin, and the length. Plotted in membrane resistivity versus path distance coordinates, the sensitivity functions display common features: along any coordinate there are low and high ranges, in which the sensitivity, respectively, increases and decreases. The ranges and corresponding rates depend on morphology and boundary conditions in a characteristic manner. These features predict existence of the geometry-dependent range of membrane resistivity (the earlier unattended mid-conductance state), such that the dendrites with a given metrical asymmetry are most distinguished in their transfer properties and electrical states if membrane resistivity is within the range and are not otherwise.
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Ascoli G, Krichmar J, Nasuto S, Senft S (2001) Generation, description and storage of dendritic morphology data. Philos Trans R Soc Lond B Biol Sci 256: 1131–1145
Barrett J (1975) Motoneuron dendrites: role in synaptic integration. Fed Proc 34(5): 1398–1407
Barrett J, Crill W (1974) Influence of dendritic location and membrane properties on the effectiveness of synapses of cat motoneurones. J Physiol (Lond) 239: 325–345
Bras H, Lahjouji F, Korogod S, Kulagina I, Barbe A (2003) Heterogeneous synaptic covering and differential charge transfer sensitivity among the dendrites of a reconstructed abducens motor neurone: correlations between electron microscopic and computer simulation data. J Neurocytol 32: 5–24
Cuntz H, Borst A, Segev I (2007) Optimization principles of dendritic structure. Theor Biol Med Model 4: 21
Destexhe A, Rudolph M, Paré D (2003) The high-conductance state of neocortical neurons in vivo. Nat Rev Neurosci 4: 739–751
Djurisic M, Antic S, Chen W, Zecevic D (2004) Voltage imaging from dendrites of mitral cells: EPSP attenuation and spike trigger zones. J Neurosci 24: 6703–6714
Gogan P, Schmiedel-Jakob I, Chitti Y, Tyč-Dumont S (1995) Fluorescence imaging of local membrane electric fields during the excitation of single neurons in culture. Biophys J 69: 299–310
Horcholle-Bossavit G, Gogan P, Ivanov Y, Korogod S, Tyč-Dumont S (2000) The problem of morphological noise in reconstructed dendritic arborization. J Neurosci Methods 95: 83–93
Jaffe D, Carnevale N (1999) Passive normalization of synaptic integration influenced by dendritic architecture. J Neurophysiol 82: 3268–3285
Koch C (1999) Biophysics of computation: information processing in single neurons. Computational Neuroscience, Oxford university press, New York, Oxford
Korogod S (1996) Electro-geometrical coupling in non-uniform branching dendrites. Biol Cybern 74: 85–93
Korogod S, Bras H, Sarana V, Gogan P, Tyč-Dumont S (1994) Electrotonic clusters in the dendritic arborization of abducens motoneurons of the rat. Eur J Neurosci 6: 1517–1527
Korogod S, Kulagina I, G Horcholle-Bossavit G, Gogan P, Tyč-Dumont S (2000) Activity-dependent reconfiguration of the effective dendritic field of motoneurons. J Comp Neurol 422: 18–34
Larkum M, Zhu J, Sakmann B (1999) A new cellular mechanism for coupling inputs arriving at different cortical layers. Nature 398(6725): 338–341
Larkum M, Zhu J, Sakmann B (2001) Dendritic mechanisms underlying the coupling of the dendritic with the axonal action potential initiation zone of adult rat layer 5 pyramidal neurons. J Physiol 533.1: 447–466
London M, Meunier C, Segev I (1999) Signal transfer in passive dendrites with nonuniform membrane conductance. J Neurosci 19(19): 8219–8233
Matlab (2000) Using MATLAB. The Mathworks, Inc.
Rall W (1977) Core conductor theory and cable properties of neurons. In: Kandel E (eds) Handbook of physiology, vol 1. American Physiological Society, Bethesda, pp 39–98
Rozenwasser E, Yusupov R (2000) Sensitivity of automatic control systems. CRC, Boca Raton
Rudolph M, Destexhe A (2003) A fast-conducting stochastic integrative mode for neocortical neurons in vivo. J Neurosci 23: 2466–2476
Savtchenko L, Gogan P, Korogod S, Tyč-Dumont S (2001) Imaging stochastic spatial variability of active channel clusters during excitation of single neurons. Neurosci Res 39: 431–446
Segev I, London M (1999) A theoretical view of passive and active dendrites. In: Stuart G, Spuston N, Hausser M (eds) Dendrites. Oxford University Press, New York, pp 205–230
Sholl D (1953) Dendritic organization in the neurons of the visual and motor cortices of the cat. J Anat 87: 387–406
Tsypkin Y (1977) The foundation of the theory of automatic systems. Nauka, Moscow
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Korogod, S.M., Kaspirzhny, A.V. Parameter sensitivity of distributed transfer properties of neuronal dendrites: a passive cable approximation. Biol Cybern 98, 87–100 (2008). https://doi.org/10.1007/s00422-007-0204-y
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DOI: https://doi.org/10.1007/s00422-007-0204-y