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Biophysics of ComputationInformation Processing in Single Neurons$
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Christof Koch

Print publication date: 1998

Print ISBN-13: 9780195104912

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780195104912.001.0001

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Synaptic Input to a Passive Tree

Synaptic Input to a Passive Tree

Chapter:
(p.402) 18 Synaptic Input to a Passive Tree
Source:
Biophysics of Computation
Author(s):

Christof Koch

Publisher:
Oxford University Press
DOI:10.1093/oso/9780195104912.003.0024

Now that we have quantified the behavior of the cell in response to current pulses and current steps as delivered by the physiologist's microelectrode, let us study the behavior of the cell responding to a more physiological input. For instance, a visual stimulus in the environment will activate cells in the retina and its target, neurons in the lateral geniculate nucleus. These, in turn, make on the order of 50 excitatory synapses onto the apical tree of a layer 5 pyramidal cell in primary visual cortex such as the one we use throughout the book, and about 100-150 synapses onto a layer 4 spiny stellate cell (Peters and Payne, 1993; Ahmed et al., 1994, 1996; Peters, Payne, and Rudd, 1994). All of these synapses will be triggered within a fraction of a millisecond (Alonso, Usrey, and Reid, 1996). Thus, any sensory input to a neuron is likely to activate on the order of 102 synapses, rather than one or two very specific synapses as envisioned in Chap. 5 in the discussion of synaptic AND-NOT logic. This chapter will reexamine the effect of synaptic input to a realistic dendritic tree. We will commence by considering a single synaptic input as a sort of baseline condition. This represents a rather artificial condition; but because the excitatory postsynaptic potential and current at the soma are frequently experimentally recorded and provide important insights into the situation prevailing in the presence of massive synaptic input, we will discuss them in detail. Next we will treat the case of many temporally dispersed synaptic inputs to a leaky integrate-and-fire model and to the passive dendritic tree of the pyramidal cell. In particular, we are interested in uncovering the exact relationship between the temporal input jitter and the output jitter. The bulk of this chapter deals with the effect of massive synaptic input onto the firing behavior of the cell, by making use of the convenient fiction that the detailed temporal arrangement of action potentials is irrelevant for neuronal information processing. This allows us to derive an analytical expression relating the synaptic input to the somatic current and ultimately to the output frequency of the cell.

Keywords:   Adaptive gain control, Cable theory, Distal synaptic input, Electrotonic distance, Facilitation, Leak conductance, Membrane resistance, Neuromodulators, Purkinje cells

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