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Dendritic computation

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Passive contributions to computation Active contributions to computation Dendrites as computational elements: Examples Dendritic computation

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r V m = I m R m Current flows uniformly out through the cell: I m = I 0 /4 r 2 Input resistance is defined as R N = V m (t)/I 0 = R m /4 r 2 Injecting current I 0 Geometry matters: the isopotential cell

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r m and r i are the membrane and axial resistances, i.e. the resistances of a thin slice of the cylinder Linear cable theory

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riri rmrm cmcm For a length L of membrane cable: r i r i L r m r m / L c m c m L Axial and membrane resistance

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(1) (2) (1) or where Time constant Space constant The cable equation

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0 Decay of voltage in space for current injection at x=0, T + I ext (x,t)

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Electrotonic length Properties of passive cables

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Johnson and Wu Electrotonic length

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Properties of passive cables Electrotonic length Current can escape through additional pathways: speeds up decay

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Johnson and Wu Voltage rise time Current can escape through additional pathways: speeds up decay

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Koch Impulse response

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General solution as a filter

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Step response

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Electrotonic length Current can escape through additional pathways: speeds up decay Cable diameter affects input resistance Properties of passive cables

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Electrotonic length Current can escape through additional pathways: speeds up decay Cable diameter affects input resistance Cable diameter affects transmission velocity Properties of passive cables

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Step response

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Other factors Finite cables Active channels

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Rall model Impedance matching: If a 3/2 = d 1 3/2 + d 2 3/2 can collapse to an equivalent cylinder with length given by electrotonic length

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Active conductances New cable equation for each dendritic compartment

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Wholl be my Rall model, now that my Rall model is gone, gone Genesis, NEURON

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Passive computations London and Hausser, 2005

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Linear filtering: Inputs from dendrites are broadened and delayed Alters summation properties.. coincidence detection to temporal integration Segregation of inputs Nonlinear interactions within a dendrite -- sublinear summation -- shunting inhibition Delay lines Dendritic inputs labelled Passive computations

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Spain; Scholarpedia Delay lines: the sound localization circuit

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Passive computations London and Hausser, 2005

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Mechanisms to deal with the distance dependence of PSP size Subthreshold boosting: inward currents with reversal near rest Eg persistent Na + Synaptic scaling Dendritic spikes Na +, Ca 2+ and NMDA Dendritic branches as mini computational units backpropagation: feedback circuit Hebbian learning through supralinear interaction of backprop spikes with inputs Active dendrites

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Segregation and amplification

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The single neuron as a neural network

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Currents Potential Distal: integration Proximal: coincidence Magee, 2000 Synaptic scaling

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Synaptic potentialsSomatic action potentials Magee, 2000 Expected distance dependence

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CA1 pyramidal neurons

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Passive properties

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Active properties: voltage-gated channels Na +, Ca 2+ or NDMA receptor block eliminates supralinearity For short intervals (0-5ms), summation is linear or slightly supralinear For longer intervals (5-100ms), summation is sublinear I h and K + block eliminates sublinear temporal summation

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Active properties: voltage-gated channels Major player in synaptic scaling: hyperpolarization activated K current, I h Increases in density down the dendrite Shortens EPSP duration, reduces local summation

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Synaptic properties While active properties contribute to summation, dont explain normalized amplitude Shape of EPSC determines how it is filtered.. Adjust ratio of AMPA/NMDA receptors

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Rall; fig London and Hausser Direction selectivity

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Back-propagating action potentials

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Johnson and Wu, Foundations of Cellular Physiology, Chap 4 Koch, Biophysics of Computation Magee, Dendritic integration of excitatory synaptic input, Nature Reviews Neuroscience, 2000 London and Hausser, Dendritic Computation, Annual Reviews in Neuroscience, 2005 References

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