Dendritic computation Passive contributions to computation - PowerPoint Presentation

Slide1

Dendritic computation

Slide2

Passive contributions to computation

Active contributions to computation

Dendrites as computational elements:

Examples

Dendritic

computation

Slide3

r

V

m

=

I

m

Rm

Current flows uniformly out through the cell:

I

m

=

I

0

/4pr2

Input resistance is defined as RN = Vm(t∞)/I0 = Rm/4pr2

Injecting current I

0

Geometry matters: the

isopotential cell

Slide4

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

Slide5

r

i

r

m

c

m

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

Slide6

(1)

(2)

(1)



or

where

Time constant

Space constant

The cable equation

Slide7

0

Decay of voltage in space for current injection at

x

=0, T



∞

+

I

ext

(x,t

)

Slide8

 Electrotonic length

Properties of passive cables

Slide9

Johnson and Wu

Electrotonic

length

Slide10

Properties of passive cables



Electrotonic

length

 Current can escape through additional pathways: speeds up decay

Slide11

Johnson and Wu

Voltage rise time

 Current can escape through additional pathways: speeds up decay

Slide12

Koch

Imp

ulse

response

Slide13

General solution as a filter

Slide14

Step response

Slide15

 Electrotonic length

 Current can escape through additional pathways: speeds up decay

 Cable diameter affects input resistance

Properties of passive cables

Slide16

 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

Slide17

Step response

Slide18

Step response

Slide19

Other factors

Finite cables

Active channels

Slide20

Rall

model

Impedance matching:

If a

3/2

= d

1

3/2 + d23/2

can collapse to an equivalent

c

ylinder with length given

b

y

electrotonic

length

Slide21

Active

conductances

New cable equation for each

dendritic

compartment

Slide22

Who’ll be my

Rall

model, now that my

Rall

model is gone, gone

Genesis, NEURON

Slide23

Passive computations

London and Hausser, 2005

Slide24

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

Slide25

Spain;

Scholarpedia

Delay lines: the sound localization circuit

Slide26

Passive computations

London and Hausser, 2005

Slide27

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 throughsupralinear interaction of backprop

spikes with inputs

Active dendrites

Slide28

Segregation and amplification

Slide29

Segregation and amplification

Slide30

Segregation and amplification

The single neuron as a neural network

Slide31

Currents

Potential

Distal: integration

Proximal: coincidence

Magee, 2000

Synaptic scaling

Slide32

Synaptic potentials

Somatic action potentials

Magee, 2000

Expected distance dependence

Slide33

CA1 pyramidal neurons

Slide34

Passive properties

Slide35

Passive properties

Slide36

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 sublinearIh

and K

+

block eliminates

sublinear

temporal summation

Slide37

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

Slide38

Synaptic properties

While active properties contribute to summation, don’t explain normalized amplitude

Shape of EPSC determines how it is filtered .. Adjust ratio of AMPA/NMDA receptors

Slide39

Rall

; fig London and

H

ausser

Direction selectivity

Slide40

Back-propagating action potentials

Slide41

Johnson and Wu, Foundations of Cellular Physiology

, Chap 4

Koch,

Biophysics of Computation

Magee, Dendritic

integration of excitatory synaptic input, Nature Reviews Neuroscience, 2000London and Hausser,

Dendritic Computation, Annual Reviews in Neuroscience, 2005

References