dendritic computation
DESCRIPTION
Dendritic computation. Dendritic computation. Dendrites as computational elements:. Passive contributions to computation. Active contributions to computation. Examples. r. Geometry matters: the isopotential cell. Injecting current I 0. V m = I m R m. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/1.jpg)
Dendritic computation
![Page 2: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/2.jpg)
Passive contributions to computation
Active contributions to computation
Dendrites as computational elements:
Examples
Dendritic computation
![Page 3: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/3.jpg)
r
Vm = Im Rm
Current flows uniformly out through the cell: Im = I0/4pr2
Input resistance is defined as RN = Vm(t∞)/I0
= Rm/4pr2
Injecting current I0
Geometry matters: the isopotential cell
![Page 4: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/4.jpg)
rm and ri are the membrane and axial resistances, i.e.the resistances of a thin slice of the cylinder
Linear cable theory
![Page 5: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/5.jpg)
ri
rmcm
For a length L of membrane cable:
ri ri Lrm rm / Lcm cm L
Axial and membrane resistance
![Page 6: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/6.jpg)
(1)
(2)
(1)
or
where Time constant
Space constant
The cable equation
![Page 7: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/7.jpg)
0
Decay of voltage in space for current injection at x=0, T ∞
+ Iext(x,t)
![Page 8: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/8.jpg)
Electrotonic length
Properties of passive cables
![Page 9: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/9.jpg)
Johnson and Wu
Electrotonic length
![Page 10: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/10.jpg)
Properties of passive cables
Electrotonic length
Current can escape through additional pathways: speeds up decay
![Page 11: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/11.jpg)
Johnson and Wu
Voltage rise time
Current can escape through additional pathways: speeds up decay
![Page 12: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/12.jpg)
Koch
Impulse response
![Page 13: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/13.jpg)
General solution as a filter
![Page 14: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/14.jpg)
Step response
![Page 15: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/15.jpg)
Electrotonic length
Current can escape through additional pathways: speeds up decay
Cable diameter affects input resistance
Properties of passive cables
![Page 16: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/16.jpg)
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
![Page 17: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/17.jpg)
Step response
![Page 18: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/18.jpg)
Step response
![Page 19: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/19.jpg)
Other factors
Finite cables
Active channels
![Page 20: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/20.jpg)
Rall model
Impedance matching:
If a3/2 = d13/2 + d2
3/2
can collapse to an equivalentcylinder with length givenby electrotonic length
![Page 21: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/21.jpg)
Active conductances
New cable equation for each dendritic compartment
![Page 22: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/22.jpg)
Who’ll be my Rall model, now that my Rall model is gone, gone
Genesis, NEURON
![Page 23: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/23.jpg)
Passive computations
London and Hausser, 2005
![Page 24: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/24.jpg)
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
![Page 25: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/25.jpg)
Spain; Scholarpedia
Delay lines: the sound localization circuit
![Page 26: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/26.jpg)
Passive computations
London and Hausser, 2005
![Page 27: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/27.jpg)
Mechanisms to deal with the distance dependence of PSP size
Subthreshold boosting: inward currents with reversal near restEg persistent Na+
Synaptic scaling
Dendritic spikesNa+, Ca2+ and NMDADendritic branches as mini computational units
backpropagation: feedback circuit Hebbian learning throughsupralinear interaction of backprop spikes with inputs
Active dendrites
![Page 28: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/28.jpg)
Segregation and amplification
![Page 29: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/29.jpg)
Segregation and amplification
![Page 30: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/30.jpg)
Segregation and amplification
The single neuron as a neural network
![Page 31: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/31.jpg)
Currents
Potential Distal: integrationProximal: coincidence
Magee, 2000
Synaptic scaling
![Page 32: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/32.jpg)
Synaptic potentials Somatic action potentials
Magee, 2000
Expected distance dependence
![Page 33: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/33.jpg)
CA1 pyramidal neurons
![Page 34: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/34.jpg)
Passive properties
![Page 35: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/35.jpg)
Passive properties
![Page 36: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/36.jpg)
Active properties: voltage-gated channels
Na +, Ca 2+ or NDMA receptor block eliminates supralinearity
For short intervals (0-5ms), summation is linear or slightly supralinearFor longer intervals (5-100ms), summation is sublinear
Ih and K+ block eliminates sublinear temporal summation
![Page 37: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/37.jpg)
Active properties: voltage-gated channels
Major player in synaptic scaling: hyperpolarization activated K current, Ih
Increases in density down the dendriteShortens EPSP duration, reduces local summation
![Page 38: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/38.jpg)
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
![Page 39: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/39.jpg)
Rall; fig London and Hausser
Direction selectivity
![Page 40: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/40.jpg)
Back-propagating action potentials
![Page 41: Dendritic computation](https://reader036.vdocuments.us/reader036/viewer/2022081505/56816380550346895dd46351/html5/thumbnails/41.jpg)
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