1. Dendritic computation

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

3. 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

4. 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

5. 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

6. (1) (2) (1) or where Time constant Space constant The cable equation

7. 0 Decay of voltage in space for current injection at x=0, T + I ext (x,t)

8. Electrotonic length Properties of passive cables

9. Johnson and Wu Electrotonic length

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

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

12. Koch Impulse response

13. General solution as a filter

14. Step response

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

16. 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

17. Step response

19. Other factors Finite cables Active channels

20. 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

21. Active conductances New cable equation for each dendritic compartment

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

23. Passive computations London and Hausser, 2005

24. 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

25. Spain; Scholarpedia Delay lines: the sound localization circuit

26. Passive computations London and Hausser, 2005

27. 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

28. Segregation and amplification

30. The single neuron as a neural network

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

32. Synaptic potentialsSomatic action potentials Magee, 2000 Expected distance dependence

33. CA1 pyramidal neurons

34. Passive properties

36. 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

37. 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

38. 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

39. Rall; fig London and Hausser Direction selectivity

40. Back-propagating action potentials

41. 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