AACIMP 2011 Summerschool. Neuroscience Stream. Lecture by Anton Chizhov

3. Leaky Integrate-and-Fire neuron (LIF) E X P E R I M E N T LIF - M O D E L V is the membrane potential ; I is the input (synaptic) current; s is the input (synaptic) conductance; C is the membrane capacity ; g L is the membrane conductance ; V rest is the rest potential ; V T is the threshold potential ; V reset is the reset potential .

4. Steady-state firing rate dependence on current and conductance LIF, no noise LIF with noise

6. PSC and PSP: single-compartmental neuron model Parameters found to fit PSC and PSP : How does the model fit to simultaneously recorded PSC and PSP? Parameters found by fitting :

7. PSC and PSP: Model of concentrated soma and cylindrical dendrite (“model S-D”) [W.Rall, 1959] Two boundary problems: A ) current-clamp to register PSP: B ) voltage-clamp to register PSC, i.e. at the end of dendrite , : Parameters : . at soma , : X=0 X=L X=0 X=L

8. At dendrite : Subtracting (2), obtain: Eqs. (1),(2) and (3) are equivalent to PSC and PSP: 2- compartmental model B ) Voltage-clamp mode Assume the potential V(X) to be linear, i.e. Model S-D As current through synapse is (1) A ) Current-clamp mode (2) because where is the dendrite conductance Model S-D At soma : (3) At dendrite : V L X=0 X=L V=0 X=0 X=L V L V 0

9. PSC and PSP: Fitting experimental PSP and PSC from [Karnup and Stelzer, 1999] Parameters found by fitting, given fixed : for 2-compartmental model: for 1-compartmental model: EPSC and EPSP IPSC and IPSP Conclusion. Solution of voltage - and current-clamp boundary problems by 2-compartmental model describes well the PSP-on-PSC dependence.

10. V – somatic potential; V d – dendritic potential; I s – registered on soma current through synapses located near soma; I d – registered on soma current through synapses located on dendrites;  m – membrane time constant;  – ratio of dendritic to somatic conductances; G s – specific somatic conductance. C V d V d V d V d V s V s I d I s Figure Transient activation of somatic and delayed activation of dendritic inhibitory conductances in experiment (solid lines) and in the model (small circles) . A, Experimental configuration. B , Responses to alveus stimulation without (left) and with ( right ) somatic V-clamp. C , In a different cell, responses to dynamic current injection in the dendrite; conductance time course (g) in green, 5-nS peak amplitude , V rev =-85 mV . Parameters of the model:  m = 33 ms ,  = 3.5 , G s = 6 nS in B and 2.4 nS in C A B [F.Pouille, M.Scanziani (2004) Nature , v. 429(6993):717-23 ] PSC and PSP: Fitting experimental PSP and PSC from [Pouille and Scanziani, 2004]

11. h [ Покровский, 19 78] φ ≈0 r V(x) V(x+ Δ x ) i m j m C Внутри Снаружи V g K g Na V Na V rest V K Hodgkin-Huxley model Approximations of ionic channels: Parameters:

12. Set of experimental data for Hodgkin-Huxley approximations

13. Approximations for are taken from [L.Graham, 1999]; I AHP is from [N.Kopell et al., 2000] Color noise model for synaptic current I S is the Ornstein-Uhlenbeck process : Model of pyramidal neuron Model with noise E X P Е R I М Е N Т

14. Control parameters of neuron Property: Neuron is controlled by two parameters [Pokrovskiy , 19 78] [Hodgkin, Huxley, 1952] Voltage-gated channels kinetics : EXPERIMENT

15. , The case of many voltage-independent synapses

16. “ Current clamp” , V(t) is registered “ Voltage clamp” , I(t) is registered Whole-cell patch-clamp: Current- and Voltage-Clamp modes const

17. Warning! The input in current clamp corresponds to negative synaptic conductance! Current-clamp is here!

19. “ Current clamp” Conductance clamp (Dynamic clamp): I ( V(t) )= s ( V(t) - V DC )+u is injected

20. Dynamic clamp for synaptic current [ Sharp AA, O'Neil MB, Abbott LF, Marder E. Dynamic clamp: computer-generated conductances in real neurons. // J. Neurophysiol. 1993 , 69(3):992-5 ]

21. Dynamic clamp for spontaneous potassium channels Control artificial K-channels

22. Experiment : pyramidal cell of visual cortex in vivo Model [Graham, 1999] of CA1 pyramidal neuron Dynamic clamp to study firing properties of neuron

23. Experiment Model u=7.7 mkA/cm 2 S=0.4 mS/cm 2 u=1.7 mkA/cm 2 S=0.024 mS/cm 2 u=2.7 mkA/cm 2 S=0.06 mS/cm 2 u=4 mkA/cm 2 S=0.15 mS/cm 2 Bottom point Top point

24. Divisive effect of shunting inhibition is due to spike threshold sensitivity to slow inactivation of sodium channels

25. Total Response (all spikes during 500ms-step) Only 1 st spikes Only 1 st interspike intervals

26. Hippocampal Pyramidal Neuron In Vitro Dynamic clamp for voltage-gated current: compensation of I NaP [Vervaeke K, Hu H., Graham L.J., Storm J.F. Contrasting effects of the persistent Na+ current on neuronal excitability and spike timing, Neuron, v49, 2006]

27. Effect of “negative conductance” by I NaP plays a role of negative conductance

28. Dynamic clamp for electric couplings between real and modeled neurons Medium electric conductance High electric conductance

29. “ Threshold-Clamp”

30. Dynamic clamp for synaptic conductance estimations in-vivo 1s 20 mV 10 nS 5 nS Эксперимент [Lyle Graham et al.]: Внутриклеточные измерения patch-clamp в зрительной коре кошки in vivo . Стимул – движущаяся полоска. Preferred direction Null direction

31. « Firing-Clamp » - method of synaptic conductance estimation Idea : a patched neuron is forced to spike with a constant rate; g E , g I , are estimated from values of subthreshold voltage and spike amplitude . Threshold voltage , V T Peak voltage, V P MODEL 1 ms τ (V)

32. Measuring system is a neuron: Firing-Clamp EXPERIMENT

33. Calibration: Firing-Clamp Cell 16_28_28 Cell 16_29_40 Cell 16_33_14 V T V peak EXPERIMENT

34. Measurements: Firing-Clamp Cell 16_27_50 Cell 16_27_5 V T V peak EXPERIMENT