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@? #" `W2 0|  N? @? #" `.=2 1|  T?d @? #" `B+2 2|  N? @? #" `.^X2 3|  T?d @? #" `Rr02 4|  N? @? #" `\  I  5|  " I  6|   jB~C`DEPFZd@ `ZSB#$*MHZ`Z7T`B~*x*ZB1NZ``*,@`#" `r   7|   JBC6DE@FJd@  xN $06$$Nx"$@`#" `   8|   JB<CDE@FJd@ 6Z0~6~<Z6B0***0B6Z6Z"$@`#" `  I n 9|   *BCDE0F:d@  r H6 r r r @`#" `   :|   rBCDETF^@  r`N5*e_ /$ HZr )A) r r,0@`#" ` Y  ;|   BCDE`Fj@ B w$HZrwZ`rZB0H24@`#" `q + v <|   2B+CDEFd@ ,,Z* 6HZl ~*Z~+l+Z+H6`0~ lZ H60`  6%H%Z%l~[\@`@`#" `  b    =| # "  2 >|  H?? #" `  2 ?|  N?d? #" `  2 @|  H?? #" `7% w 2 A|  N?d? #" `R5 d  B| <ܑe "*p e LUSQdkYkHrh7h_   C| 0e " `   e NUSQdkYkHroRh7h_  D| 6e #" `` ` e H*0 E| 6e #" ``  e J* 0 F| 6̡e #" `` ` e J* 0B | s *޽h ? h___PPT10i. +D=' d= @B + 0N0 0 (     6$2 P  Single Neuron Models (1)c      f5 ?? P%@ b LECTURE 3 ( `a  H  0޽h ? ̙33y___PPT10Y+D=' d= @B +  0N0 @ \$(  \ \ 6e P >6.___PPT9 @:Overview Single-Compartment Models " Integrate-and-Fire Models " Firing rate models " The Hodgkin-Huxley Model " Synaptic conductance description " The Runge-Kutta method III. Multi-Compartment Models " Two-Compartment Models  cgg e ae eeec eae ggc  E $e$ $g$$g$$c$(E(,e,0g04g4 8g8  # BCDE@F o @`(P(`@ (H @     "<  x @H>  # BCDE@F o @`(P(`@ (H @     "<  XP >   # t9BCDE@F o @`(P(`@ (H @     "<   >   # BCDE@F o @`(P(`@ (H @     "<   >   # BCDE@F o @`(P(`@ (H @     "<   P H>   # t9BCDE@F o @`(P(`@ (H @     "<    >   # .BCDE@F o @`(P(`@ (H @     "<   `0X >  # |xBCDE@F o @`(P(`@ (H @     "<  x 0H >  # BCDE@F o @`(P(`@ (H @     "<      <hoFV L Axon hillock$ 0 'RB  s *D>H`H  0޽h ? ̙33___PPT10i.Oi+D=' d= @B +  0N0  D6(  D  D 6=h @0 >6.___PPT9 R:Overview Single-Compartment Models " Integrate-and-Fire Models " Firing rate models " The Hodgkin-Huxley Model " Synaptic conductance description " The Runge-Kutta method III. Multi-Compartment Models " Two-Compartment Models  gccg e ae eeec eae ggc  E $e$ $g$$g$$c$(E(,e,0g04g4 8g86.___PPT9 B:Overview Single-Compartment Models " Integrate-and-Fire Models " Firing rate models " The Hodgkin-Huxley Model " Synaptic conductance description " The Runge-Kutta method III. Multi-Compartment Models " Two-Compartment Models  gcgg e a eeec eae ggc  E $e$ $g$$g$$c$(E(,e,0g04g4 8g8H  0޽h ? 33___PPT10i.Q$ +D=' d= @B + 0 @ (   S  0 00 ,$D0 7Supra- Threshold: The shape of the action potentials are more or less the same At the synapse, the action potential events translate into transmitter release As far as neuronal communication is concerned, the exact shape of the action potentials is not important, rather its time of occurrence is importantl.!u$&H  0޽h ? 33___PPT10n.Qd+ DB' d= @B D' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* 8%(+  0 2 * `'  (     0 P `p Supra- Threshold: If the voltage hits the threshold at time t0: a spike at time t0 will be registered The membrane potential will be reset to a reset value (Vreset) The system will remain there for a refractory period (t ref)Z.ZZ+L:?RB  s *D>y 9RB  s *D>99   BCpDE(FԔ p( P0Pt( @   9 yXB  0Do0 0 RB  s *DԔ9 yXB  0DoyyhF ` p0      9 ZB  s *DԔ`@ `0    S BPCDEF1(P`0P@  `   !  < pg  Pt020#+RB " s *D&>y1 y # <P ri  kVth20#+ $ <  nVreset20#+ %  BCpDE(FԔ p( P0Pt( @   9 1 1 y & <R aj  =V 0# ' <Ia  =t 0#H  0޽h ? 33___PPT10i.S|+D=' d= @B +  0 p t(   2  0 TAS ? ?d S"`?Ay``  d^  0 TA ? ?d S"`?  $D 0 d  H| d @   H  0޽h ? 33___PPT10.S5)+gPD|' = @B D7' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* +  0  6(     68 @0 >6.___PPT9 R:Overview Single-Compartment Models " Integrate-and-Fire Models " Firing rate models " The Hodgkin-Huxley Model " Synaptic conductance description " The Runge-Kutta method III. Multi-Compartment Models " Two-Compartment Models  gcgg e ae eeac eae ggc  E $e$ $g$$g$$c$(E(,e,0g04g4 8g8??p B   `D&>??p`P H  0޽h ? 33___PPT10.aiE+(z3D|' = @B D7' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* + 0   (   X  0A$?    0\5 P I5The firing rate is a function of the membrane voltage   07  P0` `g is usually a monotonically increasing function. These models mostly differ in the choice of g..a]v  NA ??= P   <<  ?f"0c  Z?? 0  Z??P  <0`]w ?g"0cB  3 rDԔ??0   0WW  P p  ASigmoid function H  0޽h ? 33___PPT10i.bPSK+D=' d= @B +Y0 1 ) @  (      0A  ? ?S"`?0 x  dRB  s *D RB  s *D `RB  s *DԔ RB  s *D>R  <G5   =V 0b  <K5i c =f 0bRB  s *D 0 0 RB  s *D0 XB  0DorE U rXB  0Do @ r  <P5V  =I 0b  <T5 `  =f 0b   BPCDEFԔd@8(P@  0 i `  6LS"`? D Tr  <X5  b B100 Hz 0bX  0`  <\5, QPhysiological Range"0b  0a5  pp ,Linear-Threshold model: ^  0 TA3 ? ?d S"`?1 $D 0 5d  0d5  @0  VBBased on the observation of the gain function in cortical neurons:H  0޽h ? 33___PPT10.b+]D|' = @B D7' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* +  0 P j(   2  6H C"?@0 >6.___PPT9 f:Overview Single-Compartment Models " Integrate-and-Fire Models " Firing rate models " The Hodgkin-Huxley Model " Synaptic conductance description " The Runge-Kutta method III. Multi-Compartment Models " Two-Compartment Models  gcgg e ae eeec eaae ggc  E $e$ $g$$g$$c$(E(,e,0g04g4 8g8  Z ??  VSingle-channel probabilistic formulations Macroscopic deterministic descriptionsB+00'0W   `Z8??PpP  0 TA8 a? ?d p a E  Zx ?? p@l  the conductance of an open channel the density of channels in the membrane the fraction of channels that are open at that time0H  0޽h ? 33___PPT10i.i+D=' d= @B + 0  (   r  S  d    -  Z ??  PK = nk^0 K   K   Z??PB  3 rDԔ??    0@WW 0 p  R"a gating or an activation variable##G  Z ?? `| OActivation of the conductance: Opening of the gate Deactivation: gate closingRP0& & 2   ` ??@   0WW C"? S(k = 4)0   H  0޽h ? 33___PPT10i.kpc+D=' d= @B +  0     : (   r  S Ld        0 ZA< h? ?d S" @P1 h   0 ZA> n? ?d S"  P `}  n   0 ZA= l? ?d S" @P `  l   0 ZA9 q? ?d S"  T P q B  3 rDԔ??p  Z ?? D opening rate 0 B  @ 3 rDԔ??  Z ??  D closing rate 0 H  Zh ??p @ B For a fixed voltage V, n approaches the limiting value n"(V) exponentially with time constant n(V)d0I!I,7#H  0޽h ? 33___PPT10i.mX+D=' d= @B + 0   (   F T \   P2XN  F    T    <| F  zJopen closed n (1-n)KK `B   0DjJ `B  B 0DjJll n   s *A. a?? an   s *A/ b??+   bn   0>"`T \r  S d  0   v  NAB ?? P v  NAD ?? P@0H  0޽h ? 33___PPT10i.no>+D=' d= @B + 0   (   r  S d  P0   I  Z ??   PNa = mkhn 0 K   K C $  Z??PB  3 rD>??   0h(WW   P  Cactivation variable2   ` ??@@0   0,,WW C"? S(k = 3)0   B  3 rD>??    01WW  P  Einactivation variableH  0޽h ? 33___PPT10i.oL+D=' d= @B +M 0 d\ (   v  NA; ??`    0 ZA' ? ?d S" P 5  B  3 rDԔ??  ZH; ??Ppp >m or h0H  0޽h ? 33___PPT10i.t+D=' d= @B + 0 @ K(   x  c $?d      0  `A@ ? ?d S" Pp   2v  NAA ??p>   0 ZA ? ?d S"  Po X   2  Zx@?? `  GGating equation0B  @  fD>??0  0 H  0޽h ? 33___PPT10i.tP>+D=' d= @B + 0 `  (   r  S Id  `}   v  NAC ?? `B  3 rD8>??  ZK8??p deinactivation40e    B  3 rD8>??@ ` `   Z\R8??P @ p  H inactivation 0 B   3 rD>??    ZV??  F activation 0    Z^?? x deactivation4 0e   B   3 rD>?? H  0޽h ? 33___PPT10i.u&2+D=' d= @B +  0   P P * (  P x P c $Cx    W P Z ??P 08___PPT10N___PPT90( ';Connor-Stevens Model (HH + transient A-current K+) (EA~ EK)<02ccaaiaaaia; v P NA+ ??e P Z ??@P   +?transient Ca2+ conductance (L, T, N, and P types. ECaT = 120mV)@0 cck caai a.2    v P NA, ??  x P Z ?? p rCa2+-dependent K+ conductance spike-rate adaptation`:0K Kv  P NA- ?? ,  P  f ?? P  R type I behavior (continuous firing rate)(*0)(  P Z ??   f Ca2+ spike, burst spiking, thalamic relay neurons404H P 0޽h ? +T3f3f___PPT10i.R\U+D=' d= @B +  0 P f(   .  6| C"?@0 >6.___PPT9 b:Overview Single-Compartment Models " Integrate-and-Fire Models " Firing rate models " The Hodgkin-Huxley Model " Synaptic conductance description " The Runge-Kutta method III. Multi-Compartment Models " Two-Compartment Models  gcgg e ae eeec eaee ggc  A $a$ $g$$g$$c$(E(,e,0g04g4 8g8??& 6  Zf??f@  WSynaptic open probability"0B   3 rDf>??  6   Zf??f `  ]Transmitter release probability" 0    0 TA ? ?d g@   H  0޽h ? +T3f3f___PPT10i.{?+D=' = @B +  0    $ (  $ r $ S d }    $ Z81 ??@  Metabotropic: Many neuromodulators including serotonin, dopamine, norepinephrine, and acetylcholine. GABAB receptors. Ionotropic: AMPA, NMDA, and GABAA receptors0 &^I &I H  ( $B $  `DfԔ?? P ,  $ Z8\2f??   &-aminobutyric acidF0B  $ 3 rDf>??    $ Z` 1f?? Pp uGlutamate, Es = 0mVF0 B  $ 3 rDf>??p@ B  $ @ 3 rDf>?? P p B $  `DfԔ??@@B $  `DfԔ?? p H $ 0޽h ? 33___PPT10i.|0+D=' = @B + 0  l(   x  c $+1d 00  1   Z-1 ??`E  *Inhibitory synapses: reversal potentials being less than the threshold for action potential generation (GABAA , Es = -80mV) Excitatory synapses: those with more depolarizing reversal potentials (AMPA, NMDA, Es = 0mV)  !!nKK  !!RH  0޽h ? +T3f3f___PPT10i.R@. +D=' = @B + 0 -% ( (  ( r ( S C1d 0  1 v ( NAG ??q n v ( NAE ?? bv ( NAF ?? @# ov  ( NAI ?? PQ v  ( NAK ?? P B  ( 3 rDf>?? 00  ( Z G1f??pj iT = 1msF0H ( 0޽h ? 33___PPT10i.~`t+D=' = @B +l 0 { 0 (  0 r 0 S 21d `  1 v 0 NAH ??qNPv 0 NAL ??pev 0 NAN ??b`v 0 NAO ??  v  0 NAM ??C  0  fP1 ??`4 U(Dayan and Abbott 2001)"0fH 0 0޽h ? 33___PPT10i.`ov+D=' = @B + 0 4 )(  4 r 4 S e1d  `  1 v 4 NAQ ??0 v 4 NAR ?? 4 ZXg1 ?? `PH@___PPT9" AWhen the postsynaptic neuron is near its resting potential, NMDA receptors are blocked by Mg2+ ions. To activate the conductance, the postsynaptic neuron must be depolarized to knock out the blocking ions 2. 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