Model neurons ynapses uggested reading: Chapter 5.8 in Dayan,. & Abbott, L., Theoretical Neuroscience, MIT ress, 200. Model neurons: ynapse Contents: ynapses ynaptic input into the RC-circuit pike-rate adaptation Refractory period Examles of apses robability of transmitter release
ynapses Model neurons: ynapses 3 The apse is remarkably complex and involves many simultaneous processes such as the production and degredation of neurotransmitter. The neurotransmitters directly (A) or indirectly (B) binds to a aptic channel and activates it. ynaptic conductances Model neurons: ynapses 4 ynaptic transmission begins when an action potential invades the preaptic terminal and activates voltage dependent Ca 2+ channels. This causes transmitter molecules to enter the cleft and bind to receptors on the postaptic neuron. As a result ion channels open, which modifies the conductance of the postaptic neuron
Model neurons: ynapses 5 ynaptic input into the RC-circuit Model neurons: ynapses 6 - I g ( Vm E) dvm C + g dvm ( V m E m V ) + m V R ( + Rg ) V + Rg E rest 0 + V rest
ynaptic input into RC-Circuit Model neurons: ynapses 7 g const t e t t peak E I I g( Vm E) dv m (t) E E E #V m # RI (t)e + V rest 80mV 20mV 0mV (relative to rest) ynaptic conductances (probabilities) Model neurons: ynapses 8 ynaptic conductance: g s g s : open channel probability s rel rel : probability of transmitter release s : probability that post. channel opens
ostaptic conductance Model neurons: ynapses 9 # $ & % d ( # ) # const. closing rate of the channel opening rate imple model of transmitter release: Transmitter concentration T t 0 t t 0 : (0) > ignore during the opening process pike Model neurons: ynapses 0 This simplification leads us to the following equation d # + with the solution 0 e #$t + With the boundary conditions above, we obtain: t + ( (0) ) e for 0 t T ( T ) e ( t T ) for t T if there is no aptic release immediately before the release at t0 ( 0) 0 max ( T ) e T
Model neurons: ynapses t + ( (0) ) e for 0 t T ( T ) e ( t T ) for t T using max e # T we can write in the general case ( T ) (0) + max( (0)) Example Model neurons: ynapses 2 t + ( (0) ) e for 0 t T ( T ) e ( t T ) for t T 0.93ms # $ 0.9ms # T ms A fit of the model to the average EC (excitatory postaptic current) recorded from mossy fiber input to a CA3 pyramidal cell in a hippocampal slice preparation. The smooth line is the theoretical curve and the wiggly line is the result of averaging recordings from a number of trials.
Fast apse Model neurons: ynapses 3 For a fast apse the rise of the conductance following a preaptic action potential can be approximated as instantaneous. For a single preaptic action potential occurring at t0 we can write t max e with A sequence of action potentials at arbitrary times can be modeled with an exponential decay d and by updating the probability after each action potential with + ( ) max low apse Model neurons: ynapses 4 For an isolated preaptic action potential occurring at t0 we can use a difference of two exponentials (e.g. GABA A and NMDA) max & B$ e $ % t ' ( ' e t ' ( 2 # > 2 ' %'( 2 B % % && ( ( $ # rise /( '( 2 % & ( ( $ # rise /( 2 $ # or the alpha function rise 2 2 B is a normalization factor and ensures that the peak value is equal to max max t e t with a peak value at t
Examples of apses ingle exp. decay Diff of two exp. Model neurons: ynapses 5 For a fast apse (AMA) the rise of the conductance following a preaptic action potential can be approximated as instantaneous. Examples of apses Model neurons: ynapses 6 Glutamate activates two different kinds of receptors: AMA and NMDA. Both receptors lead to an excitation of the membrane. AMA is fast NMDA is voltage dependent and slow (20ms rise) GABA (-aminobutyric acid) is the principal inhibitory neurotransmitter. There are two main receptors for GABA, GABA A and GABA B. GABA A is responsible for fast inhibition and requires only brief stimuli to produce a response. GABA B involves so-called second messengers.
Examples of apses: AMA Model neurons: ynapses 7 Glutamate activates two different kinds of receptors: AMA and NMDA. Both receptors lead to an excitation of the membrane. AMA: i AMA g ( V EAMA) AMA d ( # ) # fast Examples of apses: NMDA NMDA: i NMDA g GNMDA( V ) ( V ENMDA) NMDA Model neurons: ynapses 8 d ( # ) # low (20ms rise) hysiological correlate of the Hebb learning rule since both, the preaptic and postaptic cell have to be active. Dependence of the NMDA conductance on the membrane potential V and the extracellular Mg 2+ concentration. The voltage dependence is mediated by magnesium ions which normally block NDMA receptors. The postaptic cell must be sufficiently depolarized to knock out the blocking ions.
Examples of apses: NMDA Model neurons: ynapses 9 NMDA receptors contain binding sites for glutamate and the co-activator glycine, as well as an Mg 2+ binding site in the pore of the channel. At hyperpolarized potentials, the electrical driving force on Mg 2+ drives this ion into the pore of the receptor and blocks it. Examples of apses: GABA A Model neurons: ynapses 20 GABA (-aminobutyric acid) is the principal inhibitory neurotransmitter. There are two main receptors for GABA, GABA A and GABA B. GABA A GABA A is responsible for fast inhibtion and require only brief stimuli to produce a response. i GABA g ( )( ) A GABA t V EGABA A A d ( # ) #
Examples of apses: GABA B Model neurons: ynapses 2 GABA B is a much more complex receptor. It involves socalled second messengers. GABA B responses occur when the GABA binds to another compound (G-potein) which in turn binds to a otassim channel and opens it up. It takes 4 activated G-proteins to open the channel. i GABA g GABA ( V E B B 4 + K d dr K 4 3 r r d K 4 ( # ) # r r K ) Model neurons: ynapses 22 Examples of apses: Gap junctions Gap junctions are not chemical apses but electrical in nature. The produce a current proportional to the difference between pre-and postaptic potential. No transmitter or action potential is involved. Many non-neural cells, e.g. muscle, glia, are coupled in this manner. i g gap C ( Vpost Vpre)
robability of transmitter release Model neurons: ynapses 23 ynaptic conductance: g s : open channel probability s rel g s rel : probability of transmitter release s : probability that post. channel opens The probability of transmitter release and the magnitude of the resulting conductance change in the postaptic neuron can depend on the history of activity at a apse. The effects of activity on aptic conductances are termed shortand long-term. hort-term plasticity refers to a number of phenomena that affect the probability that a preaptic action potential opens postaptic channels. Long-term plasticity involves structural changes which are extremely persistent (learning). robability of transmitter release Model neurons: ynapses 24 The probability of transmitter release can be used to model aptic depression (A) and facilitation (B) of excitatory intercortical apses A) Depression of an excitatory apse between two layer 5 pyramidal cells recorded in a slice of rat somatosensory cortex. pikes were evoked by current injection into the preaptic neuron and postaptic currents were recorded with a second electrode. B) Facilitation of an excitatory apse from a pyramidal neuron to an inhibitory interneuron in layer 2/3 of rat somatosensory cortex. (A from Markram and Tsodyks, 996; B from Markram et al., 998.)
robability of transmitter release and short-term plasticity Model neurons: ynapses 25 Depression (D) and facilitation (F) of excitatory intercortical apses d rel 0 rel Update after each spike: + f rel rel rel D rel F ( rel f Threshold ) with 0 the release probability after a long period of silence robability of transmitter release and short-term plasticity Average steady-state release probability for a preaptic oisson spike-train (Dayan & Abbott, p. 87): 0 + f Fr p rel 0 rel + f r + ( f ) r F p Model neurons: ynapses 26 D p Facilitating apse Depressing apse r rel : ynaptic transmission
robability of transmitter release and short-term plasticity Model neurons: ynapses 27 Facilitating apse Depressing apse In facilitating apses, isolated spikes in low-frequency trains are transmitted with lower probability than spikes occurring within highfrequency bursts. ynapses that depress do not convey information about the values of constant high, preaptic firing rates to their postaptic targets.