How do synapses transform inputs?

Transcription

1 Neurons to networks

2 How do synapses transform inputs?

3 Excitatory synapse Input spike! Neurotransmitter release binds to/opens Na channels Change in synaptic conductance! Na+ influx E.g. AMA synapse! Depolarization due to ES (excitatory postsynaptic potential) Vocab: Depolarization means make V less neg = more positive

4 Inhibitory synapse Input spike! Neurotransmitter release binds to/opens K channels Change in synaptic conductance K+ leaves cell! Hyperpolarization due to IS (inhibitory postsynaptic potential) Vocab: hyperpolarization means make V more negative

5 Modeling a synaptic input to a (RC) neuron Synaptic conductance V R

6 Modeling a synaptic input to a (RC) neuron Synaptic conductance V R robability of postsynaptic channel opening (= fraction of channels opened) robability of transmitter release given an input spike

7 Basic synapse model Assume rel = 1 (for now) What does a single spike input do to s? Kinetic model: closed αs open d dt s = α (1 ) β s open s βs s s closed Fraction of channels open Opening rate Closing rate Fraction of channels closed here:

8 Synaptic filters Exponential Difference of exponentials A difference of exponentials model better fits biological data for GABA, NMDA synapse types

9 Simplified synaptic models Difference of exponentials: s s τ1 τ 2 ( t) = const ( e e max t t ) t Alpha function: s ( t) = const τ t peak e τ t peak

10 What happens with a sequence of input spikes? Biological synapses are dynamic! Short-term facilitation Short-term depression Input (Markram & Tsodyks, 1998)

11 Short-term synaptic plasticity: describe this via _rel Recall definition of synaptic conductance: g s = g s, max rel Idea: Specify how rel changes as a function of consecutive input spikes s Input τ d dt rel If input spike: f rel = 0 D rel rel Between input spikes, rel decays exponentially back to 0 depression: decrement rel [sketch on board] Abbott et al 1997

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13 Lab exercise: Write a code that implements the Abbott et al mechanism for synaptic depression. Drive the synapse with spikes occurring regularly at 20 Hz, as in Fig. 1A of Abbott et al 97. Can you reproduce that figure? Hint: this should be a few lines of code.

14 Impact of synaptic depression Key result (a few lines of calculation, see (7) in paper [ESB notes]): If synapse receives input spikes at rate r, then the steady state value of _rel (r) ~ 1/r

15 Consequences of synaptic depression: steady state depression average transmission rate At steady state, Constant synaptic input for Wide range of inputs! Steady-state gain control Input Rate average release probability

16 Consequences of synaptic depression: dynamic response Input rates r Steady-state transmission rates are similar for different rates Transient inputs are amplified relative to steady-state inputs In fact: an equal-percent change from baseline gives an equal transient response. Who cares? Abbott et al 97: Neuron gets inputs from 1000 s of upstream cells, each of which fires at Hz. How can we be responsive to all? Synaptic depression yields gain control to satisfy this. vs. Adaptation or inhibition, does so in an INUT-SECIFIC way!

17 Extending the model to include facilitation Recall definition of synaptic conductance: g s = g s, max rel s If input spike: f rel rel D rel rel + f 1 F ( rel ) depression: decrement rel facilitation: increment rel Between input spikes, rel still decays exponentially back to 0 Abbott et al 1997

18 Effects of synaptic facilitation & depression facilitation depression average release probability Input Rate average transmission rate Input Rate

19 More detailed plasticity model Incoming spike activates a fraction of recovered resources R to become effective (E) Amount of effective resources E govern size of gs(t) Effective resources rapidly inactivate (msec) Inactivated recover (100s of msec) E(t) determines postsynaptic current I R E Markram and Tsodyks, NAS 1997

20 Match between model and experiment

21 Summary: Synapses provide an additional layer of dynamics and computation, beyond that occurring in single neurons!

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