Synapses are everywhere 10 11 neurons 10 14 synapses Synapse change continuously –From msec –To hours (memory) Lack HH type model for the synapse.
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Synapses are everywhere 10 11 neurons 10 14 synapses Synapse change continuously –From msec –To hours (memory) Lack HH type model for the synapse
Synaptic Interactions An action potential arrives at the presynaptic cell. Voltage gated calcium channels open leading to an influx of calcium. Calcium leads to transmitter vesicles docked to the cell membrane to release transmitter molecules into the synaptic cleft. The transmitter diffuses across the cleft, and binds to postsynaptic channels. Postsynaptic channels open, ions cross the membrane. The channels close stochastically after some period of time.
What is the synaptic efficacy? (roughly … ) Time of presynaptic spike Average open time of channel Diffusion process dynamics Synaptic reversal potential
What determines G? The number of postsynaptic receptors The maximal conductance of the postsynaptic channels The number of presynaptic vesicles available for release The probability of presynaptic release upon action potential
Types of plasticity Short term - related to internal system dynamics –Milliseconds to seconds –Adaptation Long term - Related to modification of behavior –Minutes to hours –Involve the cell nucleus and gene expression –Learning
Short term plasticity Depression, facilitation, … –Details depend on precise of activity timing –Modify filtering properties of synapses –Dynamics of network must include synapse dynamics “ We cannot understand neural coding and information processing without taking into account neural dynamics ” “ We are beginning to see neurons and synapses on a more equal footing with regard to their role in computation ” (Abbott & Regehr 2004)
Long term plasticity Possible use: Development Learning (reinforcement) Memory “ When an axon of cell A is near enough to excite cell B or repeatedly or persistently takes part in firing it, some growth or metabolic change takes place in one or both cells such that A's efficiency, as one of the cells firing B, is increased.'' Donald Hebb, The Organization of Behavior, 1949
Dayan & Abbott Figure 8.1 LTP and LTD in hippocampus Points denote FP evoked by a constant stimulus Long term plasticity
Where does LTP/LTD occur? Recall –80% cortical neurons excitatory –20% inhibitory Well studied in EX EX synapses –Parts of biophysical mechanisms understood EX INH and INH EX –Observed but little understood
Modeling implications Long term changesShort term changes Equation must be augmented with synaptic change equations
Gerstner/Kistler Figure 10.2: LTP induction paradigm Weak test pulse Strong test pulse Action potential Weak test pulse - later Stronger response EPSP Long term plasticity Change persists for hours Purely postsynaptic explanation may suffice
Figure Gerstner/Kistler 10.3 Stimulate W Postsynaptic neuron fires due to S w Increases S causes spikes W does not cause spikes Neither S nor W alone lead to LTP in w Cooperativity
Synaptic Plasticity and learning Learning is a behavioral process Synaptic plasticity is an internal process Question: how do these two relate?
Model desiderata Locality Cooperativity (associativity) Potentiation and depression Boundedness Competition Long term stability Mainly consider phenomenological models Start with rate-based models
1 - Locality Locality More generally Global signal – e.g. reward
2- Cooperativity Both presynaptic and postsynaptic activity must occur Correlations a-la Hebb
3-4 Depression and boundedness Depression –E.g. add term Boundedness –An explicit mechanism needed for preventing weight increase
5-6 Competition and stability Resources are limited –An increase in a weight should lead to a decrease of a nearby weight, e.g. (Oja ’ s rule) How to reconcile short term synaptic change with long-lasting modification? –Discuss later in context of STDP
Example - the BCM rule Consider Expand to linear order in and all orders in Good biological evidence for this rule
Stability of the BCM rule The fixed point is unstable –Weight increases without bound Allow adaptive threshold Example But, non-local in time Temporal average
Spike Time Dependent Plasticity Observations: The nature of the synaptic changes depends on the temporal order of pre- and post spiking activity. In most cases –pre then post strengthen –post then pre weaken Temporal window a few milliseconds Seems to be in agreement with Hebb's philosophy –Pre neuron firing before the post neuron takes part in causing the latter to fire There are cases where the behavior is reversed. The precise cellular mechanism is not understood. –The NMDA receptor plays an important role - discuss this later.
Evolution of the weights Pre before post Post before pre
STDP - Synaptic distribution Rubin, Sompolinsky 2001
Glutamate transmission Coincidence detection: –For NMDA receptors to pass calcium, both pre- and postsynaptic cells must be active Hebbian mechanism
Presynaptic and postsynaptic plasticity Postsynaptic – e.g. activation of AMPA receptors Presynaptic – e.g. facilitation of Glutamate release –Requires retrograde messenger –Controversial
Early phase LTP Normal, low frequency transmission NMDA channel blocked Polarized postsynaptic cell Ca ++ enters thru NMDA Sequence of processes lead to increased sensitivity of NMDA channels (postsynaptic) Presynaptic plasticity (controversial)
Molecular cascades and memory Long term memory requires changes in gene expression Sequence –NMDA receptors –Calcium influx –Protein kinases –CREB-activated genes –Protein synthesis –Synapse change