Spike-timing-dependent plasticity (STDP) and its relation to differential Hebbian learning

Overview over different methods You are here !

  Early: “Bell” Late: “Food” x Differential Hebb Learning Rule XiXi X0X0 Simpler Notation x = Input u = Traced Input V V’(t) uiui u0u0

Defining the Trace In general there are many ways to do this, but usually one chooses a trace that looks biologically realistic and allows for some analytical calculations, too. EPSP-like functions:  -function: Double exp.: This one is most easy to handle analytically and, thus, often used. Dampened Sine wave: Shows an oscillation. k kk

Produces asymmetric weight change curve (if the filters h produce unimodal „humps“) Derivative of the Output Filtered Input Output  T Differential Hebbian Learning

Weight-change curve (Bi&Poo, 2001) T=t Post - t Pre ms Pre follows Post: Long-term Depression Pre t Pre Post t Post Synaptic change % Pre t Pre Post t Post Pre precedes Post: Long-term Potentiation Spike-timing-dependent plasticity (STDP): Some vague shape similarity

Hebbian learning A B A B t When an axon of cell A excites cell B and repeatedly or persistently takes part in firing it, some growth processes or metabolic change takes place in one or both cells so that A‘s efficiency... is increased. Donald Hebb (1949)

Conventional LTP Symmetrical Weight-change curve Pre t Pre Post t Post Synaptic change % Pre t Pre Post t Post The temporal order of input and output does not play any role

Plastic Synapse NMDA/AMPA Postsynaptic: Source of Depolarization The biophysical equivalent of Hebb’s postulate Presynaptic Signal (Glu) Pre-Post Correlation, but why is this needed?

Plasticity is mainly mediated by so called N-methyl-D-Aspartate (NMDA) channels. These channels respond to Glutamate as their transmitter and they are voltage depended:

Biophysical Model: Structure x NMDA synapse v Hence NMDA-synapses (channels) do require a (hebbian) correlation between pre and post-synaptic activity! Source of depolarization: 1) Any other drive (AMPA or NMDA) 2) Back-propagating spike

Local Events at the Synapse  Local Current sources “under” the synapse: Synaptic current I synaptic  Global I BP Influence of a Back-propagating spike Currents from all parts of the dendritic tree I Dendritic u1u1 x1x1 v

  Pre-syn. Spike BP- or D-Spike * V*h g NMDA On „Eligibility Traces“ Membrane potential: Weight Synaptic input Depolarization source

Dendritic compartment Plastic synapse with NMDA channels Source of Ca 2+ influx and coincidence detector Plastic Synapse NMDA/AMPA g BP spike Source of Depolarization Dendritic spike Source of depolarization: 1. Back-propagating spike 2. Local dendritic spike Model structure

Plasticity Rule (Differential Hebb) NMDA synapse - Plastic synapse NMDA/AMPA g Source of depolarization Instantenous weight change: Presynaptic influence Glutamate effect on NMDA channels Postsynaptic influence

Normalized NMDA conductance: NMDA channels are instrumental for LTP and LTD induction (Malenka and Nicoll, 1999; Dudek and Bear,1992) Pre-synaptic influence NMDA synapse - Plastic synapse NMDA/AMPA g Source of depolarization

Dendritic spikes Back- propagating spikes (Larkum et al., 2001 Golding et al, 2002 Häusser and Mel, 2003) (Stuart et al., 1997) Depolarizing potentials in the dendritic tree

NMDA synapse - Plastic synapse NMDA/AMPA g Source of depolarization The time course of the [Ca 2+ ] concentration is important in defining the direction and degree of synaptic modifications. (Yang et al., 1999; Bi, 2002) Filtered Membrane potential = source of depolarization Low-pass filter Filter h is adjusted to account for steep rise and long tail of the observed Calcium transients induced by back-propagating spikes and dendritic spikes (Markram et al., 1995; Wessel et al, 1999) Postsyn. Influence

Some Signals F

Back-propagating spike Weight change curve T NMDAr activation Back-propagating spike T=t Post – t Pre Weight Change Curves Source of Depolarization: Back-Propagating Spikes

Dendritic spikeWeight change curve T NMDAr activation T=t Post – t Pre Dendritic spike Weight Change Curves Source of Depolarization: Dendritic Spike

The same learning rule: Local Learning Rules Correlations beyond +-30 ms are mostly random Differential Hebbian learning for proximal synapses Hebbian learning for distal synapses Saudargiene et al Neural Comp. 2004

X X... v h 11 u  nn 11 00 h nn v n v 1 h n x 0 x n x 1 u n u 1 u 0 v’ n v’ 1 h 1 h 0 T   T  n Site-specific learning using the same learning rule Biologically inspired Artificial Neural Network algorithm which implements local learning rules: Circuit Diagram Representation

An example Application: developing velocity sensitivity

STDP LTP

After learning the cell becomes sensitive to stimulus velocity 1/vel.

Figure 1. Dendritic Excitability Creates a Switchable, Spatial Gradient of Plasticity in L5 Pyramids (Left) Short bursts of somatic spikes elicit bAPs that fail to backpropagate fully to distal dendrites. The result, as shown in Sjöström and Häusser (2006), is LTP of synchronously active proximal synapses, but LTD or no plasticity at distal synapses. (Middle) Cooperative activation of additional synapses depolarizes the dendrite and boosts bAP propagation into distal dendrites. This cooperativity serves as a switch to enable distal LTP (Sjöström and Häusser, 2006). (Right) Plasticity also varies with firing mode of these neurons: when bAPs are coupled with strong distal input, bAP-activated calcium spikes (BACs) are evoked in the apical tuft, which enables robust LTP (Kampa et al., 2006).Sjöström and Häusser (2006)Sjöström and Häusser, 2006Kampa et al., 2006

Here we need a slide to explain why LTD at a distal dendrite in NOT in conflict with the models shown before. The argument would be to claim that there was never enough activation AT ALL to get the Ca above the LTP threshold.

Here comes a slide on the phosphorilation of AMPA and the different effects of gradient and concentration of Ca

I NMDA + Back-propagating spike Ca 2+ concentration Calmodulin Ca 2+ /CaM Kinase IICalcineurin Phosporylation Synapse gets stronger=LTP Dephosporylation Synapse gets weaker-LTD AMPA receptors Modeling Ca 2+ pathways Some more physiological complications ! We are modeling Ca2+ rise and fall with just one diff. hebb rule. More detailed models look at LTP and LTD as two different processes.

Temporally local Learning

Hebbian Learning Self-Influencing Plasticity

Equivalent Circuit Diagram

BP Spike:BeforeAt sameTimeAfter the DS-spike LTD dominates LTP dominates LTP weakly dominates DS-Spike Only LTD weakly dominates BP-Spike Only BP before DS = Acausal DS before BP = Causal Displacement BP vs DS spike T zero-crossing LTD dominates LTP dominates - +

} } } Local DS-Spike only weak hebbian learning Cluster 2 Cluster 1 DS- and BP-Spike pronounced STDP Somatic Firing Threshold passed

Why might this make sense ?? Single phase learning will lead to weight growth regardless Tamosiunaite et al. Comp. Nsci. in press