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

2. Overview over different methods
You are here !

3. V’(t) Simpler Notation x = Input u = Traced Input
Differential Hebb Learning Rule
V’(t)
Simpler Notation
x = Input
u = Traced Input x Xi w V ui
Early: “Bell” S X0 u0
Late: “Food”

4. a-function: 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:
a-function: k
Shows an oscillation.
Dampened
Sine wave: k
Double exp.: k
This one is most easy to handle analytically and, thus, often used.

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

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

7. Hebbian learning
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) A B A t B

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

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

10. 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:

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

12. Local Events at the Synapsex1
Current sources “under” the synapse:
Synaptic current
Isynaptic
Currents from all parts of the dendritic tree
IDendritic
Local
IBP
Influence of a Back-propagating or dendritic spike u1
Global v

13. * Pre-syn. Spike On „Eligibility Traces“ gNMDA w S BP- or D-Spike V*h
Membrane potential:
Weight
Synaptic input
Depolarization source
Pre-syn. Spike
BP- or D-Spike
On „Eligibility Traces“
V*h
gNMDA * w S

14. Model structure Dendritic compartment Source of Plastic Depolarization
Plastic synapse with NMDA channels
Source of Ca2+ influx and coincidence detector
BP spike
Source of
Depolarization
Dendritic spike
Source of depolarization:
1. Back-propagating spike
2. Local dendritic spike
Plastic
Synapse
NMDA/AMPA
NMDA/AMPA g

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

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

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

18. Postsyn. Influence Filtered Membrane potential =
NMDA synapse -Plastic synapse
NMDA/AMPA g
Source of depolarization
Postsyn. Influence
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)
The time course of the [Ca2+] concentration is important in defining the
direction and degree of synaptic modifications. (Yang et al., 1999; Bi, 2002)

19. What triggers LTP/LTD: The role of Ca2+
Differential threshold hypothesis
(Artola and Singer, 1993; Lisman 1989)
LTD: low intrinsic [Ca2+] threshold
LTP: higher intrinsic [Ca2+] threshold
Problems:

20. STDP pre before post: post before pre: NMDAR is already open
Mg2+ is then removed
much Ca2+ influx
post before pre:
Mg2+ is already removed
NMDAR opens (a slow process!)
little Ca2+ influx
pre long before post:
NMDAR starts to close
Mg2+ is then removed
little Ca2+ influx
But no late LTD window found ??

21. temporal development of Ca2+ matters (Ca-gradient)!

22. STDP pre before post: post before pre: NMDAR is already open
Mg2+ is then removed
FAST Ca2+ influx
post before pre:
Mg2+ is already removed
NMDAR opens (a slow process!)
SLOW Ca2+ influx
pre long before post:
NMDAR starts to close
Mg2+ is then removed
FAST (but little) Ca2+ influx
no late LTD window found

23. Some more physiological complications !
Modeling Ca2+ pathways I
NMDA
+ Back-propagating spike
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.
Ca2+ concentration and gradient
Calmodulin
Ca2+/CaM Kinase II
Calcineurin
Phosporylation
Synapse gets stronger=LTP
AMPA receptors
Dephosporylation
Synapse gets weaker-LTD

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

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

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

27. Postsyn. Influence Filtered Membrane potential =
NMDA synapse -Plastic synapse
NMDA/AMPA g
Source of depolarization
Postsyn. Influence
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)
The time course of the [Ca2+] concentration is important in defining the
direction and degree of synaptic modifications. (Yang et al., 1999; Bi, 2002)

28. Some Signals F

29. Source of Depolarization: Back-Propagating Spikes
Weight Change Curves
Source of Depolarization: Back-Propagating Spikes
Back-propagating spike
Weight change curve
NMDAr activation
Back-propagating
spike T
T=tPost – tPre

30. Source of Depolarization: Dendritic Spike
Weight Change Curves
Source of Depolarization: Dendritic Spike
Dendritic spike
Weight change curve
NMDAr activation
Dendritic
spike T
T=tPost – tPre

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

32. 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).

33. Circuit Diagram Representation
Biologically inspired Artificial Neural Network algorithm which implements local learning rules:
Circuit Diagram Representation T
w1
wn vn u X
v’n
hnn un xn hn v1 . . X
v’1
h11 . u1 w1 wn x1 h1 v w0  u0 x0 h0
Site-specific learning using the same learning rule

34. An example Application: developing velocity sensitivity

35. LTP
STDP

36. After learning the cell becomes sensitive to stimulus velocity

37. Temporally local Learning

38. Self-Influencing Plasticity
Hebbian Learning

39. Equivalent Circuit Diagram

40. Displacement BP vs DS spike
LTP weakly dominates
DS-Spike Only
Displacement BP vs DS spike
T zero-crossing
LTD dominates
LTP dominates - +
LTD weakly dominates
BP-Spike Only
BP before DS =
Acausal
DS before BP =
Causal
BP Spike:
Before
At sameTime
After the DS-spike
LTD dominates
LTP dominates

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

42. Single phase learning will lead to weight growth regardless
Why might this make sense ??
Single phase learning will lead to weight growth regardless

44. Calcium protocols
From the viewpoint of the cell these two peaks are almost of equal quality (height and rise phase). Hence chances for LTP and LTD are equal.

45. Solution? long-lasting low frequency stimulation
short burst-like high frequency stimulation
Look at the scaling and compare to last slide!