Synaptic plasticity: Introduction
• Different induction protocols
• Calcium, NMDA receptors
-And we will also have some formal stuff withhow do we mathematically describe receptors, and talk some more about ODE’s
Rate based induction(show on board)
But: Heterosynaptic LTD – from Abraham(note – in vivo)
Note about the different meanings of hetero
Christie et. Al 1995
Pairing induced plasticity
Feldman, 2000
Show voltage clamp
Spike timing dependent plasticity
Markram et. al. 1997
Anatomy figure from Markram 97
Spike timing dependent plasticity
Markram et. al. 1997
Bi and Poo J. Neurosci. 1998
Some properties (observations) of synaptic plasticity
• Synapse specificity (but)
• Associatively: LTP when pre and post occur together.
• Cooperativety: Two different input pathways can boost each other.
Some key elements of the biophysics of induction
1. NMDA receptors are necessary (in many systems) for the induction of LTP and LTD
Bi and Poo, 1998
Control
With APV
Same holds for LTD – but some forms of plasticity are NMDAR independent
Partial blockade of NMDA-R
Cummings et. al , 1996
There are two major types of excitatory glutamate receptors in the CNS:•AMPA receptorsAnd• NMDA receptors
II. Postsynaptic, channel openings.
• Voltage dependent
• Calcium permeable
• Slow dynamics
Openings, look like:
but actually
Openings, look like:
How do we model this?
][Glu
][Glu
rN sssrs
s NNNGludt
dN )()(
How do we model this?A simple option:
sssss PPGludt
dP )1()(
][)( GlukGlus constents
Assume for simplicity that:
Furthermore, that glutamate is briefly at a high value Amax and then goes back to zero.
SHOW ALSO MATRIX FORM
sssss PPGludt
dP )1()(
][)( GlukGlus constents
Assume for simplicity that:
Examine two extreme cases:1) Rising phase, αs(Glumax )>>βs:
)0())(exp(1))(0()(()(
)1()(
sssss
sss
PGlutPGlutP
PGludt
dP
)0(]))[exp(1))(0(()( max sss PGluktPkGtP
Rising phase, time constant = 1/ αs(Glumax )
Where the time constant, τrise = 1/(αs[Glu])
τrise
2) Falling phase, [Glu]=0:
)exp((max))( tPtP
Pdt
dP
sss
sss
rising phase
combined
Simple algebraic form of synaptic conductance:
))/exp()/(exp( 21max ttBPPs Where B is a normalization constant, and τ1 > τ2 is
the fall time.
Or the even simpler ‘alpha’ function:
which peaks at t= τs
)/exp(maxs
ss t
tPP
A more realistic model of an AMPA receptor
Closed Open Bound 1
Bound 2
Desensitized 1
Markov model as in Lester and Jahr, (1992), Franks et. al. (2003).
K1[Glu] K2[Glu]
K-2K-1
K3
K-3
K-dKd
MATRIX FORM !!!
NMDA receptors are also voltage dependent:
Jahr and Stevens; 90
1)13.16/exp(
57.3
][1
2
VmM
MgGNMDA
Can this also be done with a dynamical equation?Why is the use this algebraic form justified?
The complete equation for current through the NMDAR should have several components:
1.Time dependence:
2.Multiply by voltage dependence of the conductance
3.And … how do you get a current for the conductance?
2. Calcium influx is necessary for plasticity
and its level determines the sign and magnitude of plasticity
(Cho et. al. 2001)
And might be sufficient
Yang, Tang Zucker, 1999
• Moderate, but prolonged calcium elevation = LTD
• High calcium elevation = LTP ( brief is sufficient, but what will long do? )
Yang, Tang Zucker, 1999
High/Correlated activity
High High CalciumCalcium
LTP
LTP
Low/uncorrelated activity
ModerateModerate CalciumCalcium
LTD
LTDLTD
Magic Magic
High NMDA-Ractivation
Modelrate NMDA-Ractivation
High/Correlated activity
High High CalciumCalcium
LTP
LTP
Low/uncorrelated activity
ModerateModerate CalciumCalcium
LTD
LTDLTD
Magic Magic
High NMDA-Ractivation
Modelrate NMDA-Ractivation
Oconnor et al. 2005
What did we learn today?