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?