Synaptic transmission

• Presynaptic release of neurotransmitter• Quantal analysis• Postsynaptic receptors• Single channel transmission• Models of AMPA and NMDA receptors• Analysis of two state models• Realistic models

Synaptic transmission:

CNS synapse

PNS synapse

Neuromuscular junction

Much of what we know comes from the more accessible large synapses of the neuromuscular junction.

This synapse never shows failures.

Different sizes and shapes

I. Presynaptic release

II. Postsynaptic, channel openings.

I. Presynaptic release: The Quantal Hypothesis

A single spontaneous release event – mini.

Mini amplitudes, recorded postsynaptically are variable.

I. Presynaptic release

Assumption: minis result from a release of a single ‘quanta’.

The variability can come from recording noise or from variability in quantal size.

Quanta = vesicle

A single mini

Induced release is multi-quantal

Statistics of the quantal hypothesis:

•N available vesicles•Pr- prob. Of release

Binomial statistics:

K

NKNr

Kr PPNKP )1()()|(

•N available vesicles•Pr- prob. Of release

Binomial statistics: Examples

K

NKr

Kr PPNKP )1()()|(

mean:

variance:

NPK r

)1(2rr PPN

Note – in real data, the variance is larger

Yoshimura Y, Kimura F, Tsumoto T, 1999

Example of cortical quantal release

Short term synaptic dynamics:

depression facilitation

Synaptic depression:

• Nr- vesicles available for release.

• Pr- probability of release.• Upon a release event NrPr of the vesicles are

moved to another pool, not immediately available (Nu).

• Used vesicles are recycled back to available pool, with a time constant τu

Tru

uuirrr

NNN

NttNPdt

dN

/)(

urTirrr NNttNP

dt

dN /)()(

Therefore:

And for many AP’s:

urTii

rrr NNttNP

dt

dN /)()(

NuNr

1/τu

Show examples of short term depression.

How might facilitation work?

There are two major types of excitatory glutamate receptors in the CNS:•AMPA receptorsAnd• NMDA receptors

II. Postsynaptic, channel openings.

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 Gmax and then goes back to zero.

sssss PPGludt

dP )1()(

][)( GlukGlus constents

Assume for simplicity that:

Examine two extreme cases:1) Rising phase, kGmax>>βs:

)0(]))[exp(1))(0(][()(

)1(][

sss

ss

PGluktPGluktP

PGlukdt

dP

)0(]))[exp(1))(0(()( max sss PGluktPkGtP

Rising phase, time constant= 1/(k[Glu])

Where the time constant, τrise = 1/(k[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

Variability of synaptic conductance through N receptors

(do on board)

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

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?

NMDA model is both ligand and voltage dependent

Homework 4.

a.Implement a 2 state, stochastic, receptor

Assume α=1, β=0.1, and glue is 1 between times 1 and 2.Run this stochastic model many times from time 0 to 30, show the average probability of being in an open state (proportional to current).

b. Implement using an ODE a model to calculate the average current, compare to a. and to analytical curve

][Glu

c. Implement using an ODE the following 5-state receptor:

Closed Open Bound 1

Bound 2

Desensitized 1

K1[Glu] K2[Glu]

K-2K-1

K3

K-3

K-dKd

Assume there are two pulses of [Glu]= ?, for a duration of 0.2 ms each, 10 ms apart.

Show the resulting currents

K1=13;    [mM/msec]; K-1=5.9*(10^(-3));  [1/ms] K2=13;  [mM/msec]; K-2=86;   [1/msec]K3=2.7;  [1/msec]; K-3=0.2;   [ 1/msec]Kd=0.9 [1/msec]; K-d=0.9

Summary