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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