presynaptic release of neurotransmitter quantal analysis ... · synaptic transmission •...
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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
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Synaptic transmission:
CNS synapse
PNS synapse
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Neuromuscular junction
Much of what we know comes from the more accessible large synapses of the neuromuscular junction.
This synapse never shows failures.
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Different sizes and shapes
I. Presynaptic release
II. Postsynaptic, channel openings.
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I. Presynaptic release: The Quantal Hypothesis
A single spontaneous release event – mini.
Mini amplitudes, recorded postsynaptically are variable.
I. Presynaptic release
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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
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A single mini
Induced release is multi-quantal
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Statistics of the quantal hypothesis:
• N available vesicles • Pr- prob. Of release
Binomial statistics:
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• N available vesicles • Pr- prob. Of release
Binomial statistics: Examples (note difference from previous histograms)
€
P(K |N) = (Pr)K (1− Pr )
K NK
mean:
variance:
Note – in real data, the variance is larger
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Yoshimura Y, Kimura F, Tsumoto T, 1999
Example of cortical quantal release
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Short term synaptic dynamics:
depression facilitation
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Short-term 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
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Therefore:
And for many AP’s:
Nu Nr
1/τu
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Show examples of short term depression.
How might facilitation work?
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There are two major types of excitatory glutamate receptors in the CNS: • AMPA receptors And • NMDA receptors
II. Postsynaptic, channel openings.
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Openings, look like:
but actually
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Openings, look like:
How do we model this?
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How do we model this? A simple option:
Assume for simplicity that:
Furthermore, that glutamate is briefly at a high value Gmax and then goes back to zero.
SHOW ALSO MATRIX FORM
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Assume for simplicity that:
Examine two extreme cases: 1) Rising phase, kGmax>>βs:
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Rising phase, time constant= 1/(k[Glu])
Where the time constant, τrise = 1/(k[Glu])
τrise
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2) Falling phase, [Glu]=0:
rising phase
combined
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Simple algebraic form of synaptic conductance:
Where B is a normalization constant, and τ1 > τ2 is the fall time.
Or the even simpler ‘alpha’ function:
which peaks at t= τs
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Variability of synaptic conductance through N receptors
(do on board)
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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-2 K-1
K3
K-3
K-d Kd
MATRIX FORM !!!
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NMDA receptors are also voltage dependent:
Jahr and Stevens; 90
Can this also be done with a dynamical equation? Why is the use this algebraic form justified?
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NMDA model is both ligand and voltage dependent
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Homework 4.
a. Implement a 2 state, stochastic, receptor
Assume α=1, β=0.1, and glue is 1 between times 1 and 2, and zero otherwise. 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
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c. Implement using an ODE the following 5-state receptor:
Closed Open Bound 1 Bound 2
Desensitized 1
K1[Glu] K2[Glu]
K-2 K-1
K3
K-3
K-d Kd
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=0.05
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Summary