Presynaptic release of neurotransmitter Quantal analysis ... · Synaptic transmission •...
Transcript of Presynaptic release of neurotransmitter Quantal analysis ... · Synaptic transmission •...
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:
• N available vesicles • Pr- prob. Of release
Binomial statistics: Examples (note difference from previous histograms)
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P(K |N) = (Pr)K (1− Pr )
K NK
mean:
variance:
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
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
Therefore:
And for many AP’s:
Nu Nr
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 receptors And • NMDA receptors
II. Postsynaptic, channel openings.
Openings, look like:
but actually
Openings, look like:
How do we model this?
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
Assume for simplicity that:
Examine two extreme cases: 1) Rising phase, kGmax>>βs:
Rising phase, time constant= 1/(k[Glu])
Where the time constant, τrise = 1/(k[Glu])
τrise
2) Falling phase, [Glu]=0:
rising phase
combined
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
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-2 K-1
K3
K-3
K-d Kd
MATRIX FORM !!!
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?
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, 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
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
Summary