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 P r - prob. Of release Binomial statistics:

N available vesicles P r - prob. Of release Binomial statistics: Examples 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

Synaptic depression: N r - vesicles available for release. P r - probability of release. Upon a release event N r P r of the vesicles are moved to another pool, not immediately available (N u ). Used vesicles are recycled back to available pool, with a time constant τ u

Therefore: And for many AP’s: NuNu NrNr 1/τ u

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?

A simple option: Assume for simplicity that: Furthermore, that glutamate is briefly at a high value G max and then goes back to zero.

Assume for simplicity that: Examine two extreme cases: 1) Rising phase, kG max >>β s :

Rising phase, time constant= 1/(k[Glu]) Where the time constant, τ rise = 1/(k[Glu]) τ rise

2) Falling phase, [Glu]=0: rising phase combined

Simple algebraic form of synaptic conductance: Where B is a normalization constant, and τ 1 > τ 2 is the fall time. Or the even simpler ‘alpha’ function: which peaks at t= τ s

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). K 1 [Glu] K 2 [Glu] K -2 K -1 K3K3 K -3 K -d KdKd

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. 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 K 1 [Glu] K 2 [Glu] K -2 K -1 K3K3 K -3 K -d KdKd Assume there are two pulses of [Glu]= ?, for a duration of 0.2 ms each, 10 ms apart. Show the resulting currents K 1 =13; [mM/msec]; K -1 =5.9*(10^(-3)); [1/ms] K 2 =13; [mM/msec]; K -2 =86; [1/msec] K 3 =2.7; [1/msec]; K -3 =0.2; [ 1/msec] K d =0.9 [1/msec]; K -d =0.9

Summary