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)

€

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