Synapses
Neurons Communicate
through Synapses
Neurons Communicate
through Synapses
•
Spike in presynaptic neuron travels down axon.
•
Rise in intracellular Ca causes neurotransmitter vesicles
to fuse to membrane, release their contents into synaptic
cleft (unless they don’t… more on that later)
•
Neurotransmitter molecules diffuse across cleft, bind to
receptors on postsynaptic neuron
•
This transiently opens some ion channels, changing
conductance (and therefore membrane potential) of
postsynaptic neuron
Neurons Communicate
through Synapses
Isyn (t) =
gsyn (t)(V (t)
Esyn )
Leaky integrator with conductance-based synapse:
dV
Cm
=
dt
gL (V
dV
⌧m
=
dt
EL )
V
gsyn (t)(V
gsyn (t)(V
Esyn )
Esyn )
Types of Synapses
•
Different neurotransmitters open different ion channels with
different reversal potentials
•
Excitatory neurotransmitters have reversal potentials that
are above rest, so the postsynaptic neuron typically
depolarizes in response to a presynaptic spike
•
Inhibitory neurotransmitters have reversal potentials that
are below or near rest, so the postsynaptic neuron typically
hyper-polarizes in response to a presynaptic spike
•
Dale’s Principle: A presynaptic neuron projects to all of its
postsynaptic targets with the same “type” of synapse (exc.
or inh.)
Types of Neurotransmitters
and Receptors
•
Ionotropic receptors are activated directly by
neurotransmitters. Faster.
•
Metabotropic are modulated indirectly through a second
signaling pathway. Slower, modulatory.
•
We will focus on ionotropic.
•
Glutamate: Excitatory neurotransmitter
•
•
Ionotropic receptors: AMPA and NMDA
GABA: Inhibitory
•
Ionotropic receptors: GABAB and GABAA
If Ps (0 ) = 0, as it will if there is no synaptic release immediately before the
release at t = 0, equation 5.28 simplifies to Ps (t ) = 1 − exp(−αs t ) for 0 ≤
t ≤ T, and this reaches a maximum value Pmax = Ps ( T ) = 1 − exp(−αs T ).
In terms of this parameter, a simple manipulation of equation 5.28 shows
that we can write, in the general case,
Synaptic kinetics
•
Ps ( T ) = Ps (0 ) + Pmaxmolecules
(1 − Ps (0 )) .
Binding of neurotransmitter
cause (5.30)
ion
channels
to open.
Figure 5.14 shows a fit to a recorded postsynaptic current using this for-
malism. In this case, βs was set to 0.19 ms−1 . The transmitter concentra• Unbinding
causes
them
tion was modeled
as a square
pulseto
of close.
duration T = 1 ms during which
αs = 0.93 ms−1 . Inverting these values, we find that the time constant determiningmodel:
the rapid rise seen in figure 5.14A is 0.9 ms, while the fall of the
• Kinetic
decay!
dgms.
current is an exponential with a time constant of 5.26
syn
time cnst
60 pA
rise time!
cnst
10 ms
spike time
⌧d
=
gsyn + x
dt
dx
⌧r
= x
dt
x(tspk )
x(tspk ) + Jsyn
synaptic weight
Figure 5.14: A fit of the model discussed in the text to the average EPSC (excitatory postsynaptic current) recorded from mossy fiber input to a CA3 pyramidal
Synaptic kinetics
•
Binding of neurotransmitter molecules cause ion
channels to open.
•
Unbinding causes them to close.
•
Equivalent to adding a post-synaptic conductance
waveform:
X
gsyn (t) = Jsyn
↵(t tspk )
tspk
↵(t) =
1
⌧d
When ⌧r ⌧ 1 :
⌧r
⇣
e
t/⌧d
1
↵(t) = e
⌧d
e
t/⌧r
t/⌧d
⌘
⇥(t)
⇥(t)
Figure 5.14 shows a fit to a recorded postsynaptic current using this formalism. In this case, βs was set to 0.19 ms−1 . The transmitter concentration was modeled as a square pulse of duration T = 1 ms during which
αs = 0.93 ms−1 . Inverting these values, we find that the time constant determining the rapid rise seen in figure 5.14A is 0.9 ms, while the fall of the
current is an exponential with a time constant of 5.26 ms.
60 pA
Synaptic Kinetics
10 ms
Postsynaptic current (PSC) in response to
one spike from an excitatory neuron.
Characteristic of AMPA: !
fast decay time (~3-5ms)
faster rise time (<1ms)
Figure 5.14: A fit of the model discussed in the text to the average EPSC (excitatory postsynaptic current) recorded from mossy fiber input to a CA3 pyramidal
cell in a hippocampal slice preparation. The smooth line is the theoretical curve
and the wiggly line is the result of averaging recordings from a number of trials.
(Adapted from Destexhe et al., 1994.)
Measured in voltage clamp: hold voltage at fixed
value, so you can measure current only. In this case,
current is proportional to conductance.
For a fast synapse like the one shown in figure 5.14, the rise of the conIsyn (t)
= gsyn
(t)(V
(t) is E
ductance following
a presynaptic
action
potential
so syn
rapid) that it can
be approximated as instantaneous. In this case, the synaptic conductance
Synaptic Kinetics
Normalized PSC
Inhibitory postsynaptic current (IPSC)
Characteristic of GABAB: !
slower decay time (~7-10ms)
slower rise time (~1-2ms)
1.0
0.8
0.6
0.4
0.2
5
10
15
20
25
30
time (ms)
Modeling Synaptic
Conductances
IAM P A (t) = gAM P A (t)(V
X
gAM P A (t) =
↵(t tj )
EAM P A )
j
↵(t) = ⇥(t)e
t/⌧AM P A
AMPA conductance
0.30
0.25
0.20
0.15
0.10
0.05
20
40
60
80
100
120
140
time (ms)
Modeling Synaptic
Conductances
IGABA (t) = gGABA (t)(V
X
gGABA (t) =
(t tj )
EGABA )
j
(t) = JGABA ⇥(t)(e
t/⌧f
e
GABAB conductance
0.20
0.15
0.10
0.05
20
40
60
80
100
120
140
time (ms)
t/⌧r
)
Modeling Synaptic
Conductances
GABAB conductance
0.20
0.15
0.10
0.05
20
gsyn (t) =
40
60
X
80
↵(t
j
where
X
S(t) =
(t
100
120
140
time (ms)
tj ) = (S ⇤ ↵)(t)
tj )
j
is a representation of the presynaptic spike train as a
point process
Modeling Synaptic
Conductances
GABAB conductance
0.20
0.15
gsyn (t) =
0.10
0.05
20
40
60
80
100
S(t) =
120
X
140
(t
X
time (ms)
j
X
↵(t
gsyn (t)
tj ) =
= (S ⇤↵(t
↵)(t)tj ) = (
j
tj )
j
The statistics of gsyn(t) can be derived from those of S(t)
But how do we quantify the statistics of a process like S(t)?