Cortex:
CNS
Orientation selective
cortical simple cell
Systems
Areas
Local Nets
Neurons
Synapses
Molekules
Layers in the Cortex:
CNS
Systems
Areas
Local Nets
Neurons
Synapses
Molekules
Local Circuits in V1:
CNS
Systems
Areas
Local Nets
Neurons
Synapses
Molekules
LGN inputs
Spiny stellate
cell
Circuit
Cell types
Smooth stellate
cell
Neurophysiological Background
“The Neuron “
Contents:
 Structure
 Electrical Membrane Properties
 Ion Channels
 Actionpotential
 Signal Propagation
 Synaptic Transmission
Nerve cell
Structure of a Neuron:
At the dendrite the incoming
signals arrive (incoming currents)
At the soma current
are finally integrated.
At the axon hillock action potential
are generated if the potential crosses the
membrane threshold
The axon transmits (transports) the
action potential to distant sites
CNS
At the synapses are the outgoing
signals transmitted onto the
dendrites of the target
neurons
Systems
Areas
Local Nets
Neurons
Synapses
Molekules
Structure of a Neuron:
At the dendrite the incoming
signals arrive (incoming currents)
At the soma current
are finally integrated.
At the axon hillock action potential
are generated if the potential crosses the
membrane threshold
The axon transmits (transports) the
action potential to distant sites
CNS
At the synapses are the outgoing
signals transmitted onto the
dendrites of the target
neurons
Systems
Areas
Local Nets
Neurons
Synapses
Molekules
Different Types of Neurons:
dendrite
dendrite
Unipolar
cell
axon
soma
(Invertebrate N.)
Bipolar
cell
soma
axon
Retinal bipolar cell
Different Types
of Multi-polar
Cells
Spinal motoneuron
Hippocampal
pyramidal cell
Purkinje cell of the
cerebellum
Cell membrane:
The cell membrane separates intra- from
extra-cellular spaces
Cl-
K+
Na+ and Cl- ions are more concentrated
outside, while negative ions (A-) and plenty
of K+ are more concentrated inside.
Due to differences in the ion-concenrations
across the membrane a potential difference
arises:
Vm
In addition, the membrane acts like a
capacitor:
Q  CVm
Current flow leads to voltage change:
dQ
dVm
IC 
C
dt
dt
Ion channels:
Ion channels consist of big (protein)
molecules which are inserted into to the
membrane and connect intra- and
extracellular space.
Channels act as a restistance against the
free flow of ions. Electrical resistor R:
1
IR  (Vm  Vrestruhe)  g (Vm  Vrest
ruhe)
R
If Vm = Vrest there is no current flow.
Channels are normally ion-selective and
will open and close in dependence on the
membrane potential (normal case) but also
on (other) ions (e.g. NMDA channels).
Channels exists for: K+, Na+, Ca2+, Cl-
Membrane - Circuit diagram:
In order to decribe the electrical properties
of a membrane you need the membrane
capacitance C, the conductivity g=1/R and
the resting potential Vrest.
Current across the membrane is given by:
dVm
Iinj  IC  IR  C
 g (Vm  Vrest
ruhe)
dt
or:
rest
Cm
dVm(t )
  g (Vm  Vrest
ruhe)  Iinj
dt
Using this equation you can calculate how
the current changes depending on an
experimentally injected current.
Membrane - Circuit Diagram (advanced version):
The whole thing gets more complicated due to the fact that there are many
different ion channels all of which have their own characteristics depending on
the momentarily existing state of the cell.
The conducitvity of a channel depends on the membrane potential and on the
concentration difference between intra- and extracellular space (and sometimes
also on other parameters).
One needs a computer simulation to describe this complex membrane behavior.
Structure of a Neuron:
At the dendrite the incoming
signals arrive (incoming currents).
Signals propagate (normally) in a
passive, electrotonic way towards the
soma
At the soma current
are finally integrated.
At the axon hillock action potential
are generated if the potential crosses the
membrane threshold
The axon transmits (transports) the
action potential to distant sites
CNS
At the synapses are the outgoing
signals transmitted onto the
dendrites of the target
neurons
Systems
Areas
Local Nets
Neurons
Synapses
Molekules
Electrotonic Signal Propagation:
Injected Current
Membrane Potential
Injected current flows out from the cell evenly across the membrane.
The cell membrane has everywhere the same potential.
The change in membrane potention follows an exponential with time constant: t = RC
Electrotonic Signal Propagation:
The potential decays along a dendrite (or axon)
according to the distance from the current injection
site.
At every location the temporal response follows an
exponential but with ever decreasing amplitude.
If plotting only the maxima against the distance then
you will get another exponential.
Different shape of the potentials in the dendrite and
the soma of a motoneuron.
Compartment-Model:
One can model the electrotonic
propagation of potentials in the
complex dendritic tree by
subdividing the tree into small
(cyklindrical) compartments. For
each compartment the membrane
equations can then be solved and
integrated. (All this is tedious and
complicated.)
Structure of a Neuron:
At the dendrite the incoming
signals arrive (incoming currents)
At the soma current
are finally integrated.
At the axon hillock action potential
are generated if the potential crosses the
membrane threshold.
The axon transmits (transports) the
action potential to distant sites
CNS
At the synapses are the outgoing
signals transmitted onto the
dendrites of the target
neurons
Systems
Areas
Local Nets
Neurons
Synapses
Molekules
Action potential
Hodgkin Huxley Model:
Cm
dVm(t )

dt
Na-Current + K-Current + Leakage Current + injec. Current
Hodgkin Huxley Model:
Cm
dVm(t )
  gNam3 h(Vm  VNa) + K-Current
dt
plus Equations for m and h
+ Leakage Current + injec.
Strom
Hodgkin Huxley Model:
Cm
dVm(t )
  gNam 3 h(Vm  VNa)  gKn 4 (Vm  VK ) + Leakage Current + injec.
dt
Current
plus Equ. for m, h and n
Hodgkin Huxley Modell:
Cm
dVm(t )
  gNam 3h(Vm  VNa)  gKn 4 (Vm  VK )  gm(Vm  Vrest
ruhe)  Iinj
dt
plus Equ. For m, h and n
Hodgkin Huxley Modell:
Cm
dVm(t )
  gNam 3h(Vm  VNa)  gKn 4 (Vm  VK )  gm(Vm  Vrest
ruhe)  Iinj
dt
plus Equ. for m, h and n
VNa= 55 mV, VK = -75 mV, Vrest = -60 mV
gNa= 120 mS/cm2, gK= 36 mS/cm2, Cm= 1 mS/cm2
V mV
@
D
Action Potential / Threshold:
40
20
0
20
40
60
80
-
Iinj = 0.42 nA
5
V mV
@
D
0
40
20
0
20
40
60
80
-
5
@
D
V mV
15
20
Iinj = 0.43 nA
0
-
@
D
10
t ms
Short, weak current pulses depolarize the
cell only a little.
40
20
0
20
40
60
80
@
D
10
t ms
15
20
Iinj = 0.44 nA
An action potential is elicited when crossing
the threshold.
0
5
@
D
10
t ms
15
20
V mV
@
D
Action Potential / Firing Latency:
-
40
20
0
20
40
60
80
Iinj = 0.45 nA
V mV
@
D
0
-
40
20
0
20
40
60
80
@
D
V mV
@
D
10
t ms
15
20
Iinj = 0.65 nA
0
-
5
5
40
20
0
20
40
60
80
@
D
10
t ms
15
20
Iinj = 0.85 nA
0
5
@
D
10
t ms
15
20
A higher current reduces the time until an
action potential is elicited.
V mV
@
D
Action Potential / Refractory Period:
40
20
0
20
40
60
80
-
Iinj = 0.5 nA
5
10
V mV
@
D
0
-
40
20
0
20
40
60
80
5
10
@
D
V mV
25
30
Iinj = 0.5 nA
0
-
@
D
15 20
t ms
40
20
0
20
40
60
80
@
D
15 20
t ms
25
30
Iinj = 0.5 nA
0
5
10
@
D
15 20
t ms
25
30
Longer current pulses will lead to more
action potentials.
However, directly after an action potential
the ion channels are in an inactive state and
cannot open. In addition, the membrane
potential is rather hyperpolarized. Thus, the
next action potential can only occur after a
“waiting period” during which the cell return
to its normal state.
This “waiting period” is called the refractory
period.
V mV
@
D
Action Potential / Firing Rate:
40
20
0
20
40
60
80
-
Iinj = 0.2 nA
20
V mV
@
D
0
-
20
@
D
V mV
80
100
Iinj = 0.3 nA
40
20
0
20
40
60
80
0
-
@
D
40
60
t ms
40
20
0
20
40
60
80
@
D
40
60
t ms
80
100
Iinj = 0.6 nA
0
20
@
D
40
60
t ms
80
When injecting current for longer durations
an increase in current strength will lead to an
increase of the number of action potentials
per time. Thus, the firing rate of the neuron
increases.
100
The maximum firing rate is limited by the
absolute refractory period.
Action Potential / Shapes:
Squid Giant Axon
Rat - Muscle
Cat - Heart
Structure of a Neuron:
At the dendrite the incoming
signals arrive (incoming currents)
At the soma current
are finally integrated.
At the axon hillock action potential
are generated if the potential crosses the
membrane threshold.
The axon transmits (transports) the
action potential to distant sites
CNS
At the synapses are the outgoing
signals transmitted onto the
dendrites of the target
neurons
Systems
Areas
Local Nets
Neurons
Synapses
Molekules
Propagation of an Action Potential:
Action potentials propagate without being
diminished (active process).
Open channels per
mm2 membrane area
Local current loops
All sites along a nerve fiber will be
depolarized until the potential passes
threshold. As soon as this happens a new
AP will be elicited at some distance to the
old one.
Main current flow is across the fiber.
Time
Distance
Structure of a Neuron:
At the dendrite the incoming
signals arrive (incoming currents)
At the soma current
are finally integrated.
At the axon hillock action potential
are generated if the potential crosses the
membrane threshold
The axon transmits (transports) the
action potential to distant sites
CNS
At the synapses are the
outgoing signals transmitted
onto the dendrites of the
target neurons
Systems
Areas
Local Nets
Neurons
Synapses
Molekules
Chemical synapse
Neurotransmitter
Receptors
Neurotransmitters
Chemicals (amino acids, peptides, monoamines) that
transmit, amplify and modulate signals between neuron and
another cell.
Cause either excitatory or inhibitory PSPs.
Glutamate – excitatory transmitter
GABA, glycine – inhibitory transmitter
Synaptic Transmission:
Synapses are used to transmit signals from the axon of a source to the dendrite of a target
neuron.
There are electrical (rare) and chemical synapses (very common)
At an electrical synapse we have direct electrical coupling (e.g., heart muscle cells).
At a chemical synapse a chemical substance (transmitter) is used to transport the signal.
Electrical synapses operate bi-directional and are extremely fast, chem. syn. operate unidirectional and are slower.
Chemical synapses can be excitatory or inhibitory
they can enhance or reduce the signal
change their synaptic strength (this is what happens during learning).
Structure of a Chemical Synapse:
Axon
Synaptic cleft
Motor Endplate
(Frog muscle)
Active
zone
vesicles
Muscle fiber
Presynaptic
membrane
Postsynaptic
membrane
Synaptic cleft
What happens at a chemical synapse during signal transmission:
Pre-synaptic
action potential
The pre-synaptic action potential depolarises the
axon terminals and Ca2+-channels open.
Ca2+ enters the pre-synaptic cell by which the
transmitter vesicles are forced to open and release
the transmitter.
Concentration of
transmitter
in the synaptic cleft
Thereby the concentration of transmitter increases
in the synaptic cleft and transmitter diffuses to the
postsynaptic membrane.
Post-synaptic
action potential
Transmitter sensitive channels at the postsyaptic
membrane open. Na+ and Ca2+ enter, K+ leaves the
cell. An excitatory postsynaptic current (EPSC) is
thereby generated which leads to an excitatory
postsynaptic potential (EPSP).
Neurotransmitters and their (main) Actions:
Transmitter
Channel-typ
Ion-current
Action
Acetylecholin
nicotin. Receptor
Na+ and K+
excitatory
Glutamate
AMPA / Kainate
Na+ and K+
excitatory
GABA
GABAA-Receptor Cl-
inhibitory
Cl-
inhibitory
Glycine
Acetylecholin
muscarin. Rec.
-
metabotropic, Ca2+ Release
Glutamate
NMDA
Na+, K+, Ca2+
voltage dependent
blocked at resting potential
Synaptic Plasticity
Long-term potentiation (LTP)
High frequency stimulation: 1s, 100Hz
Long-term depression (LTD)
Low frequency stimulation: 15min, 1Hz
Summation Properties at Synapses:
Will be treated when we start to talk about:
How to do calculations with neurons.
The whole complex neuronal structure and function can be modeled at a
first level of abstraction by a Simple Integrate-And-Fire Neuron:
ui
wi
O
O  S ( wi ui )
i
ui = signals from pre-synaptic neurons
wi = synaptic weights
S = Threshold(function)
O = Output firing rate of the neuron
•
Here Rall’s Cable Model!