Cortex:
CNS
Orientation selective
Systems
cortical simple cell
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 Cell types Circuit
Spiny stellate
cell 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 Systems
signals transmitted onto the
Areas
dendrites of the target
neurons 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 Systems
signals transmitted onto the
Areas
dendrites of the target
neurons Local Nets
Neurons
Synapses
Molekules
Different Types of Neurons:
dendrite
dendrite
Bipolar
Unipolar axon cell
cell soma
axon
soma
(Invertebrate N.) Retinal bipolar cell
Different Types
of Multi-polar
Cells
Hippocampal Purkinje cell of the
Spinal motoneuron
pyramidal cell cerebellum
Cell membrane:
The cell membrane separates intra- from
extra-cellular spaces
Cl-
Na+ and Cl- ions are more concentrated
outside, while negative ions (A-) and plenty
K+ 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 Vruhe) g (Vm Vrest )
rest
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
dVm(t )
Cm g (Vm Vruhe) Iinj
rest
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 Systems
signals transmitted onto the
Areas
dendrites of the target
neurons 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 Systems
signals transmitted onto the
Areas
dendrites of the target
neurons Local Nets
Neurons
Synapses
Molekules
Action potential
Hodgkin Huxley Model:
dVm(t )
Cm Na-Current + K-Current + Leakage Current + injec. Current
dt
Hodgkin Huxley Model:
dVm(t )
Cm gNam3h(Vm VNa) + K-Current + Leakage Current + injec.
dt Strom
plus Equations for m and h
Hodgkin Huxley Model:
dVm(t )
Cm gNam3h(Vm VNa) gKn 4 (Vm VK ) + Leakage Current + injec.
dt Current
plus Equ. for m, h and n
Hodgkin Huxley Modell:
dVm(t )
Cm gNam3h(Vm VNa) gKn 4 (Vm VK ) gm(Vm Vrest ) Iinj
ruhe
dt
plus Equ. For m, h and n
Hodgkin Huxley Modell:
dVm(t )
Cm gNam3h(Vm VNa) gKn 4 (Vm VK ) gm(Vm Vrest ) Iinj
ruhe
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
D
@ Action Potential / Threshold:
40
20
Iinj = 0.42 nA Short, weak current pulses depolarize the
0 cell only a little.
V mV
- 20
- 40
- 60
D
@
- 80
0 5 10 15 20
t ms
D
@
40
20
Iinj = 0.43 nA
0
V mV
- 20
- 40
- 60
D
@
- 80
0 5 10 15 20
t ms
D
@
40
20
Iinj = 0.44 nA
0
An action potential is elicited when crossing
V mV
- 20
- 40 the threshold.
- 60
D
@
- 80
0 5 10 15 20
t ms
D
@ Action Potential / Firing Latency:
40
20
Iinj = 0.45 nA A higher current reduces the time until an
0 action potential is elicited.
V mV
- 20
- 40
- 60
D
@
- 80
0 5 10 15 20
t ms
D
@
40
20
Iinj = 0.65 nA
0
V mV
- 20
- 40
- 60
D
@
- 80
0 5 10 15 20
t ms
D
@
40
20
Iinj = 0.85 nA
0
V mV
- 20
- 40
- 60
D
@
- 80
0 5 10 15 20
t ms
D
@ Action Potential / Refractory Period:
40
Iinj = 0.5 nA Longer current pulses will lead to more
20
0 action potentials.
V mV
- 20
- 40
- 60
However, directly after an action potential
the ion channels are in an inactive state and
D
@
- 80
0 5 10 15 20 25 30 cannot open. In addition, the membrane
t ms potential is rather hyperpolarized. Thus, the
D
@
40 next action potential can only occur after a
Iinj = 0.5 nA
20 “waiting period” during which the cell return
0
to its normal state.
V mV
- 20
- 40
- 60
This “waiting period” is called the refractory
D
@
- 80
period.
0 5 10 15 20 25 30
t ms
D
@
40
20
Iinj = 0.5 nA
0
V mV
- 20
- 40
- 60
D
@
- 80
0 5 10 15 20 25 30
t ms
D
@ Action Potential / Firing Rate:
40 Iinj = 0.2 nA When injecting current for longer durations
20
0 an increase in current strength will lead to an
V mV
- 20 increase of the number of action potentials
- 40
- 60 per time. Thus, the firing rate of the neuron
D
@
- 80 increases.
0 20 40 60 80 100
t ms The maximum firing rate is limited by the
D
@
40 Iinj = 0.3 nA absolute refractory period.
20
0
V mV
- 20
- 40
- 60
D
@
- 80
0 20 40 60 80 100
t ms
D
@
40 Iinj = 0.6 nA
20
0
V mV
- 20
- 40
- 60
D
@
- 80
0 20 40 60 80 100
t ms
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 Systems
signals transmitted onto the
Areas
dendrites of the target
neurons Local Nets
Neurons
Synapses
Molekules
Propagation of an Action Potential:
Action potentials propagate without being
diminished (active process).
mm2 membrane area
Open channels per
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
Local current loops
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 Systems
outgoing signals transmitted Areas
onto the dendrites of the Local Nets
target neurons 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 uni-
directional 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
Motor Endplate Synaptic cleft
(Frog muscle)
Active vesicles
zone
Muscle fiber
Presynaptic
membrane
Postsynaptic
membrane
Synaptic cleft
What happens at a chemical synapse during signal transmission:
The pre-synaptic action potential depolarises the
Pre-synaptic axon terminals and Ca2+-channels open.
action potential
Ca2+ enters the pre-synaptic cell by which the
transmitter vesicles are forced to open and release
the transmitter.
Concentration of Thereby the concentration of transmitter increases
transmitter
in the synaptic cleft and transmitter diffuses to the
in the synaptic cleft
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
Glycine Cl- inhibitory
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!