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Basics of Computational
Neuroscience
1) Introduction
Lecture: Computational Neuroscience,
The Basics – A reminder:
Contents
1) Brain, Maps, Areas, Networks, Neurons, and Synapses
The tough stuff:
2,3) Membrane Models
3,4) Spiking Neuron Models
5) Calculating with Neurons I: adding, subtracting, multiplying, dividing
5,6) Calculating with Neurons II: Integration, differentiation
6) Calculating with Neurons III: networks, vector-/matrix- calculus, assoc. memory
6,7) Information processing in the cortex I: Neurons as filters
7) Information processing in the cortex II:Correlation analysis of neuronal connections
7,8) Information processing in the cortex III: Neural Codes and population responses
8) Information processing in the cortex IV: Neuronal maps
Something interesting – the broader perspective
9) On Intelligence and Cognition – Computational Properties?
Motor Function
10,11) Models of Motor Control
Adaptive Mechanisms
11,12) Learning and plasticity I: Physiological mechanisms and formal learning rules
12,13) Learning and plasticity II: Developmental models of neuronal maps
13) Learning and plasticity III: Sequence learning, conditioning
Higher functions
14) Memory: Models of the Hippocampus
15) Models of Attention, Sleep and Cognitive Processes
The Interdisciplinary Nature of Computational Neuroscience
What is computational neuroscience ?
Different Approaches towards Brain and Behavior
Neuroscience:
Environment
Behavior
Stimulus
Reaction
Psychophysics (human behavioral studies):
Environment
Behavior
Stimulus
Reaction
Neurophysiology:
Environment
Behavior
Stimulus
Reaction
Theoretical/Computational Neuroscience:

Environment
Stimulus
f (x )

 dx
U
Behavior
Reaction
Levels of information processing in the nervous system
1m
CNS
10cm
Sub-Systems
1cm
Areas / „Maps“
1mm
Local Networks
100mm
Neurons
1mm
Synapses
0.1mm
Molecules
CNS (Central Nervous System):
CNS
Systems
Areas
Local Nets
Neurons
Synapses
Molekules
Cortex:
CNS
Systems
Areas
Local Nets
Neurons
Synapses
Molekules
Where are things happening in the brain.
Is the information
represented locally ?
The Phrenologists view
at the brain
(18th-19th centrury)
CNS
Systems
Areas
Local Nets
Neurons
Synapses
Molekules
Results from human surgery
CNS
Systems
Areas
Local Nets
Neurons
Synapses
Molekules
Results from imaging techniques – There are maps in the brain
CNS
Systems
Areas
Local Nets
Neurons
Synapses
Molekules
Visual System:
More than 40 areas !
Parallel processing of „pixels“ and
image parts
Hierarchical Analysis of increasingly
complex information
Many lateral and feedback
connections
CNS
Systems
Areas
Local Nets
Neurons
Synapses
Molekules
Primary visual Cortex:
CNS
Systems
Areas
Local Nets
Neurons
Synapses
Molekules
Retinotopic Maps in V1:
V1 contains a retinotopic map of the visual Field.
Adjacent Neurons represent adjacent regions in the
retina. That particular small retinal region from which a
single neuron receives its input is called the receptive
field of this neuron.
V1 receives information from both eyes. Alternating
regions in V1 (Ocular Dominanz Columns) receive
(predominantely) Input from either the left or the right
eye.
Each location in the cortex represents a different part
of the visual scene through the activity of many
neurons. Different neurons encode different aspects of
the image. For example, orientation of edges, color,
motion speed and direction, etc.
V1 decomposes an image into these components.
CNS
Systems
Areas
Local Nets
Neurons
Synapses
Molekules
Orientation selectivity in V1:
stimulus
Orientation selective neurons in V1 change
their activity (i.e., their frequency for
generating action potentials) depending on
the orientation of a light bar projected onto
the receptive Field. These Neurons, thus,
represent the orientation of lines oder edges
in the image.
Their receptive field looks like this:
CNS
Systems
Areas
Local Nets
Neurons
Synapses
Molekules
Superpositioning of maps in V1:
Thus, neurons in V1 are orientation
selective. They are, however, also
selective for retinal position and
ocular dominance as well as for
color and motion. These are called
„features“. The neurons are
therefore akin to „feature-detectors“.
For each of these parameter there
exists a topographic map.
These maps co-exist and are
superimposed onto each other. In
this way at every location in the
cortex one finds a neuron which
encodes a certain „feature“. This
principle is called „full coverage“.
CNS
Systems
Areas
Local Nets
Neurons
Synapses
Molekules
Local Circuits in V1:
stimulus
Selectivity is generated by
specific connections
Orientation selective
cortical simple cell
CNS
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
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
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.
Membrane - Circuit diagram:
rest
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
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