1. Basics of Computational Neuroscience

2. Lecture: Computational Neuroscience, Contents
1) Introduction
The Basics – A reminder:
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
Lecture: Computational Neuroscience, Contents

3. The Interdisciplinary Nature of Computational Neuroscience
What is computational neuroscience ?

4. Different Approaches towards Brain and Behavior
Neuroscience:
Environment
Stimulus
Behavior
Reaction

5. Psychophysics (human behavioral studies):
Black Box
Environment
Stimulus
Behavior
Reaction

6. Neurophysiology:
Environment
Stimulus
Behavior
Reaction

7. Theoretical/Computational Neuroscience:
Environment
Stimulus
Behavior
Reaction

8. Levels of information processing in the nervous system
CNS 1m
Sub-Systems
10cm
Areas / „Maps“
1cm
Local Networks
1mm
Neurons
100mm
Synapses
1mm
Molecules
0.1mm

9. CNS (Central Nervous System):
Systems
Areas
Local Nets
Neurons
Synapses
Molekules

10. Cortex:
CNS
Systems
Areas
Local Nets
Neurons
Synapses
Molekules

11. Where are things happening in the brain.
The Phrenologists view
at the brain
(18th-19th centrury)
Is the information
represented locally ?
Molekules
Synapses
Neurons
Local Nets
Areas
Systems
CNS

12. Results from human surgery
CNS
Systems
Areas
Local Nets
Neurons
Synapses
Molekules

13. Results from imaging techniques – There are maps in the brain
CNS
Systems
Areas
Local Nets
Neurons
Synapses
Molekules

14. 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

15. Primary visual Cortex:
CNS
Systems
Areas
Local Nets
Neurons
Synapses
Molekules

16. 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.
Molekules
Synapses
Neurons
Local Nets
Areas
Systems
CNS

17. 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:
Molekules
Synapses
Neurons
Local Nets
Areas
Systems
CNS

18. 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“.
Molekules
Synapses
Neurons
Local Nets
Areas
Systems
CNS

19. Local Circuits in V1: stimulus
Orientation selective
cortical simple cell
Local Circuits in V1:
stimulus
Selectivity is generated by specific connections
Molekules
Synapses
Neurons
Local Nets
Areas
Systems
CNS

20. Layers in the Cortex: CNS Systems Areas Local Nets Neurons Synapses
Molekules

21. Local Circuits in V1: LGN inputs Cell types Circuit Spiny stellate
Molekules
Synapses
Neurons
Local Nets
Areas
Systems
CNS
LGN inputs
Cell types
Circuit
Spiny stellate
cell
Smooth stellate
cell

22. 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
Molekules
Synapses
Neurons
Local Nets
Areas
Systems
CNS
At the synapses are the outgoing
signals transmitted onto the
dendrites of the target
neurons

23. Different Types of Neurons:
dendrite
dendrite
Bipolar
cell
Unipolar
cell
axon
soma
axon
soma
(Invertebrate N.)
Retinal bipolar cell
Different Types
of Multi-polar
Cells
Hippocampal
pyramidal cell
Purkinje cell of the
cerebellum
Spinal motoneuron

24. Cell membrane:
The cell membrane separates intra- from extra-cellular spaces 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: In addition, the membrane acts like a capacitor:
Cl- K+

25. 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.

26. Membrane - Circuit diagram:
rest

27. 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.
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).
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.

28. 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 dendrite the incoming
signals arrive (incoming currents).
Signals propagate (normally) in a passive, electrotonic way towards the soma
At the dendrite the incoming
signals arrive (incoming currents).
Signals propagate (normally) in a passive, electrotonic way towards the soma
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
Molekules
Synapses
Neurons
Local Nets
Areas
Systems
CNS
At the synapses are the outgoing
signals transmitted onto the
dendrites of the target
neurons

29. 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
Injected current flows out from the cell evenly across the membrane.
The cell membrane has everywhere the same potential.
Injected current flows out from the cell evenly across the membrane.

30. Electrotonic Signal Propagation:
The potential decays along a dendrite (or axon) according to the distance from the current injection site.
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.
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.
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.

31. 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.)

32. Structure of a Neuron: At the axon hillock action potential
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.
At the axon hillock action potential
are generated if the potential crosses the
membrane threshold.
At the axon hillock action potential
are generated if the potential crosses the
membrane threshold.
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
Molekules
Synapses
Neurons
Local Nets
Areas
Systems
CNS
At the synapses are the outgoing
signals transmitted onto the
dendrites of the target
neurons

33. Action potential

34. Action Potential / Shapes:
Cat - Heart
Rat - Muscle
Squid Giant Axon

35. Structure of a Neuron: The axon transmits (transports) the
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
The axon transmits (transports) the
action potential to distant sites
The axon transmits (transports) the
action potential to distant sites
The axon transmits (transports) the
action potential to distant sites
Molekules
Synapses
Neurons
Local Nets
Areas
Systems
CNS
At the synapses are the outgoing
signals transmitted onto the
dendrites of the target
neurons

36. Propagation of an Action Potential:
Distance
Time
Local current loops
mm2 membrane area
Open channels per
Action potentials propagate without being diminished (active process).
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.
Action potentials propagate without being diminished (active process).
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.
Action potentials propagate without being diminished (active process).

37. 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
At the synapses are the outgoing signals transmitted onto the dendrites of the target neurons
At the synapses are the outgoing signals transmitted onto the dendrites of the target neurons
At the synapses are the outgoing signals transmitted onto the dendrites of the target neurons
Systems
Areas
Local Nets
Neurons
Synapses
Molekules

38. Chemical synapse
Neurotransmitter
Receptors

39. 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

40. 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.
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).
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.
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).
Synapses are used to transmit signals from the axon of a source to the dendrite of a target neuron.
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)

41. Structure of a Chemical Synapse:
Axon
Motor Endplate
(Frog muscle)
Synaptic cleft
Active
zone
vesicles
Muscle fiber
Presynaptic
membrane
Postsynaptic
membrane
Synaptic cleft

42. What happens at a chemical synapse during signal transmission:
Pre-synaptic
action potential
Concentration of
transmitter
in the synaptic cleft
Post-synaptic
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.
Thereby the concentration of transmitter increases in the synaptic cleft and transmitter diffuses to the postsynaptic membrane.
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).
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.
Thereby the concentration of transmitter increases in the synaptic cleft and transmitter diffuses to the postsynaptic membrane.
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.
The pre-synaptic action potential depolarises the axon terminals and Ca2+-channels open.

43. 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
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
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
Transmitter Channel-typ Ion-current Action
Acetylecholin nicotin. Receptor Na+ and K+ excitatory
Glutamate AMPA / Kainate Na+ and K+ excitatory
Transmitter Channel-typ Ion-current Action
Transmitter Channel-typ Ion-current Action
Acetylecholin nicotin. Receptor Na+ and K+ excitatory
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

44. Synaptic Plasticity