Basics of ComputationalNeuroscience

What is computational neuroscience ?

The Interdisciplinary Nature of Computational Neuroscience

1. Computational neuroscience and the perspective of scientists versus that of behaving agents

2. Levels of Information processing in the brain

3. Neuron and Synapse: Biophysical properties, membrane- and action-potential

4. Calculating with Neurons I: adding, subtracting, multiplying, dividing

5. Calculating with Neurons II: Integration, differentiation

6. Calculating with Neurons III: networks, vector-/matrix- calculus, associative memory

7. Information processing in the cortex I: Correlation analysis of neuronal connections

8. Information processing in the cortex II: Neurons as filters

9. Information processing in the cortex III: Coding of behavior by poputation responses

10. Information processing in the cortex IV: Neuronal maps

11. Learning and plasticity I: Physiological mechanisms and formal learning rules

12. Learning and plasticity II: Developmental models of neuronal maps

13. Learning and plasticity III: Sequence learning, conditioning

14. Memory: Models of the Hippocampus

Lecture: Computational Neuroscience, Contents

What is computational neuroscience ?

The Interdisciplinary Nature of Computational Neuroscience

Neuroscience:

Environment

Stimulus

Behavior

Reaction

Different Approaches towards Brain and Behavior

Psychophysics (human behavioral studies):

Environment

Stimulus

Behavior

Reaction

Environment

Stimulus

Neurophysiology:

Behavior

Reaction

Environment

Stimulus

Theoretical/Computational Neuroscience:

Behavior

Reactiondx

)(xf

U

Levels of information processing in the nervous system

Molecules0.1m

Synapses1m

Neurons100m

Local Networks1mm

Areas / „Maps“ 1cm

Sub-Systems10cm

CNS1m

CNS (Central Nervous System):

Molekules

Synapses

Neurons

Local Nets

Areas

Systems

CNS

Cortex:

Molekules

Synapses

Neurons

Local Nets

Areas

Systems

CNS

Where are things happening in the brain.

Is the informationrepresented locally ?

The Phrenologists viewat the brain(18th-19th centrury)

Molekules

Synapses

Neurons

Local Nets

Areas

Systems

CNS

Untersuchungen von Patienten

Sehen != Erkennen

Molekules

Synapses

Neurons

Local Nets

Areas

Systems

CNS

Results from human surgery

Molekules

Synapses

Neurons

Local Nets

Areas

Systems

CNS

Results from imaging techniques

Molekules

Synapses

Neurons

Local Nets

Areas

Systems

CNS

Functional and anatomical subdivisions of the Cortex:

Molekules

Synapses

Neurons

Local Nets

Areas

Systems

CNS

limbic association cortex primary sensor and motor areas

Parietal-temporal-occipital assoc. cortex

Higher sensorial areasPremotor cortex

Prefrontalassociation cortex

Visual System:

More than 40 areas !

Parallel processing of „pixels“ andimage parts

Hierarchical Analysis of increasingly complex information

Many lateral and feedback connections

Molekules

Synapses

Neurons

Local Nets

Areas

Systems

CNS

Primary visual Cortex:

Molekules

Synapses

Neurons

Local Nets

Areas

Systems

CNS

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.

Molekules

Synapses

Neurons

Local Nets

Areas

Systems

CNS

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 dicomposes an image into these components.

Orientation selectivity in V1:

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.

Molekules

Synapses

Neurons

Local Nets

Areas

Systems

CNS

Their receptive field looks like this:

stimulus

HIER weiter

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

Local Circuits in V1:

Selectivity is generated by specific connections

stimulus

Orientation selectivecortical simple cell

Molekules

Synapses

Neurons

Local Nets

Areas

Systems

CNS

Layers in the Cortex:

Molekules

Synapses

Neurons

Local Nets

Areas

Systems

CNS

Local Circuits in V1:

Molekules

Synapses

Neurons

Local Nets

Areas

Systems

CNS

LGN inputs Cell types Local connections

To subcortical areasColl. Sup., Pulvinar, Pons

LGN, Claustrum

To different cortex areas

Spiny stellatecell Smooth stellate

cell

At the dendrite the incomingsignals arrive (incoming currents)

Molekules

Synapses

Neurons

Local Nets

Areas

Systems

CNS

At the soma currentare finally integrated.

At the axon hillock action potentialare generated if the potential crosses the membrane threshold

The axon transmits (transports) theaction potential to distant sites

At the synapses are the outgoingsignals transmitted onto the dendrites of the targetneurons

Structure of a Neuron: