COMPUTATIONAL NEUROSCIENCE

Instructor: Péter Érdi
Dept. Physics
Office:Olds/Upton 208B
Phone: 337-5720
email: perdi@kzoo.edu
TA: Gábor Csárdi
email: csardi@kzoo.edu

Topic: The discipline of Computational Neuroscience discusses mathematical models, computational algorithms, and simulation methods that contribute to our understanding of neural mechanisms. You will learn the basic concepts and methods of computational neuroscience research. Some brief introduction to neurobiological concepts and mathematical techniques will also be given.The techniques will be applied for describing the behavior of several brain regions. Both normal and pathological behaviors will be analyzed by using neural models.

Goal: The first goal is to teach WHY mathematical and computational methods are important in understanding the structure, function and dynamics of neural organization. The second goal is to explain HOW neural phenomena occurring at different hierarchical levels can be described by proper mathematical models.

The course is not highly technical mathematically, but teaches and uses the basic mathematical notions of dynamical system theory. Students of science majors (with some mathematical interest and skill) are expected to take the class.

Course Structure: Ten topics will be discussed. We shall spend one week on each topic. During the term it will be possible to attend demonstrations. In addition, small groups will be formed to work on specific projects. They should collect data, and run simulations.

Exam: There will be a one hour long midterm and final oral examination. Written and oral report on the group project is a prerequirement of making the final examination. Extra-class activities in connection with computational neuroscience (e.g. writing of simulation programs, participation in class discussion, active participation in the demonstrations of simulation softwares organized by the Center for Complex System Studies) will also be considered in assigning your final grade.

1 TOWARDS an INTEGRATIVE NEUROSCIENCE

Topics: The necessity of integrating structural, functional and dynamic approaches to the brain. Organizational levels, neural centers, overview of the main experimental techniques. What is computational neuroscience?

Readings:

• Towards an Integrative Neuroscience [http://geza.kzoo.edu/cns/cneukbev.pdf],
• The Brain as a Hierarchical Dynamic System [http://geza.kzoo.edu/cns/firstw2.pdf]

2-3 NEUROELECTRICITY. SINGLE CELL MODELS

Topics: Electrical properties of neurons. Single Compartmental Models. McCulloch-Pitts model. Integrate-and-fire models. Voltage-dependent conductances. The Hodgkin-Huxley model. Modeling Channels. Synaptic Conductances. Softwares (NEURON, GENESIS). Case studies pyramidal cell, some interneurons.

Readings:

• Lights, Camera, Action Potential! [http://staff.washington.edu/chudler/ap.html]
• Sounds of Neuroscience [http://staff.washington.edu/chudler/son.html]
• Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems, by Peter Dayan and L. F. Abbott, Chapter 5: Model neurons I: Neuroelectronics [http://neurotheory.columbia.edu/~larry/book/teaching.html]
• Thomas E. (2002). Realistic models of neurons and neuronal networks . [http://www.ulg.ac.be/cogsci/ethomas.html]
• The Book of Genesis [http://www.genesis-sim.org/GENESIS/bog/bog.html]

4 SYNAPSE, SYNAPTIC TRANSMISSION, NEUROCHEMISTRY, NEUROPHARMACOLOGY}

Topics: The synapse. Synaptic transmission. Neurotransmitters and Neuroactive Peptides

Readings:

• Neurotransmitters and Neuroactive Peptides [http://staff.washington.edu/chudler/chnt1.html
• Pharmacodynamics and Pharmacokinetics [http://www.muhealth.org/~pharm204/pharmacodynamics_and_pharmacok.html

5 SYNAPTIC PLASTICITY, LEARNING

Topics: Cellular basis of synaptic plasticity. Learning rules: Hebb's rule and its variations. Learning in biological and artificial networks: supervised, unsupervised and reinforcement learning. Classical conditioning and reinforcement learning. Dopamine and the prediction of reward

Readings:

• Érdi P and Somogyvári Z: Post-Hebbian learning algorithms in Handbook in Brain Theory and Neural Networks. [http://geza.kzoo.edu/cns/erdi_p2.pdf]
• Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems Peter Dayan and L. F. Abbott, Chapter 9: Classical conditioning and reinforcement learning [http://neurotheory.columbia.edu/~larry/book/teaching.html]

6 NEURAL NETWORKS, NEURAL RHYTHMICITY

Topics: Oscillation and chaos in neural networks. Linear stability analysis. Neural networks: two level dynamics.

Readings:

• Neurodynamical System Theory, 2. Brain Rhythms, Normal and Pathological [http://www.rmki.kfki.hu/biofiz/cneuro/tutorials/como/comoall/index.html]

7 COMPUTATIONAL APPROACH to the HIPPOCAMPUS

Topics: Anatomical organization, afferent and efferent systems, local circuitry. Electrical activity patterns. Long-term potentiation. Cognitive map. Navigating algorithms.

Readings:

• Anatomical organization of the Hippocampus [http://geza.kzoo.edu/cns/icannall/icann00.html]

8 MODELING of NEUROLOGICAL and PSYCHIATRICAL DISORDERS

Topics: Neural and mental disorders as dynamical diseases. Epilepsy, Alzheimer disease, Parkinson disease, anxiety, ADHD, schizophrenia

Readings:

• Péter Érdi: Neural information processing: normal and pathological. Third Conference on the Foundations of Information Science, Paris, France, 4-7 July, 2005. [http://www.kzoo.edu/physics/ccss/material.html]

9 MODELING GENERATION and CONTROL of NORMAL and PATHOLOGICAL RHYTHMS

Topics: Rhythms in the septohippocampal system and their role in mood regulation.

Readings:

• M. Hajós, WE. Hoffmann, G. Orbán, T. Kiss, P. Érdi: Modulation of septo-hippocampal theta activity by GABAA receptors: Experimental and computational approach. Neuroscience 126/3 (2004) 599--610 [http://geza.kzoo.edu/cns/Neurosci-04-proof.pdf]

10 COMPUTATIONAL NEUROSCIENCE: WHERE WE ARE NOW?

Summary. Group reports. Open discussion forum. Preparation for the exam.