Models in Neuro Omri Barak TA Friedrich Schuessler

Models in Neuro Omri Barak TA: Friedrich Schuessler

Observations in neuro • Memory can last a lifetime • Protein turnover has a timescale of days. • Recovery from brain damage • Distributed storage of information? • Variability of in-vivo firing • Despite regularity of in-vitro

Observations in neuro • Cued recall is almost boundless • But free recall is severely limited • Orientation tuning in V 1 was discovered in the 1950 s • But a 2005 paper estimated we understand at most 15% of V 1 activity. • Grid cells • Really? Hexagons? ? ?

The brain is complex • What does that mean? • Many interacting elements. • Experiments are often reductionist is nature • Underlying models (mathematical or other) stitch the pieces • Stich the pieces = consistency

Consistency • Math makes it harder to round corners. • If things are not self consistent – you notice it. • Caution: harder is not impossible.

Aims of this course • Understand how (abstract) models can be used in neuroscience. • Discuss examples where they work and fail. • Learn how to simulate and analyze simple models • Dynamical systems • Numerical simulation • Phase plane analysis

Practicalities • Lectures: • Wednesday 9: 30 – 11: 30 • Practice sessions: • Monday 12: 30 – 14: 30 • Friedrich Schuessler (There will be some schedule changes due to conferences, retreat, etc. )

What I expect you to do • Read the assigned papers. • Try to do the math yourself • Think

Warm up • Fitz. Hugh-Nagumo • • Numerical simulation Phase plane Bifurcations …

Fitzhugh Nagumo model •

• Add second, slow, equation • What happens to the graphs (go up and down, fixed point shifts) • Follow an action potential using the two graphs

• Phase space • Mechanical examples: marker, pendulum • Fitzhugh Nagumo phase space • Draw nullclines • Determine motion quadrants in all regions of phase space • Understand qualitative trajectories. • Show action potential • Separation of timescales – horizontal trajectories