1. Bioeng 376 / Bioph 317 / Neuro 317 / Physl 317M. Nelson, Spring 2004 Dayan and Abbott, 2001

2. Bioeng 376 / Bioph 317 / Neuro 317 / Physl 317M. Nelson, Spring 2004 Dayan and Abbott, 2001

3. Bioeng 376 / Bioph 317 / Neuro 317 / Physl 317M. Nelson, Spring 2004 Dayan and Abbott, 2001

4. Bioeng 376 / Bioph 317 / Neuro 317 / Physl 317M. Nelson, Spring 2004

5. Take-home Lessons neurons have diverse and complex dendritic morphologies voltage records look like “noisy baseline” + “spikes” in vitro current injection yields relatively simple voltage records with RC-like response curves, plus spikes if v > threshold in vivo recordings are generally “noisier” (synaptic activity) leaky integrate-and-fire model attempts to capture basic properties of voltage records (RC time constant, spike threshold); typically ignores complexities of neuron morphology Typical numerical parameters: resting membrane voltage: ~  70 mV spike amplitude: ~100 mV (intracellular) spike duration: ~1 msec RC time constant: ~10 msec maximum spike rate: ~100 spikes/s

6. Bioeng 376 / Bioph 317 / Neuro 317 / Physl 317M. Nelson, Spring 2004 Leaky integrate-and-fire model initialize membrane voltagev = v rest RC-circuit dynamicsdv/dt = (-v(t)/R + I(t))/C spike generation if (v  v thresh ) then generate spike voltage resetif (just spiked) then reset voltage absolute refractory periodif (time since last spike < t refract ) then don’t allow another spike For more info see: http://diwww.epfl.ch/~gerstner/SPNM/node26.html http://zadorlab.cshl.edu/rep_fire_inc/rep_fire_inc.html http://diwww.epfl.ch/~gerstner/SPNM/node26.html http://zadorlab.cshl.edu/rep_fire_inc/rep_fire_inc.html