Dynamical Systems in Neuroscience:

Electrophysiology of Neurons 43pulse size, Ap, needed toproduce 2nd spike (µA/cm2) memrane potential (mV)10050020100absoluterefractoryrelativerefractoryhyperexcitability0 5 10 15 20 25time, tp, after 1st spike (ms)tpApFigure 2.17: Refractory periods in the Hodgkin-Huxley model with I = 3.beyond the scope of this book, and the reader can consult Keener and Sneyd (1998)and references therein.2.3.4 Dendritic compartmentsModifications of the Hodgkin-Huxley model, often called Hodgkin-Huxley-type models,or conductance-based models, can describe the dynamics of spike-generation of manyif not all neurons recorded in nature. However, there is more to the computationalproperty of neurons than just the spike-generation mechanism. Many neurons havean extensive dendritic tree that can sample the synaptic input arriving at differentlocations and integrate it over space and time.Many dendrites have voltage-gated currents, so the synaptic integration is nonlinear,sometimes resulting in dendritic spikes that can propagate forward to the somaof the neuron or backwards to distant dendritic locations. Dendritic spikes are prominentin intrinsically bursting (IB) and chattering (CH) neocortical neurons consideredin Chap. 8. In that chapter we also model regular spiking (RS) pyramidal neurons,the most numerous class of neurons in mammalian neocortex, and show that theirspike-generation mechanism is one of the simplest. The computation complexity of RSneurons must be hidden then in the arbors of their dendritic trees.It is not feasible at present to study analytically or geometrically the dynamics ofmembrane potential in dendritic trees, unless dendrites are assumed to be passive (lin-