Dynamical Systems in Neuroscience:

Simple Models 319The classification of hippocampal CA1 pyramidal neurons into five different classesdoes not imply a fundamental difference in the ionic mechanism of spike-generation, butonly a quantitative difference. This follows from the observation that pharmacologicalmanipulations can gradually and reversibly transform an NB neuron into LTB IIIneuron and visa-versa by elevating the extracellular concentration of K + (Jensen et al.1994), reducing extracellular Ca 2+ (Su et al. 2001), or blocking K + M-current (Yueand Yaari 2004), or manipulating Ca 2+ current dynamics in apical dendrites (Mageeand Carruth 1999).In Fig. 8.35 we modify the simple model for neocortical RS neuron to reproducefiring patterns of hippocampal pyramidal cells. To get the continuum of responses, fromNB to LTB II, we fix all the parameters and vary only the after-spike reset parameterc in an increment of 5 mV, and the parameter d. These phenomenological parametersdescribe the effect of high-threshold inward and outward currents activated during eachspike and affecting the after-spike behavior. Increasing c corresponds to up-regulatingslow I Na,p or down-regulating slow K + currents, which leads to transition from NBto LTB III in the CA1 slice (Su et al. 2001) and in the simple model in Fig. 8.35.Interestingly, the same procedure results in transitions from RS to IB and possibly toCH classes in neocortical pyramidal neurons (Izhikevich 2003). This is consistent withthe observation by Steriade (2004) that many neocortical neurons can change theirfiring classes in vivo depending on the state of the brain.8.4.2 Spiny projection neurons of neostriatum and basal gangliaSpiny projection neurons, the major class of neurons in neostriatum and basal ganglia,display a prominent bistable behavior in vivo shown in Fig. 8.36 (Wilson and Groves1981, Wilson 1993): They shift the membrane potential from hyperpolarized to depolarizedstates in response to synchronous excitatory synaptic input from cortex and/orthalamus. In vitro studies of such neurons reveal a slowly inactivating K + A-current,which is believed to be responsible for the maintenance of the up- and down-states, inaddition to the synaptic input. Indeed, the K + current is completely deinactivated atthe hyperpolarized potentials (down-states), and reduces the response of the neuronto any synaptic input. In contrast, prolonged depolarization (up-state) inactivates thecurrent and makes the neuron more excitable and ready to fire spikes.The most remarkable feature of neostriatal spiny neurons is depicted in Fig. 8.37.In response to depolarizing current pulses, the neurons display a prominent slowlydepolarizing (ramp) potential, and hence long latency to spike discharge (Nisenbaumet al. 1994). The ramp is mostly due to the slow inactivation of K + A-current andslow charging of the dendritic tree. The delay to spike could be as long as 1 sec, butthe subsequent spike train has a shorter relatively constant period that depends on themagnitude of the injected current.Let us use the simple model (8.5, 8.6) to simulate the responses of spiny neuronsto current pulses. The resting membrane potential of the neuron in Fig. 8.37 is around