Dynamical Systems in Neuroscience:

Electrophysiology of Neurons 37pre-steppotentials-20 mVV s-80 mVstep potentialV 0I(t)peakI sinactivation10.5010.50h sinstantaneousactivation0 10 20 30 40 50 60 70time (ms)m(t)h(t)Figure 2.12: Dynamics of the current(I), activation (m) and inactivation(h) variables in the voltage-clampexperiment aimed at measuring h ∞ (V )in Fig. 2.11.In Ex. 6 we describe a better method to determine h ∞ (V ) that does not rely on thedifference between the activation and inactivation time scales.The voltage-sensitive steady-state activation and inactivation functions overlap ina shaded window depicted in Fig. 2.11. Depending on the size of the shaded area inthe figure, the overlap may result in a noticeable “window” current.2.2.4 Hyperpolarization-activated channelsMany neurons in various parts of the brain have channels that are opened by hyperpolarization.These channels produce currents that are turned on by hyperpolarizationand turned off by depolarization. Biologists refer to such currents as being“exceptional” or “weird”, and denoted them as I Q (“queer”), I f (“funny”), I h(“hyperpolarization-activated”), or I Kir (K + inward rectifier). We will consider the lasttwo currents in detail in the next chapter. Most neuroscience textbooks classify thesecurrents in a special category — hyperpolarization-activated currents. However, fromthe theoretical point of view it is inconvenient to create special categories. In this bookwe treat these currents as “normal” transient currents with the understanding that theyare always activated (either a = 0 or variable m = 1 in (2.8)), but can be inactivatedby depolarization (variable h → 0) or deinactivated by hyperpolarization (variableh → 1). Moreover, there is biophysical evidence suggesting that closing/opening ofI Kir is indeed related to the inactivation/deinactivation process (Lopatin et al. 1994).