Association between electrophysiological phenotypes and Kv2.1 potassium channel expression explained by geometrical analysis

Excitable cells exhibit different electrophysiological profiles while responding to current stimulation in current-clamp experiments. In theory, the differences could be explained by changes in the expression of proteins mediating transmembrane ion transport. Experimental verification by performing systematic, controlled variations in the expression of proteins of the same type (e.g. voltage-dependent, noninactivating Kv2.1 channels) is difficult to achieve in the absence of other changes. However, biophysical models enable this possibility and allows us to assess and characterise the electrophysiological phenotypes associated to different levels of expression of non-inactivating voltage-dependent K-channels of type Kv2.1. To do so, we use a 2-dimensional biophysical model of neuronal membrane potential and study the phase plane geometry and bifurcation structures associated with different levels of Kv2.1 expression with the input current as bifurcation parameter. We find that increasing the expression of Kv2.1 channels reduces the size of the region of the phase plane from which action potentials can be initiated. The changes in expression can also be related to different transitions between rest and repetitive firing in current clamp experiments. For instance, increasing the number of Kv2.1 channels shifts the rheobase current to higher levels, but also expands the dynamic range in which excitatory external current produces repetitive spiking. Our analysis shows that changes in the responses to increasing input currents can be associated to different sequences of fixed point bifurcations. In general, the fixed points are attracting, then repulsive, and later become attracting again as the input current increases, but the bifurcation sequences also include changes in fixed point type, and change qualitatively with the expression of Kv2.1 channels. In the non-repetitive spiking regime with low current stimulation, low expression of Kv2.1 channels yields bifurcation sequences that include transitions between 3 and 1 fixed points, and repetitive firing starts with delays that decrease with increasing current (aggregation). For higher expression of Kv2.1 channels there is only one fixed point that changes in type and attractivity as the input current increases, convergence to rest tends to be oscillatory (resonance), and repetitive spiking starts without noticeable delays. Our models explain how the same neuron is theoretically be capable of including both aggregating and resonant modes of integration for synaptic input, as shown in current clamp experiments.