Kinetics of Two-State Ion  Information Maximization in Single Neurons  Assumptions

The Kinetics of Ion Channels as a Substrate for Adaptation

Theory predicts that nerve cells will change the density and properties of voltage-dependent ion channels in the membrane to enable computation and the transmission of information. A biologically plausible realization of such an adaptation mechanism must hew to the principle of self-organization: the states of the ion channels should directly drive the process of self-modification.

In other words, each term in the learning rule

$$\Delta g_i = \eta(t) \Bigl\langle \frac{\delta}{\delta V(t)... ...(\langle V \rangle) \, m_i h_i (E_i - V) \Bigr\rangle\tag{3}$$ (3)

should be directly related to the occupancy of ion channel states and the transitions between these channel states.

Voltage-dependent ion channels have at least two states, or configurations of the ion channel protein. In general, ion channel proteins will go through several intermediate, meta-stable states en route from the more stable open, closed, or inactive states. Suppose that specific states of the ion channel can interact with second messengers, such as G-proteins, to elicit a cascade leading eventually to gene expression of the channel protein and a change in the channel density. Alternatively, imagine that the channel is subject to modification (e.g., by being phosphorylated) only when it passes through a particular state, as illustrated in the cartoon schematic of fig. 10.
 
 

 

Figure 10: An ion channel passes through several short-lived meta-stable states in switching between closed open states, indicated by asterisks in the diagram below. We hypothesize that channel modification depends on the ion channel protein being in particular states, since interaction with kinases and G-proteins is governed by the three-dimensional ion channel protein configuration.

 

 

Under this scheme, the rate of ion channel modification is directly proportional to the occupancy of particular ion channel states. For each class of ion channels in the model neuron, the conductance fraction $\langle m_i h_i \rangle$ in eq. 3 reflects the average number of ion channels that are in the open state. But even at steady state, individual channels will make frequent transitions between open and closed states. The rate at which channels make these transitions is reflected in the occupancy of the intermediate states and will be shown below to be proportional to

$$\frac{\delta}{\delta V(t)} \langle m_i h_i \rangle$$ in simple biophysical models of ion channels.
 

3/7/1998