K+ fluxes differ in several important aspects. First, they are opposite in sign for most values of membrane potential: The Na+ flux depolarizes the neuron, whereas the K+ flux hyperpolarizes the cell. Second, the Na + flux turns on ("activates") much more quickly than the K+ flux. Third, the Na+ flux turns off ("inactivates") after a brief period of depolarization. In contrast, the K + conductance remains activated in response to a prolonged depolarizing stimulus.

A watershed event in the history of neuroscience was the development by Hodgkin and Huxley of a relatively simple mathematical model, derived from voltage-clamp studies of the giant axon of the squid, that accounts for the generation and propagation of the action potential. The Hodgkin-Huxley model describes the membrane as an electrical circuit (Fig.

4a) that includes descriptions of membrane capacitance Cm; voltage-gated, Na + - and K + -selective conductances (GNa and GK, respectively), each in series with a battery representing the appropriate equilibrium potential; and a constant "leak" conductance that passes more than one ion. Mathematically, the Hodgkin-Huxley model includes four differential equations, which describe how the derivatives of membrane potential and three "gating variables" (variables that range between 0 and 1 and determine the values of voltage-gated conductances) behave. Two time- and voltage-dependent gating variables determine the size of the Na+ conductance: The m gate captures the rapid activation of the Na+ conductance after a step depolarization, whereas the h gate describes the slower inactivation process by which the

Figure 4 The Hodgkin-Huxley model of voltage-gated Na+ and K+ conductances. (a) Electrical circuit representation of the Hodgkin-Huxley model of squid giant axon under space-clamped conditions. (b-d) Responses of the Hodgkin-Huxley gating variables to a voltage-clamp step from Vhold = —90mV to Vclamp = 0mV. The m and h gates determine the value of GNapm3h. The n gate determines the value of GKpn4. (e) Steady-state values of m, h, and n for the entire physiologically relevant range of membrane potential Vm. (f)Time constants describing how quickly the gating variables m, h, and n reach their steady-state values, plotted vs Vm. Note the log scale on the y-axis.

Figure 4 The Hodgkin-Huxley model of voltage-gated Na+ and K+ conductances. (a) Electrical circuit representation of the Hodgkin-Huxley model of squid giant axon under space-clamped conditions. (b-d) Responses of the Hodgkin-Huxley gating variables to a voltage-clamp step from Vhold = —90mV to Vclamp = 0mV. The m and h gates determine the value of GNapm3h. The n gate determines the value of GKpn4. (e) Steady-state values of m, h, and n for the entire physiologically relevant range of membrane potential Vm. (f)Time constants describing how quickly the gating variables m, h, and n reach their steady-state values, plotted vs Vm. Note the log scale on the y-axis.

Table I

Definitions and Units of Mathematical Symbols

Table I

Definitions and Units of Mathematical Symbols

Was this article helpful?

Everything you ever wanted to know about. We have been discussing depression and anxiety and how different information that is out on the market only seems to target one particular cure for these two common conditions that seem to walk hand in hand.

## Post a comment