In a simple model, the Na+ and K+ ions are considered to flow through ion channels where a series of gates determine the conductance of the ion channel. The macroscopic conductances of the Hodgkin & Huxley model arise from the combined effects of a large number of microscopic ion channels embedded in the membrane. Each individual ion channel can be thought of as containing one or more physical gates that regulate the flow of ions through the channel. The variation in g values is determined by the set of gate variables n, m and h. The of the conductance depends upon the membrane voltage V because the values of n, m and h depend on time, their previous value at an earlier time and the membrane voltage. The rates of change of the gate variables are (12) where the the and are rate constants ’s ’s rate of closed gates opening rate of open gates closing fraction of gates opening per second fraction of closing per second If the membrane voltage is clamped at some value V, then values of the gate variables n, m and h will reach a steady state value n, m and h x n or m or h and the steady state (equilibrium) value is given by (13) If at time t = 0, x(0) = x0, then a solution of equation (12) is (14) the time x constant for the evolution of x is (15) The K+ channel is controlled by 4n activation gates (16) The Na+ channel is controlled by 3m activation gates and 1h inactivation gate
In a simple model, the Na+ and K+ ions are considered to flow through ion channels where a series of gates determine the conductance of the ion channel. The macroscopic conductances of the Hodgkin & Huxley model arise from the combined effects of a large number of microscopic ion channels embedded in the membrane. Each individual ion channel can be thought of as containing one or more physical gates that regulate the flow of ions through the channel. The variation in g values is determined by the set of gate variables n, m and h. The of the conductance depends upon the membrane voltage V because the values of n, m and h depend on time, their previous value at an earlier time and the membrane voltage. The rates of change of the gate variables are (12) where the the ’s and ’s are rate constants rate of closed gates opening rate of open gates closing fraction of gates opening per second fraction of closing per second If the membrane voltage is clamped at some value V, then values of the gate variables n, m and h will reach a steady state value n, m and h x n or m or h and the steady state (equilibrium) value is given by (13) If at time t = 0, x(0) = x0, then a solution of equation (12) is (14) the time x constant for the evolution of x is (15) The K+ channel is controlled by 4n activation gates (16) The Na+ channel is controlled by 3m activation gates and 1h inactivation gate
bp_HH_01.docx