Difference between revisions of "DiffEqs"
From Sean_Carver
(→Bilayer Membrane with Na/K Pumps) |
(→Plain Bilayer Membrane) |
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== Plain Bilayer Membrane == | == Plain Bilayer Membrane == | ||
| − | + | Remember the capacitor equation: | |
<math> C \frac{dV(t)}{dt} = I(t) </math> | <math> C \frac{dV(t)}{dt} = I(t) </math> | ||
| Line 7: | Line 7: | ||
<math> V(0) = 0 </math> | <math> V(0) = 0 </math> | ||
| − | Here ''C'' is a constant (parameter) | + | Here ''C'' is a constant (a parameter): the ''capacitance'' of the membrane. |
| − | Next ''V(t)'' is the membrane potential. | + | Next ''V(t)'' is the membrane potential. Typically ''V(t)'' is the quantity of interest -- and it is the quantity that is usually measure. |
| − | Next ''I(t)'' is the | + | Next ''I(t)'' is the capacitive current into the cell. The capacitive current involves the ionic currents into the cell as well as the injected current. For a plain lipid bilayer, it is just the injected current. |
| − | Finally ''V(0)'' is the initial membrane potential of the cell. | + | Finally ''V(0)'' is the initial membrane potential of the cell, the constant of integration required for a definite solution to the equation. |
| + | |||
| + | We can solve this equation | ||
| + | |||
| + | <math> V(t) = V(0) + \frac{1}{C} \int_0^t I(s) ds </math> | ||
== Bilayer Membrane with Na/K Pumps == | == Bilayer Membrane with Na/K Pumps == | ||
Revision as of 22:20, 10 February 2009
Contents
Plain Bilayer Membrane
Remember the capacitor equation:
Here C is a constant (a parameter): the capacitance of the membrane.
Next V(t) is the membrane potential. Typically V(t) is the quantity of interest -- and it is the quantity that is usually measure.
Next I(t) is the capacitive current into the cell. The capacitive current involves the ionic currents into the cell as well as the injected current. For a plain lipid bilayer, it is just the injected current.
Finally V(0) is the initial membrane potential of the cell, the constant of integration required for a definite solution to the equation.
We can solve this equation
Bilayer Membrane with Na/K Pumps
Same, except that the initial condition is different.
