Model Overview
Our model will apply a modified form of the Hodgkin-Huxley equations. We plan to quantitatively examine the effect of increased chlorine conductance on the action potential due to the presence of alcohol. We begin with the following equations
α is the rate at which channels go from closed to open, and β is the rate at which channels go from open to close. m is the proportion of sodium activation gates in the open state, n refers to the potassium gates, and h refers to the sodium inactivation gates. The last equation incorporates the time-dependent voltage and expresses the total ionic flow.
Cm is membrane capacitance, g is the conductance to a specific ion, and Iapp is the applied current. L refers to the leak channels, which includes chlorine. We see that our model will examine a change in gL as alcohol concentration increases. MATLAB will be used to generate plots of membrane voltage over time as gL is increased.
The following plots show the response of a system to varying values of the chloride conductance in a Hodgkin Huxley approximation of cell membrane response to an action potential. We chose values of g = 0.1, 1.0, 1.5, 1.65, 1.698, and 1.70 V/m^2. No noticeable change in membrane voltage occurred until g = 1.0. Between g = 1.0 and 1.7, the magnitude of the action potential decreased until depolarization did not reach the threshold for an action potential to occur. Based on this simulation, g = 1.689 was the largest value for an action potential to still form.
The following plots show the response of a system to varying values of the chloride conductance in a Hodgkin Huxley approximation of cell membrane response to an action potential. We chose values of g = 0.1, 1.0, 1.5, 1.65, 1.698, and 1.70 V/m^2. No noticeable change in membrane voltage occurred until g = 1.0. Between g = 1.0 and 1.7, the magnitude of the action potential decreased until depolarization did not reach the threshold for an action potential to occur. Based on this simulation, g = 1.689 was the largest value for an action potential to still form.
Figure 10: g = 0.1 V/m^2. Normal physiological conductance level, resulting in a depolarization the cell to 40 mV
Figure 11: g = 1.0 V/m^2. First noticeable decrease in depolarization level following an action potential.
Figure 12: g = 1.5 V/m^2. The strength of the action potential continues to decrease.
Figure 13: g = 1.65 V/m^2
Figure 14: g = 1.689 V/m^2. The conductance reaches a critical value for action potential formation.
Figure 15: g = 1.70 V/m^2. The membrane voltage does not reach the threshold to produce an action potential.
