Computer Simulation of Action Potentials in Squid Axon - Assignment Example

Analyzing action potentials is important in understanding the mechanisms of signal transmission in nerves. To do this, an experiment using a computer program to study the generation of action potentials using electrical stimuli was conducted. By modifying the strength and duration of stimuli, the changes in the action potential’s latency and strength were observed. During the experiment, it was seen that the latency of the response was dependent on the strength of the stimulus, and not on the duration by which the membrane is exposed to the stimulus. However, in contrast to latency, the strength of the action potential was not modified by either strength or duration of stimulus. As well, it was observed that another stimulus cannot produce an action potential if given immediately after a previous stimulus. This refractory period is caused by the deactivation of voltage-gated Na+ channels and opening of K+ channels, resulting to the return of the membrane potential to its negative state. In conclusion, the action potential, and subsequently the signal transmission based on it, is dependent on the opening and closing of ion channels present along the membrane. INTRODUCTION Action potentials are rapid changes in the membrane potential. In turn, this potential is based upon the differences in concentrations of ions, each of which is charged either negative (anion) or positive (cation), across the membrane. The concentration difference is due to a selectively permeable membrane, which prevents the ions from transferring sides to equalize the number of ions between inside and outside a cell. But why is there a concentration gradient in the first place? The Na+-K+ pumps along the cell membrane force three Na+ outside and two K+ inside the cell. As a result, there is a net deficit of positive ions and a resulting negative potential inside the cell. In a resting state, the membrane potential is -90 millivolts (90 mV). Upon depolarization, the membrane rapidly becomes very permeable to Na+, through its voltage-gated channels, allowing the excess of Na+ to pass through into the cell. As a result, the resting potential is changed to as much as +35 mV. Through repolarization, the resting potential is gained back not long after depolarization, when Na+ voltage-gated channels close and K+ passively diffuse down its concentration gradient through its own voltage-gated channels (Guyton and Hall, 2006). However, entry of Na+ does not immediately cause depolarization. The number of Na+ that enter the cell must be more than the amount of K+ that gets out of the cell since the membrane is more permeable to K+ than Na+. Thus, the sudden change of membrane potential to -65 mV is the said threshold for stimulating the action potential (Guyton and Hall, 2006). Any electrical stimuli above this threshold produce an action potential with the same amount of strength, as stated by the all-or-none concept (Purves et al., 2004). In addition, a new action potential cannot occur unless the membrane is still depolarized. This is because the Na+ voltage-gated channels necessary for depolarization is still deactivated during repolarization. At this point, called the refractory period, no amount of stimulus can initiate action potential (Finkler). Hodgkin and Huxley characterized the voltage-gated channels involved in the generation of action potential. According to these scientists, the Na channels have two gates (the activation and inactivation gates), while K channels only have one. At resting state, the Na+ channels have the activation gate (facing extracellularly) closed while the other gate is opened. At this time the K+ channels are closed as well. When the channels are activated, both the activation and inactivation gates of Na+ channels are opened. Finally, upon repolarization, the inactivation gate is closed, while the other is opened. K+ channels are opened as well. To mathematically describe the effects of such changes on membrane potential, they also provided equations to describe the relationship among Na+ conductance, K+ conductance, and membrane potential after stimulation (Guyton and Hall, 2006). This experiment used a computer program based on the Hogkin and Huxley equations in describing the changes in membrane potential before, during and after electrical stimulation. Its aim is. MATERIALS AND METHODS First, using a computer program, a single electrical stimulus with varying amplitudes, 50, 20, 10, 7, 5, and 2 µA/cm2, was applied for 1 ms onto a cellular membrane. The changes in membrane potential, Na+ conductance and K+ conductance over time were then plotted, and the peak height, amplitude, latency and threshold of the action potential produced at different times after stimulation were determined. Next, the response of the membrane potential was observed when a second stimulus (50 or 100 µA/cm2 for 0.5 ms) was applied 4 or 7 ms after exposure to first stimulus (50 µA/cm2 for 0.5 ms). RESULTS Table 1. The presence (X) or absence (0) of action potential after exposure to varying amounts and duration of stimulus Stimulus strength (µA/cm2) Stimulus duration (ms) 0.1 0.5 1 2 5 50 0 X X X X 20 0 X X X X 10 0 0 X X X 7 0 0 X X X 5 0 0 0 X X 2 0 0 0 0 0 Table 1 shows the presence of action potentials after exposure to varying amounts of stimulus and/or applied for increasing periods of time. No amount of stimulus applied for 0.1 ms was able to induce action potential, while the minimum strength (2 µA/cm2) was unable to stimulate the cellular membrane as well. This indicates that a larger amount stimulus only needs to be applied for less time to stimulate the membrane. In contrast, a smaller amount of stimulus should be applied longer for it to induce an action potential. Table 2. Detailed descriptions of the response to exposure to various stimulus strengths and duration. Observed in the resulting action potential, if any, were peak height (mV), amplitude (mV), latency (ms) and threshold voltage (mV). Absence of action potential is depicted in this table as the rows enclosed in gray cells. Stimulus Response Strength (µA/cm2) Duration (ms) Peak height (mV) Amplitude (mV) Latency (ms) Threshold voltage (mV) 2 0.1 - - - - 0.5 - - - - 1 - - 2.66 -89 2 - - 2.66 -87 5 - - 2.88 -87 5 0.1 - - - - 0.5 - - - - 1 - - - - 2 14 104 2.33 -71 5 15 105 2.2 -78 7 0.1 - - - - 0.5 - - - - 1 12 102 4.18 -69 2 15 105 1.90 -73 5 16 106 1.86 -74 10 0.1 - - - - 0.5 - - - - 1 15 105 1.81 -71` 2 16 106 1.56 -68 5 16 106 1.60 -65 20 0.1 - - - - 0.5 15 105 1.67 -70 1 16 106 0.95 -67 2 17 107 0.85 -72 5 17 107 0.91 -69 50 0.1 - - - - 0.5 15 105 1.63 -89 1 16 106 0.95 -67 2 17 107 0.85 -72 5 17 107 0.72 -76 Graph 1. Observed relationship of stimulus strength (µA/cm2) and response latency measured at different duration of stimulus exposure, using the data from table 2. Absent action potentials (with infinite latency) were not depicted in this graph. Graph 2. Observed relationship of stimulus duration (ms) and response latency measured using different stimulus amplitude (µA/cm2). Absent action potentials (with infinite latency) were not depicted in this graph. Data used for this graph were those summarized in Table 2. Graph 1 shows that the plots of responses from stimuli applied at 3 (green) and 5 ms (purple) merged across all data points, while that of 1 ms merged only upon using a stimulus of 10 µA/cm2 and above. This is better shown using Graph 2, when the plots turn to be somewhat horizontal, especially at duration of 2 ms and above. This might imply that the duration of stimulus application might not affect the latency of the response, especially at greater stimulus strengths. On the other hand, latency seems to decrease with increasing strength of stimulus. However, there might be a limit to this decrease in latency as the plot of 20 µA/cm2 is seen to be almost similar to that of 50 µA/cm2. Thus, the latency of response is more likely a function of stimulus strength rather than duration. Looking at the other characteristics of the action potentials (Table 2), it can be seen that the peak height and amplitude slightly increase while threshold voltage seem to decrease upon raising the stimulus strength or the duration of stimulus applied on the membrane (graph/s not shown). In the experiment using dual stimuli, it was observed that another action potential was generated by a stronger second stimulus at 7 ms delay, but not with 4 ms. DISCUSSION An action potential can be described by many of its characteristics. Initially, one describes its latency, which is defined as the time between the start of the stimulus to the onset of the action potential (http://www.medicine.mcgill.ca/physio/vlab/cap/character.htm). Of course, if there is no stimulus, then latency will turn out to be infinity, as observed in this experiment conducted. Certain characteristics of the stimulus affect the latency of the resulting action potential. As seen in the experiment, the latency is inversely affected by the strength of the stimulus. This is because the strength of the stimulus affects the frequency of the action potential rather than its amplitude (Purves et al., 2004). As well, in accordance to the all-or-none law, which states that the strength of the action potential remains the same regardless of the amplitude of the stimulus used to induce it, what was observed in the experiment as a slight increase in the amplitude of action potential upon using a greater strength or a longer duration of stimulus might have been insignificant (Purves et al., 2004). Thus, it can be said that action potentials always have the same strength and duration, and that they are independent of the strength and duration of stimuli used to induce them (Pearson Education). In the generation of action potential, the depolarization causing the opening of voltage-gated Na+ channels results to the entry of Na+ ions into the cell. The positive charge the ions bring results to further depolarization of the membrane. This positive feedback loop therefore produces a faster the conversion of the initially negative membrane potential to positive that happens in depolarization (Figure 3) (Pearson Education). Graph 3. Positive feedback cycle during the rapid depolarization in the generation of action potential. This positive feedback loop is interrupted by the closing of the voltage-gated Na+ channels by their time-sensitive inactivation gates. As well, the voltage-gated K+ channels open to allow K+ ions to get out of the cell. These two processes decrease the membrane potential, and disrupt the positive feedback loop. This results to repolarization, and hyperpolarization of the membrane (Pearson Education). Immediately after the action potential, which in this experiment is represented at 4 ms after the first stimulus, another action potential was generated because the Na+ channels are inactive and the K+ channels are still open to allow the exit of K+ ions. This period is called the absolute refractory period. Afterwards (at 7 ms after first stimulus), at the relative refractory period, the neuron was able to initiate an action potential, although it needed a stronger stimulus (100 µA/cm2) that can initiate a membrane potential more positive than the threshold to produce an action potential. These refractory periods are important in neurophysiology as they determine the speed of action potential generation and subsequently, signal transmission (Pearson Education). The number of action potentials that a neuron can generate is thus dependent on the amount and types of voltage-gated ions its membrane has. As well, it prevents the stimulation of the initiating membrane and the subsequent backward transmission of signals. This allows the action potential to propagate toward the nerve endings of neurons (Purves et al., 2004) In conclusion, action potentials are generated by stimulus that can initiate membrane potentials greater than the nerve’s threshold. The membrane depolarizes rapidly through the positive feedback loop, until it is interrupted by the deactivation of voltage-gated Na+ channels and opening of K+ channels, resulting to the membrane’s return to its negative potential. These states of the channels prevent the production of another action potential, thus averting the backward propagation of signals along the nerve. The refractory periods also determine the amount of signal certain nerves can generate. REFERENCES Benjamin Cummings. The Action Potential. [online] Available at: [Accessed 31 December 2011]. Finkler, M. S. Lab#6: Neurophysiology Stimulation. [online] Available at: [Accessed 31 December 2011]. Guyton, A. C. and Hall, J. E., 2006. Textbook of Medical Physiology. Philadelphia: Elsevier, Inc. Purves, D. Augustine, G. J., Fitzpatrick, D., Hall, W. C., Lamantia, A., McNamara, J. O., and Williams, S. M. eds., 2004. Neuroscience. Massachusetts: Sinauer. Compound Action Potential. [online] Available at: [Accessed 31 December 2011]. Read More