Exemplary Results Draft 2

Author: Catherine Osborn

Results

Replicating Figure 1

We first ran the model using the given initial conditions with an injected current of 1 nA for 1 ms. Upon providing this injection, the shape of the output was not that of an action potential (Figure 1). We decided to examine the voltage of the hypoglossal motoneuron without providing an injection. We found that the voltage was not stable with the given initial conditions. Without stimulating the cell, we examined all of the state variables individually to determine the time at which all were stable. This point occurred when time was equal to 6000 ms. We solved all of the state variables at this time point and used those values as the new initial conditions. These new initial conditions are shown in Table 1.

Figure 1. Action potential simulation after injection of 1 nA for 1 ms using the provided initial condition.

Table 2: Initial Conditions
V[0] = -71.630 mV
mNa[0] = 0.015
hNa[0] = 0.981
mNaP[0] = 0.0025
hNaP[0] = 0.790
n[0] = 0.159
mT[0] = 0.0012
hT[0] = 0.554
mP[0] = 1.235 x 10-8
mN[0] = 0.00097
hN[0] = 0.633,
zSK[0] = 0.002
mA[0] = 0.0579
hA[0] = 0.318
mH[0] = 0.176
[Ca+2]i[0] = 0.000135

When we reran the model with the new initial conditions for the state variables, the output was the same as Figure 1 from Purvis and Butera (Figure 2). The action potential we produced is shown in Figure 3. The stimulus is required to elicit an action potential in the hypoglossal motor neuron. When the stimulus is detected, sodium channels are opened (I_Na and I_NaP are activated), allowing for a rush of sodium into the cell and a rapid depolarization (the upward climb of the action potential spike). The repolarization is caused by sodium current inactivation and activation of the potassium currents (I_K and I_A), which causes potassium ions to rush out of the cell (the descent of the action potential spike). Both figures display the fast after-hyperpolarization period (fAHP), the the slight after-depolarization peak (ADP), and the medium duration after-hyperpolarization period (mAHP). The fAHP is caused by the I_Na, I_NaP, I_K, I_A, and the calcium currents (I_N, I_T, and I_P). The large depolarization produced by the sodium currents activates the calcium currents. These inward currents cause calcium to rush into the motoneuron and depolarize the membrane after the cell has repolarized, which leads to the ADP. The mAHP is attributed to the calcium-dependent potassium current I_SK. The buildup of internal calcium caused by the inward calcium currents activated during the action potential activates the outward SK current. The SK current in the model does not show inactivation, so it remains activated until the internal calcium concentration is decreased.

Purvis and Butera Results	Our Results
Figure 2. Purvis ad Butera. Action potential after stimulation of 1 nA for 1 ms.	Figure 3. Group Simulation. Action potential after 1 nA for 1 ms pulse.

Replicating Figure 2

Figure 2 in Purvis and Butera (2005) shows the change in current over time during an action potential (stimulated by an injection of current of 1 nA for 1 ms) for all of the different channels except I_H (Figure 4). We were able to replicate these figures by plotting the change in I_ionic for each of the different currents (Figure 5). Figure 4A shows the activation of the sodium currents of a 2 ms time scale. Again, sodium rushes into the cell, resulting in depolarization, and the current is then inactivated. Figure 4B shows the changes in inward calcium flow for each of the specific calcium currents. The flow of calcium into the cell occurs over a 20 ms period -- much slower than the influx of sodium ions. The blue line represents the total calcium current (I_Ca = I_P+I_T+I_N). Figure 4C shows the changes in the outward flow of potassium currents. These currents are activated quickly like the sodium currents. The leak current (as shown in Figure 2C) makes only minor changes in current conductance during the action potential when compared to the other two voltage dependent potassium currents. Figure 4D depicts the I_SK current. This current is only activated after the calcium currents are activated and remains active throughout the mAHP.

Purvis and Butera Results	Our Results
Figure 4. Purvis and Butera. Ionic currents during an action potential	Figure 5, A and C. A) Sodium currents. INa is blue, INaP is red. C) Potassium currents. IK is blue, IA is red, Ileak is green.	Figure 5, B and D. B) Calcium currents. ICa is blue, IT is green, IN is red, and IP is orange. D) Calcium-dependent potassium current, ISK.

Replicating Figure 3

Figure 3 from Purvis and Butera (Figure 6) looks at how the ADP is both calcium- (Figure 6A) and voltage-dependent (Figure 6B). We were able to recreate this with varying levels of success. Our calcium-dependent comparison of the ADP (Figure 7A) was produced by varying the g_T parameter. The red line is when g_T = 0.15 μS, the green line is when g_T = 0.125 μS, and the blue line is when g_T = 0.1 μS. Increasing the g_T parameter raises the amplitude of the ADP.

Our Figure 7B was an attempt to recreate Figure 3B from Purvis and Butera (Figure 6B). As In their paper, we gave pre-pulses of 0 nA (blue line), -0.1 nA (green line), or -0.2nA (red line) to hyperpolarize the cell to -72 mV, -75 mV, or -78 mV respectively. At these voltages, we stimulated the cell with a current of 1 nA for 1 ms. Purvis and Butera superimposed the graphs so as to only compare the change in amplitude from the starting voltage (-72 mV, -75 mV, or -78 mV), to the ADP by making the beginnings of the action potentials appear as if they all start at the same voltage and the ADP occur at different voltages. We have chosen to show these voltage-dependent ADP comparisons differently. Figure 7B shows that the traces start at 0 ms with an initial voltage of about -72 mV and, in the case of the -0.1 nA and -0.2 nA pre-pulses, hyperpolarize the cell for 5 ms before the action potential was stimulated. Because the cell voltage when this action potential was stimulated varies between the trials, and the ADP appears to occur at the same voltages, one can see that the starting voltage-to-ADP amplitude increased as the cell was hyperpolarized.

Figure 6. Purvis and Butera Results	Figure 7. Our Results
Figure 6. A) Calcium-Dependent ADP. B) Voltage-Dependent ADP.	Figure 7. A) Calcium-Dependent ADP. gT = 0.15 μS (red), gT = 0.125 μS (green), and gT = 0.1 μS (blue). B) Voltage-Dependent ADP. Pre-pulses: 0 nA (blue), -0.1 nA (green), and -0.2nA (red).

Replicating Figure 4

Figure 4 from Purvis and Butera (Figure 8) demonstrates the effects of removing the SK channel from the voltage equation for both single pulse (Figure 8A) and a held pulse (Figure 8B). To block the SK channels, thus replicating the effects of treating the motoneuron with apamin, we removed the SK current by setting g_SK to 0. We were able to replicate these results in Figure 9. As seen in Figure 9A. Removing the I_SK during a single pulse removes the mAHP caused by the outward-flow of potassium ions which further depolarize the cell. Figure 9B shows that at a decreased conductance (g_SK= 0.03 μS) during a held pulse, there are no mAHP produced and the action potentials decrease in frequency (adaptation).

Figure 8. Purvis and Butera Results	Figure 9. Our Results
Figure 8. A) Comparison of action potential from single 1.0 nA pulse when gSK = 0 (dotted) or gSK = 0.3 μS (bold). B) Held 0.33 nA current when gSK = 0.03 μS.	Figure 9. A) Comparison of action potential from single 1.0 nA pulse when gSK = 0 (red) or gSK = 0.3 μS (blue). B) Held 0.33 nA current when gSK = 0.03 μS.

Replicating Figure 5

Figure 5 from Purvis and Butera shows the results of stimulation with a held current of 0.22 nA (Figure 10). This stimulation current is near the threshold for firing action potentials. We can see that adaptation of firing frequency occurs during the stimulation and eventually the motoneuron ceases to fire (Figure 10A). Figure 10B shows a close-up view of the first action potential. This peak displays a delayed-excitation period before firing begins. We were able to replicate these results (Figure 11).

Figure 10. Purvis and Butera Results	Figure 11. Our Results
Figure 10. A) Action potentials stimulated by 2500 ms of 0.22 nA current. B) Close up showing delayed excitation before the first peak.	Figure 11. A) Action potentials stimulated by 2500 ms of 0.22 nA current. B) Close up showing delayed excitation before the first peak.

Replicating Figure 6

Purvis and Butera went on to examine how stimuli above threshold may result in adaption ('Figure 12). Figure 12A shows action potentials from a 250-ms held current of 2.0 nA. Adaptation is visible between the first and second peaks. When we attempted to replicate this figure (Figure 13) using the given parameters, we found that the second spike was appeared to be barely more than a large ADP. Using manipulate, we determined that higher values of the stimulus (I_stim = 2.23 in Figure 13A) would yield what appeared to be a second action potential. There was no mention that any other parameters were changed, however, we manipulated the value of g_T to produce the appropriate shape of the second action potential. Only at values of g_T below 0.05 was the second action potential peak greater than 0 mV and included a small ADP. Smaller values of g_T are associated with greater levels of adaptation of firing. Figure 13A shows our recreation of Figure 6A (Figure 12A) when I_stim = 2.23 nA and g_T = 0.04 μS. Reasons for this discrepancy will be explored in the Discussion section.

Purvis and Butera Results	Our Results
Figure 12. Purvis ad Butera. Istim = 2.0 nA for 250 ms. gT = 0.1.	Figure 13. Group Stimulation. Istim = 2.23 nA for 250 ms. gT = 0.04.

Replicating Figure 8

The biological hypothesis of this model was to explore whether the age-dependent changes seen in the rats could be attributed to varying the densities of g_T and g_N to account for the switch from an adapting to an accelerating firing pattern of action potentials. Purvis and Butera calculated the interspike intervals between the first and second, and then the second and third action potentials. When the second ISI is higher than the first ISI, that means that the firing pattern is adapting (firing is slowing down). If the first ISI is higher than the second ISI, the firing pattern is accelerating. Purvis and Butera found that varying the g_T parameter resulted in the switch in firing patterns (Figure 14). Our data replicates this finding (Figure 15).

Purvis and Butera Results	Our Results
Figure 14. Purvis ad Butera. Age-dependent changes related to variations in gT and gN.	Figure 15. Group Stimulation. Modulating the gT. The first interspike intervals are red and the second interspike intervals are shown in blue. Calculated during a 1 nA held current.

We anticipate calculating the interspike intervals found g_N and comparing them to the Purvis and Butera figures. These preliminary results suggest that changes in the densities of these currents could be responsible for the changes in firing patterns seen in the transition from neonates to adult rats hypoglossal motoneuron.