Calcium-activated SK channels control firing regularity by modulating sodium channel availability in midbrain dopamine neurons

Abstract

Dopamine neurons in the substantia nigra pars compacta and ventral tegmental area regulate behaviours such as reward-related learning, and motor control. Dysfunction of these neurons is implicated in Schizophrenia, addiction to drugs, and Parkinson's disease. While some dopamine neurons fire single spikes at regular intervals, others fire irregular single spikes interspersed with bursts. Pharmacological inhibition of calcium-activated potassium (SK) channels increases the variability in their firing pattern, sometimes also increasing the number of spikes fired in bursts, indicating that SK channels play an important role in maintaining dopamine neuron firing regularity and burst firing. However, the exact mechanisms underlying these effects are still unclear. Here, we develop a biophysical model of a dopamine neuron incorporating ion channel stochasticity that enabled the analysis of availability of ion channels in multiple states during spiking. We find that decreased firing regularity is primarily due to a significant decrease in the AHP that in turn resulted in a reduction in the fraction of available voltage-gated sodium channels due to insufficient recovery from inactivation. Our model further predicts that inhibition of SK channels results in a depolarisation of action potential threshold along with an increase in its variability.

Figure 1

Dopamine neuron model. (A) A single spherical compartment of diameter 10 μm and capacitance 1 μF represents the dopamine neuron soma. It is incorporated with those ionic conductances known to be sufficient to reproduce the basic electrophysiological features associated with these neurons, such as the Na (sodium channel) and K (delayed rectifier potassium channel) that regulate the generation and repolarisation of the action potential respectively; the A (A-type potassium channel) that helps maintain firing frequency; CaL (L-type calcium channel) that provides the bulk of intracellular calcium; SK (calcium-activated potassium channel of the SK type) that maintains firing regularity. (B) The Hodgkin-Huxley style equivalent electrical circuit for the model schematic in (A). The sodium and delayed rectifier potassium channels are modelled as stochastic, keeping all other ion channels deterministic. The neuronal membrane is considered as a capacitor with capacitance C_M and with ion channels in parallel to each other. E_ion is the electromotive force that represents the reversal potential of the respective ion channel, I_ion represents the current flowing through them, and Ca is the intracellular calcium ion concentration. (C,D) Markov gating schemes for sodium and potassium channels respectively. Each sodium channel can exist in one of activated/open, inactivated or closed states while each potassium channel can either be open or closed.

Figure 2

Spontaneous spike train and action potential characteristics obtained from simulations. (A) The in silico dopamine neuron fired spontaneously at a rate of 3.6 Hz and the CV of ISIs is equal to 0.13. The spike train was characterised by slow depolarisation preceding the spike, followed by a pronounced post-spike AHP. (B) Average action potential waveforms obtained from the model superimposed with those obtained from the SNc and VTA. The average waveforms were aligned at the point of maximum rate of rise. (Experimental waveforms adapted from ref. 55).

Figure 3

Effects of simulated inhibition of ion channels regulating spontaneous firing in the model dopamine neuron. (A) Under control conditions the in silico neuron fired spontaneously at a rate of 3.6 Hz (left). (B) When the maximal conductance of A-type potassium channels is reduced by 50% from 4 mS/cm² to 2 mS/cm² we observed a 1.8% increase in firing rate. As we can see from the ISI histogram, there was no change in the CV of ISI, indicating that A-type channels are involved in regulating firing rate and not firing regularity. (C) When the L-type calcium channel was inhibited by reducing the maximal conductance from 15 mS/cm² to 5 mS/cm² there was a marked decrease in firing regularity as can be seen from the spike train (left) and the ISI histogram. The CV of ISI increased from 0.13 to 0.35, which is a similar increase observed during SK channel inhibition. (D) Simulating a sodium channel block resulted in a cessation of firing indicating that sodium channels are essential for spike production.

Figure 4

Simulated inhibition of SK channels decreases firing regularity and increases firing rate. (A) The model dopamine neuron fired spontaneously at a slow and rhythmic rate of 3.6 Hz (left) with CV of ISI = 0.13 (right). (B) Simulated SK channel inhibition resulted in a decrease in the firing regularity (left) and the CV of ISI increased to 0.32 (right). (C) This was accompanied by a decrease in the AHP of the action potential (top), quantified by a significant decrease in peak AHP (bottom). (D) Somatic currents prominent during the ISI. Error bars represent mean ± S.E.M, not visible due to small errors.

Figure 5

SK channel inhibition causes a decrease in rate of rise in membrane voltage. Phase-plane plot showed a clear reduction in rate of change in membrane voltage during a simulated SK channel inhibition (red) compared to control (black). (B) This was quantified by a significant decrease in the maximum value of rate of rise of membrane voltage, which is indicative of sodium channel unavailability. Error bars indicate mean ± S.E.M, not visible due to small errors.

Figure 6

Action potential threshold depolarises and becomes more variable with simulated SK channel inhibition. (A,B) When SK channels were inhibited in the model, action potential threshold depolarised and became more variable (B) compared to control (A). The red and black dots indicate spike threshold. (C) Quantification of depolarisation in spike threshold as an effect of SK channel block in the model. Error bars represent mean ± S.E.M, not visible due to small errors.

Figure 7

Failure of recovery from inactivation of sodium channels underlies decrease in firing regularity with SK channel inhibition. Shows the availability of sodium channels (ii–iv) during the course of the action potential (i). The number of sodium channels open increased steadily with depolarisation (ii) following the start of the action potential. This was accompanied by a steady increase in the number of inactivated channels (iii). While the number of open channels went back to zero as soon as the action potential had passed, there was a significant difference between the number of channels that remained in the inactivated state (iii). As the channels recovered from inactivation, they became closed (iv); however once again, a large number of channels failed to go into the closed state because they remained inactivated. Shaded region in (A) represents standard deviation around the mean. (B) Although we cannot see a reduction in the number of open channels during the peak of the action potential, there is a small yet statistically significant reduction in the number of open channels during the spike. (C) The reduction in recovery from inactivation is explained by the reduction in the h parameter of sodium channels inactivation dynamics. h was calculated at minimum membrane voltage attained after spike. Error bars represent mean ± S.E.M, not visible due to small errors.

Figure 8

Method for calculation of action potential threshold. Action potential is calculated as the voltage corresponding to the maximum value of the third derivative of the membrane potential.