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.