Tabak et al. (2007), Dopamine
December 2007, model of the month by Lu Li
Original model: BIOMD0000000138
It is well known that dopamine (DA), through D2 receptors, tonically inhibits the prolactin secretion by pituitary lactotrophs . This is because D2 receptor activation can induce membrane hyperpolarisation by opening potassium channels, which in turn prevents action potential and associated Ca2+ influx, thus reducing the intracellular concentration of Ca2+ and hormone secretion . In contrast, low concentrations of dopamine have been found to stimulate the release of prolactin [3,4]. However, the underlying mechanism remains unexplained.
An earlier study  showed that the large-conductance calcium-activated K+ current (BK) increases hormone release by changing the spiking pattern during an action potential. This transformation of spiking waveform increases Ca2+ entry into the cells, thus increasing the release of prolactin. Although this induced K+ current is very brief, it effectively reduces the activation of the delayed rectifier (DR) K+ channel that is primarily responsible for terminating the action potential.
There are two types of fast K+ current whose conductances can be increased by DA, one is through BK channels, the other through inactivating A-type K+ channels [6,7].
Thus, putting the above all together, the questions are: (1) If low concentrations of DA can increase the conductance of either BK channels or A-type K+ channels, will these additional currents change the spiking pattern of the membrane potential, increase Ca concentration, and raise the hormone secretion? (2) if so, will the effects of these two types of K+ current be mediated via the same mechanism?
In order to answer these questions, Tabak et al.  set up a minimal electrophysiological model of a lactotroph (BIOMD0000000138). At the beginning, the membrane potential is only controlled by three voltage-gated currents, a Ca2+ current, a delayed-rectifier K+ current and a slow, Ca2+-activated K+ current. Then, the effect of a low dose of DA is simulated by adding current from either the BK channel or the A-type K+ channel.
Simulation results showed that the addition of either type of K+ current could convert membrane potential from spiking into bursting. However, this patterning change is not sufficient to increase the average Ca2+ concentration in the cell. Additionally, the BK channel and the A-type K+ channel transform spiking patterns through distinct mechanisms.
Figure 1: Effect of the conductance of BK channels (gBK) on intracellular Ca2+ concentration ([Ca]) and prolactin release (PRL). Figure taken from 
Figure 2: Effect of the conductance of A-type K+ channels (gA) on intracelluar Ca2+ concentration ([Ca]) and prolactin release (PRL). Figure taken from 
As shown in Figure 1, by increasing the conductance of BK channels, the membrane potential is finally converted from spiking into bursting, Ca2+ concentration is increased, and the release of prolactin is greatly raised. On the other hand, although the raise of conductance of A-type K+ channels does change the pattern of membrane potential, when the conductance is raised to a certain level, this bursting pattern is eventually associated with decreased Ca2+ levels, as shown in Figure 2.
Tabak et al. further investigated how the two channels could trigger the same spiking pattern but distinct Ca2+ levels. Phase plane analysis, regarding calcium concentration as constant at each steady state, illustrated that the higher conductance of BK channels produces a region of bistability (Figure 3). However, since ionic permeability and membrane potential closely affect each other, what we actually observe are periodic changes of the membrane potential with slow variation in Ca2+ concentration, where the system switches between low and high steady state. Since this periodic orbit can be found further to the right of the [Ca2+] axis than in the low conductance case, the average Ca2+ concentration is increased.
Figure 3: Phase plane analysis of BK channel current. V denotes membrane potential; [Ca], the intracellular Ca2+ concentration; gBK, the conductance of BK channels. In all panels, the z-shaped curves indicate the steady state of the system when Ca2+ is treated as constant and the ε-shaped curves indicate the minimum and maximum of the periodic orbit. Figure taken from 
In the case of A-type K+ channels, bursting pattern appears even for moderate conductance (Figure 4, middle panel). However this bursting pattern is not associated with bistability, and the range of Ca2+ concentrations covered remains the same. When the conductance of A-type K+ channel is increased to a certain level (Figure 4, right panel), although there is a region of the bistability, the periodic orbits moves, to the left of the [Ca2+] axis, rather than to the right. Thus, the average Ca2+ concentration is decreased.
Figure 4: Phase plane analysis of A-type K+ channel current. V denotes membrane potential; [Ca], the intracellular Ca2+ concentration; gA, the conductance of A-type K+ channel. In all panels, the z-shaped curves indicate the steady state of the system when Ca2+ is treated as constant and the ε- shaped curves indicate the minimum and maximum of periodic orbits. Figure taken from 
To summarise, with this computational model Tabak et al. provided support for the notion that the fast K+ current, which is triggered by low doses of DA might be the underlying reason for the stimulatory effect on prolactin secretion. Increasing the conductance of BK channels always results in an increase of Ca2+ concentration and thus hormone secretion, while this is not always the case when the conductance of A-type K+ channels is increased. Thus, transforming spiking patterns into bursting is necessary, but not sufficient, for the stimulatory effect of DA.
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