Modelling the molecular basis of cardiac repolarization

Abstract

Aims

To study the properties of ion-channel gating ( I_Ks , the slow delayed rectifier K ⁺ channel) that underlie the channel's participation in rate-dependent repolarization of the cardiac action potential (AP).

Methods

Computational biology approach was used to simulate the channel gating and the AP of a mammalian ventricular myocyte.

Results

At fast rate, channels accumulate at closed state near the open state, from which they can rapidly open to generate large repolarizing current late during the AP, effectively shortening its duration.

Conclusion

I_Ks builds an ‘available reserve’ of channels that can open ‘on-demand’ to repolarize the AP and shorten its duration at fast rate (‘rate-adaptation’). This property also makes I_Ks effective in providing repolarization reserve when other repolarizing currents are compromised by disease or drugs.

Introduction

Unlike the normal action potential (AP) depolarization, which is dominated by a single type of ion channel (the sodium channel), AP repolarization is determined by a delicate balance between inward and outward currents carried by a variety of ion channels. This multi-current mechanism provides for precise control of the AP duration (APD) and its rate dependence (adaptation). The balance of currents is determined by the gating kinetic properties of ion channels that participate in the repolarization process. Therefore, it is important to study the molecular gating processes of repolarizing currents during the AP. Moreover, abnormal AP repolarization underlies various cardiac arrhythmias (hereditary and acquired), which adds important clinical relevance and motivation for such studies. ¹

This conference article summarizes the previously published work that utilized a computational biology approach to gain insight into the molecular mechanisms of repolarization. Details can be found in the original publications. ^{2 , 3}

Methods

Markov models of ion-channel kinetics were developed for the sodium current ( I_Na ), ^{4 , 5} L-type calcium current ( I_Ca(L) ), ⁶ the rapid delayed rectifier potassium current ( I_Kr ), ^{2 , 7} and the slow delayed rectifier potassium current ( I_Ks ). ^{2 , 3} By inserting these models into detailed, integrated models of the cardiac ventricular myocyte, ^{3 , 4} the role of each channel in shaping the AP can be determined. Moreover, in the Markovian scheme, the gating transitions between kinetic states of the channel during the AP can be obtained. In this paper, we focus on I_Ks and its molecular transitions during gating. The I_Ks model was incorporated into the Luo-Rudy dynamic model (LRd) of a mammalian ventricular cell ^{8 , 9} (available in the research section of http://www.rudylab.wustl.edu ). Prior to stimulation at various pacing rates, cells were kept quiescent for 10 min to achieve steady-state resting conditions before all pacing protocols.

Results

Markov model of I_Ks

Like other cardiac K ⁺ channels, I_Ks has a tetrameric structure with four identical α-subunits (KCNQ1), each with six transmembrane-spanning segments. ¹⁰ In addition, a β–subunit (KCNE1) is incorporated in the channel assembly. The S4 segment of each α-subunit is positively charged and serves as the voltage sensor of the channel. Upon depolarization, all four voltage sensors move in response to the changing electric field, causing the channel to open. It has been shown that each voltage sensor undergoes at least two transitions prior to channel opening. ^{11 , 12} Considering all possible combinations of voltage sensors positions (e.g. three at the rest position and one in excited position 1; two at rest, one at excited position 1 and one at excited position 2, etc.) leads to 15 closed states of the channel prior to opening. This provides the basis for the Markov I_Ks model in Figure  1 A . The model contains 15 closed states (C ₁ to C ₁₅ ) and two open states (O ₁ and O ₂ ). The closed states are divided into two zones: Zone 2 (green) contains channels for which at least one subunit is still in its rest position and has to make a first transition to state 1; Zone 1 (blue) contains channels with voltage sensors that have already made the first transition and only need to make the second transition into state 2. The first voltage-sensor transition (left to right in the diagram of Figure  1 A ) is slow (transition rate α = 4.4 s ⁻¹ ), whereas the second transition (top to bottom) is fast ( γ = 44.7 s ⁻¹ ). These kinetic properties are the basis for the effectiveness of I_Ks as a repolarizing current and as a determinant of APD and its rate dependence.

Kinetic transitions of I_Ks during the action potential

Figure  1 B shows the AP and I_Ks current (top) and channel-state occupancy (bottom) during pacing at slow rate [cycle length (CL) = 1000 ms]. Figure  1 C provides similar information for fast pacing (CL = 300 ms). At the fast rate, I_Ks increases faster during the AP and reaches a higher peak magnitude than at slow rate. The larger I_Ks acts to shorten APD at fast rate, a phenomenon called APD adaptation (compare Figure  1 B and Figure  1 C ). At the slow rate, 60% of channels reside in Zone 2 before AP depolarization ( Figure  1 B , bottom) and must make a slow transition to Zone 1 before opening. At this rate, only 40% of channels reside in Zone 1 before the AP onset, from which they can quickly transition to the open state. In contrast ( Figure  1 C , bottom), at the fast rate, nearly 75% of channels accumulate in Zone 1 before AP depolarization. This facilitates fast channel openings and rapid rise of I_Ks during the AP (note the correspondence of the I_Ks curves in the upper panels to the open-state occupancy curves in the lower panels). Thus, at fast rate, channels accumulate between beats in Zone 1, creating an ‘available reserve’ of channels that can open rapidly and generate a large current which shortens APD.

Discussion

The simulations presented here demonstrate the intimate link between an ion-channel molecular structure that determines its gating properties and its function during the AP. As a result of two-stage voltage sensor activation, I_Ks channels accumulate at fast rate in Zone 1 of closed states that are close to the open state. At fast rate, there is not sufficient time between APs for channels to transition back to Zone 2 before the next AP. Traditionally, it has been accepted that increased repolarizing current, at fast rate, results from channel accumulation in the open state. I_Ks provides a greater current at fast rate by building an available reserve in closed (not open) states from which channels can open rapidly, ‘on demand’. This behaviour has been confirmed by AP-clamp experiments ¹³ showing a rapid increase in I_Ks at fast rate, but no instantaneous current (indicating no open-state accumulation) at AP initiation. This mechanism makes I_Ks a very effective repolarizing current, because it promotes channel openings during the late plateau and repolarization phase of the AP, when its influence on the membrane potential is greatest ( Figure  1 ). As a consequence, I_Ks can provide effective ‘repolarization reserve’ when other repolarizing currents (e.g. I_Kr ) are reduced by mutations that cause the long QT syndrome or by drugs. An example of this property was discussed previously (Silva and Rudy ² , Figure 7), where I_Ks eliminated arrhythmogenic after depolarizations in the presence of I_Kr block.

Conflict of interest : none declared.

Funding

National Institutes of Health (RO1-HL49 054, R37-HL33 343) to Y.R.

References