MarkoLAB: A simulator to study ionic channel's stochastic behavior.

Mathematical models of the cardiac cell have started to include markovian representations of the ionic channels instead of the traditional Hodgkin & Huxley formulations. There are many reasons for this: Markov models are not restricted to the idea of independent gates defining the channel, they allow more complex description with specific transitions between open, closed or inactivated states, and more importantly those states can be closely related to the underlying channel structure and conformational changes. METHODS: We used the LabVIEW® and MATLAB® programs to implement the simulator MarkoLAB that allow a dynamical 3D representation of the markovian model of the channel. The Monte Carlo simulation was used to implement the stochastic transitions among states. The user can specify the voltage protocol by setting the holding potential, the step-to voltage and the duration of the stimuli. RESULTS: The most studied feature of a channel is the current flowing through it. This happens when the channel stays in the open state, but most of the time, as revealed by the low open probability values, the channel remains on the inactive or closed states. By focusing only when the channel enters or leaves the open state we are missing most of its activity. MarkoLAB proved to be quite useful to visualize the whole behavior of the channel and not only when the channel produces a current. Such dynamic representation provides more complete information about channel kinetics and will be a powerful tool to demonstrate the effect of gene mutations or drugs on the channel function. CONCLUSIONS: MarkoLAB provides an original way of visualizing the stochastic behavior of a channel. It clarifies concepts, such as recovery from inactivation, calcium- versus voltage-dependent inactivation, and tail currents. It is not restricted to ionic channels only but it can be extended to other transporters, such as exchangers and pumps. This program is intended as a didactical tool to illustrate the dynamical behavior of a channel. It has been implemented in two platforms MATLAB® and LabVIEW® to enhance the target users of this new didactical tool. The computational cost of implementing a stochastic simulation is within the range of a personal computer performance; making MarkoLAB suitable to be run during a lecture or presentation.

Atrial-selective targeting of arrhythmogenic phase-3 early afterdepolarizations in human myocytes.

BACKGROUND: We have previously shown that non-equilibrium Na(+) current (INa) reactivation drives isoproterenol-induced phase-3 early afterdepolarizations (EADs) in mouse ventricular myocytes. In these cells, EAD initiation occurs secondary to potentiated sarcoplasmic reticulum Ca(2+) release and enhanced Na(+)/Ca(2+) exchange (NCX). This can be abolished by tetrodotoxin-blockade of INa, but not ranolazine, which selectively inhibits ventricular late INa. AIM: Since repolarization of human atrial myocytes is similar to mouse ventricular myocytes in that it is relatively rapid and potently modulated by Ca(2+), we investigated whether similar mechanisms can evoke EADs in human atrium. Indeed, phase-3 EADs have been shown to re-initiate atrial fibrillation (AF) during autonomic stimulation, which is a well-recognized initiator of AF. METHODS: We integrated a Markov model of INa gating in our human atrial myocyte model. To simulate experimental results, we rapidly paced this cell model at 10Hz in the presence of 0.1µM acetylcholine and 1µM isoproterenol, and assessed EAD occurrence upon return to sinus rhythm (1Hz). RESULTS: Cellular Ca(2+) loading during fast pacing results in a transient period of hypercontractility after return to sinus rhythm. Here, fast repolarization and enhanced NCX facilitate INa reactivation via the canonical gating mode (i.e., not late INa burst mode), which drives EAD initiation. Simulating ranolazine administration reduces atrial peak INa and leads to faster repolarization, during which INa fails to reactivate and EADs are prevented. CONCLUSIONS: Non-equilibrium INa reactivation can critically contribute to arrhythmias, specifically in human atrial myocytes. Ranolazine might be beneficial in this context by blocking peak (not late) atrial INa.

How to make calcium-sensitive minielectrodes.

In this protocol we describe how to make and use minielectrodes for measuring [Ca(2+)] in small volumes of solution. The minielectrodes are ~2 mm in diameter and have sufficiently low resistances to be used with a standard pH meter. They are made by dipping polyethylene or borosilicate glass tubes (~5 cm long) in a membrane solution. Although the chemicals used to make these Ca(2+)-sensitive minielectrodes are expensive, they can be used to make hundreds of electrodes, each with a useful life of several months.

Simulation of Ca-calmodulin-dependent protein kinase II on rabbit ventricular myocyte ion currents and action potentials.

Ca-calmodulin-dependent protein kinase II (CaMKII) was recently shown to alter Na(+) channel gating and recapitulate a human Na(+) channel genetic mutation that causes an unusual combined arrhythmogenic phenotype in patients: simultaneous long QT syndrome and Brugada syndrome. CaMKII is upregulated in heart failure where arrhythmias are common, and CaMKII inhibition can reduce arrhythmias. Thus, CaMKII-dependent channel modulation may contribute to acquired arrhythmic disease. We developed a Markovian Na(+) channel model including CaMKII-dependent changes, and incorporated it into a comprehensive myocyte action potential (AP) model with Na(+) and Ca(2+) transport. CaMKII shifts Na(+) current (I(Na)) availability to more negative voltage, enhances intermediate inactivation, and slows recovery from inactivation (all loss-of-function effects), but also enhances late noninactivating I(Na) (gain of function). At slow heart rates, with long diastolic time for I(Na) recovery, late I(Na) is the predominant effect, leading to AP prolongation (long QT syndrome). At fast heart rates, where recovery time is limited and APs are shorter, there is little effect on AP duration, but reduced availability decreases I(Na), AP upstroke velocity, and conduction (Brugada syndrome). CaMKII also increases cardiac Ca(2+) and K(+) currents (I(Ca) and I(to)), complicating CaMKII-dependent AP changes. Incorporating I(Ca) and I(to) effects individually prolongs and shortens AP duration. Combining I(Na), I(Ca), and I(to) effects results in shortening of AP duration with CaMKII. With transmural heterogeneity of I(to) and I(to) downregulation in heart failure, CaMKII may accentuate dispersion of repolarization. This provides a useful initial framework to consider pathways by which CaMKII may contribute to arrhythmogenesis.

Quantitative assessment of the SR Ca2+ leak-load relationship.

Increased diastolic SR Ca2+ leak (J(leak)) could depress contractility in heart failure, but there are conflicting reports regarding the J(leak) magnitude even in normal, intact myocytes. We have developed a novel approach to measure SR Ca2+ leak in intact, isolated ventricular myocytes. After stimulation, myocytes were exposed to 0 Na+, 0 Ca2+ solution +/-1 mmol/L tetracaine (to block resting leak). Total cell [Ca2+] does not change under these conditions with Na+-Ca2+ exchange inhibited. Resting [Ca2+]i declined 25% after tetracaine addition (126+/-6 versus 94+/-6 nmol/L; P<0.05). At the same time, SR [Ca2+] ([Ca2+](SRT)) increased 20% (93+/-8 versus 108+/-6 micromol/L). From this Ca2+ shift, we calculate J(leak) to be 12 micromol/L per second or 30% of the SR diastolic efflux. The remaining 70% is SR pump unidirectional reverse flux (backflux). The sum of these Ca2+ effluxes is counterbalanced by unidirectional forward Ca2+ pump flux. J(leak) also increased nonlinearly with [Ca2+](SRT) with a steeper increase at higher load. We conclude that J(leak) is 4 to 15 micromol/L cytosol per second at physiological [Ca2+](SRT). The data suggest that the leak is steeply [Ca2+](SRT)-dependent, perhaps because of increased [Ca2+]i sensitivity of the ryanodine receptor at higher [Ca2+](SRT). Key factors that determine [Ca2+](SRT) in intact ventricular myocytes include (1) the thermodynamically limited Ca2+ gradient that the SR can develop (which depends on forward flux and backflux through the SR Ca2+ ATPase) and (2) diastolic SR Ca2+ leak (ryanodine receptor mediated).