Ionic mechanisms and Ca2+ dynamics underlying the glucose response of pancreatic β cells: a simulation study

To clarify the mechanisms underlying the pancreatic β-cell response to varying glucose concentrations ([G]), electrophysiological findings were integrated into a mathematical cell model. The Ca2+ dynamics of the endoplasmic reticulum (ER) were also improved. The model was validated by demonstrating quiescent potential, burst–interburst electrical events accompanied by Ca2+ transients, and continuous firing of action potentials over [G] ranges of 0–6, 7–18, and >19 mM, respectively. These responses to glucose were completely reversible. The action potential, input impedance, and Ca2+ transients were in good agreement with experimental measurements. The ionic mechanisms underlying the burst–interburst rhythm were investigated by lead potential analysis, which quantified the contributions of individual current components. This analysis demonstrated that slow potential changes during the interburst period were attributable to modifications of ion channels or transporters by intracellular ions and/or metabolites to different degrees depending on [G]. The predominant role of adenosine triphosphate–sensitive K+ current in switching on and off the repetitive firing of action potentials at 8 mM [G] was taken over at a higher [G] by Ca2+- or Na+-dependent currents, which were generated by the plasma membrane Ca2+ pump, Na+/K+ pump, Na+/Ca2+ exchanger, and TRPM channel. Accumulation and release of Ca2+ by the ER also had a strong influence on the slow electrical rhythm. We conclude that the present mathematical model is useful for quantifying the role of individual functional components in the whole cell responses based on experimental findings

ポリエチレンチューブによる心筋細胞活動電位の記録

金沢大学医薬保健研究域保健学

Gradient-based parameter optimization method to determine membrane ionic current composition in human induced pluripotent stem cell-derived cardiomyocytes

Premature cardiac myocytes derived from human induced pluripotent stem cells (hiPSC-CMs) show heterogeneous action potentials (APs), probably due to different expression patterns of membrane ionic currents. We developed a method for determining expression patterns of functional channels in terms of whole-cell ionic conductance (Gx) using individual spontaneous AP configurations. It has been suggested that apparently identical AP configurations can be obtained using different sets of ionic currents in mathematical models of cardiac membrane excitation. If so, the inverse problem of Gx estimation might not be solved. We computationally tested the feasibility of the gradient-based optimization method. For a realistic examination, conventional 'cell-specific models' were prepared by superimposing the model output of AP on each experimental AP recorded by conventional manual adjustment of Gxs of the baseline model. Gxs of 4–6 major ionic currents of the 'cell-specific models' were randomized within a range of ± 5–15% and used as an initial parameter set for the gradient-based automatic Gxs recovery by decreasing the mean square error (MSE) between the target and model output. Plotting all data points of the MSE–Gx relationship during optimization revealed progressive convergence of the randomized population of Gxs to the original value of the cell-specific model with decreasing MSE. The absence of any other local minimum in the global search space was confirmed by mapping the MSE by randomizing Gxs over a range of 0.1–10 times the control. No additional local minimum MSE was obvious in the whole parameter space, in addition to the global minimum of MSE at the default model parameter

Time-dependent changes in membrane excitability during glucose-induced bursting activity in pancreatic β cells

In our companion paper, the physiological functions of pancreatic β cells were analyzed with a new β-cell model by time-based integration of a set of differential equations that describe individual reaction steps or functional components based on experimental studies. In this study, we calculate steady-state solutions of these differential equations to obtain the limit cycles (LCs) as well as the equilibrium points (EPs) to make all of the time derivatives equal to zero. The sequential transitions from quiescence to burst–interburst oscillations and then to continuous firing with an increasing glucose concentration were defined objectively by the EPs or LCs for the whole set of equations. We also demonstrated that membrane excitability changed between the extremes of a single action potential mode and a stable firing mode during one cycle of bursting rhythm. Membrane excitability was determined by the EPs or LCs of the membrane subsystem, with the slow variables fixed at each time point. Details of the mode changes were expressed as functions of slowly changing variables, such as intracellular [ATP], [Ca2+], and [Na+]. In conclusion, using our model, we could suggest quantitatively the mutual interactions among multiple membrane and cytosolic factors occurring in pancreatic β cells

Magnesium gating of cardiac gap junction channels.

We aimed to study kinetics of modulation by intracellular Mg(2+) of cardiac gap junction (Mg(2+) gate). Paired myocytes of guinea-pig ventricle were superfused with solutions containing various concentrations of Mg(2+). In order to rapidly apply Mg(2+) to one aspect of the gap junction, the non-junctional membrane of one of the pair was perforated at nearly the connecting site by pulses of nitrogen laser beam. The gap junction conductance (G(j)) was measured by clamping the membrane potential of the other cell using two-electrode voltage clamp method. The laser perforation immediately increased G(j), followed by slow G(j) change with time constant of 3.5 s at 10 mM Mg(2+). Mg(2+) more than 1.0 mM attenuated dose-dependently the gap junction conductance and lower Mg(2+) (0.6 mM) increased G(j) with a Hill coefficient of 3.4 and a half-maximum effective concentration of 0.6 mM. The time course of G(j) changes was fitted by single exponential function, and the relationship between the reciprocal of time constant and Mg(2+) concentration was almost linear. Based on the experimental data, a mathematical model of Mg(2+) gate with one open state and three closed states well reproduced experimental results. One-dimensional cable model of thirty ventricular myocytes connected to the Mg(2+) gate model suggested a pivotal role of the Mg(2+) gate of gap junction under pathological conditions