Dynamical Mechanisms of Pacemaker Generation in IK1-Downregulated Human Ventricular Myocytes: Insights from Bifurcation Analyses of a Mathematical Model

Abstract

Dynamical mechanisms of the biological pacemaker (BP) generation in human ventricular myocytes were investigated by bifurcation analyses of a mathematical model. Equilibrium points (EPs), periodic orbits, stability of EPs, and bifurcation points were determined as functions of bifurcation parameters, such as the maximum conductance of inward-rectifier K+ current (I(K1)), for constructing bifurcation diagrams. Stable limit cycles (BP activity) abruptly appeared around an unstable EP via a saddle-node bifurcation when I(K1) was suppressed by 84.6%. After the bifurcation at which a stable EP disappears, the I(K1)-reduced system has an unstable EP only, which is essentially important for stable pacemaking. To elucidate how individual sarcolemmal currents contribute to EP instability and BP generation, we further explored the bifurcation structures of the system during changes in L-type Ca2+ channel current (I(Ca,L)), delayed-rectifier K+ currents (I(K)), or Na(+)/Ca2+ exchanger current (I(NaCa)). Our results suggest that 1), I(Ca,L) is, but I(K) or I(NaCa) is not, responsible for EP instability as a requisite to stable BP generation; 2), I(K) is indispensable for robust pacemaking with large amplitude, high upstroke velocity, and stable frequency; and 3), I(NaCa) is the dominant pacemaker current but is not necessarily required for the generation of spontaneous oscillations.

Roles of hyperpolarization-activated current If in sinoatrial node pacemaking: insights from bifurcation analysis of mathematical models

“…Moreover, as reported previously, investigating bifurcation structures of SAN or ventricular models is also useful for elucidating the dynamical mechanisms of abnormal automaticity (4,5,15,23,29,50,52) and triggered activity (14). Thus the nonlinear dynamical approach would be necessary for general understanding and systematic descriptions of the mechanisms of normal and abnormal pacemaker activities, possibly leading to the construction of a general theory for pacemaker mechanisms.…”

“…Thus we first examined the influences of I f on stability and bifurcation of EPs during I bias applications, i.e., whether I f enlarges the unstable V E (and I bias ) region in the I bias -V E curve, for the model cells. This approach would reveal the contributions of I f to EP (V E ) instability, as well as robustness against hyperpolarizing and depolarizing loads (22)(23)(24)(25)52). Figure 1 shows the effects of increasing g f on stability and bifurcation during I bias applications of the Kurata et al central (21) and peripheral (25) Bifurcation points on the I bias -V E curve were determined with changing g f and plotted as functions of g f on both the potential (V E ) and current (I bias ) coordinates.…”

“…In our laboratory's previous studies, bifurcation structures (i.e., ways of changes in the number or stability of equilibrium and periodic states) of ventricular or SAN model systems were investigated for elucidating the dynamic mechanisms of normal and abnormal pacemaker activities (22)(23)(24)(25). These theoretical works indicate that the initiation and cessation of pacemaker activity are considered as bifurcation phenomena, and that the mathematical approach-bifurcation analysis-provides a convenient way of understanding how individual currents contribute to pacemaker activities.…”

Genetically engineered cardiac pacemaker: Stem cells transfected with HCN2 gene and myocytes—A model

“…This indicates the change from oscillatory to excitable but quiescent behavior occurs through a homoclinic bifurcation [24], [14]). Cell pair model A "cell pair", consisting of a myocyte and a stem cell coupled together is described by the following set of equations : …”

M3 Muscarinic Receptor Signaling Stabilizes a Novel Mutant Human Ether-a-Go-Go-Related Gene Channel Protein via Phosphorylation of Heat Shock Factor 1 in Transfected Cells

“…The changes in immunoreactivities were confirmed by quantification of the signal activities ( Figure 3B). Figure 4A shows the original traces of E4031-sensitive hERG using mathematical models developed by Kurata et al 19 and O'Hara et al 20 A mid-myocardial (M) cell version of the Kurata et al model was developed on the basis of the transmural heterogeneity in densities of sarcolemmal ion channels, transporters and SR Ca 2+ uptake/release rates, as summarized by O'Hara et al 20 We used the M cell versions of the two HVM models because they have larger ICaL, as well as smaller IKr and IKs, thus being much more vulnerable to EAD formation than the endocardial and epicardial versions. 20 Whether the carbachol-induced modification of the mutant hERG current inhibits EAD formation in the LQT2 HVMs was tested, as shown in the supplementary material.…”