Characterization of Intracellular Ca2+ Transient by the Hybrid Logistic Function in Aequorin-Injected Rabbit and Mouse Papillary Muscles

Abstract

Myocardial intracellular calcium (Ca 2+ ) transients (CaTs) regulate tension generation and relaxation. Isometric tension curves are often analyzed using exponential equations; however, we previously demonstrated that hybrid logistic (HL) functions, which describe the difference between two S-shaped logistic functions, provide more accurate representations. In the present study, we investigated the potential application of HL functions for analyzing CaTs directly. CaTs were measured using the calcium-sensitive bioluminescent protein, aequorin, in 7 isolated rabbit right ventricular and 15 isolated mouse left ventricular papillary muscles. CaT data were fit by the least-squares method using HL and polynomial exponential (PE) function equations. The mean correlation coefficient (r) values of HL and PE fits were 0.9934 vs. 0.9523 in rabbit and 0.9980 vs. 0.9407 in mouse, respectively. The Z transformation of r value and the adjusted coefficient of determination (r squares) were higher, and the residual mean squares and Akaike information criterion values, which estimate goodness of fit between functions with different numbers of parameters, were lower for the HL curves than for the PE curves in both rabbit and mouse. There were significant correlations between the calculated values from the best-fit HL function curve and the primary CaT data. Thus the HL function curves more accurately described the amplitudes and time courses of CaTs in both rabbit and mouse papillary muscles. We speculate that the first logistic component curve reflects the concentration and time course of Ca 2+ inflow into the cytoplasmic space, and that the second logistic component curve reflects the concentrations and time courses of Ca 2+ removal from the cytoplasmic space as well as Ca 2+ binding to troponin. This approach might provide a more robust model for studying CaTs and cardiac cycle regulation.Key words: myocardium, calcium, curve fit, cardiac cycle, excitation-contraction coupling. Myocardial intracellular calcium (Ca 2+ ) concentrationis an important determinant of mammalian myocardial tension generation and relaxation [1]. Changes in cytoplasmic Ca 2+ , i.e., Ca 2+ transients (CaTs), are related to the generated tension curves [2], and the increase and decrease in cytoplasmic Ca 2+ concentration regulate myocardial contraction and relaxation, respectively. Additionally, changes in the Ca 2+ sensitivity of cardiac troponin (Tn) substantially influence the contractile forces by altering the actin-myosin cross-bridge (CB) interaction.The tension waveform in the myocardium and left ventricular (LV) pressure waveform in the heart provide valuable information for evaluating myocardial and cardiac performance, including inotropism and lusitropism. In this paradigm, the myocardium and LV are viewed as nonlinear oscillators that generate tension and LV pressure over time. To maximize the amount of useful information extracted from the isometric tension and isovolumic LV pressure curve waveforms, many investigators have attempte...

Calcium-induced calcium release from the sarcoplasmic reticulum can be evaluated with a half-logistic function model in aequorin-injected cardiac muscles

“…In a previous study, we reported that the logistic function curve-fits well the ascending phase from twitch stimulation to the peak Ca 2? concentration [7]. A computer simulation of the CaT also provided a characterization of the logistic function [17].…”

“…The experimental procedures have been previously described in detail [4,6,7]. In short, seven albino rabbits (Japan White; body weight 2.0-2.5 kg) and 15 mice (C57BL/6; body weight 25-30 g) were anesthetized with intravenous (1.5-2.0 mg/kg) and intraperitoneal (15-20 mg/kg) pentobarbital sodium, respectively.…”

Half-Logistic Time Constants as Inotropic and Lusitropic Indices for Four Sequential Phases of Isometric Tension Curves in Isolated Rabbit and Mouse Papillary Muscles

“…39) We speculate that the tension waveform in Phase I is mainly related to the contraction process; that is, the rapid increase in intracellular Ca 2+ concentration due to Ca 2+ inflow into the cytoplasm, Ca 2+ -induced Ca 2+ release from the SR, Ca 2+ binding to troponin C, and cross-bridge association. 5,7) Conversely, the tension waveform in Phase IV is mainly related to the relaxation process; that is, the decrease in intracellular Ca 2+ concentration due to Ca 2+ dissociation from troponin C and Ca 2+ removal from the cytoplasm, and cross-bridge dissociation.…”

“…1,2) Nonlinear regression and curve-fitting may contribute to resolution of the mechanism, summarize information, remove noise, allow speculation regarding unmeasured data, and separate the effects of multiple factors. In an effort to maximize the amount of useful information that can be extracted from the waveforms of the tension and LV pressure curves, these curves have been studied by curve-fitting with mathematical models including sinusoidal, 3) polynomial-exponential, 4) hybrid-logistic, [5][6][7][8][9][10] and hybridWeibull functions. 11) Many attempts have also been made to derive reliable lusitropic indices from the minimum of the first order time derivative of LV pressure (dP/dt min ).…”