Background: Myocardial contraction and relaxation are regulated by increases and decreases in intracellular cytoplasmic calcium (Ca2+) concentration ([Ca2+]i). In previous studies, we found that a half-logistic (h-L) function, which represents a half-curve of a symmetrical sigmoid logistic function with a boundary at the inflection point, curve-fits the first half of the ascending phase (CaTI) and the second half of the descending phase of the [Ca2+]i transient curve (CaTIV) better than a mono-exponential (m-E) function. In the present study, we investigated the potential application of an h-L function to the analysis of the second half of the ascending phase of the [Ca2+]i transient curve (CaTII).
Methods: The [Ca2+]i transient was measured using the Ca2+-sensitive photoprotein aequorin, which was microinjected into 15 isolated left ventricular (LV) papillary muscles of mice. The observed CaTII data during the time duration from the point corresponding to the maximum ofthe first-order time derivative of Ca2+ concentration (dCa/dtmax) to the point corresponding to the peak Ca2+ concentration was curve-fitted by the least-squares method using the h-L and m-E function equations.
Results: The mean correlation coefficient (r) values ofthe h-L and m-E curve-fits for CaTII were 0.9996 and 0.9984, respectively. The Z transformation of h-L r was larger than that of m-E r (p < 0.0001). H-L residual mean square (RMS) was smaller than m-E RMS (p < 0.001).
Conclusions: The h-L function tracks the magnitudes and time courses of CaTII more accurately than the m-E function in isolated aequorin-injected mouse LV papillary muscle. Compared with the m-E time constant, the h-L time constant of CaTII is a more reliable index for evaluating the time duration of the change in the increase in [Ca2+]i during the combination of the middle part of the contraction process and the early part of the relaxation process. CaTII can be assessed by the h-L function model in cardiac muscles. The h-Lapproach may provide a more useful model for studying each process in myocardial Ca2+ handling.