Analysing force–pCa curves

We investigated three forms of the Hill equation used to fit force–calcium data from skinned muscle experiments; Two hyperbolic forms that relate force to calcium concentration directly, and a sigmoid form that relates force to the −log10 of the calcium concentration (pCa). The equations were fit to force–calcium data from 39 cardiac myocytes (up to five myocytes from each of nine mice) and the Hill coefficient and the calcium required for half maximal activation, expressed as a concentration (EC50) and as a pCa value (pCa50) were obtained. The pCa50 values were normally distributed and the EC50 values were found to approximate a log-normal distribution. Monte Carlo simulations confirmed that these distributions were intrinsic to the Hill equation. Statistical tests such as the t-test are robust to moderate levels of departure from normality as seen here, and either EC50 or pCa50 may be used to test for significant differences so long as it is kept in mind that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Updelta\hbox{EC}_{50}$$\end{document} is an additive measure of change and that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Updelta\hbox{pCa}_{50}$$\end{document} is a ratiometric measure of change. The Hill coefficient was found to be sufficiently log-normally distributed that log-transformed values should be used to test for statistically significant differences.