Evaluation and propagation of confidence intervals in nonlinear, asymmetrical variance spaces. Analysis of ligand-binding data.

Two problems that are often overlooked in studies employing nonlinear least-squares techniques for parameter estimation are confidence-interval estimation and propagation. When the parameters are correlated, the variance space and consequently the confidence intervals are nonlinear and asymmetrical. The presented mathematical method for the evaluation of confidence intervals and error propagation addresses these problems. The examples employed to demonstrate these methods include linear least-squares and the nonlinear least-squares analysis of ligand-binding problems, such as hormone receptor interactions and oxygen binding to human hemoglobin. The mathematical procedures have proven very useful for analyzing the molecular mechanism of cooperativity in human hemoglobin (Johnson, M. L., and G. K. Ackers, 1982. Biochemistry 21:201-211).