Correlation Analysis: A Tool for Comparing Relaxation-Type Models to Experimental Data

Maurizio Tomaiuolo, Joel Tabak, Richard Bertram

We describe a new technique for comparing mathematical models to the biological systems that they describe. This technique is appropriate for systems that produce relaxation oscillations or bursting oscillations, and takes advantage of noise that is inherent to all biological systems. Both types of oscillations are composed of active phases of activity followed by silent phases, repeating periodically. The presence of noise adds variability to the durations of the different phases. The central idea of the technique is that the active phase duration may be correlated with either/both the previous or next silent phase duration, and the resulting correlation pattern provides information about the dynamic structure of the system. Correlation patterns can easily be determined by making scatter plots and applying correlation analysis to the cluster of data points. This could be done both with experimental data and with model simulation data. If the model correlation pattern is in general agreement with the experimental data, then this adds support for the validity of the model. Otherwise, the model must be corrected. While this tool is only one test of many required to validate a mathematical model, it is easy to implement and is non-invasive.