Overcoming data limitations to identify a static nonlinearity in a biological signaling cascade

One important challenge in modeling biological systems is that of structure identification: how do we characterize unknown parts of a system using knowledge of the rest of the system along with data gathered from the input and output? Biological systems are particularly difficult to identify this way because measurements of such systems are often noisy. Furthermore, these measurements can be sparse-widely and unevenly spaced in time-when collecting samples from the system requires considerable time and effort. These two issues severely limit the information available to accurately identify the unknown structure. Here, we consider the specific problem of identifying a static nonlinearity in a biological signaling cascade using noisy, sparse experimental measurements. By making the input and output subsystems in the cascade normalizable and normalizing the data gathered from those subsystems, we effectively incorporate additional information into each data point to reduce measurement noise. We then interpolate the normalized data to generate continuous input and output signals, which we can apply to the input and output subsystems in order to identify the nonlinearity connecting them. We demonstrate the effectiveness of this procedure by using it to identify the mechanism for ergosterol sensing by the Sre1 and Scp1 proteins in fission yeast.