On Parameter Identifiability in Non-Linear Biophysical Models

Abstract

The quantitative modeling of biological phenomena allows for a deeper understanding of underlying mechanisms as well as the determination of biophysical parameters. However, we note that in many systems, the unique identification of relevant parameters is not possible with common experimental methods. The parameters of a model are said to be identifiable if there a unique point in parameter space that leads to an optimal agreement with particular data. In common non-linear models, however, there is not a unique map from parameter space to data space, and the confusion resulting from this lack of parameter identifiability may be slowing progress in many fields of biophysics. We use a simple example model to show analytically that this problem often results from rank-difficient regression, i.e., there are an infinite number of ways for the model parameters to fit the data equally well. Further, we use the same model to show that the identifiability problem can be resolved if additional experimental data is included for model constraint. Unfortunately, most models of interest will not be amenable to analytical examination. We present a numerical method based on Markov chain Monte Carlo (MCMC) sampling which can be used for any data and any model and will allow the diagnosis of these issues. We provide example uses of MCMC to asses parameter identifiability in a variety of systems. This method is an important tool that provides the ability to assess parameter identifiability for a given model and various potential experimental manipulations. This new kind of power analysis will lead to more precise conclusion and more fruitful experimentation.