A unified framework for estimating parameters of kinetic biological models

Utilizing kinetic models of biological systems commonly require computational approaches to estimate parameters, posing a variety of challenges due to their highly non-linear and dynamic nature, which is further complicated by the issue of non-identifiability. We propose a novel parameter estimation framework by combining approaches for solving identifiability with a recently introduced filtering technique that can uniquely estimate parameters where conventional methods fail. This framework first conducts a thorough analysis to identify and classify the non-identifiable parameters and provides a guideline for solving them. If no feasible solution can be found, the framework instead initializes the filtering technique with informed prior to yield a unique solution.

This framework has been applied to uniquely estimate parameter values for the sucrose accumulation model in sugarcane culm tissue and a gene regulatory network. In the first experiment the results show the progression of improvement in reliable and unique parameter estimation through the use of each tool to reduce and remove non-identifiability. The latter experiment illustrates the common situation where no further measurement data is available to solve the non-identifiability. These results show the successful application of the informed prior as well as the ease with which parallel data sources may be utilized without increasing the model complexity.

The proposed unified framework is distinct from other approaches by providing a robust and complete solution which yields reliable and unique parameter estimation even in the face of non-identifiability.