Abstract
BackgroundUnderstanding the dynamics of biological processes can substantially be supported by computational models in the form of nonlinear ordinary differential equations (ODE). Typically, this model class contains many unknown parameters, which are estimated from inadequate and noisy data. Depending on the ODE structure, predictions based on unmeasured states and associated parameters are highly uncertain, even undetermined. For given data, profile likelihood analysis has been proven to be one of the most practically relevant approaches for analyzing the identifiability of an ODE structure, and thus model predictions. In case of highly uncertain or non-identifiable parameters, rational experimental design based on various approaches has shown to significantly reduce parameter uncertainties with minimal amount of effort.ResultsIn this work we illustrate how to use profile likelihood samples for quantifying the individual contribution of parameter uncertainty to prediction uncertainty. For the uncertainty quantification we introduce the profile likelihood sensitivity (PLS) index. Additionally, for the case of several uncertain parameters, we introduce the PLS entropy to quantify individual contributions to the overall prediction uncertainty. We show how to use these two criteria as an experimental design objective for selecting new, informative readouts in combination with intervention site identification. The characteristics of the proposed multi-criterion objective are illustrated with an in silico example. We further illustrate how an existing practically non-identifiable model for the chlorophyll fluorescence induction in a photosynthetic organism, D. salina, can be rendered identifiable by additional experiments with new readouts.ConclusionsHaving data and profile likelihood samples at hand, the here proposed uncertainty quantification based on prediction samples from the profile likelihood provides a simple way for determining individual contributions of parameter uncertainties to uncertainties in model predictions. The uncertainty quantification of specific model predictions allows identifying regions, where model predictions have to be considered with care. Such uncertain regions can be used for a rational experimental design to render initially highly uncertain model predictions into certainty. Finally, our uncertainty quantification directly accounts for parameter interdependencies and parameter sensitivities of the specific prediction.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-014-0436-5) contains supplementary material, which is available to authorized users.
Highlights
Understanding the dynamics of biological processes can substantially be supported by computational models in the form of nonlinear ordinary differential equations (ODE)
Several excellent publications have appeared over the last years, which focus on identification of computational models for biochemical systems by applying a variety of methodological optimal experimental design approaches, e.g. [3-8]
Predictions on unmeasured states are highly uncertain as is illustrated by the extreme trajectories of each parameter derived from the simulated samples along the profile likelihood (Figure 1(c))
Summary
Understanding the dynamics of biological processes can substantially be supported by computational models in the form of nonlinear ordinary differential equations (ODE). This model class contains many unknown parameters, which are estimated from inadequate and noisy data. Advances in technology and biotechnology in particular allow us to look inside biological cells and observe dynamic processes occurring at the molecular level Still, many of these processes can only partially be observed in experiments hampering the experimental exploration of interaction mechanisms. A computational abstraction of the dynamic biochemical process in the form of an ordinary differential equation system (ODE) with unknown parameters can provide answers to the dynamics of unmeasured states that in turn give information on interaction mechanisms. Several excellent publications have appeared over the last years, which focus on identification of computational models for biochemical systems by applying a variety of methodological optimal experimental design approaches, e.g. [3-8]
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.