Abstract
Motivation: Experiment design strategies for biomedical models with the purpose of parameter estimation or model discrimination are in the focus of intense research. Experimental limitations such as sparse and noisy data result in unidentifiable parameters and render-related design tasks challenging problems. Often, the temporal resolution of data is a limiting factor and the amount of possible experimental interventions is finite. To address this issue, we propose a Bayesian experiment design algorithm to minimize the prediction uncertainty for a given set of experiments and compare it to traditional A-optimal design.Results: In an in depth numerical study involving an ordinary differential equation model of the trans-Golgi network with 12 partly non-identifiable parameters, we minimized the prediction uncertainty efficiently for predefined scenarios. The introduced method results in twice the prediction precision as the same amount of A-optimal designed experiments while introducing a useful stopping criterion. The simulation intensity of the algorithm's major design step is thereby reasonably affordable. Besides smaller variances in the predicted trajectories compared with Fisher design, we could also achieve smaller parameter posterior distribution entropies, rendering this method superior to A-optimal Fisher design also in the parameter space.Availability: Necessary software/toolbox information are available in the supplementary material. The project script including example data can be downloaded from http://www.ist.uni-stuttgart.de/%7eweber/BayesFisher2012.Contact: patrick.weber@ist.uni-stuttgart.deSupplementary Information: Supplementary data are available at Bioinformatics online.
Highlights
Regulation models are preferably used to describe intra- and inter-cellular interactions of biomolecules
We address the problem of efficiently selecting experiments to improve the prediction capabilities of a given ordinary differential equation (ODE) model of the following form: x(t;u,θ ) = f (x(t;u,θ ),u(t),θ ) x(0;u,θ ) = x0(u,θ ) y(t;u,θ ) = h(x(t;u,θ),u(t),θ), (1)
The stopping criterion was reached by the Bayesian routine after four experiments in all five runs, while requesting a total of 12 data points. This means that we expect the trained model to be able to make predictions for all 27 experiments in which all trajectory variances are below the threshold
Summary
Regulation models are preferably used to describe intra- and inter-cellular interactions of biomolecules. Claiming that ODE model predictions improve when reducing parameter uncertainty intervals, these methods design optimal experiments for parameter estimation (OED/PE). Models can be used to make precise predictions despite sloppy parameters with large confidence intervals (Brown et al, 2004; Klinke, 2009). This is rendering OED/PE an indirect method to improve predictions. Methods have been developed to directly address experiment design for better model predictions (Casey et al, 2007; Vanlier et al, 2012), which we here refer to as OED/MP. We use a Bayesian posterior inference method and predict experimentally feasible scenarios to purposively reduce uncertainty in the model trajectories. The method is successfully applied to reduce prediction uncertainty of an ODE model of secretory pathway control at the trans-Golgi network. In an intense comparison study, we were able to outperform Aoptimal designed experiments in both prediction uncertainty and posterior distribution entropy, with affordable computational effort
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