Elsevier

Biosystems

Volume 102, Issues 2–3, November–December 2010, Pages 157-167
Biosystems

A hierarchical approach to model parameter optimization for developmental systems

https://doi.org/10.1016/j.biosystems.2010.09.002Get rights and content

Abstract

In the context of Systems Biology, computer simulations of gene regulatory networks provide a powerful tool to validate hypotheses and to explore possible system behaviors. Nevertheless, modeling a system poses some challenges of its own: especially the step of model calibration is often difficult due to insufficient data. For example when considering developmental systems, mostly qualitative data describing the developmental trajectory is available while common calibration techniques rely on high-resolution quantitative data.

Focusing on the calibration of differential equation models for developmental systems, this study investigates different approaches to utilize the available data to overcome these difficulties. More specifically, the fact that developmental processes are hierarchically organized is exploited to increase convergence rates of the calibration process as well as to save computation time.

Using a gene regulatory network model for stem cell homeostasis in Arabidopsis thaliana the performance of the different investigated approaches is evaluated, documenting considerable gains provided by the proposed hierarchical approach.

Section snippets

Background

Mathematical modeling is one of the key tools assisting researchers when studying gene regulatory networks; it not only helps to visualize complex interactions, but in particular allows to validate hypothesis concerning system structure and dynamics in silico before actual experiments are carried out (Amonlirdviman et al., 2005, Bouyer et al., 2008, Geier et al., 2008, Jönsson et al., 2005, Nakamasu et al., 2009, von Dassow et al., 2000, Yamaguchi et al., 2007). With regard to developmental

Model system background

To evaluate the possible impact of considering information on the developmental trajectory of a system during the parameter calibration process of respective models, the proposed techniques are tested on a partial differential equation model describing autonomous SAM maintenance in A. thaliana. Model details are presented in (Hohm et al., 2010) and only a brief review on the underlying processes is given here.

Approach

The aim of model calibration is to identify a parameter setting in the model parameter space that minimizes the deviation between model output and available data. For the real-valued parameter space Xn considered for the example system SAM in A. thaliana such a parameter setting is described by the following expression:argminxXf(x),where f(x) quantifies the model fit by measuring the degree of dissimilarity between experimental data and model. Identifying such a parameter setting poses two

Results and discussion

In the following, it is investigated how experimental data can be used in the process of model calibration or model parameter optimization. In this regard hypotheses are tested that the inclusion of information on intermediate system states can facilitate parameter optimization for GRN models in developmental biology for which mostly qualitative data is available. As example system the model for emergence and maintenance of the SAM in A. thaliana presented in Hohm et al. (2010) is used.

Conclusions

In this study we addressed the problem of model calibration for differential equation models in the area of developmental biology. In this domain, researchers are interested in understanding the emergence of patterns with respect to gene expression profiles in considered tissues. The calibration of such time and space dependent models is difficult due to the usually non-linear dependences between model entities as well as due to the fact that it is difficult to acquire high-resolution

Acknowledgements

The authors would like to thank Ralf Müller and Rüdiger Simon for providing the in situ hybridization images shown in Fig. 1.

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