A hierarchical approach to model parameter optimization for developmental systems
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 considered for the example system SAM in A. thaliana such a parameter setting is described by the following expression: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.
References (55)
- et al.
Interdomain signaling in stem cell maintenance of plant shoot meristems
Mol. Cells
(2009) - et al.
The CLAVATA1 gene encodes a putative receptor kinase that controls shoot and floral meristem size in arabidopsis
Cell
(1997) - et al.
Role of WUSCHEL in regulating stem cell fate in the Arabidopsis shoot meristem
Cell
(1998) - et al.
Connectionist model of development
J. Theor. Biol.
(1991) - et al.
Mathematical modeling of planar cell polarity to understand domineering nonautonomy
Science
(2005) - et al.
Performance evaluation of an advanced local search evolutionary algorithm
- et al.
Two-dimensional patterning by a trapping/depletion mechanism: the role of TTG1 and GL3 in Arabidopsis trichome formation
PLoS Biol.
(2008) - et al.
Dependendence of stem cell fate in arabidopsis on a feedback loop regulated by CLV3 activity
Science
(2000) - et al.
Do additional objectives make a problem harder?
Practical Nonparametric Statistics
(1999)
Multi-Objective Optimization Using Evolutionary Algorithms
Signaling of cell fate decisions by CLAVATA3 in Arabidopsis shoot meristems
Science
Evolutionary computation
Nat. Rev. Genet.
A quantitative and dynamic model for plant cell regulation
PLoS ONE
Pattern formation during de novo assembly of the Arabidopsis shoot meristem
Development
WUSCHEL signaling functions in interregional communication during Arabidopsis ovule development
Gene Dev.
Multiobjectivization by decomposition of scalar cost functions
Investigations into the effect of multiobjectivization in protein structure prediction
Completely derandomized self-adaptation in evolution strategies
Evol. Comput.
Modeling the shoot apical meristem in A. thaliana: parameter estimation for spatial pattern formation
A multiobjective evolutionary algorithm for numerical parameter space characterization of reaction diffusion systems
Multicellular pattern formation: parameter estimation for ODE-based gene regulatory network models
IEEE Eng. Med. Biol.
Multiobjectivization for parameter estimation: a case-study on the segment polarity network of drosophila
A dynamic model for stem cell homeostasis and patterning in Arabidopsis meristems
PLoS ONE
Introduction to Global Optimization
Covariance matrix adaptation for multi-objective optimization
Evol. Comput.
The Arabidopsis CLAVATA2 gene encodes a receptor-like protein required for the stability of the CLAVATA1 receptor-like kinase
Plant Cell
Cited by (1)
Evolving reaction-diffusion systems on GPU
2011, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)