Parameter estimation and determinability analysis applied to Drosophila gap gene circuits

BackgroundMathematical modeling of real-life processes often requires the estimation of unknown parameters. Once the parameters are found by means of optimization, it is important to assess the quality of the parameter estimates, especially if parameter values are used to draw biological conclusions from the model.ResultsIn this paper we describe how the quality of parameter estimates can be analyzed. We apply our methodology to assess parameter determinability for gene circuit models of the gap gene network in early Drosophila embryos.ConclusionOur analysis shows that none of the parameters of the considered model can be determined individually with reasonable accuracy due to correlations between parameters. Therefore, the model cannot be used as a tool to infer quantitative regulatory weights. On the other hand, our results show that it is still possible to draw reliable qualitative conclusions on the regulatory topology of the gene network. Moreover, it improves previous analyses of the same model by allowing us to identify those interactions for which qualitative conclusions are reliable, and those for which they are ambiguous.

[1]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[2]  John Reinitz,et al.  A database for management of gene expression data in situ , 2004, Bioinform..

[3]  A. Simcox,et al.  When does determination occur in Drosophila embryos? , 1983, Developmental biology.

[4]  Norbert Perrimon,et al.  Activation of posterior gap gene expression in the Drosophila blastoderm , 1995, Nature.

[5]  Lennart Ljung,et al.  System identification (2nd ed.): theory for the user , 1999 .

[6]  John Reinitz,et al.  Registration of the expression patterns of Drosophila segmentation genes by two independent methods , 2001, Bioinform..

[7]  M. Akam,et al.  The molecular basis for metameric pattern in the Drosophila embryo. , 1987, Development.

[8]  C. W. Gear,et al.  Numerical initial value problem~ in ordinary differential eqttations , 1971 .

[9]  David H. Sharp,et al.  Mechanism of eve stripe formation , 1995, Mechanisms of Development.

[10]  Douglas B. Kell,et al.  Non-linear optimization of biochemical pathways: applications to metabolic engineering and parameter estimation , 1998, Bioinform..

[11]  Leon Glass,et al.  Reverse Engineering the Gap Gene Network of Drosophila melanogaster , 2006, PLoS Comput. Biol..

[12]  Dmitri Papatsenko,et al.  A self-organizing system of repressor gradients establishes segmental complexity in Drosophila , 2003, Nature.

[13]  Richard F. Gunst,et al.  Applied Regression Analysis , 1999, Technometrics.

[14]  Gene H. Golub,et al.  Matrix computations , 1983 .

[15]  Christopher R. Myers,et al.  Universally Sloppy Parameter Sensitivities in Systems Biology Models , 2007, PLoS Comput. Biol..

[16]  B. Alberts,et al.  Studies of nuclear and cytoplasmic behaviour during the five mitotic cycles that precede gastrulation in Drosophila embryogenesis. , 1983, Journal of cell science.

[17]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[18]  N. Rashevsky,et al.  Mathematical biology , 1961, Connecticut medicine.

[19]  David H. Sharp,et al.  Dynamic control of positional information in the early Drosophila embryo , 2004, Nature.

[20]  Clifford H. Thurber,et al.  Parameter estimation and inverse problems , 2005 .

[21]  Johannes Jaeger,et al.  On the dynamic nature of positional information. , 2006, BioEssays : news and reviews in molecular, cellular and developmental biology.

[22]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[23]  Gaudenz Danuser,et al.  Linking data to models: data regression , 2006, Nature Reviews Molecular Cell Biology.

[24]  David H. Sharp,et al.  Dynamical Analysis of Regulatory Interactions in the Gap Gene System of Drosophila melanogaster , 2004, Genetics.

[25]  Jaap A. Kaandorp,et al.  Efficient parameter estimation for spatio-temporal models of pattern formation: case study of Drosophila melanogaster , 2007, Bioinform..

[26]  Piet Hemker,et al.  Numerical methods for differential equations in system simulation and in parameter estimation : (analysis and simulation of biochemical systems; proc. of the 8th febs meeting, amsterdam, 1972, p 59-80) , 1972 .

[27]  David H. Sharp,et al.  Known maternal gradients are not sufficient for the establishment of gap domains in Drosophila melanogaster , 2007, Mechanisms of Development.