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Tailored parameter optimization methods for ordinary differential equation models with steady-state constraints

Overview of attention for article published in BMC Systems Biology, August 2016
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Title
Tailored parameter optimization methods for ordinary differential equation models with steady-state constraints
Published in
BMC Systems Biology, August 2016
DOI 10.1186/s12918-016-0319-7
Pubmed ID
Authors

Anna Fiedler, Sebastian Raeth, Fabian J. Theis, Angelika Hausser, Jan Hasenauer

Abstract

Ordinary differential equation (ODE) models are widely used to describe (bio-)chemical and biological processes. To enhance the predictive power of these models, their unknown parameters are estimated from experimental data. These experimental data are mostly collected in perturbation experiments, in which the processes are pushed out of steady state by applying a stimulus. The information that the initial condition is a steady state of the unperturbed process provides valuable information, as it restricts the dynamics of the process and thereby the parameters. However, implementing steady-state constraints in the optimization often results in convergence problems. In this manuscript, we propose two new methods for solving optimization problems with steady-state constraints. The first method exploits ideas from optimization algorithms on manifolds and introduces a retraction operator, essentially reducing the dimension of the optimization problem. The second method is based on the continuous analogue of the optimization problem. This continuous analogue is an ODE whose equilibrium points are the optima of the constrained optimization problem. This equivalence enables the use of adaptive numerical methods for solving optimization problems with steady-state constraints. Both methods are tailored to the problem structure and exploit the local geometry of the steady-state manifold and its stability properties. A parameterization of the steady-state manifold is not required. The efficiency and reliability of the proposed methods is evaluated using one toy example and two applications. The first application example uses published data while the second uses a novel dataset for Raf/MEK/ERK signaling. The proposed methods demonstrated better convergence properties than state-of-the-art methods employed in systems and computational biology. Furthermore, the average computation time per converged start is significantly lower. In addition to the theoretical results, the analysis of the dataset for Raf/MEK/ERK signaling provides novel biological insights regarding the existence of feedback regulation. Many optimization problems considered in systems and computational biology are subject to steady-state constraints. While most optimization methods have convergence problems if these steady-state constraints are highly nonlinear, the methods presented recover the convergence properties of optimizers which can exploit an analytical expression for the parameter-dependent steady state. This renders them an excellent alternative to methods which are currently employed in systems and computational biology.

Twitter Demographics

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Mendeley readers

The data shown below were compiled from readership statistics for 35 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
Germany 2 6%
United Kingdom 1 3%
Unknown 32 91%

Demographic breakdown

Readers by professional status Count As %
Student > Ph. D. Student 12 34%
Researcher 8 23%
Student > Master 4 11%
Other 2 6%
Professor 2 6%
Other 3 9%
Unknown 4 11%
Readers by discipline Count As %
Biochemistry, Genetics and Molecular Biology 9 26%
Engineering 6 17%
Agricultural and Biological Sciences 4 11%
Computer Science 3 9%
Medicine and Dentistry 2 6%
Other 4 11%
Unknown 7 20%

Attention Score in Context

This research output has an Altmetric Attention Score of 1. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 24 August 2016.
All research outputs
#6,276,099
of 8,272,014 outputs
Outputs from BMC Systems Biology
#621
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Outputs of similar age
#180,338
of 253,543 outputs
Outputs of similar age from BMC Systems Biology
#27
of 40 outputs
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