Name
Title | ||
|---|---|---|
An Adjoint-Based Parameter Identification Algorithm Applied to Planar Cell Polarity Signaling |
Abstract | ||
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This paper presents an adjoint-based algorithm for performing automatic parameter identification on differential equation models of biological systems. The algorithm locally solves an optimization problem, in which the cost reflects the deviation between the observed data and the output of the parameter- ized mathematical model, and the constraints are the governing parameterized equations. The tractability and the speed of conver- gence (to local minima) of the algorithm are strongly favorable to numerical parameter search algorithms which do not make use of the adjoint. Furthermore, initializing the algorithm with different instantiations of the parameters allows one to effectively search the parameter space. Results of the application of this algorithm to a previously presented mathematical model of planar cell polarity (PCP) signaling in the wings of Drosophila melanogaster are presented, and some new insights into the PCP mechanism that are enabled by the algorithm are described. the model structure may be brought into question, and the simu- lation results may be used to indicate how the structure could be changed (11), (23). The model is tested against the actual data and for its predictive capabilities. As new data and/or new un- derstanding arises, the structure of the model may be altered and new parameters selected (10). In protein regulatory networks, the number of states to model is typically large and depends on the number of proteins of in- terest, the parameter spaces are large, and the most appropriate models are often nonlinear functions of the states and parame- ters. Due to this and the need to efficiently test the feasibility of different model structures, it is becoming increasingly impor- tant to develop fast, efficient, scalable methods for large-scale parameter identification. In this paper, we present an algorithm for performing auto- matic parameter identification on differential equation models of biological systems. The algorithm attempts to minimize an objective function which encodes the deviation between the ob- served data of the system and the output of the parameterized model, with the governing parameterized equations forming the constraints of this optimization problem. The algorithm relies on the adjoint method, which efficiently calculates the gradient of the objective function with respect to the unknown parameters, essentially describing analytically how to minimize the objec- tive by varying the parameters. We augment this gradient-based method by using additional information provided by the deriva- tive of the gradient to give well-conditioned optimization even when the optimal parameter values are several orders of mag- nitude different from each other. While the adjoint method is a technique familiar to optimal control and has been used to great extent in areas such as aerodynamic design (12), its application to the kinds of ordinary differential equation (ODE) and partial differential equation (PDE) models of protein regulatory net- works requires elucidation. We state and justify conditions on the model and the objective function so that the adjoint method may be applied. In addition, we discuss its implementation and |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1109/TAC.2007.911362 | IEEE Transactions on Circuits and Systems I-regular Papers |
Keywords | Field | DocType |
Parameter estimation,Signal processing,Biological system modeling,Differential equations,Biological systems,Systems biology,Constraint optimization,Mathematical model,Testing,Proteins | Differential equation,Mathematical optimization,Parameterized complexity,Optimal control,Search algorithm,Control theory,Algorithm,Maxima and minima,Parameter space,System identification,Optimization problem,Mathematics | Journal |
Volume | Issue | ISSN |
53 | Special Is | 0018-9286 |
Citations | PageRank | References |
8 | 0.82 | 3 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Robin L. Raffard | 1 | 63 | 6.64 |
| Keith Amonlirdviman | 2 | 13 | 1.45 |
| Jeffrey D. Axelrod | 3 | 19 | 2.41 |
| Claire J. Tomlin | 4 | 1491 | 158.05 |