Abstract
BackgroundMathematical models play a key role in systems biology: they summarize the currently available knowledge in a way that allows to make experimentally verifiable predictions. Model calibration consists of finding the parameters that give the best fit to a set of experimental data, which entails minimizing a cost function that measures the goodness of this fit. Most mathematical models in systems biology present three characteristics which make this problem very difficult to solve: they are highly non-linear, they have a large number of parameters to be estimated, and the information content of the available experimental data is frequently scarce. Hence, there is a need for global optimization methods capable of solving this problem efficiently.ResultsA new approach for parameter estimation of large scale models, called Cooperative Enhanced Scatter Search (CeSS), is presented. Its key feature is the cooperation between different programs (“threads”) that run in parallel in different processors. Each thread implements a state of the art metaheuristic, the enhanced Scatter Search algorithm (eSS). Cooperation, meaning information sharing between threads, modifies the systemic properties of the algorithm and allows to speed up performance. Two parameter estimation problems involving models related with the central carbon metabolism of E. coli which include different regulatory levels (metabolic and transcriptional) are used as case studies. The performance and capabilities of the method are also evaluated using benchmark problems of large-scale global optimization, with excellent results.ConclusionsThe cooperative CeSS strategy is a general purpose technique that can be applied to any model calibration problem. Its capability has been demonstrated by calibrating two large-scale models of different characteristics, improving the performance of previously existing methods in both cases. The cooperative metaheuristic presented here can be easily extended to incorporate other global and local search solvers and specific structural information for particular classes of problems.
Highlights
Mathematical models play a key role in systems biology: they summarize the currently available knowledge in a way that allows to make experimentally verifiable predictions
Testing the performance of our method with this problem has two advantages: first, the benchmark is well known in the largescale global optimization community, which facilitates the critical examination of the results; and second, the objective function selected from the benchmark has a smaller computational cost than the ones from our models, which allows to carry out more extensive tests in less time
From them it is concluded that enhanced Scatter Search (eSS) performs well with the benchmark problem, and that its performance is considerably improved by using its cooperative version, Cooperative enhanced Scatter Search (CeSS)
Summary
Mathematical models play a key role in systems biology: they summarize the currently available knowledge in a way that allows to make experimentally verifiable predictions. Model building is a complex task that usually follows an iterative process [1,2,3,4,5,6,7] It begins with the definition of the purpose of the model, this is, with the determination of the questions that the model should be able to answer. The step is to propose a mathematical structure with the necessary level of detail, which will in general include a number of unknown, non-measurable parameters An estimation of these parameters is needed in order to obtain quantitative predictions; this is the step, which is commonly known as parameter estimation or identification, data fitting, or model calibration [1,4,5,6]. The final step is model validation, which entails testing the model with new data; if this reveals modeling errors, the process should be iteratively repeated
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