Parameter estimation with bio-inspired meta-heuristic optimization: modeling the dynamics of endocytosis

Ljupčo Todorovski,Sašo Džeroski,Katerina Tashkova,Jurij Šilc,Peter Korošec

doi:10.1186/1752-0509-5-159

Ljupčo Todorovski, Sašo Džeroski + Show 3 more

Open Access

https://doi.org/10.1186/1752-0509-5-159

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Abstract

BackgroundWe address the task of parameter estimation in models of the dynamics of biological systems based on ordinary differential equations (ODEs) from measured data, where the models are typically non-linear and have many parameters, the measurements are imperfect due to noise, and the studied system can often be only partially observed. A representative task is to estimate the parameters in a model of the dynamics of endocytosis, i.e., endosome maturation, reflected in a cut-out switch transition between the Rab5 and Rab7 domain protein concentrations, from experimental measurements of these concentrations. The general parameter estimation task and the specific instance considered here are challenging optimization problems, calling for the use of advanced meta-heuristic optimization methods, such as evolutionary or swarm-based methods.ResultsWe apply three global-search meta-heuristic algorithms for numerical optimization, i.e., differential ant-stigmergy algorithm (DASA), particle-swarm optimization (PSO), and differential evolution (DE), as well as a local-search derivative-based algorithm 717 (A717) to the task of estimating parameters in ODEs. We evaluate their performance on the considered representative task along a number of metrics, including the quality of reconstructing the system output and the complete dynamics, as well as the speed of convergence, both on real-experimental data and on artificial pseudo-experimental data with varying amounts of noise. We compare the four optimization methods under a range of observation scenarios, where data of different completeness and accuracy of interpretation are given as input.ConclusionsOverall, the global meta-heuristic methods (DASA, PSO, and DE) clearly and significantly outperform the local derivative-based method (A717). Among the three meta-heuristics, differential evolution (DE) performs best in terms of the objective function, i.e., reconstructing the output, and in terms of convergence. These results hold for both real and artificial data, for all observability scenarios considered, and for all amounts of noise added to the artificial data. In sum, the meta-heuristic methods considered are suitable for estimating the parameters in the ODE model of the dynamics of endocytosis under a range of conditions: With the model and conditions being representative of parameter estimation tasks in ODE models of biochemical systems, our results clearly highlight the promise of bio-inspired meta-heuristic methods for parameter estimation in dynamic system models within system biology.

Highlights

We address the task of parameter estimation in models of the dynamics of biological systems based on ordinary differential equations (ODEs) from measured data, where the models are typically non-linear and have many parameters, the measurements are imperfect due to noise, and the studied system can often be only partially observed
The theoretical and experimental approach [16] undertaken to model the endocytosis rely on the mutual exclusiveness of the Rab5 and Rab7 domains
For each model, simulated with the best parameter estimates obtained by a single method in a single case, we report the corresponding Root mean squared error (RMSE) and RMSEm values and expect that the optimization method that led to the best RMSE would lead to the best RMSEm

Summary

Introduction

We address the task of parameter estimation in models of the dynamics of biological systems based on ordinary differential equations (ODEs) from measured data, where the models are typically non-linear and have many parameters, the measurements are imperfect due to noise, and the studied system can often be only partially observed. A. Due to the highly nonlinear dynamics and the limited measurability of biological systems, the parameter estimation task is challenging and computationally expensive. For the few ones that can be measured, measured data are noisy and taken at a coarse time resolution All these constraints, combined with the complex dynamic of the considered models, can lead to identifiability problems, i.e, the impossibility of unique estimation of the unknown model parameters, making the parameter estimation an even harder optimization task [3]

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