A dual-parameter identification approach for data-based predictive modeling of hybrid gene regulatory network-growth kinetics in Pseudomonas putida mt-2.

Data integration to model-based description of biological systems incorporating gene dynamics improves the performance of microbial systems. Bioprocess performance, typically predicted using empirical Monod-type models, is essential for a sustainable bioeconomy. To replace empirical models, we updated a hybrid gene regulatory network-growth kinetic model, predicting aromatic pollutants degradation and biomass growth in Pseudomonas putida mt-2. We modeled a complex biological system including extensive information to understand the role of the regulatory elements in toluene biodegradation and biomass growth. The updated model exhibited extra complications such as the existence of oscillations and discontinuities. As parameter estimation of complex biological models remains a key challenge, we used the updated model to present a dual-parameter identification approach (the 'dual approach') combining two independent methodologies. Approach I handled the complexity by incorporation of demonstrated biological knowledge in the model-development process and combination of global sensitivity analysis and optimisation. Approach II complemented Approach I handling multimodality, ill-conditioning and overfitting through regularisation estimation, global optimisation, and identifiability analysis. To systematically quantify the biological system, we used a vast amount of high-quality time-course data. The dual approach resulted in an accurately calibrated kinetic model (NRMSE: 0.17055) efficiently handling the additional model complexity. We tested model validation using three independent experimental data sets, achieving greater predictive power (NRMSE: 0.18776) than the individual approaches (NRMSE I: 0.25322, II: 0.25227) and increasing model robustness. These results demonstrated data-driven predictive modeling potentially leading to bioprocess' model-based control and optimisation.

Parameter estimation in models of biological oscillators: an automated regularised estimation approach.

BACKGROUND: Dynamic modelling is a core element in the systems biology approach to understanding complex biosystems. Here, we consider the problem of parameter estimation in models of biological oscillators described by deterministic nonlinear differential equations. These problems can be extremely challenging due to several common pitfalls: (i) a lack of prior knowledge about parameters (i.e. massive search spaces), (ii) convergence to local optima (due to multimodality of the cost function), (iii) overfitting (fitting the noise instead of the signal) and (iv) a lack of identifiability. As a consequence, the use of standard estimation methods (such as gradient-based local ones) will often result in wrong solutions. Overfitting can be particularly problematic, since it produces very good calibrations, giving the impression of an excellent result. However, overfitted models exhibit poor predictive power. Here, we present a novel automated approach to overcome these pitfalls. Its workflow makes use of two sequential optimisation steps incorporating three key algorithms: (1) sampling strategies to systematically tighten the parameter bounds reducing the search space, (2) efficient global optimisation to avoid convergence to local solutions, (3) an advanced regularisation technique to fight overfitting. In addition, this workflow incorporates tests for structural and practical identifiability. RESULTS: We successfully evaluate this novel approach considering four difficult case studies regarding the calibration of well-known biological oscillators (Goodwin, FitzHugh-Nagumo, Repressilator and a metabolic oscillator). In contrast, we show how local gradient-based approaches, even if used in multi-start fashion, are unable to avoid the above-mentioned pitfalls. CONCLUSIONS: Our approach results in more efficient estimations (thanks to the bounding strategy) which are able to escape convergence to local optima (thanks to the global optimisation approach). Further, the use of regularisation allows us to avoid overfitting, resulting in more generalisable calibrated models (i.e. models with greater predictive power).