Inference of Biological S-System Using the Separable Estimation Method and the Genetic Algorithm

Abstract

Reconstruction of a biological system from its experimental time series data is a challenging task in systems biology. The S-system which consists of a group of nonlinear ordinary differential equations (ODEs) is an effective model to characterize molecular biological systems and analyze the system dynamics. However, inference of S-systems without the knowledge of system structure is not a trivial task due to its nonlinearity and complexity. In this paper, a pruning separable parameter estimation algorithm (PSPEA) is proposed for inferring S-systems. This novel algorithm combines the separable parameter estimation method (SPEM) and a pruning strategy, which includes adding an l₁ regularization term to the objective function and pruning the solution with a threshold value. Then, this algorithm is combined with the continuous genetic algorithm (CGA) to form a hybrid algorithm that owns the properties of these two combined algorithms. The performance of the pruning strategy in the proposed algorithm is evaluated from two aspects: the parameter estimation error and structure identification accuracy. The results show that the proposed algorithm with the pruning strategy has much lower estimation error and much higher identification accuracy than the existing method.

Comprehensive Review of Models and Methods for Inferences in Bio-Chemical Reaction Networks

“…Regularization of optimization problems is a strategy to deal with ill-conditioned problems due to insufficient or noisy data for a given number of parameters to be estimated (Gábor and Banga, 2014;Gábor et al, 2017). In particular, regularization introduces additional constraints to penalize complexity or constraints on parameters values using prior knowledge which can trade-off estimator bias with its variance while not over-fitting model (Kravaris et al, 2013;Jang et al, 2016;Liu et al, 2012). Alternatively, perturbation method has been developed to for fitting data in (Shiang, 2009).…”

“…S-system model is a set of decoupled non-linear ODEs in the form of product of powerlaw functions (Chou et al, 2006;Liu et al, 2012;Meskin et al, 2011;Iwata et al, 2014). Such model is justified by multivariate linearization in logarithmic coordinates.…”

“…Computationally efficient tensor representation of BRNs to facilitate parameter estimation and sensitivity analysis is devised in (Liao et al, 2015a). Other computational models for qualitative description of interactions and behavioral logic in BRNs involve Petri nets (Mazur, 2012;Sun et al, 2012;Schnoerr et al, 2017), probabilistic Boolean networks (Mizera et al, 2014;Liu et al, 2012;Mazur, 2012), continuous time recurrent neural networks (Berrones et al, 2016), and agent based model (ABM) . Hardware description language (HDL) which is normally used to describe logic of electronic circuits is adopted for the case of spatially-dependent biological systems described by PDEs in (Rosati et al, 2018).…”

“…Genetic programming and PSO are combined in (Nobile et al, 2013) whereas fuzzy logic based PSO is developed in . Regularization, pruning and continuous genetic algorithm (CGA) are combined in (Liu et al, 2012).…”

PSO Based PI Controller Design for a Solar Charger System

“…The second stage uses a DC/DC buck converter [10], which controls the charging system by battery voltage and current feedback for the lithium battery, so as to make the system attain constant voltage, current, and voltage charge. The PI controller based on optimal algorithm is designed to achieve the charge control of second stage [11, 12]. This two-stage system can achieve simultaneous MPPT of solar energy and lithium charge control.…”