Estimation of Small-Scale Kinetic Parameters of Escherichia coli (E. coli) Model by Enhanced Segment Particle Swarm Optimization Algorithm ESe-PSO

The ability to create “structured models” of biological simulations is becoming more and more commonplace. Although computer simulations can be used to estimate the model, they are restricted by the lack of experimentally available parameter values, which must be approximated. In this study, an Enhanced Segment Particle Swarm Optimization (ESe-PSO) algorithm that can estimate the values of small-scale kinetic parameters is described and applied to E. coli’s main metabolic network as a model system. The glycolysis, phosphotransferase system, pentose phosphate, the TCA cycle, gluconeogenesis, glyoxylate pathways, and acetate formation pathways of Escherichia coli are represented by the Differential Algebraic Equations (DAE) system for the metabolic network. However, this algorithm uses segments to organize particle movements and the dynamic inertia weight (ω) to increase the algorithm’s exploration and exploitation potential. As an alternative to the state-of-the-art algorithm, this adjustment improves estimation accuracy. The numerical findings indicate a good agreement between the observed and predicted data. In this regard, the result of the ESe-PSO algorithm achieved superior accuracy compared with the Segment Particle Swarm Optimization (Se-PSO), Particle Swarm Optimization (PSO), Genetic Algorithm (GA), and Differential Evolution (DE) algorithms. As a result of this innovative approach, it was concluded that small-scale and even entire cell kinetic model parameters can be developed.

An Enhanced Segment Particle Swarm Optimization Algorithm for Kinetic Parameters Estimation of the Main Metabolic Model of Escherichia Coli

Building a biologic model that describes the behavior of a cell in biologic systems is aimed at understanding the physiology of the cell, predicting the production of enzymes and metabolites, and providing a suitable data that is valid for bio-products. In addition, building a kinetic model requires the estimation of the kinetic parameters, but kinetic parameters estimation in kinetic modeling is a difficult task due to the nonlinearity of the model. As a result, kinetic parameters are mostly reported or estimated from different laboratories in different conditions and time consumption. Hence, based on the aforementioned problems, the optimization algorithm methods played an important role in addressing these problems. In this study, an Enhanced Segment Particle Swarm Optimization algorithm (ESe-PSO) was proposed for kinetic parameters estimation. This method was proposed to increase the exploration and the exploitation of the Segment Particle Swarm Optimization algorithm (Se-PSO). The main metabolic model of E. coli was used as a benchmark which contained 172 kinetic parameters distributed in five pathways. Seven kinetic parameters were well estimated based on the distance minimization between the simulation and the experimental results. The results revealed that the proposed method had the ability to deal with kinetic parameters estimation in terms of time consumption and distance minimization.

Finite-time parametric identification for the model representing the metabolic and genetic regulatory effects of sequential aerobic respiration and anaerobic fermentation processes in Escherichia coli

Mathematical modelling applied to biological systems allows for the inferring of changes in the dynamic behaviour of organisms associated with variations in the environment. Models based on ordinary differential equations are most commonly used because of their ability to describe the mechanisms of biological systems such as transcription. The disadvantage of using this approach is that there is a large number of parameters involved and that it is difficult to obtain them experimentally. This study presents an algorithm to obtain a finite-time parameter characterization of the model used to describe changes in the metabolic behaviour of Escherichia coli associated with environmental changes. In this scheme, super-twisting algorithm was proposed to recover the derivative of all the proteins and mRNA of E. coli associated to changes in the concentration of oxygen available in the growth media. The 75 identified parameters in this study maintain the biological coherence of the system and they were estimated with no more than 20% error with respect to the real ones included in the proposed model.

The best models of metabolism

Biochemical systems are among of the oldest application areas of mathematical modeling. Spanning a time period of over one hundred years, the repertoire of options for structuring a model and for formulating reactions has been constantly growing, and yet, it is still unclear whether or to what degree some models are better than others and how the modeler is to choose among them. In fact, the variety of options has become overwhelming and difficult to maneuver for novices and experts alike. This review outlines the metabolic model design process and discusses the numerous choices for modeling frameworks and mathematical representations. It tries to be inclusive, even though it cannot be complete, and introduces the various modeling options in a manner that is as unbiased as that is feasible. However, the review does end with personal recommendations for the choices of default models. WIREs Syst Biol Med 2017, 9:e1391. doi: 10.1002/wsbm.1391 For further resources related to this article, please visit the WIREs website.

Kriging-Based Parameter Estimation Algorithm for Metabolic Networks Combined with Single-Dimensional Optimization and Dynamic Coordinate Perturbation

The metabolic network model allows for an in-depth insight into the molecular mechanism of a particular organism. Because most parameters of the metabolic network cannot be directly measured, they must be estimated by using optimization algorithms. However, three characteristics of the metabolic network model, i.e., high nonlinearity, large amount parameters, and huge variation scopes of parameters, restrict the application of many traditional optimization algorithms. As a result, there is a growing demand to develop efficient optimization approaches to address this complex problem. In this paper, a Kriging-based algorithm aiming at parameter estimation is presented for constructing the metabolic networks. In the algorithm, a new infill sampling criterion, named expected improvement and mutual information (EI&MI), is adopted to improve the modeling accuracy by selecting multiple new sample points at each cycle, and the domain decomposition strategy based on the principal component analysis is introduced to save computing time. Meanwhile, the convergence speed is accelerated by combining a single-dimensional optimization method with the dynamic coordinate perturbation strategy when determining the new sample points. Finally, the algorithm is applied to the arachidonic acid metabolic network to estimate its parameters. The obtained results demonstrate the effectiveness of the proposed algorithm in getting precise parameter values under a limited number of iterations.