Parameter estimation in kinetic models for large scale biotechnological systems with advanced mathematical programming techniques (2025)

Hybrid dynamic modeling of Escherichia coli central metabolic network combining Michaelis-Menten and approximate kinetic equations

Bio Systems, 2010

The construction of dynamic metabolic models at reaction network level requires the use of mechanistic enzymatic rate equations that comprise a large number of parameters. The lack of knowledge on these equations and the difficulty in the experimental identification of their associated parameters, represent nowadays the limiting factor in the construction of such models. In this study, we compare four alternative modeling approaches based on Michaelis–Menten kinetics for the bi-molecular reactions and different types of simplified rate equations for the remaining reactions (generalized mass action, convenience kinetics, lin-log and power-law). Using the mechanistic model for Escherichia coli central carbon metabolism as a benchmark, we investigate the alternative modeling approaches through comparative simulations analyses. The good dynamic behavior and the powerful predictive capabilities obtained using the hybrid model composed of Michaelis–Menten and the approximate lin-log kinetics indicate that this is a possible suitable approach to model complex large-scale networks where the exact rate laws are unknown.

Large-Scale Kinetic Parameters Estimation of Metabolic Model of Escherichia Coli

International Journal of Machine Learning and Computing

In the last few decades, the metabolic model of E.coli has attracted the attention of many researchers in the area of biological system modeling. Metabolic models are constructed using mass-balance equations with kinetic-rate computation to simulate the behavior of the metabolic system over time. However, in the development of the metabolic model, large-scale kinetic parameters affect the model response if the parameter values are not assigned accurately, which, in turn, propagates the errors in the ordinary differential equations (ODEs)-the mass balance equations associated with the model. This situation emphasizes the need to adopt a global optimization technique to compute the kinetic parameters such that the errorsthe discrepancy between actual biological data and the model response-are minimized. In this work, the PSO algorithm has been adopted to estimate the kinetic parameters by minimizing the errors of the large-scale of metabolic model response of E. coli with reference to real experimental data. Seven highly sensitive kinetic parameters in the model response were considered in the optimization problem. Estimation of the 7 th kinetic parameters by the PSO method provides a good performance of the model in terms of accuracy.

On a general model structure for macroscopic biological reaction rates

Journal of Biotechnology, 2007

Macroscopic modelling of bioprocesses requires the determination of a biological reaction scheme and a kinetic model. The a priori selection of an appropriate kinetic model structure is usually made difficult by the lack of detailed bioprocess knowledge and the profusion of apparently similar biological kinetic laws. Moreover, parameter identification is made arduous and time-consuming by the strong non-linearities involved in kinetic laws. In most cases, these kinetic structures are non-linearizable and no first parameter estimation can be deduced easily. In order to avoid such identification problems, Bogaerts et al. . A general mathematical modelling technique for bioprocesses in engineering applications. Syst. Anal. Model. Simul. 35, have developed a general linearizable kinetic structure which allows the representation of activation and/or inhibition effects of each component in the culture. This paper further generalizes this structure in order to improve the way saturation effects are taken into account, and in turn, improve the biological interpretation of the model parameters. The main advantage of the proposed structure lies in an associated systematic estimation procedure. The usefulness of the proposed model is tested with simulated as well as with experimental data.

Modeling metabolic networks in C. glutamicum: a comparison of rate laws in combination with various parameter optimization strategies

BMC Systems Biology, 2009

Background: To understand the dynamic behavior of cellular systems, mathematical modeling is often necessary and comprises three steps: (1) experimental measurement of participating molecules, (2) assignment of rate laws to each reaction, and (3) parameter calibration with respect to the measurements. In each of these steps the modeler is confronted with a plethora of alternative approaches, e. g., the selection of approximative rate laws in step two as specific equations are often unknown, or the choice of an estimation procedure with its specific settings in step three. This overall process with its numerous choices and the mutual influence between them makes it hard to single out the best modeling approach for a given problem.

Model and global sensitivity analysis of E. coli central metabolism

2009

This work provides analysis of kinetic behavior of the central metabolism of E. coli upon glucose impulse during the initial transients of 15 seconds. The analysis is based on the model derived from dynamic measurements of the key intracellular metabolites. Response of the central carbon metabolism (glycolysis and pentose phosphate pathway) is decoupled from the anabolic and TCA systems by the transient measurements of the cofactors and oxaloacetate concentrations. The kinetic parameters are initially estimated by the nonlinear Least Squares Method (with Marqardt minimization) and improved by several global optimization algorithms (simplex Nelder-Mead, Simulated Annealing and Differential Evolution). However, due to severe ill-conditioned problem, large errors in the estimates are inherently present. The focus of this research is to reveal which are the most important enzyme effectors, reflected by the corresponding kinetic parameters, responsible for modeling of the input-output fluxes of the central metabolism. Applied is the Fourier Amplitude Sensitivity Test (FAST) for global sensitivity analysis. Identified are the key kinetic parameters responsible for the following fluxes: phosphotransferase system (PTS), nucleotide biosynthesis and pyruvate to biomass. The results could be potentially applicable for understanding of the metabolism regulation and for rational application of genetic engineering.

Analysis of Bioprocesses. Dynamic Modeling is a Must

Materials Today: Proceedings, 2016

BioPreDyn-bench: benchmark problems for kinetic modelling in systems biology

Dynamic modelling is one of the cornerstones of systems biology. Many research efforts are currently being invested in the development and exploitation of large-scale kinetic models. The associated problems of parameter estimation (model calibration) and optimal experimental design are particularly challenging. The community has already developed many methods and software packages which aim to facilitate these tasks. However, there is a lack of suitable benchmark problems which allow a fair and systematic evaluation and comparison of these contributions. Here we present BioPreDyn-bench, a set of challenging parameter estimation problems which aspire to serve as reference test cases in this area. This set comprises six problems including medium and large-scale kinetic models of the bacterium E. coli, baker's yeast S. cerevisiae, the vinegar fly D. melanogaster, Chinese Hamster Ovary cells, and a generic signal transduction network. The level of description includes metabolism, transcription, signal transduction, and development. For each problem we provide (i) a basic description and formulation, (ii) implementations ready-to-run in several formats, (iii) computational results obtained with specific solvers, (iv) a basic analysis and interpretation. This suite of benchmark problems can be readily used to evaluate and compare parameter estimation methods. Further, it can also be used to build test problems for sensitivity and identifiability analysis, model reduction and optimal experimental design methods. The suite, including codes and documentation, can be freely downloaded from http://www.iim.csic.es/˜gingproc/biopredynbench/

Model Identification, Parameter Estimation, and Dynamic Flux Analysis of E. coli Central Metabolism

Chemical and Biochemical Engineering Quarterly

In this work are applied three global optimisation algorithms for adaptation of the mathematical model of the central metabolism of Escherichia coli to data obtained in the experiment with response to glucose impulse. Applied is the adaptive simplex method by Nelder-Mead, evolutionary algorithms of differential evolution, and simulated annealing. The original model has been modified by the following steps: closure of Entner- -Doudoroff pathway with pyruvate balance, introduction of phosphoenolpyruavate carboxylase and carboxykinase reactions in the balance of phosphoenolypyravate, account for loss of pyruvate in biomass synthesis, change in kinetic rate expressions for several enzymes, and partial re-estimation of the kinetic parameters by the global optimisation algorithms. The modified model correctly predicts observed oscillatory response to glucose impulse in concentrations of pyruvate and D-ribose-5-phosphate. To discern metabolic control, evaluated are dynamic intracellular fl...

Non-linear optimization of biochemical pathways: applications to metabolic engineering and parameter estimation

Bioinformatics/computer Applications in The Biosciences, 1998

Motivation: The simulation of biochemical kinetic systems is a powerful approach that can be used for: (i) checking the consistency of a postulated model with a set of experimental measurements, (ii) answering 'what if?' questions and (iii) exploring possible behaviours of a model. Here we describe a generic approach to combine numerical optimization methods with biochemical kinetic simulations, which is suitable for use in the rational design of improved metabolic pathways with industrial significance (metabolic engineering) and for solving the inverse problem of metabolic pathways, i.e. the estimation of parameters from measured variables. Results: We discuss the suitability of various optimization methods, focusing especially on their ability or otherwise to find global optima. We recommend that a suite of diverse optimization methods should be available in simulation software as no single one performs best for all problems. We describe how we have implemented such a simulation-optimization strategy in the biochemical kinetics simulator Gepasi and present examples of its application. Availability: The new version of Gepasi (3.20), incorporating the methodology described here, is available on the Internet at

Modeling of enzyme production kinetics

Applied Microbiology and Biotechnology, 2006

Models of single cells, cell populations, and cultures can be most useful in organizing information in a comprehensive system description, as well as in optimizing and controlling actual production operations. Models discussed in this article are of various degrees of biological structure and mathematical complexity. The models are developed based on the biomass formation, substrate consumption, and product formation. The potentials and the limitations of all the models have been reported. The parameter estimation by different methods has been discussed in this communication. These parameters will be helpful to explore the areas where future-modeling studies may be especially valuable.