Generalized Mass Action Model Research Articles

Newton Competitive Genetic Algorithm Method for Optimization the Production of Biochemical Systems

In this work, the optimization of biochemical systems production is performed by using a hybrid method of Newton competitive genetic algorithm is presented. The proposed method works by representing the biochemical systems as a generalized mass action model, where it leads to the process of solving a complex non-linear equations system. The optimization process becomes hard and difficult when it involves multi-objective problem. This is where two objectives, namely the maximize the biochemical systems production and minimize the total amount of chemical concentrations involves. To deal with the problem, this work proposed a hybrid method of the Newton method, genetic algorithm, and competitive co-evolutionary algorithm. The proposed method was experimentally applied on the benchmark biochemical systems and the experimental results showed that the proposed method achieved better results compared to the existing works.

A newton cooperative genetic algorithm method for in silico optimization of metabolic pathway production.

This paper presents an in silico optimization method of metabolic pathway production. The metabolic pathway can be represented by a mathematical model known as the generalized mass action model, which leads to a complex nonlinear equations system. The optimization process becomes difficult when steady state and the constraints of the components in the metabolic pathway are involved. To deal with this situation, this paper presents an in silico optimization method, namely the Newton Cooperative Genetic Algorithm (NCGA). The NCGA used Newton method in dealing with the metabolic pathway, and then integrated genetic algorithm and cooperative co-evolutionary algorithm. The proposed method was experimentally applied on the benchmark metabolic pathways, and the results showed that the NCGA achieved better results compared to the existing methods.

Parameter estimation of dynamic biological network models using integrated fluxes

BackgroundParameter estimation is often the bottlenecking step in biological system modeling. For ordinary differential equation (ODE) models, the challenge in this estimation has been attributed to not only the lack of parameter identifiability, but also computational issues such as finding globally optimal parameter estimates over highly multidimensional search space. Recent methods using incremental estimation approach could alleviate the computational difficulty by performing the parameter estimation one-reaction-at-a-time. However, incremental estimation strategies usually require data smoothing and are known to produce biased parameter estimates.ResultsIn this article, we presented a new parameter estimation method called integrated flux parameter estimation (IFPE). We employed the integral form of the ODE such that we could compute the integral of reaction fluxes from time-series concentration data without data smoothing. Here, we formulated the parameter estimation as a nested optimization problem. In the outer optimization, we performed a minimization of model prediction errors over parameters associated with a subset of reactions labeled as independent. The dimension of the independent reaction subset was equal to the degrees of freedom in the calculation of integrated fluxes (IF) from concentration data. We selected the independent reactions such that given their IF values, the IFs of the remaining (dependent) reactions could be uniquely determined. Meanwhile, in the inner optimization, we estimated the model parameters associated with the dependent reactions, one-reaction-at-a-time, by minimizing the dependent IF prediction errors. We demonstrated the performance of the IFPE method using two case studies: a generalized mass action model of a branched pathway and a lin-log ODE model of Lactococcus lactis glycolytic pathway.ConclusionsThe IFPE significantly outperformed standard simultaneous parameter estimation in terms of computational efficiency and scaling. In comparison to incremental parameter estimation (IPE) method, the IFPE produced parameter estimates with significantly lower bias and did not require time-series data smoothing. The advantages of IFPE over the IPE however came at the cost of a small increase in the computational time.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-014-0127-x) contains supplementary material, which is available to authorized users.

Simulation of the Denitrification Process of Waste Water with a Biochemical Systems Model: A Non-Conventional Approach

Abstract Matching experimental and theoretical approaches have often been fruitful in the investigation of complex biological processes. Here we develop a novel non-conventional model for the denitrification of waste water. Earlier models of the denitrification process were compiled by the International Association on Water Quality group. The Activated Sludge Models 1–3, which are the most frequently used all over the world, are presently not adapted towards the integration of both nitrous and nitric oxide emissions during the denitrification process. In the present work, a Generalized Mass Action model, based on Biochemical Systems Theory, was designed to simulate the nitrate reduction observed in specific experimental conditions. The model was implemented and analysed with the software package PLAS. Data from a representative experiment were chosen (T=10°C, pH=7, C/N=3, with acetate as carbon source) to simulate greenhouse NO and N2O gas emissions, in order to test hypotheses about the corresponding bacterial metabolic pathways. The results show that the reduction of nitrate and nitrite is kinetically limiting and that nitrate reduction is limited by diffusion and support that distinct microbial subpopulations are involved in the denitrification pathway, which has consequences for NO emissions.

Modeling and validation of autoinducer-mediated bacterial gene expression in microfluidic environments.

Biosensors exploiting communication within genetically engineered bacteria are becoming increasingly important for monitoring environmental changes. Currently, there are a variety of mathematical models for understanding and predicting how genetically engineered bacteria respond to molecular stimuli in these environments, but as sensors have miniaturized towards microfluidics and are subjected to complex time-varying inputs, the shortcomings of these models have become apparent. The effects of microfluidic environments such as low oxygen concentration, increased biofilm encapsulation, diffusion limited molecular distribution, and higher population densities strongly affect rate constants for gene expression not accounted for in previous models. We report a mathematical model that accurately predicts the biological response of the autoinducer N-acyl homoserine lactone-mediated green fluorescent protein expression in reporter bacteria in microfluidic environments by accommodating these rate constants. This generalized mass action model considers a chain of biomolecular events from input autoinducer chemical to fluorescent protein expression through a series of six chemical species. We have validated this model against experimental data from our own apparatus as well as prior published experimental results. Results indicate accurate prediction of dynamics (e.g., 14% peak time error from a pulse input) and with reduced mean-squared error with pulse or step inputs for a range of concentrations (10 μM-30 μM). This model can help advance the design of genetically engineered bacteria sensors and molecular communication devices.

An Improved Geometric Programming Approach for Optimization of Biochemical Systems

This paper proposes an improved geometric programming approach to address the optimization of biochemical systems. In the proposed method we take advantage of a special and interesting class of nonlinear kinetic models known as generalized mass action (GMA) models. In most situations optimization problems with GMA models are nonconvex and difficult problems to solve for global optimality. To deal with this difficulty, in this work, some transformation strategy is first used to convert the optimization problem with GMA models into an equivalent problem. Then a convexification technique is applied to transform this resulting optimization problem into a series of standard geometric programming problems that can be solved to reach a global solution. Two case studies are presented to demonstrate the advantages of the proposed method in terms of computational efficiency.

Steady-state optimization of biochemical systems through geometric programming

This paper presents an iterative strategy to address the steady-state optimization of biochemical systems. In the method we take advantage of a special class of nonlinear kinetic models known as Generalized Mass Action (GMA) models. These systems are interesting in that they allow direct merging of stoichiometric and S-system models. In most cases nonconvex steady-state optimization problems with GMA models cannot be transformed into tractable convex formulations, but an iterative strategy can be used to compute the optimal solution by solving a series of geometric programming. The presented framework is applied to several case studies and shown to the tractability and effectiveness of the method. The simulation is also studied to investigate the convergence properties of the algorithm and to give a performance comparison of our proposed and other approaches.

Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models

BackgroundDesign of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization.ResultsBased on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity.ConclusionsOur results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task.

Outer approximation-based algorithm for biotechnology studies in systems biology

Optimization methods play a central role in systems biology studies as they can help in identifying key processes that can be experimentally changed so that specific biological goals can be attained. Standard optimization methods used in this field rely on simplified linear models that may fail in capturing the underlying complexity of the target metabolic network. Within this general context, we present a novel approach to globally optimize metabolic networks. The approach presented relies on (1) adopting a general modeling framework for metabolic networks: the Generalized Mass Action (GMA) representation; (2) posing the optimization task as a non-convex nonlinear programming (NLP) problem; and (3) devising an efficient solution method for globally optimizing the resulting NLP that embeds a GMA model of the metabolic network. The capabilities of our method are illustrated through two case studies: the anaerobic fermentation pathway in Saccharomyces cerevisiae and the citric acid production using Aspergillus niger. Numerical results show that the method presented provides near optimal solutions in low CPU times even in cases where the commercial global optimization package BARON fails to close the optimality gap.

Optimization and evolution in metabolic pathways: Global optimization techniques in Generalized Mass Action models

Cells are natural factories that can adapt to changes in external conditions. Their adaptive responses to specific stress situations are a result of evolution. In theory, many alternative sets of coordinated changes in the activity of the enzymes of each pathway could allow for an appropriate adaptive readjustment of metabolism in response to stress. However, experimental and theoretical observations show that actual responses to specific changes follow fairly well defined patterns that suggest an evolutionary optimization of that response. Thus, it is important to identify functional effectiveness criteria that may explain why certain patterns of change in cellular components and activities during adaptive response have been preferably maintained over evolutionary time. Those functional effectiveness criteria define sets of physiological requirements that constrain the possible adaptive changes and lead to different operation principles that could explain the observed response. Understanding such operation principles can also facilitate biotechnological and metabolic engineering applications. Thus, developing methods that enable the analysis of cellular responses from the perspective of identifying operation principles may have strong theoretical and practical implications. In this paper we present one such method that was designed based on nonlinear global optimization techniques. Our methodology can be used with a special class of nonlinear kinetic models known as GMA models and it allows for a systematic characterization of the physiological requirements that may underlie the evolution of adaptive strategies.

Multi-objective steady state optimization of biochemical reaction networks using a constrained genetic algorithm

A hybrid genetic algorithm-based method to solve constrained multi-objective optimization problems is proposed. Considering operation around a steady state of a dynamical system, the task of the algorithm consists on finding a set of optimal, but constrained solutions. The method is exemplified on a (bio)chemical reaction network in Saccharomyces cerevisiae. In the steady state the model reduces to a system of non-linear equations which must be solved by a search method. This iterative search was integrated into a genetic algorithm in order to look up for optimal steady states. The basic idea is to use individuals of the genetic algorithm as starting points for the search algorithm. The optimization goal was to simultaneously maximize ethanol production and reduce metabolic burden. Two alternative kinetic approaches are compared to Michaelis Menten-type kinetics: a S-System and a generalized mass action model, both based on Power-Law kinetics.

Modeling and simulation of intracellular dynamics: choosing an appropriate framework.

Systems biology is a reemerging paradigm which, among other things, focuses on mathematical modeling and simulation of biochemical reaction networks in intracellular processes. For most simulation tools and publications, they are usually characterized by either preferring stochastic simulation or rate equation models. The use of stochastic simulation is occasionally accompanied with arguments against rate equations. Motivated by these arguments, we discuss in this paper the relationship between these two forms of representation. Toward this end, we provide a novel compact derivation for the stochastic rate constant that forms the basis of the popular Gillespie algorithm. Comparing the mathematical basis of the two popular conceptual frameworks of generalized mass action models and the chemical master equation, we argue that some of the arguments that have been put forward are ignoring subtle differences and similarities that are important for answering the question in which conceptual framework one should investigate intracellular dynamics.

Power-law modeling based on least-squares criteria: consequences for system analysis and simulation

The power-law formalism was initially derived as a Taylor series approximation in logarithmic space for kinetic rate-laws. The resulting models, either as generalized mass action (GMA) or as S-systems models, allow to characterize the target system and to simulate its dynamical behavior in response to external perturbations and parameter changes. This approach has been succesfully used as a modeling tool in many applications from cell metabolism to population dynamics. Without leaving the general formalism, we recently proposed to derive the power-law representation in an alternative way that uses least-squares (LS) minimization instead of the traditional derivation based on Taylor series [B. Hernández-Bermejo, V. Fairén, A. Sorribas, Math. Biosci. 161 (1999) 83–94]. It was shown that the resulting LS power-law mimics the target rate-law in a wider range of concentration values than the classical power-law, and that the prediction of the steady-state using the LS power-law is closer to the actual steady-state of the target system. However, many implications of this alternative approach remained to be established. We explore some of them in the present work. Firstly, we extend the definition of the LS power-law within a given operating interval in such a way that no preferred operating point is selected. Besides providing an alternative to the classical Taylor power-law, that can be considered a particular case when the operating interval is reduced to a single point, the LS power-law so defined is consistent with the results that can be obtained by fitting experimental data points. Secondly, we show that the LS approach leads to a system description, either as an S-system or a GMA model, in which the systemic properties (such as the steady-state prediction or the log-gains) appear averaged over the corresponding interval when compared with the properties that can be computed from Taylor-derived models in different operating points within the considered operating range. Finally, we also show that the LS description leads to a global, accurate description of the system when it is submitted to external forcing.