Modeling and simulation: tools for metabolic engineering.

Mathematical modeling is one of the key methodologies of metabolic engineering. Based on a given metabolic model different computational tools for the simulation, data evaluation, systems analysis, prediction, design and optimization of metabolic systems have been developed. The currently used metabolic modeling approaches can be subdivided into structural models, stoichiometric models, carbon flux models, stationary and nonstationary mechanistic models and models with gene regulation. However, the power of a model strongly depends on its basic modeling assumptions, the simplifications made and the data sources used. Model validation turns out to be particularly difficult for metabolic systems. The different modeling approaches are critically reviewed with respect to their potential and benefits for the metabolic engineering cycle. Several tools that have emerged from the different modeling approaches including structural pathway synthesis, stoichiometric pathway analysis, metabolic flux analysis, metabolic control analysis, optimization of regulatory architectures and the evaluation of rapid sampling experiments are discussed.     

A structured approach for selection among candidate metabolic network models and estimation of unknown stoichiometric coefficients

A metabolic network model is one of the cornerstones of the emerging Metabolic Engineering methodology. In this article, special attention is therefore, given to the phase of model building. A five-stage structured approach to metabolic network modeling is introduced. The basic steps are: (1) to collect a priori knowledge on the reaction network and to build candidate network models, (2) to perform an a priori check of the model, (3) to estimate the unknown parameters in the model, (4) to check the identified model for acceptability from a biological and thermodynamic point of view, and (5) to validate the model with new data. The approach is illustrated with a growth system involving baker's yeast growing on mixtures of substrates. Special attention is given to the central uncertainties in metabolic network modeling, i.e., estimation of energetic parameters in the network and the choice of the source of anabolic reducing equivalents NADPH.     

A decompositional approach to parameter estimation in pathway modeling: a case study of the Akt and MAPK pathways and their crosstalk

Parameter estimation is a critical problem in modeling biological pathways. It is difficult because of the large number of parameters to be estimated and the limited experimental data available. In this paper, we propose a decompositional approach to parameter estimation. It exploits the structure of a large pathway model to break it into smaller components, whose parameters can then be estimated independently. This leads to significant improvements in computational efficiency. We present our approach in the context of Hybrid Functional Petri Net modeling and evolutionary search for parameter value estimation. However, the approach can be easily extended to other modeling frameworks and is independent of the search method used. We have tested our approach on a detailed model of the Akt and MAPK pathways with two known and one hypothesized crosstalk mechanisms. The entire model contains 84 unknown parameters. Our simulation results exhibit good correlation with experimental data, and they yield positive evidence in support of the hypothesized crosstalk between the two pathways.     

Parameter estimation in models combining signal transduction and metabolic pathways: the dependent input approach

Biological complexity and limited quantitative measurements pose severe challenges to standard engineering methodologies for modelling and simulation of genes and gene products integrated in a functional network. In particular, parameter quantification is a bottleneck, and therefore parameter estimation, identifiability, and optimal experiment design are important research topics in systems biology. An approach is presented in which unmodelled dynamics are replaced by fictitious 'dependent inputs'. The dependent input approach is particularly useful in validation experiments, because it allows one to fit model parameters to experimental data generated by a reference cell type ('wild-type') and then test this model on data generated by a variation ('mutant'), so long as the mutations only affect the unmodelled dynamics that produce the dependent inputs. Another novel feature of the approach is in the inclusion of a priori information in a multi-objective identification criterion, making it possible to obtain estimates of parameter values and their variances from a relatively limited experimental data set. The pathways that control the nitrogen uptake fluxes in baker's yeast (Saccharomyces cerevisiae) have been studied. Well-defined perturbation experiments were performed on cells growing in steady-state. Time-series data of extracellular and intracellular metabolites were obtained, as well as mRNA levels. A nonlinear model was proposed and was shown to be structurally identifiable given data of its inputs and outputs. The identified model is a reliable representation of the metabolic system, as it could correctly describe the responses of mutant cells and different perturbations.     

Integrative top-down system metabolic modeling in experimental disease states via data-driven Bayesian methods

Multivariate metabolic profiles from biofluids such as urine and plasma are highly indicative of the biological fitness of complex organisms and can be captured analytically in order to derive top-down systems biology models. The application of currently available modeling approaches to human and animal metabolic pathway modeling is problematic because of multicompartmental cellular and tissue exchange of metabolites operating on many time scales. Hence, novel approaches are needed to analyze metabolic data obtained using minimally invasive sampling methods in order to reconstruct the patho-physiological modulations of metabolic interactions that are representative of whole system dynamics. Here, we show that spectroscopically derived metabolic data in experimental liver injury studies (induced by hydrazine and alpha-napthylisothiocyanate treatment) can be used to derive insightful probabilistic graphical models of metabolite dependencies, which we refer to as metabolic interactome maps. Using these, system level mechanistic information on homeostasis can be inferred, and the degree of reversibility of induced lesions can be related to variations in the metabolic network patterns. This approach has wider application in assessment of system level dysfunction in animal or human studies from noninvasive measurements.     

Plant Metabolic Modeling: Achieving New Insight into Metabolism and Metabolic Engineering

Models are used to represent aspects of the real world for specific purposes, and mathematical models have opened up new approaches in studying the behavior and complexity of biological systems. However, modeling is often time-consuming and requires significant computational resources for data development, data analysis, and simulation. Computational modeling has been successfully applied as an aid for metabolic engineering in microorganisms. But such model-based approaches have only recently been extended to plant metabolic engineering, mainly due to greater pathway complexity in plants and their highly compartmentalized cellular structure. Recent progress in plant systems biology and bioinformatics has begun to disentangle this complexity and facilitate the creation of efficient plant metabolic models. This review highlights several aspects of plant metabolic modeling in the context of understanding, predicting and modifying complex plant metabolism. We discuss opportunities for engineering photosynthetic carbon metabolism, sucrose synthesis, and the tricarboxylic acid cycle in leaves and oil synthesis in seeds and the application of metabolic modeling to the study of plant acclimation to the environment. The aim of the review is to offer a current perspective for plant biologists without requiring specialized knowledge of bioinformatics or systems biology.     

湖泊生态系统动力学模型研究进展

从系统分析在湖泊生态系统动力学研究中的作用出发,对湖泊生态系统的动力学建模过程、方法和软件等进行了总结.在此基础上,综述了国内外湖泊生态系统动力学模型的发展.从1960年代至今,湖泊生态系统动力学模型从简单的零维模型发展到复杂的水质水动力学生态综合模型和生态结构动力学模型,如LakeWeb模型.中国的湖泊生态系统动力学模型研究始于20世纪80年代,主要集中在滇池、太湖、东湖和巢湖等富营养化严重的湖泊以及其他水体.目前,已经开发一些软件用于湖泊生态系统动力学模拟,主要有CEQUALICM、WASP、AQUATOX、PAMOLARE、CAEDYM等,以及用来模拟湖泊能流的软件ECOPATH.湖泊生态系统动力学模型还在监测、数据共享和模型结构、参数选取和不确定性分析等方面存在不足,需在今后的研究中加以改进.     

Estimating parameters of a forest ecosystem C model with measurements of stocks and fluxes as joint constraints

We conducted an inverse modeling analysis, using a variety of data streams (tower-based eddy covariance measurements of net ecosystem exchange, NEE, of CO₂, chamber-based measurements of soil respiration, and ancillary ecological measurements of leaf area index, litterfall, and woody biomass increment) to estimate parameters and initial carbon (C) stocks of a simple forest C-cycle model, DALEC, using Monte Carlo procedures. Our study site is the spruce-dominated Howland Forest AmeriFlux site, in central Maine, USA. Our analysis focuses on: (1) full characterization of data uncertainties, and treatment of these uncertainties in the parameter estimation; (2) evaluation of how combinations of different data streams influence posterior parameter distributions and model uncertainties; and (3) comparison of model performance (in terms of both predicted fluxes and pool dynamics) during a 4-year calibration period (1997–2000) and a 4-year validation period (“forward run”, 2001–2004). We find that woody biomass increment, and, to a lesser degree, soil respiration, measurements contribute to marked reductions in uncertainties in parameter estimates and model predictions as these provide orthogonal constraints to the tower NEE measurements. However, none of the data are effective at constraining fine root or soil C pool dynamics, suggesting that these should be targets for future measurement efforts. A key finding is that adding additional constraints not only reduces uncertainties (i.e., narrower confidence intervals) on model predictions, but at the same time also results in improved model predictions by greatly reducing bias associated with predictions during the forward run.     

Subcellular metabolic organization in the context of dynamic energy budget and biochemical systems theories

The dynamic modelling of metabolic networks aims to describe the temporal evolution of metabolite concentrations in cells. This area has attracted increasing attention in recent years owing to the availability of high-throughput data and the general development of systems biology as a promising approach to study living organisms. Biochemical Systems Theory (BST) provides an accurate formalism to describe biological dynamic phenomena. However, knowledge about the molecular organization level, used in these models, is not enough to explain phenomena such as the driving forces of these metabolic networks. Dynamic Energy Budget (DEB) theory captures the quantitative aspects of the organization of metabolism at the organism level in a way that is non-species-specific. This imposes constraints on the sub-organismal organization that are not present in the bottom-up approach of systems biology. We use in vivo data of lactic acid bacteria under various conditions to compare some aspects of BST and DEB approaches. Due to the large number of parameters to be estimated in the BST model, we applied powerful parameter identification techniques. Both models fitted equally well, but the BST model employs more parameters. The DEB model uses similarities of processes under growth and no-growth conditions and under aerobic and anaerobic conditions, which reduce the number of parameters. This paper discusses some future directions for the integration of knowledge from these two rich and promising areas, working top-down and bottom-up simultaneously. This middle-out approach is expected to bring new ideas and insights to both areas in terms of describing how living organisms operate.     

A glucose-insulin pharmacodynamic surface modeling validation and comparison of metabolic system models

Metabolic system modeling for model-based glycaemic control is becoming increasingly important. Few metabolic system models are clinically validated for both fit to the data and prediction ability. This research introduces a new additional form of pharmaco-dynamic (PD) surface comparison for model analysis and validation. These 3D surfaces are developed for 3 clinically validated models and 1 model with an added saturation dynamic. The models include the well-known Minimal Model. They are fit to two different data sets of clinical PD data from hyperinsulinaemic clamp studies at euglycaemia and/or hyperglycaemia. The models are fit to the first data set to determine an optimal set of population parameters. The second data set is used to test trend prediction of the surface modeling as it represents a lower insulin sensitivity cohort and should thus require only scaling in these (or related) parameters to match this data set. This particular approach clearly highlights differences in modeling methods, and the model dynamics utilized that may not appear as clearly in other fitting or prediction validation methods.Across all models saturation of insulin action is seen to be an important determinant of prediction and fit quality. In particular, the well-reported under-modeling of insulin sensitivity in the Minimal Model can be seen in this context to be a result of a lack of saturation dynamics, which in turn affects its ability to detect differences between cohorts. The overall approach of examining PD surfaces is seen to be an effective means of analyzing and thus validating a metabolic model's inherent dynamics and basic trend prediction on a population level, but is not a replacement for data driven, patient-specific fit and prediction validation for clinical use. The overall method presented could be readily generalized to similar PD systems and therapeutics.     

Diverse metabolic model parameters generate similar methionine cycle dynamics

Parameter estimation constitutes a major challenge in dynamic modeling of metabolic networks. Here we examine, via computational simulations, the influence of system nonlinearity and the nature of available data on the distribution and predictive capability of identified model parameters. Simulated methionine cycle metabolite concentration data (both with and without corresponding flux data) was inverted to identify model parameters consistent with it. Thousands of diverse parameter families were found to be consistent with the data to within moderate error, with most of the parameter values spanning over 1000-fold ranges irrespective of whether flux data was included. Due to strong correlations within the extracted parameter families, model predictions were generally reliable despite the broad ranges found for individual parameters. Inclusion of flux data, by strengthening these correlations, resulted in substantially more reliable flux predictions. These findings suggest that, despite the difficulty of extracting biochemically accurate model parameters from system level data, such data may nevertheless prove adequate for driving the development of predictive dynamic metabolic models.     

Bringing metabolic networks to life: integration of kinetic, metabolic, and proteomic data

Background

Translating a known metabolic network into a dynamic model requires reasonable guesses of all enzyme parameters. In Bayesian parameter estimation, model parameters are described by a posterior probability distribution, which scores the potential parameter sets, showing how well each of them agrees with the data and with the prior assumptions made.

Results

We compute posterior distributions of kinetic parameters within a Bayesian framework, based on integration of kinetic, thermodynamic, metabolic, and proteomic data. The structure of the metabolic system (i.e., stoichiometries and enzyme regulation) needs to be known, and the reactions are modelled by convenience kinetics with thermodynamically independent parameters. The parameter posterior is computed in two separate steps: a first posterior summarises the available data on enzyme kinetic parameters; an improved second posterior is obtained by integrating metabolic fluxes, concentrations, and enzyme concentrations for one or more steady states. The data can be heterogenous, incomplete, and uncertain, and the posterior is approximated by a multivariate log-normal distribution. We apply the method to a model of the threonine synthesis pathway: the integration of metabolic data has little effect on the marginal posterior distributions of individual model parameters. Nevertheless, it leads to strong correlations between the parameters in the joint posterior distribution, which greatly improve the model predictions by the following Monte-Carlo simulations.

Conclusion

We present a standardised method to translate metabolic networks into dynamic models. To determine the model parameters, evidence from various experimental data is combined and weighted using Bayesian parameter estimation. The resulting posterior parameter distribution describes a statistical ensemble of parameter sets; the parameter variances and correlations can account for missing knowledge, measurement uncertainties, or biological variability. The posterior distribution can be used to sample model instances and to obtain probabilistic statements about the model's dynamic behaviour.     

PEtab—Interoperable specification of parameter estimation problems in systems biology

Reproducibility and reusability of the results of data-based modeling studies are essential. Yet, there has been—so far—no broadly supported format for the specification of parameter estimation problems in systems biology. Here, we introduce PEtab, a format which facilitates the specification of parameter estimation problems using Systems Biology Markup Language (SBML) models and a set of tab-separated value files describing the observation model and experimental data as well as parameters to be estimated. We already implemented PEtab support into eight well-established model simulation and parameter estimation toolboxes with hundreds of users in total. We provide a Python library for validation and modification of a PEtab problem and currently 20 example parameter estimation problems based on recent studies.     

A Bayesian framework for parameter estimation in dynamical models

Mathematical models in biology are powerful tools for the study and exploration of complex dynamics. Nevertheless, bringing theoretical results to an agreement with experimental observations involves acknowledging a great deal of uncertainty intrinsic to our theoretical representation of a real system. Proper handling of such uncertainties is key to the successful usage of models to predict experimental or field observations. This problem has been addressed over the years by many tools for model calibration and parameter estimation. In this article we present a general framework for uncertainty analysis and parameter estimation that is designed to handle uncertainties associated with the modeling of dynamic biological systems while remaining agnostic as to the type of model used. We apply the framework to fit an SIR-like influenza transmission model to 7 years of incidence data in three European countries: Belgium, the Netherlands and Portugal.     

Modeling and simulation of molecular biology systems using petri nets: modeling goals of various approaches

Petri nets are a discrete event simulation approach developed for system representation, in particular for their concurrency and synchronization properties. Various extensions to the original theory of Petri nets have been used for modeling molecular biology systems and metabolic networks. These extensions are stochastic, colored, hybrid and functional. This paper carries out an initial review of the various modeling approaches based on Petri net found in the literature, and of the biological systems that have been successfully modeled with these approaches. Moreover, the modeling goals and possibilities of qualitative analysis and system simulation of each approach are discussed.     

Are Assumptions about the Model Type Necessary in Reaction-Diffusion Modeling? A FRAP Application

At present, fluorescence recovery after photobleaching (FRAP) data are interpreted using various types of reaction-diffusion (RD) models: the model type is usually fixed first, and corresponding model parameters are inferred subsequently. In this article, we describe what we believe to be a novel approach for RD modeling without using any assumptions of model type or parameters. To the best of our knowledge, this is the first attempt to address both model-type and parameter uncertainties in inverting FRAP data. We start from the most general RD model, which accounts for a flexible number of molecular fractions, all mobile, with different diffusion coefficients. The maximal number of possible binding partners is identified and optimal parameter sets for these models are determined in a global search of the parameter-space using the Simulated Annealing strategy. The numerical performance of the described techniques was assessed using artificial and experimental FRAP data. Our general RD model outperformed the standard RD models used previously in modeling FRAP measurements and showed that intracellular molecular mobility can only be described adequately by allowing for multiple RD processes. Therefore, it is important to search not only for the optimal parameter set but also for the optimal model type.     

Cellular signaling identifiability analysis: A case study

Two primary purposes for mathematical modeling in cell biology are (1) simulation for making predictions of experimental outcomes and (2) parameter estimation for drawing inferences from experimental data about unobserved aspects of biological systems. While the former purpose has become common in the biological sciences, the latter is less common, particularly when studying cellular and subcellular phenomena such as signaling—the focus of the current study. Data are difficult to obtain at this level. Therefore, even models of only modest complexity can contain parameters for which the available data are insufficient for estimation. In the present study, we use a set of published cellular signaling models to address issues related to global parameter identifiability. That is, we address the following question: assuming known time courses for some model variables, which parameters is it theoretically impossible to estimate, even with continuous, noise-free data? Following an introduction to this problem and its relevance, we perform a full identifiability analysis on a set of cellular signaling models using DAISY (Differential Algebra for the Identifiability of SYstems). We use our analysis to bring to light important issues related to parameter identifiability in ordinary differential equation (ODE) models. We contend that this is, as of yet, an under-appreciated issue in biological modeling and, more particularly, cell biology.     

Metabolic engineering of Bacillus subtilis fueled by systems biology: Recent advances and future directions

By combining advanced omics technology and computational modeling, systems biologists have identified and inferred thousands of regulatory events and system-wide interactions of the bacterium Bacillus subtilis, which is commonly used both in the laboratory and in industry. This dissection of the multiple layers of regulatory networks and their interactions has provided invaluable information for unraveling regulatory mechanisms and guiding metabolic engineering. In this review, we discuss recent advances in the systems biology and metabolic engineering of B. subtilis and highlight current gaps in our understanding of global metabolism and global pathway engineering in this organism. We also propose future perspectives in the systems biology of B. subtilis and suggest ways that this approach can be used to guide metabolic engineering. Specifically, although hundreds of regulatory events have been identified or inferred via systems biology approaches, systematic investigation of the functionality of these events in vivo has lagged, thereby preventing the elucidation of regulatory mechanisms and further rational pathway engineering. In metabolic engineering, ignoring the engineering of multilayer regulation hinders metabolic flux redistribution. Post-translational engineering, allosteric engineering, and dynamic pathway analyses and control will also contribute to the modulation and control of the metabolism of engineered B. subtilis, ultimately producing the desired cellular traits. We hope this review will aid metabolic engineers in making full use of available systems biology datasets and approaches for the design and perfection of microbial cell factories through global metabolism optimization.