Dynamics of Positional Enrichment: Theoretical Development and Application to Carbon Labeling in Zymomonas mobilis

Biochemical Systems Theory: A Review

Biochemical systems theory (BST) is the foundation for a set of analytical andmodeling tools that facilitate the analysis of dynamic biological systems. This paper depicts major developments in BST up to the current state of the art in 2012. It discusses its rationale, describes the typical strategies and methods of designing, diagnosing, analyzing, and utilizing BST models, and reviews areas of application. The paper is intended as a guide for investigators entering the fascinating field of biological systems analysis and as a resource for practitioners and experts.

Mathematical modeling and validation of the ergosterol pathway in Saccharomyces cerevisiae

The de novo biosynthetic machinery for both sphingolipid and ergosterol production in yeast is localized in the endoplasmic reticulum (ER) and Golgi. The interconnections between the two pathways are still poorly understood, but they may be connected in specialized membrane domains, and specific knockouts strongly suggest that both routes have different layers of mutual control and are co-affected by drugs. With the goal of shedding light on the functional integration of the yeast sphingolipid-ergosterol (SL-E) pathway, we constructed a dynamic model of the ergosterol pathway using the guidelines of Biochemical Systems Theory (BST) (Savageau., J. theor. Biol., 25, 365–9, 1969). The resulting model was merged with a previous mathematical model of sphingolipid metabolism in yeast (Alvarez-Vasquez et al., J. theor. Biol., 226, 265–91, 2004; Alvarez-Vasquez et al., Nature433, 425–30, 2005). The S-system format within BST was used for analyses of consistency, stability, and sensitivity of the SL-E model, while the GMA format was used for dynamic simulations and predictions. Model validation was accomplished by comparing predictions from the model with published results on sterol and sterol-ester dynamics in yeast. The validated model was used to predict the metabolomic dynamics of the SL-E pathway after drug treatment. Specifically, we simulated the action of drugs affecting sphingolipids in the endoplasmic reticulum and studied changes in ergosterol associated with microdomains of the plasma membrane (PM).

Recent developments in parameter estimation and structure identification of biochemical and genomic systems

The organization, regulation and dynamical responses of biological systems are in many cases too complex to allow intuitive predictions and require the support of mathematical modeling for quantitative assessments and a reliable understanding of system functioning. All steps of constructing mathematical models for biological systems are challenging, but arguably the most difficult task among them is the estimation of model parameters and the identification of the structure and regulation of the underlying biological networks. Recent advancements in modern high-throughput techniques have been allowing the generation of time series data that characterize the dynamics of genomic, proteomic, metabolic, and physiological responses and enable us, at least in principle, to tackle estimation and identification tasks using 'top-down' or 'inverse' approaches. While the rewards of a successful inverse estimation or identification are great, the process of extracting structural and regulatory information is technically difficult. The challenges can generally be categorized into four areas, namely, issues related to the data, the model, the mathematical structure of the system, and the optimization and support algorithms. Many recent articles have addressed inverse problems within the modeling framework of Biochemical Systems Theory (BST). BST was chosen for these tasks because of its unique structural flexibility and the fact that the structure and regulation of a biological system are mapped essentially one-to-one onto the parameters of the describing model. The proposed methods mainly focused on various optimization algorithms, but also on support techniques, including methods for circumventing the time consuming numerical integration of systems of differential equations, smoothing overly noisy data, estimating slopes of time series, reducing the complexity of the inference task, and constraining the parameter search space. Other methods targeted issues of data preprocessing, detection and amelioration of model redundancy, and model-free or model-based structure identification. The total number of proposed methods and their applications has by now exceeded one hundred, which makes it difficult for the newcomer, as well as the expert, to gain a comprehensive overview of available algorithmic options and limitations. To facilitate the entry into the field of inverse modeling within BST and related modeling areas, the article presented here reviews the field and proposes an operational 'work-flow' that guides the user through the estimation process, identifies possibly problematic steps, and suggests corresponding solutions based on the specific characteristics of the various available algorithms. The article concludes with a discussion of the present state of the art and with a description of open questions.