Design principles and operating principles: the yin and yang of optimal functioning

Analysis of systemic effects of dioxin on human health through template-and-anchor modeling

Dioxins are persistent environmental pollutants known for their multiple health effects, from skin rashes to liver dysfunction, reproductive toxicity and cancer. While the hazards of dioxins have been well documented, the challenge of developing a comprehensive understanding of the overall health impact of dioxins remains. We propose to address this challenge with a new approach methodology (NAM) consisting of a novel adaptation of the Template-and-Anchor (T&A) modeling paradigm. Generically, the template model is defined as a high-level coarse-grained model capturing the main physiological processes of the system. The variables of this template model are anchor models, which represent component sub-systems in greater detail at lower biological levels. For the case of dioxin, we design the template to capture the systemic effects of dioxin on the body's handling of cholesterol. Two new anchor models within this template elucidate the effects of dioxin on cholesterol transport in the bloodstream and on sex hormone steroidogenesis and the menstrual cycle. A third anchor model, representing dioxin-mediated effects on cholesterol biosynthesis via the mevalonate pathway, had been developed previously. The T&A modeling paradigm enables a holistic evaluation of the impact of toxicants, which in the future may be translated into a powerful tool for comprehensive computational health risk assessments, personalized medicine, and the development of virtual clinical trials.

Engineering microbial chemical factories using metabolic models

Living organisms in analogy with chemical factories use simple molecules such as sugars to produce a variety of compounds which are necessary for sustaining life and some of which are also commercially valuable. The metabolisms of simple (such as bacteria) and higher organisms (such as plants) alike can be exploited to convert low value inputs into high value outputs. Unlike conventional chemical factories, microbial production chassis are not necessarily tuned for a single product overproduction. Despite the same end goal, metabolic and industrial engineers rely on different techniques for achieving productivity goals. Metabolic engineers cannot affect reaction rates by manipulating pressure and temperature, instead they have at their disposal a range of enzymes and transcriptional and translational processes to optimize accordingly. In this review, we first highlight how various analytical approaches used in metabolic engineering and synthetic biology are related to concepts developed in systems and control engineering. Specifically, how algorithmic concepts derived in operations research can help explain the structure and organization of metabolic networks. Finally, we consider the future directions and challenges faced by the field of metabolic network modeling and the possible contributions of concepts drawn from the classical fields of chemical and control engineering. The aim of the review is to offer a current perspective of metabolic engineering and all that it entails without requiring specialized knowledge of bioinformatics or systems biology.

Perspective: Dimensions of the scientific method

The scientific method has been guiding biological research for a long time. It not only prescribes the order and types of activities that give a scientific study validity and a stamp of approval but also has substantially shaped how we collectively think about the endeavor of investigating nature. The advent of high-throughput data generation, data mining, and advanced computational modeling has thrown the formerly undisputed, monolithic status of the scientific method into turmoil. On the one hand, the new approaches are clearly successful and expect the same acceptance as the traditional methods, but on the other hand, they replace much of the hypothesis-driven reasoning with inductive argumentation, which philosophers of science consider problematic. Intrigued by the enormous wealth of data and the power of machine learning, some scientists have even argued that significant correlations within datasets could make the entire quest for causation obsolete. Many of these issues have been passionately debated during the past two decades, often with scant agreement. It is proffered here that hypothesis-driven, data-mining-inspired, and "allochthonous" knowledge acquisition, based on mathematical and computational models, are vectors spanning a 3D space of an expanded scientific method. The combination of methods within this space will most certainly shape our thinking about nature, with implications for experimental design, peer review and funding, sharing of result, education, medical diagnostics, and even questions of litigation.

Quantitative Operating Principles of Yeast Metabolism during Adaptation to Heat Stress

Microorganisms evolved adaptive responses to survive stressful challenges in ever-changing environments. Understanding the relationships between the physiological/metabolic adjustments allowing cellular stress adaptation and gene expression changes being used by organisms to achieve such adjustments may significantly impact our ability to understand and/or guide evolution. Here, we studied those relationships during adaptation to various stress challenges in Saccharomyces cerevisiae, focusing on heat stress responses. We combined dozens of independent experiments measuring whole-genome gene expression changes during stress responses with a simplified kinetic model of central metabolism. We identified alternative quantitative ranges for a set of physiological variables in the model (production of ATP, trehalose, NADH, etc.) that are specific for adaptation to either heat stress or desiccation/rehydration. Our approach is scalable to other adaptive responses and could assist in developing biotechnological applications to manipulate cells for medical, biotechnological, or synthetic biology purposes.

Metrics for regulated biochemical pathway systems

MOTIVATION

The assessment of graphs through crisp numerical metrics has long been a hallmark of biological network analysis. However, typical graph metrics ignore regulatory signals that are crucially important for optimal pathway operation, for instance, in biochemical or metabolic studies. Here we introduce adjusted metrics that are applicable to both static networks and dynamic systems.

RESULTS

The metrics permit quantitative characterizations of the importance of regulation in biochemical pathway systems, including systems designed for applications in synthetic biology or metabolic engineering. They may also become criteria for effective model reduction.

AVAILABILITY AND IMPLEMENTATION

The source code is available at https://gitlab.com/tienbien44/metrics-bsa.

Underlying Principles of Natural Selection in Network Evolution: Systems Biology Approach

Systems biology is a rapidly expanding field that integrates diverse areas of science such as physics, engineering, computer science, mathematics, and biology toward the goal of elucidating the underlying principles of hierarchical metabolic and regulatory systems in the cell, and ultimately leading to predictive understanding of cellular response to perturbations. Because post-genomics research is taking place throughout the tree of life, comparative approaches offer a way for combining data from many organisms to shed light on the evolution and function of biological networks from the gene to the organismal level. Therefore, systems biology can build on decades of theoretical work in evolutionary biology, and at the same time evolutionary biology can use the systems biology approach to go in new uncharted directions. In this study, we present a review of how the post-genomics era is adopting comparative approaches and dynamic system methods to understand the underlying design principles of network evolution and to shape the nascent field of evolutionary systems biology. Finally, the application of evolutionary systems biology to robust biological network designs is also discussed from the synthetic biology perspective.

Perspective: On the importance of hydrodynamic interactions in the subcellular dynamics of macromolecules

An outstanding challenge in computational biophysics is the simulation of a living cell at molecular detail. Over the past several years, using Stokesian dynamics, progress has been made in simulating coarse grained molecular models of the cytoplasm. Since macromolecules comprise 20%-40% of the volume of a cell, one would expect that steric interactions dominate macromolecular diffusion. However, the reduction in cellular diffusion rates relative to infinite dilution is due, roughly equally, to steric and hydrodynamic interactions, HI, with nonspecific attractive interactions likely playing rather a minor role. HI not only serve to slow down long time diffusion rates but also cause a considerable reduction in the magnitude of the short time diffusion coefficient relative to that at infinite dilution. More importantly, the long range contribution of the Rotne-Prager-Yamakawa diffusion tensor results in temporal and spatial correlations that persist up to microseconds and for intermolecular distances on the order of protein radii. While HI slow down the bimolecular association rate in the early stages of lipid bilayer formation, they accelerate the rate of large scale assembly of lipid aggregates. This is suggestive of an important role for HI in the self-assembly kinetics of large macromolecular complexes such as tubulin. Since HI are important, questions as to whether continuum models of HI are adequate as well as improved simulation methodologies that will make simulations of more complex cellular processes practical need to be addressed. Nevertheless, the stage is set for the molecular simulations of ever more complex subcellular processes.

A metabolite-centric view on flux distributions in genome-scale metabolic models

Background

Genome-scale metabolic models are important tools in systems biology. They permit the in-silico prediction of cellular phenotypes via mathematical optimisation procedures, most importantly flux balance analysis. Current studies on metabolic models mostly consider reaction fluxes in isolation. Based on a recently proposed metabolite-centric approach, we here describe a set of methods that enable the analysis and interpretation of flux distributions in an integrated metabolite-centric view. We demonstrate how this framework can be used for the refinement of genome-scale metabolic models.

Results

We applied the metabolite-centric view developed here to the most recent metabolic reconstruction of Escherichia coli. By compiling the balance sheets of a small number of currency metabolites, we were able to fully characterise the energy metabolism as predicted by the model and to identify a possibility for model refinement in NADPH metabolism. Selected branch points were examined in detail in order to demonstrate how a metabolite-centric view allows identifying functional roles of metabolites. Fructose 6-phosphate aldolase and the sedoheptulose bisphosphate bypass were identified as enzymatic reactions that can carry high fluxes in the model but are unlikely to exhibit significant activity in vivo. Performing a metabolite essentiality analysis, unconstrained import and export of iron ions could be identified as potentially problematic for the quality of model predictions.

Conclusions

The system-wide analysis of split ratios and branch points allows a much deeper insight into the metabolic network than reaction-centric analyses. Extending an earlier metabolite-centric approach, the methods introduced here establish an integrated metabolite-centric framework for the interpretation of flux distributions in genome-scale metabolic networks that can complement the classical reaction-centric framework. Analysing fluxes and their metabolic context simultaneously opens the door to systems biological interpretations that are not apparent from isolated reaction fluxes. Particularly powerful demonstrations of this are the analyses of the complete metabolic contexts of energy metabolism and the folate-dependent one-carbon pool presented in this work. Finally, a metabolite-centric view on flux distributions can guide the refinement of metabolic reconstructions for specific growth scenarios.

Mesoscopic modeling as a starting point for computational analyses of cystic fibrosis as a systemic disease

Probably the most prominent expectation associated with systems biology is the computational support of personalized medicine and predictive health. At least some of this anticipated support is envisioned in the form of disease simulators that will take hundreds of personalized biomarker data as input and allow the physician to explore and optimize possible treatment regimens on a computer before the best treatment is applied to the actual patient in a custom-tailored manner. The key prerequisites for such simulators are mathematical and computational models that not only manage the input data and implement the general physiological and pathological principles of organ systems but also integrate the myriads of details that affect their functionality to a significant degree. Obviously, the construction of such models is an overwhelming task that suggests the long-term development of hierarchical or telescopic approaches representing the physiology of organs and their diseases, first coarsely and over time with increased granularity. This article illustrates the rudiments of such a strategy in the context of cystic fibrosis (CF) of the lung. The starting point is a very simplistic, generic model of inflammation, which has been shown to capture the principles of infection, trauma, and sepsis surprisingly well. The adaptation of this model to CF contains as variables healthy and damaged cells, as well as different classes of interacting cytokines and infectious microbes that are affected by mucus formation, which is the hallmark symptom of the disease (Perez-Vilar and Boucher, 2004) [1]. The simple model represents the overall dynamics of the disease progression, including so-called acute pulmonary exacerbations, quite well, but of course does not provide much detail regarding the specific processes underlying the disease. In order to launch the next level of modeling with finer granularity, it is desirable to determine which components of the coarse model contribute most to the disease dynamics. The article introduces for this purpose the concept of module gains or ModGains, which quantify the sensitivity of key disease variables in the higher-level system. In reality, these variables represent complex modules at the next level of granularity, and the computation of ModGains therefore allows an importance ranking of variables that should be replaced with more detailed models. The "hot-swapping" of such detailed modules for former variables is greatly facilitated by the architecture and implementation of the overarching, coarse model structure, which is here formulated with methods of biochemical systems theory (BST). This article is part of a Special Issue entitled: Computational Proteomics, Systems Biology & Clinical Implications. Guest Editor: Yudong Cai.

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.

Identifying the preferred subset of enzymatic profiles in nonlinear kinetic metabolic models via multiobjective global optimization and Pareto filters

Optimization models in metabolic engineering and systems biology focus typically on optimizing a unique criterion, usually the synthesis rate of a metabolite of interest or the rate of growth. Connectivity and non-linear regulatory effects, however, make it necessary to consider multiple objectives in order to identify useful strategies that balance out different metabolic issues. This is a fundamental aspect, as optimization of maximum yield in a given condition may involve unrealistic values in other key processes. Due to the difficulties associated with detailed non-linear models, analysis using stoichiometric descriptions and linear optimization methods have become rather popular in systems biology. However, despite being useful, these approaches fail in capturing the intrinsic nonlinear nature of the underlying metabolic systems and the regulatory signals involved. Targeting more complex biological systems requires the application of global optimization methods to non-linear representations. In this work we address the multi-objective global optimization of metabolic networks that are described by a special class of models based on the power-law formalism: the generalized mass action (GMA) representation. Our goal is to develop global optimization methods capable of efficiently dealing with several biological criteria simultaneously. In order to overcome the numerical difficulties of dealing with multiple criteria in the optimization, we propose a heuristic approach based on the epsilon constraint method that reduces the computational burden of generating a set of Pareto optimal alternatives, each achieving a unique combination of objectives values. To facilitate the post-optimal analysis of these solutions and narrow down their number prior to being tested in the laboratory, we explore the use of Pareto filters that identify the preferred subset of enzymatic profiles. We demonstrate the usefulness of our approach by means of a case study that optimizes the ethanol production in the fermentation of Saccharomyces cerevisiae.

On the Interplay between the Evolvability and Network Robustness in an Evolutionary Biological Network: A Systems Biology Approach

In the evolutionary process, the random transmission and mutation of genes provide biological diversities for natural selection. In order to preserve functional phenotypes between generations, gene networks need to evolve robustly under the influence of random perturbations. Therefore, the robustness of the phenotype, in the evolutionary process, exerts a selection force on gene networks to keep network functions. However, gene networks need to adjust, by variations in genetic content, to generate phenotypes for new challenges in the network's evolution, ie, the evolvability. Hence, there should be some interplay between the evolvability and network robustness in evolutionary gene networks. In this study, the interplay between the evolvability and network robustness of a gene network and a biochemical network is discussed from a nonlinear stochastic system point of view. It was found that if the genetic robustness plus environmental robustness is less than the network robustness, the phenotype of the biological network is robust in evolution. The tradeoff between the genetic robustness and environmental robustness in evolution is discussed from the stochastic stability robustness and sensitivity of the nonlinear stochastic biological network, which may be relevant to the statistical tradeoff between bias and variance, the so-called bias/variance dilemma. Further, the tradeoff could be considered as an antagonistic pleiotropic action of a gene network and discussed from the systems biology perspective.

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

Background

Design 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.

Results

Based 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.

Conclusions

Our 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.

Analysis of operating principles with S-system models

Operating principles address general questions regarding the response dynamics of biological systems as we observe or hypothesize them, in comparison to a priori equally valid alternatives. In analogy to design principles, the question arises: Why are some operating strategies encountered more frequently than others and in what sense might they be superior? It is at this point impossible to study operation principles in complete generality, but the work here discusses the important situation where a biological system must shift operation from its normal steady state to a new steady state. This situation is quite common and includes many stress responses. We present two distinct methods for determining different solutions to this task of achieving a new target steady state. Both methods utilize the property of S-system models within Biochemical Systems Theory (BST) that steady states can be explicitly represented as systems of linear algebraic equations. The first method uses matrix inversion, a pseudo-inverse, or regression to characterize the entire admissible solution space. Operations on the basis of the solution space permit modest alterations of the transients toward the target steady state. The second method uses standard or mixed integer linear programming to determine admissible solutions that satisfy criteria of functional effectiveness, which are specified beforehand. As an illustration, we use both methods to characterize alternative response patterns of yeast subjected to heat stress, and compare them with observations from the literature.

Robust model matching design methodology for a stochastic synthetic gene network

Synthetic biology has shown its potential and promising applications in the last decade. However, many synthetic gene networks cannot work properly and maintain their desired behaviors due to intrinsic parameter variations and extrinsic disturbances. In this study, the intrinsic parameter uncertainties and external disturbances are modeled in a non-linear stochastic gene network to mimic the real environment in the host cell. Then a non-linear stochastic robust matching design methodology is introduced to withstand the intrinsic parameter fluctuations and to attenuate the extrinsic disturbances in order to achieve a desired reference matching purpose. To avoid solving the Hamilton-Jacobi inequality (HJI) in the non-linear stochastic robust matching design, global linearization technique is used to simplify the design procedure by solving a set of linear matrix inequalities (LMIs). As a result, the proposed matching design methodology of the robust synthetic gene network can be efficiently designed with the help of LMI toolbox in Matlab. Finally, two in silico design examples of the robust synthetic gene network are given to illustrate the design procedure and to confirm the robust model matching performance to achieve the desired behavior in spite of stochastic parameter fluctuations and environmental disturbances in the host cell.

Identifying quantitative operation principles in metabolic pathways: a systematic method for searching feasible enzyme activity patterns leading to cellular adaptive responses

BACKGROUND

Optimization methods allow designing changes in a system so that specific goals are attained. These techniques are fundamental for metabolic engineering. However, they are not directly applicable for investigating the evolution of metabolic adaptation to environmental changes. Although biological systems have evolved by natural selection and result in well-adapted systems, we can hardly expect that actual metabolic processes are at the theoretical optimum that could result from an optimization analysis. More likely, natural systems are to be found in a feasible region compatible with global physiological requirements.

RESULTS

We first present a new method for globally optimizing nonlinear models of metabolic pathways that are based on the Generalized Mass Action (GMA) representation. The optimization task is posed as a nonconvex nonlinear programming (NLP) problem that is solved by an outer-approximation algorithm. This method relies on solving iteratively reduced NLP slave subproblems and mixed-integer linear programming (MILP) master problems that provide valid upper and lower bounds, respectively, on the global solution to the original NLP. The capabilities of this method are illustrated through its application to the anaerobic fermentation pathway in Saccharomyces cerevisiae. We next introduce a method to identify the feasibility parametric regions that allow a system to meet a set of physiological constraints that can be represented in mathematical terms through algebraic equations. This technique is based on applying the outer-approximation based algorithm iteratively over a reduced search space in order to identify regions that contain feasible solutions to the problem and discard others in which no feasible solution exists. As an example, we characterize the feasible enzyme activity changes that are compatible with an appropriate adaptive response of yeast Saccharomyces cerevisiae to heat shock

CONCLUSION

Our results show the utility of the suggested approach for investigating the evolution of adaptive responses to environmental changes. The proposed method can be used in other important applications such as the evaluation of parameter changes that are compatible with health and disease states.

On the estimation of robustness and filtering ability of dynamic biochemical networks under process delays, internal parametric perturbations and external disturbances

Inherently, biochemical regulatory networks suffer from process delays, internal parametrical perturbations as well as external disturbances. Robustness is the property to maintain the functions of intracellular biochemical regulatory networks despite these perturbations. In this study, system and signal processing theories are employed for measurement of robust stability and filtering ability of linear and nonlinear time-delay biochemical regulatory networks. First, based on Lyapunov stability theory, the robust stability of biochemical network is measured for the tolerance of additional process delays and additive internal parameter fluctuations. Then the filtering ability of attenuating additive external disturbances is estimated for time-delay biochemical regulatory networks. In order to overcome the difficulty of solving the Hamilton Jacobi inequality (HJI), the global linearization technique is employed to simplify the measurement procedure by a simple linear matrix inequality (LMI) method. Finally, an example is given in silico to illustrate how to measure the robust stability and filtering ability of a nonlinear time-delay perturbative biochemical network. This robust stability and filtering ability measurement for biochemical network has potential application to synthetic biology, gene therapy and drug design.

A systematic design method for robust synthetic biology to satisfy design specifications

BACKGROUND

Synthetic biology is foreseen to have important applications in biotechnology and medicine, and is expected to contribute significantly to a better understanding of the functioning of complex biological systems. However, the development of synthetic gene networks is still difficult and most newly created gene networks are non-functioning due to intrinsic parameter uncertainties, external disturbances and functional variations of intra- and extra-cellular environments. The design method for a robust synthetic gene network that works properly in a host cell under these intrinsic parameter uncertainties and external disturbances is the most important topic in synthetic biology.

RESULTS

In this study, we propose a stochastic model that includes parameter fluctuations and external disturbances to mimic the dynamic behaviors of a synthetic gene network in the host cell. Then, based on this stochastic model, four design specifications are introduced to guarantee that a synthetic gene network can achieve its desired steady state behavior in spite of parameter fluctuations, external disturbances and functional variations in the host cell. We propose a systematic method to select a set of appropriate design parameters for a synthetic gene network that will satisfy these design specifications so that the intrinsic parameter fluctuations can be tolerated, the external disturbances can be efficiently filtered, and most importantly, the desired steady states can be achieved. Thus the synthetic gene network can work properly in a host cell under intrinsic parameter uncertainties, external disturbances and functional variations. Finally, a design procedure for the robust synthetic gene network is developed and a design example is given in silico to confirm the performance of the proposed method.

CONCLUSION

Based on four design specifications, a systematic design procedure is developed for designers to engineer a robust synthetic biology network that can achieve its desired steady state behavior under parameter fluctuations, external disturbances and functional variations in the host cell. Therefore, the proposed systematic design method has good potential for the robust synthetic gene network design.

A systematic molecular circuit design method for gene networks under biochemical time delays and molecular noises

Background

Gene networks in nanoscale are of nonlinear stochastic process. Time delays are common and substantial in these biochemical processes due to gene transcription, translation, posttranslation protein modification and diffusion. Molecular noises in gene networks come from intrinsic fluctuations, transmitted noise from upstream genes, and the global noise affecting all genes. Knowledge of molecular noise filtering and biochemical process delay compensation in gene networks is crucial to understand the signal processing in gene networks and the design of noise-tolerant and delay-robust gene circuits for synthetic biology.

Results

A nonlinear stochastic dynamic model with multiple time delays is proposed for describing a gene network under process delays, intrinsic molecular fluctuations, and extrinsic molecular noises. Then, the stochastic biochemical processing scheme of gene regulatory networks for attenuating these molecular noises and compensating process delays is investigated from the nonlinear signal processing perspective. In order to improve the robust stability for delay toleration and noise filtering, a robust gene circuit for nonlinear stochastic time-delay gene networks is engineered based on the nonlinear robust H_∞ stochastic filtering scheme. Further, in order to avoid solving these complicated noise-tolerant and delay-robust design problems, based on Takagi-Sugeno (T-S) fuzzy time-delay model and linear matrix inequalities (LMIs) technique, a systematic gene circuit design method is proposed to simplify the design procedure.

Conclusion

The proposed gene circuit design method has much potential for application to systems biology, synthetic biology and drug design when a gene regulatory network has to be designed for improving its robust stability and filtering ability of disease-perturbed gene network or when a synthetic gene network needs to perform robustly under process delays and molecular noises.

Robust H infinity-stabilization design in gene networks under stochastic molecular noises: fuzzy-interpolation approach

Molecular noises in gene networks come from intrinsic fluctuations, transmitted noise from upstream genes, and the global noise affecting all genes. Knowledge of molecular noise filtering in gene networks is crucial to understand the signal processing in gene networks and to design noise-tolerant gene circuits for synthetic biology. A nonlinear stochastic dynamic model is proposed in describing a gene network under intrinsic molecular fluctuations and extrinsic molecular noises. The stochastic molecular-noise-processing scheme of gene regulatory networks for attenuating these molecular noises is investigated from the nonlinear robust stabilization and filtering perspective. In order to improve the robust stability and noise filtering, a robust gene circuit design for gene networks is proposed based on the nonlinear robust H infinity stochastic stabilization and filtering scheme, which needs to solve a nonlinear Hamilton-Jacobi inequality. However, in order to avoid solving these complicated nonlinear stabilization and filtering problems, a fuzzy approximation method is employed to interpolate several linear stochastic gene networks at different operation points via fuzzy bases to approximate the nonlinear stochastic gene network. In this situation, the method of linear matrix inequality technique could be employed to simplify the gene circuit design problems to improve robust stability and molecular-noise-filtering ability of gene networks to overcome intrinsic molecular fluctuations and extrinsic molecular noises.

On the robust circuit design schemes of biochemical networks: steady-state approach

Based on the steady-state analyses of the synergism and saturation system (S-system) model, a robust control method is proposed for biochemical networks via feedback and feedforward biochemical circuits. Two robust biochemical circuit design schemes are developed. One scheme is to improve the system's structural stability so as to tolerate larger kinetic parameter variations, whereas the other is to compensate for the kinetic parameter variations to eliminate their effects. In addition, a multi-objective biochemical circuit design scheme is introduced for both the robust design against kinetic parameter variations and a desired sensitivity design to eliminate the effect of external disturbance simultaneously. The proposed robust circuit design schemes will provide a systematic method with potential applications in synthetic circuit design for biotechnological purpose and drug design purpose. Recent advances in both metabolic and genetic engineering have made the robust biochemical circuit control approach feasible through the design and implementation of synthetic biological networks amenable to mathematical modeling and quantitative analysis. Finally, several examples including the robust circuit design of the tricarboxylic acid cycle are used in silico to illustrate the design procedure and to confirm the performance of the proposed design method.

Engineering primary metabolic pathways of industrial micro-organisms

Metabolic engineering is a powerful tool for the optimisation and the introduction of new cellular processes. This is mostly done by genetic engineering. Since the introduction of this multidisciplinary approach, the success stories keep accumulating. The primary metabolism of industrial micro-organisms has been studied for long time and most biochemical pathways and reaction networks have been elucidated. This large pool of biochemical information, together with data from proteomics, metabolomics and genomics underpins the strategies for design of experiments and choice of targets for manipulation by metabolic engineers. These targets are often located in the primary metabolic pathways, such as glycolysis, pentose phosphate pathway, the TCA cycle and amino acid biosynthesis and mostly at major branch points within these pathways. This paper describes approaches taken for metabolic engineering of these pathways in bacteria, yeast and filamentous fungi.

Use of physiological constraints to identify quantitative design principles for gene expression in yeast adaptation to heat shock

Background

Understanding the relationship between gene expression changes, enzyme activity shifts, and the corresponding physiological adaptive response of organisms to environmental cues is crucial in explaining how cells cope with stress. For example, adaptation of yeast to heat shock involves a characteristic profile of changes to the expression levels of genes coding for enzymes of the glycolytic pathway and some of its branches. The experimental determination of changes in gene expression profiles provides a descriptive picture of the adaptive response to stress. However, it does not explain why a particular profile is selected for any given response.

Results

We used mathematical models and analysis of in silico gene expression profiles (GEPs) to understand how changes in gene expression correlate to an efficient response of yeast cells to heat shock. An exhaustive set of GEPs, matched with the corresponding set of enzyme activities, was simulated and analyzed. The effectiveness of each profile in the response to heat shock was evaluated according to relevant physiological and functional criteria. The small subset of GEPs that lead to effective physiological responses after heat shock was identified as the result of the tuning of several evolutionary criteria. The experimentally observed transcriptional changes in response to heat shock belong to this set and can be explained by quantitative design principles at the physiological level that ultimately constrain changes in gene expression.

Conclusion

Our theoretical approach suggests a method for understanding the combined effect of changes in the expression of multiple genes on the activity of metabolic pathways, and consequently on the adaptation of cellular metabolism to heat shock. This method identifies quantitative design principles that facilitate understating the response of the cell to stress.

Analysis of dynamic labeling data

Comprehensive assessments of the organization and regulation of metabolic pathways cannot be limited to steady-state measurements alone but require dynamic time series data. One experimental means of generating such data consists of radioactively labeling precursors and measuring their fate over time. While labeling experiments belong to the standard repertoire of biological laboratory techniques, corresponding mathematical tools for analyzing the non-linear dynamics of tracers are scarce. The article addresses this issue, using Biochemical Systems Theory as the modeling framework. The description of the dynamics of labeled metabolites alone is difficult, but it is demonstrated that these difficulties are easily overcome by setting up dynamic models in two or three blocks, one for the kinetics of the total pools, the second just for the labeled portions, and the third, optional, block for the remaining unlabeled components. Since the dynamic model is not limited in complexity and can account for linear pathways, converging and diverging branches, cycles, and the various observed modes of regulation, the proposed method of non-linear tracer analysis is rather general and permits simulations of most standard labeling experiments, both at steady state and during transients.

Integration of kinetic information on yeast sphingolipid metabolism in dynamical pathway models

For the first time, kinetic information from the literature was collected and used to construct integrative dynamical mathematical models of sphingolipid metabolism. One model was designed primarily with kinetic equations in the tradition of Michaelis and Menten whereas the other two models were designed as alternative power-law models within the framework of Biochemical Systems Theory. Each model contains about 50 variables, about a quarter of which are dependent (state) variables, while the others are independent inputs and enzyme activities that are considered constant. The models account for known regulatory signals that exert control over the pathway. Standard mathematical testing, repeated revisiting of the literature, and numerous rounds of amendments and refinements resulted in models that are stable and rather insensitive to perturbations in inputs or parameter values. The models also appear to be compatible with the modest amount of experimental experience that lends itself to direct comparisons. Even though the three models are based on different mathematical representations, they show dynamic responses to a variety of perturbations and changes in conditions that are essentially equivalent for small perturbations and similar for large perturbations. The kinetic information used for model construction and the models themselves can serve as a starting point for future analyses and refinements.