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.

A major factor contributing to the etiology of depression is a neurochemical imbalance of the dopaminergic and serotonergic systems, which is caused by persistently high levels of circulating stress hormones. Here, a computational model is proposed to investigate the interplay between dopaminergic and serotonergic-kynurenine metabolism under cortisolemia and its consequences for the onset of depression. The model was formulated as a set of nonlinear ordinary differential equations represented with power-law functions. Parameter values were obtained from experimental data reported in the literature, biological databases, and other general information, and subsequently fine-tuned through optimization. Model simulations predict that changes in the kynurenine pathway, caused by elevated levels of cortisol, can increase the risk of neurotoxicity and lead to increased levels of 3,4-dihydroxyphenylaceltahyde (DOPAL) and 5-hydroxyindoleacetaldehyde (5-HIAL). These aldehydes contribute to alpha-synuclein aggregation and may cause mitochondrial fragmentation. Further model analysis demonstrated that the inhibition of both serotonin transport and kynurenine-3-monooxygenase decreased the levels of DOPAL and 5-HIAL and the neurotoxic risk often associated with depression. The mathematical model was also able to predict a novel role of the dopamine and serotonin metabolites DOPAL and 5-HIAL in the ethiology of depression, which is facilitated through increased cortisol levels. Finally, the model analysis suggests treatment with a combination of inhibitors of serotonin transport and kynurenine-3-monooxygenase as a potentially effective pharmacological strategy to revert the slow-down in monoamine neurotransmission that is often triggered by inflammation.

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.

The complexity of morphogenesis poses a fundamental challenge to understanding the mechanisms governing the formation of biological patterns and structures. Over the past century, numerous processes have been identified as critically contributing to morphogenetic events, but the interplay between the various components and aspects of pattern formation have been much harder to grasp. The combination of traditional biology with mathematical and computational methods has had a profound effect on our current understanding of morphogenesis and led to significant insights and advancements in the field. In particular, the theoretical concepts of reaction-diffusion systems and positional information, proposed by Alan Turing and Lewis Wolpert, respectively, dramatically influenced our general view of morphogenesis, although typically in isolation from one another. In recent years, agent-based modeling has been emerging as a consolidation and implementation of the two theories within a single framework. Agent-based models (ABMs) are unique in their ability to integrate combinations of heterogeneous processes and investigate their respective dynamics, especially in the context of spatial phenomena. In this review, we highlight the benefits and technical challenges associated with ABMs as tools for examining morphogenetic events. These models display unparalleled flexibility for studying various morphogenetic phenomena at multiple levels and have the important advantage of informing future experimental work, including the targeted engineering of tissues and organs.

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. The traditional scientific method: Hypothesis-driven deductionResearch is the undisputed core activity defining science.Without research, the advancement of scientific knowledge would come to a screeching halt.While it is evident that researchers look for new information or insights, the term "research" is somewhat puzzling.Never mind the prefix "re," which simply means "coming back and doing it again and again," the word "search" seems to suggest that the research process is somewhat haphazard, that not much of a strategy is involved in the process.One might argue that research a few hundred years ago had the character of hoping for enough luck to find something new.The alchemists come to mind in their quest to turn mercury or lead into gold, or to discover an elixir for eternal youth, through methods we nowadays consider laughable.

MOTIVATION: Most metabolic pathways contain more reactions than metabolites and therefore have a wide stoichiometric matrix that corresponds to infinitely many possible flux distributions that are perfectly compatible with the dynamics of the metabolites in a given dataset. This under-determinedness poses a challenge for the quantitative characterization of flux distributions from time series data and thus for the design of adequate, predictive models. Here we propose a method that reduces the degrees of freedom in a stepwise manner and leads to a dynamic flux distribution that is, in a statistical sense, likely to be close to the true distribution. RESULTS: We applied the proposed method to the lignin biosynthesis pathway in switchgrass. The system consists of 16 metabolites and 23 enzymatic reactions. It has seven degrees of freedom and therefore admits a large space of dynamic flux distributions that all fit a set of metabolic time series data equally well. The proposed method reduces this space in a systematic and biologically reasonable manner and converges to a likely dynamic flux distribution in just a few iterations. The estimated solution and the true flux distribution, which is known in this case, show excellent agreement and thereby lend support to the method. AVAILABILITY AND IMPLEMENTATION: The computational model was implemented in MATLAB (version R2014a, The MathWorks, Natick, MA). The source code is available at https://github.gatech.edu/VoitLab/Stepwise-Inference-of-Likely-Dynamic-Flux-Distributions and www.bst.bme.gatech.edu/research.php . CONTACT: [email protected] or [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: Large amounts of metabolomics data have been accumulated in recent years and await analysis. Previously, we had developed a systems biology approach to infer biochemical mechanisms underlying metabolic alterations observed in cancers and other diseases. The method utilized the typical Euclidean distance for comparing metabolic profiles. Here, we ask whether any of the numerous alternative metrics might serve this purpose better. METHODS AND FINDINGS: We used enzymatic alterations in purine metabolism that were measured in human renal cell carcinoma to test various metrics with the goal of identifying the best metrics for discerning metabolic profiles of healthy and diseased individuals. The results showed that several metrics have similarly good performance, but that some are unsuited for comparisons of metabolic profiles. Furthermore, the results suggest that relative changes in metabolite levels, which reduce bias toward large metabolite concentrations, are better suited for comparisons of metabolic profiles than absolute changes. Finally, we demonstrate that a sequential search for enzymatic alterations, ranked by importance, is not always valid. CONCLUSIONS: We identified metrics that are appropriate for comparisons of metabolic profiles. In addition, we constructed strategic guidelines for the algorithmic identification of biochemical mechanisms from metabolomics data.

The article demonstrates that computational modeling has the capacity to convert metabolic snapshots, taken sequentially over time, into a description of cellular, dynamic strategies. The specific application is a detailed analysis of a set of actions with which Saccharomyces cerevisiae responds to heat stress. Using time dependent metabolic concentration data, we use a combination of mathematical modeling, reverse engineering, and optimization to infer dynamic changes in enzyme activities within the sphingolipid pathway. The details of the sphingolipid responses to heat stress are important, because they guide some of the longer-term alterations in gene expression, with which the cells adapt to the increased temperature. The analysis indicates that all enzyme activities in the system are affected and that the shapes of the time trends in activities depend on the fatty-acyl CoA chain lengths of the different ceramide species in the system.

This year we celebrate the 150th anniversary of the law of mass action. This law is often assumed to have been "there" forever, but it has its own history, background, and a definite starting point. The law has had an impact on chemistry, biochemistry, biomathematics, and systems biology that is difficult to overestimate. It is easily recognized that it is the direct basis for computational enzyme kinetics, ecological systems models, and models for the spread of diseases. The article reviews the explicit and implicit role of the law of mass action in systems biology and reveals how the original, more general formulation of the law emerged one hundred years later ab initio as a very general, canonical representation of biological processes.

Stability and sensitivity analyses of biological systems require the ad hocwriting of computer code, which is highly dependent on the particular model and burdensome for large systems. We propose a very accurate strategy to overcome this challenge. Its core concept is the conversion of the model into the format of biochemical systems theory (BST), which greatly facilitates the computation of sensitivities. First, the steady state of interest is determined by integrating the model equations toward the steady state and then using a Newton-Raphson method to fine-tune the result. The second step of conversion into the BST format requires several instances of numerical differentiation. The accuracy of this task is ensured by the use of a complex-variable Taylor scheme for all differentiation steps. The proposed strategy is implemented in a new software program, COSMOS, which automates the stability and sensitivity analysis of essentially arbitrary ODE models in a quick, yet highly accurate manner. The methods underlying the process are theoretically analyzed and illustrated with four representative examples: a simple metabolic reaction model; a model of aspartate-derived amino acid biosynthesis; a TCA-cycle model; and a modified TCA-cycle model. COSMOS has been deposited to https://github.com/BioprocessdesignLab/COSMOS.

The regulatory roles of sphingolipids in diverse cell functions have been characterized extensively. However, the dynamics and interactions among the different sphingolipid species are difficult to assess, because de novo biosynthesis, metabolic inter-conversions, and the retrieval of sphingolipids from membranes form a complex, highly regulated pathway system. Here we analyze the heat stress response of this system in the yeast Saccharomyces cerevisiae and demonstrate how the cell dynamically adjusts its enzyme profile so that it is appropriate for operation under stress conditions before changes in gene expression become effective. The analysis uses metabolic time series data, a complex mathematical model, and a custom-tailored optimization strategy. The results demonstrate that all enzyme activities rapidly increase in an immediate response to the elevated temperature. After just a few minutes, different functional clusters of enzymes follow distinct activity patterns. Interestingly, starting after about six minutes, both de novo biosynthesis and all exit routes from central sphingolipid metabolism become blocked, and the remaining metabolic activity consists entirely of an internal redistribution among different sphingoid base and ceramide pools. After about 30 minutes, heat stress is still in effect and the enzyme activity profile is still significantly changed. Importantly, however, the metabolites have regained concentrations that are essentially the same as those under optimal conditions.

Lignin is a polymer in secondary cell walls of plants that is known to have negative impacts on forage digestibility, pulping efficiency, and sugar release from cellulosic biomass. While targeted modifications of different lignin biosynthetic enzymes have permitted the generation of transgenic plants with desirable traits, such as improved digestibility or reduced recalcitrance to saccharification, some of the engineered plants exhibit monomer compositions that are clearly at odds with the expected outcomes when the biosynthetic pathway is perturbed. In Medicago, such discrepancies were partly reconciled by the recent finding that certain biosynthetic enzymes may be spatially organized into two independent channels for the synthesis of guaiacyl (G) and syringyl (S) lignin monomers. Nevertheless, the mechanistic details, as well as the biological function of these interactions, remain unclear. To decipher the working principles of this and similar control mechanisms, we propose and employ here a novel computational approach that permits an expedient and exhaustive assessment of hundreds of minimal designs that could arise in vivo. Interestingly, this comparative analysis not only helps distinguish two most parsimonious mechanisms of crosstalk between the two channels by formulating a targeted and readily testable hypothesis, but also suggests that the G lignin-specific channel is more important for proper functioning than the S lignin-specific channel. While the proposed strategy of analysis in this article is tightly focused on lignin synthesis, it is likely to be of similar utility in extracting unbiased information in a variety of situations, where the spatial organization of molecular components is critical for coordinating the flow of cellular information, and where initially various control designs seem equally valid.

The entanglement of lignin polymers with cellulose and hemicellulose in plant cell walls is a major biological barrier to the economically viable production of biofuels from woody biomass. Recent efforts of reducing this recalcitrance with transgenic techniques have been showing promise for ameliorating or even obviating the need for costly pretreatments that are otherwise required to remove lignin from cellulose and hemicelluloses. At the same time, genetic manipulations of lignin biosynthetic enzymes have sometimes yielded unforeseen consequences on lignin composition, thus raising the question of whether the current understanding of the pathway is indeed correct. To address this question systemically, we developed and applied a novel modeling approach that, instead of analyzing the pathway within a single target context, permits a comprehensive, simultaneous investigation of different datasets in wild type and transgenic plants. Specifically, the proposed approach combines static flux-based analysis with a Monte Carlo simulation in which very many randomly chosen sets of parameter values are evaluated against kinetic models of lignin biosynthesis in different stem internodes of wild type and lignin-modified alfalfa plants. In addition to four new postulates that address the reversibility of some key reactions, the modeling effort led to two novel postulates regarding the control of the lignin biosynthetic pathway. The first posits functionally independent pathways toward the synthesis of different lignin monomers, while the second postulate proposes a novel feedforward regulatory mechanism. Subsequent laboratory experiments have identified the signaling molecule salicylic acid as a potential mediator of the postulated control mechanism. Overall, the results demonstrate that mathematical modeling can be a valuable complement to conventional transgenic approaches and that it can provide biological insights that are otherwise difficult to obtain.

BACKGROUND: Determining the parameters of a mathematical model from quantitative measurements is the main bottleneck of modelling biological systems. Parameter values can be estimated from steady-state data or from dynamic data. The nature of suitable data for these two types of estimation is rather different. For instance, estimations of parameter values in pathway models, such as kinetic orders, rate constants, flux control coefficients or elasticities, from steady-state data are generally based on experiments that measure how a biochemical system responds to small perturbations around the steady state. In contrast, parameter estimation from dynamic data requires time series measurements for all dependent variables. Almost no literature has so far discussed the combined use of both steady-state and transient data for estimating parameter values of biochemical systems. RESULTS: In this study we introduce a constrained optimization method for estimating parameter values of biochemical pathway models using steady-state information and transient measurements. The constraints are derived from the flux connectivity relationships of the system at the steady state. Two case studies demonstrate the estimation results with and without flux connectivity constraints. The unconstrained optimal estimates from dynamic data may fit the experiments well, but they do not necessarily maintain the connectivity relationships. As a consequence, individual fluxes may be misrepresented, which may cause problems in later extrapolations. By contrast, the constrained estimation accounting for flux connectivity information reduces this misrepresentation and thereby yields improved model parameters. CONCLUSION: The method combines transient metabolic profiles and steady-state information and leads to the formulation of an inverse parameter estimation task as a constrained optimization problem. Parameter estimation and model selection are simultaneously carried out on the constrained optimization problem and yield realistic model parameters that are more likely to hold up in extrapolations with the model.

MOTIVATION: At the center of computational systems biology are mathematical models that capture the dynamics of biological systems and offer novel insights. The bottleneck in the construction of these models is presently the identification of model parameters that make the model consistent with observed data. Dynamic flux estimation (DFE) is a novel methodological framework for estimating parameters for models of metabolic systems from time-series data. DFE consists of two distinct phases, an entirely model-free and assumption-free data analysis and a model-based mathematical characterization of process representations. The model-free phase reveals inconsistencies within the data, and between data and the alleged system topology, while the model-based phase allows quantitative diagnostics of whether--or to what degree--the assumed mathematical formulations are appropriate or in need of improvement. Hallmarks of DFE are the facility to: diagnose data and model consistency; circumvent undue compensation of errors; determine functional representations of fluxes uncontaminated by errors in other fluxes and pinpoint sources of remaining errors. Our results suggest that the proposed approach is more effective and robust than presently available methods for deriving metabolic models from time-series data. Its avoidance of error compensation among process descriptions promises significantly improved extrapolability toward new data or experimental conditions.

BACKGROUND: Structure identification of dynamic models for complex biological systems is the cornerstone of their reverse engineering. Biochemical Systems Theory (BST) offers a particularly convenient solution because its parameters are kinetic-order coefficients which directly identify the topology of the underlying network of processes. We have previously proposed a numerical decoupling procedure that allows the identification of multivariate dynamic models of complex biological processes. While described here within the context of BST, this procedure has a general applicability to signal extraction. Our original implementation relied on artificial neural networks (ANN), which caused slight, undesirable bias during the smoothing of the time courses. As an alternative, we propose here an adaptation of the Whittaker's smoother and demonstrate its role within a robust, fully automated structure identification procedure. RESULTS: In this report we propose a robust, fully automated solution for signal extraction from time series, which is the prerequisite for the efficient reverse engineering of biological systems models. The Whittaker's smoother is reformulated within the context of information theory and extended by the development of adaptive signal segmentation to account for heterogeneous noise structures. The resulting procedure can be used on arbitrary time series with a nonstationary noise process; it is illustrated here with metabolic profiles obtained from in-vivo NMR experiments. The smoothed solution that is free of parametric bias permits differentiation, which is crucial for the numerical decoupling of systems of differential equations. CONCLUSION: The method is applicable in signal extraction from time series with nonstationary noise structure and can be applied in the numerical decoupling of system of differential equations into algebraic equations, and thus constitutes a rather general tool for the reverse engineering of mechanistic model descriptions from multivariate experimental time series.

BACKGROUND: Expression microarray analysis is one of the most popular molecular diagnostic techniques in the post-genomic era. However, this technique faces the fundamental problem of potential cross-hybridization. This is a pervasive problem for both oligonucleotide and cDNA microarrays; it is considered particularly problematic for the latter. No comprehensive multivariate predictive modeling has been performed to understand how multiple variables contribute to (cross-) hybridization. RESULTS: We propose a systematic search strategy using multiple multivariate models [multiple linear regressions, regression trees, and artificial neural network analyses (ANNs)] to select an effective set of predictors for hybridization. We validate this approach on a set of DNA microarrays with cytochrome p450 family genes. The performance of our multiple multivariate models is compared with that of a recently proposed third-order polynomial regression method that uses percent identity as the sole predictor. All multivariate models agree that the 'most contiguous base pairs between probe and target sequences,' rather than percent identity, is the best univariate predictor. The predictive power is improved by inclusion of additional nonlinear effects, in particular target GC content, when regression trees or ANNs are used. CONCLUSION: A systematic multivariate approach is provided to assess the importance of multiple sequence features for hybridization and of relationships among these features. This approach can easily be applied to larger datasets. This will allow future developments of generalized hybridization models that will be able to correct for false-positive cross-hybridization signals in expression experiments.

RATIONALE: Modern molecular biology is generating data of unprecedented quantity and quality. Particularly exciting for biochemical pathway modeling and proteomics are comprehensive, time-dense profiles of metabolites or proteins that are measurable, for instance, with mass spectrometry, nuclear magnetic resonance or protein kinase phosphorylation. These profiles contain a wealth of information about the structure and dynamics of the pathway or network from which the data were obtained. The retrieval of this information requires a combination of computational methods and mathematical models, which are typically represented as systems of ordinary differential equations. RESULTS: We show that, for the purpose of structure identification, the substitution of differentials with estimated slopes in non-linear network models reduces the coupled system of differential equations to several sets of decoupled algebraic equations, which can be processed efficiently in parallel or sequentially. The estimation of slopes for each time series of the metabolic or proteomic profile is accomplished with a 'universal function' that is computed directly from the data by cross-validated training of an artificial neural network (ANN). CONCLUSIONS: Without preprocessing, the inverse problem of determining structure from metabolic or proteomic profile data is challenging and computationally expensive. The combination of system decoupling and data fitting with universal functions simplifies this inverse problem very significantly. Examples show successful estimations and current limitations of the method. AVAILABILITY: A preliminary Web-based application for ANN smoothing is accessible at http://bioinformatics.musc.edu/webmetabol/. S-systems can be interactively analyzed with the user-friendly freeware PLAS (http://correio.cc.fc.ul.pt/~aenf/plas.html) or with the MATLAB module BSTLab (http://bioinformatics.musc.edu/bstlab/), which is currently being beta-tested.

MOTIVATION: Modern methods of genomics have produced an unprecedented amount of raw data. The interpretation and explanation of these data constitute a major, well-recognized challenge. RESULTS: Biochemical Systems Theory (BST) is the mathematical basis of a well-established methodological framework for analyzing networks of biochemical reactions. An existing BST model of yeast glycolysis is used here to explain and interpret the glycolytic gene expression pattern of heat shocked yeast. Our analysis demonstrates that the observed gene expression profile satisfies the primary goals of increased ATP, trehalose, and NADPH production, while maintaining intermediate metabolites at reasonable levels. Based on a systematic exploration of alternative, hypothetical expression profiles, we show that the observed profile outperforms other profiles. CONCLUSION: BST is a useful framework for combining DNA microarray data with enzymatic process information to yield new insights into metabolic pathway regulation. AVAILABILITY: All analyses were executed with the software PLAS(Copyright), which is freely available at http://correio.cc.fc.ul.pt/~aenf/plas.html for academic use. CONTACT: [email protected]