Determination of causal connectivities of species in reaction networks

A query-response causal analysis of reaction events in biochemical reaction networks

The stochastic kinetics of biochemical reaction networks is described by a chemical master equation (CME) and the underlying laws of mass action. Assuming network-free simulations of the rule-based models of biochemical reaction networks (BRNs), this paper departs from the usual analysis of network dynamics as the time-dependent distributions of chemical species counts, and instead considers statistically evaluating the sequences of reaction events generated from the stochastic simulations. The reaction event-time series can be used for reaction clustering, identifying rare events, and recognizing the periods of increased or steady-state activity. However, the main aim of this paper is to device an effective method for identifying causally and anti-causally related sub-sequences of reaction events using their empirical probabilities. This allows discovering some of the causal dynamics of BRNs as well as uncovering their short-term deterministic behaviors. In particular, it is proposed that the reaction sub-sequences that are conditionally nearly certain or nearly uncertain can be considered as being causally related. Moreover, since the time-ordering of reaction events is locally irrelevant, the reaction sub-sequences can be transformed into the reaction sets or multi-sets. The distance metrics can be then used to define the equivalences among the reaction events. The proposed method for identifying the causally related reaction sub-sequences has been implemented as a computationally efficient query-response mechanism. The method was evaluated for five models of genetic networks in seven defined numerical experiments. The models were simulated in BioNetGen using the open-source network-free simulator NFsim. This simulator had to be modified first to allow recording the traces of reaction events, and it is available in the Github repository, ploskot/nfsim_1.20. The generated event time-series were analyzed with Python and Matlab scripts. The whole process of data generation, analysis and visualization has been nearly fully automated using shell scripts. This demonstrates the opportunities for substantially increasing the research productivity by creating automated data generation and processing pipelines.

Programming Bacteria With Light-Sensors and Applications in Synthetic Biology

Photo-receptors are widely present in both prokaryotic and eukaryotic cells, which serves as the foundation of tuning cell behaviors with light. While practices in eukaryotic cells have been relatively established, trials in bacterial cells have only been emerging in the past few years. A number of light sensors have been engineered in bacteria cells and most of them fall into the categories of two-component and one-component systems. Such a sensor toolbox has enabled practices in controlling synthetic circuits at the level of transcription and protein activity which is a major topic in synthetic biology, according to the central dogma. Additionally, engineered light sensors and practices of tuning synthetic circuits have served as a foundation for achieving light based real-time feedback control. Here, we review programming bacteria cells with light, introducing engineered light sensors in bacteria and their applications, including tuning synthetic circuits and achieving feedback controls over microbial cell culture.

Stoichiometric Correlation Analysis: Principles of Metabolic Functionality from Metabolomics Data

Recent advances in metabolomics technologies have resulted in high-quality (time-resolved) metabolic profiles with an increasing coverage of metabolic pathways. These data profiles represent read-outs from often non-linear dynamics of metabolic networks. Yet, metabolic profiles have largely been explored with regression-based approaches that only capture linear relationships, rendering it difficult to determine the extent to which the data reflect the underlying reaction rates and their couplings. Here we propose an approach termed Stoichiometric Correlation Analysis (SCA) based on correlation between positive linear combinations of log-transformed metabolic profiles. The log-transformation is due to the evidence that metabolic networks can be modeled by mass action law and kinetics derived from it. Unlike the existing approaches which establish a relation between pairs of metabolites, SCA facilitates the discovery of higher-order dependence between more than two metabolites. By using a paradigmatic model of the tricarboxylic acid cycle we show that the higher-order dependence reflects the coupling of concentration of reactant complexes, capturing the subtle difference between the employed enzyme kinetics. Using time-resolved metabolic profiles from Arabidopsis thaliana and Escherichia coli, we show that SCA can be used to quantify the difference in coupling of reactant complexes, and hence, reaction rates, underlying the stringent response in these model organisms. By using SCA with data from natural variation of wild and domesticated wheat and tomato accession, we demonstrate that the domestication is accompanied by loss of such couplings, in these species. Therefore, application of SCA to metabolomics data from natural variation in wild and domesticated populations provides a mechanistic way to understanding domestication and its relation to metabolic networks.

Nonlinear response theory in chemical kinetics

A theory of nonlinear response of chemical kinetics, in which multiple perturbations are used to probe the time evolution of nonlinear chemical systems, is developed. Expressions for nonlinear chemical response functions and susceptibilities, which can serve as multidimensional measures of the kinetic pathways and rates, are derived. A new class of multidimensional measures that combine multiple perturbations and measurements is also introduced. Nonlinear fluctuation-dissipation relations for steady-state chemical systems, which replace operations of concentration measurement and perturbations, are proposed. Several applications to the analysis of complex reaction mechanisms are provided.

Computational study of collisions between O(3P) and NO(2Π) at temperatures relevant to the hypersonic flight regime

Reactions involving N and O atoms dominate the energetics of the reactive air flow around spacecraft when reentering the atmosphere in the hypersonic flight regime. For this reason, the thermal rate coefficients for reactive processes involving O((3)P) and NO((2)Π) are relevant over a wide range of temperatures. For this purpose, a potential energy surface (PES) for the ground state of the NO2 molecule is constructed based on high-level ab initio calculations. These ab initio energies are represented using the reproducible kernel Hilbert space method and Legendre polynomials. The global PES of NO2 in the ground state is constructed by smoothly connecting the surfaces of the grids of various channels around the equilibrium NO2 geometry by a distance-dependent weighting function. The rate coefficients were calculated using Monte Carlo integration. The results indicate that at high temperatures only the lowest A-symmetry PES is relevant. At the highest temperatures investigated (20,000 K), the rate coefficient for the "O1O2+N" channel becomes comparable (to within a factor of around three) to the rate coefficient of the oxygen exchange reaction. A state resolved analysis shows that the smaller the vibrational quantum number of NO in the reactants, the higher the relative translational energy required to open it and conversely with higher vibrational quantum number, less translational energy is required. This is in accordance with Polanyi's rules. However, the oxygen exchange channel (NO2+O1) is accessible at any collision energy. Finally, this work introduces an efficient computational protocol for the investigation of three-atom collisions in general.

Systems Biology Strategy Reveals PKCδ is Key for Sensitizing TRAIL-Resistant Human Fibrosarcoma

Cancer cells are highly variable and largely resistant to therapeutic intervention. Recently, the use of the tumor necrosis factor related apoptosis-inducing ligand (TRAIL) induced treatment is gaining momentum due to TRAIL’s ability to specifically target cancers with limited effect on normal cells. Nevertheless, several malignant cancer types still remain non-sensitive to TRAIL. Previously, we developed a dynamic computational model, based on perturbation-response differential equations approach, and predicted protein kinase C (PKC) as the most effective target, with over 95% capacity to kill human fibrosarcoma (HT1080) in TRAIL stimulation (1). Here, to validate the model prediction, which has significant implications for cancer treatment, we conducted experiments on two TRAIL-resistant cancer cell lines (HT1080 and HT29). Using PKC inhibitor bisindolylmaleimide I, we demonstrated that cell viability is significantly impaired with over 95% death of both cancer types, in consistency with our previous model. Next, we measured caspase-3, Poly (ADP-ribose) polymerase (PARP), p38, and JNK activations in HT1080, and confirmed cell death occurs through apoptosis with significant increment in caspase-3 and PARP activations. Finally, to identify a crucial PKC isoform, from 10 known members, we analyzed each isoform mRNA expressions in HT1080 cells and shortlisted the highest 4 for further siRNA knock-down (KD) experiments. From these KDs, PKCδ produced the most cancer cell death in conjunction with TRAIL. Overall, our approach combining model predictions with experimental validation holds promise for systems biology based cancer therapy.

Metabolic network discovery by top-down and bottom-up approaches and paths for reconciliation

The primary focus in the network-centric analysis of cellular metabolism by systems biology approaches is to identify the active metabolic network for the condition of interest. Two major approaches are available for the discovery of the condition-specific metabolic networks. One approach starts from genome-scale metabolic networks, which cover all possible reactions known to occur in the related organism in a condition-independent manner, and applies methods such as the optimization-based Flux-Balance Analysis to elucidate the active network. The other approach starts from the condition-specific metabolome data, and processes the data with statistical or optimization-based methods to extract information content of the data such that the active network is inferred. These approaches, termed bottom-up and top-down, respectively, are currently employed independently. However, considering that both approaches have the same goal, they can both benefit from each other paving the way for the novel integrative analysis methods of metabolome data- and flux-analysis approaches in the post-genomic era. This study reviews the strengths of constraint-based analysis and network inference methods reported in the metabolic systems biology field; then elaborates on the potential paths to reconcile the two approaches to shed better light on how the metabolism functions.

Computational strategies for a system-level understanding of metabolism

Cell metabolism is the biochemical machinery that provides energy and building blocks to sustain life. Understanding its fine regulation is of pivotal relevance in several fields, from metabolic engineering applications to the treatment of metabolic disorders and cancer. Sophisticated computational approaches are needed to unravel the complexity of metabolism. To this aim, a plethora of methods have been developed, yet it is generally hard to identify which computational strategy is most suited for the investigation of a specific aspect of metabolism. This review provides an up-to-date description of the computational methods available for the analysis of metabolic pathways, discussing their main advantages and drawbacks. In particular, attention is devoted to the identification of the appropriate scale and level of accuracy in the reconstruction of metabolic networks, and to the inference of model structure and parameters, especially when dealing with a shortage of experimental measurements. The choice of the proper computational methods to derive in silico data is then addressed, including topological analyses, constraint-based modeling and simulation of the system dynamics. A description of some computational approaches to gain new biological knowledge or to formulate hypotheses is finally provided.

A systems biology approach to suppress TNF-induced proinflammatory gene expressions

Background

Tumor necrosis factor (TNF) is a widely studied cytokine (ligand) that induces proinflammatory signaling and regulates myriad cellular processes. In major illnesses, such as rheumatoid arthritis and certain cancers, the expression of TNF is elevated. Despite much progress in the field, the targeted regulation of TNF response for therapeutic benefits remains suboptimal. Here, to effectively regulate the proinflammatory response induced by TNF, a systems biology approach was adopted.

Results

We developed a computational model to investigate the temporal activations of MAP kinase (p38), nuclear factor (NF)-κB, and the kinetics of 3 groups of genes, defined by early, intermediate and late phases, in murine embryonic fibroblast (MEF) and 3T3 cells. To identify a crucial target that suppresses, and not abolishes, proinflammatory genes, the model was tested in several in silico knock out (KO) conditions. Among the candidate molecules tested, in silico RIP1 KO effectively regulated all groups of proinflammatory genes (early, middle and late). To validate this result, we experimentally inhibited TNF signaling in MEF and 3T3 cells with RIP1 inhibitor, Necrostatin-1 (Nec-1), and investigated 10 genes (Il6, Nfkbia, Jun, Tnfaip3, Ccl7, Vcam1, Cxcl10, Mmp3, Mmp13, Enpp2) belonging to the 3 major groups of upregulated genes. As predicted by the model, all measured genes were significantly impaired.

Conclusions

Our results demonstrate that Nec-1 modulates TNF-induced proinflammatory response, and may potentially be used as a therapeutic target for inflammatory diseases such as rheumatoid arthritis and osteoarthritis.

Identification of regulatory structure and kinetic parameters of biochemical networks via mixed-integer dynamic optimization

Background

Recovering the network topology and associated kinetic parameter values from time-series data are central topics in systems biology. Nevertheless, methods that simultaneously do both are few and lack generality.

Results

Here, we present a rigorous approach for simultaneously estimating the parameters and regulatory topology of biochemical networks from time-series data. The parameter estimation task is formulated as a mixed-integer dynamic optimization problem with: (i) binary variables, used to model the existence of regulatory interactions and kinetic effects of metabolites in the network processes; and (ii) continuous variables, denoting metabolites concentrations and kinetic parameters values. The approach simultaneously optimizes the Akaike criterion, which captures the trade-off between complexity (measured by the number of parameters), and accuracy of the fitting. This simultaneous optimization mitigates a possible overfitting that could result from addition of spurious regulatory interactions.

Conclusion

The capabilities of our approach were tested in one benchmark problem. Our algorithm is able to identify a set of plausible network topologies with their associated parameters.

Statistical Model for Biochemical Network Inference

We describe a statistical method for predicting most likely reactions in a biochemical reaction network from the longitudinal data on species concentrations. Such data is relatively easily available in biochemical laboratories, for instance, via the popular RT-PCR technology. Under the assumed kinetics of the law of mass action, we also propose the data-based algorithms for estimating the prediction errors and for network dimension reduction. The second algorithm allows in particular for the application of the original algebraic inferential procedure described in [4] without the unnecessary restrictions on the dimension of the network stoichiometric space. Simulated examples of biochemical networks are analyzed, in order to assess the proposed methods' performance.

A graphical user interface for a method to infer kinetics and network architecture (MIKANA)

One of the main challenges in the biomedical sciences is the determination of reaction mechanisms that constitute a biochemical pathway. During the last decades, advances have been made in building complex diagrams showing the static interactions of proteins. The challenge for systems biologists is to build realistic models of the dynamical behavior of reactants, intermediates and products. For this purpose, several methods have been recently proposed to deduce the reaction mechanisms or to estimate the kinetic parameters of the elementary reactions that constitute the pathway. One such method is MIKANA: Method to Infer Kinetics And Network Architecture. MIKANA is a computational method to infer both reaction mechanisms and estimate the kinetic parameters of biochemical pathways from time course data. To make it available to the scientific community, we developed a Graphical User Interface (GUI) for MIKANA. Among other features, the GUI validates and processes an input time course data, displays the inferred reactions, generates the differential equations for the chemical species in the pathway and plots the prediction curves on top of the input time course data. We also added a new feature to MIKANA that allows the user to exclude a priori known reactions from the inferred mechanism. This addition improves the performance of the method. In this article, we illustrate the GUI for MIKANA with three examples: an irreversible Michaelis–Menten reaction mechanism; the interaction map of chemical species of the muscle glycolytic pathway; and the glycolytic pathway of Lactococcus lactis. We also describe the code and methods in sufficient detail to allow researchers to further develop the code or reproduce the experiments described. The code for MIKANA is open source, free for academic and non-academic use and is available for download (Information S1).

Automated refinement and inference of analytical models for metabolic networks

The reverse engineering of metabolic networks from experimental data is traditionally a labor-intensive task requiring a priori systems knowledge. Using a proven model as a test system, we demonstrate an automated method to simplify this process by modifying an existing or related model--suggesting nonlinear terms and structural modifications--or even constructing a new model that agrees with the system's time series observations. In certain cases, this method can identify the full dynamical model from scratch without prior knowledge or structural assumptions. The algorithm selects between multiple candidate models by designing experiments to make their predictions disagree. We performed computational experiments to analyze a nonlinear seven-dimensional model of yeast glycolytic oscillations. This approach corrected mistakes reliably in both approximated and overspecified models. The method performed well to high levels of noise for most states, could identify the correct model de novo, and make better predictions than ordinary parametric regression and neural network models. We identified an invariant quantity in the model, which accurately derived kinetics and the numerical sensitivity coefficients of the system. Finally, we compared the system to dynamic flux estimation and discussed the scaling and application of this methodology to automated experiment design and control in biological systems in real time.

Macroscopic law of conservation revealed in the population dynamics of Toll-like receptor signaling

Stimulating the receptors of a single cell generates stochastic intracellular signaling. The fluctuating response has been attributed to the low abundance of signaling molecules and the spatio-temporal effects of diffusion and crowding. At population level, however, cells are able to execute well-defined deterministic biological processes such as growth, division, differentiation and immune response. These data reflect biology as a system possessing microscopic and macroscopic dynamics. This commentary discusses the average population response of the Toll-like receptor (TLR) 3 and 4 signaling. Without requiring detailed experimental data, linear response equations together with the fundamental law of information conservation have been used to decipher novel network features such as unknown intermediates, processes and cross-talk mechanisms. For single cell response, however, such simplicity seems far from reality. Thus, as observed in any other complex systems, biology can be considered to possess order and disorder, inheriting a mixture of predictable population level and unpredictable single cell outcomes.

Metabolomics: an integral technique in systems biology

Metabolomics is the unbiased identification and state-specific quantification of all metabolites in a cell, tissue or whole organism, and has developed rapidly into one of the cornerstones of postgenomic techniques for the quantitative analysis of molecular phenotypes. These large-scale analyses of metabolites are intimately bound to advancements in MS technologies and have emerged in parallel with the development of novel mass analyzers and hyphenated techniques, as well as with the combination of different techniques to cope with the physicochemical diversity of a metabolome. This review gives a brief description of the development and applications of these technologies in biochemistry and systems biology, and discusses their significance in the postgenomic era. Especially, the systematic relation between high-throughput metabolomic data and their interpretation with respect to the underlying biochemical regulatory network is discussed.

Gaussian graphical modeling reconstructs pathway reactions from high-throughput metabolomics data

Background

With the advent of high-throughput targeted metabolic profiling techniques, the question of how to interpret and analyze the resulting vast amount of data becomes more and more important. In this work we address the reconstruction of metabolic reactions from cross-sectional metabolomics data, that is without the requirement for time-resolved measurements or specific system perturbations. Previous studies in this area mainly focused on Pearson correlation coefficients, which however are generally incapable of distinguishing between direct and indirect metabolic interactions.

Results

In our new approach we propose the application of a Gaussian graphical model (GGM), an undirected probabilistic graphical model estimating the conditional dependence between variables. GGMs are based on partial correlation coefficients, that is pairwise Pearson correlation coefficients conditioned against the correlation with all other metabolites. We first demonstrate the general validity of the method and its advantages over regular correlation networks with computer-simulated reaction systems. Then we estimate a GGM on data from a large human population cohort, covering 1020 fasting blood serum samples with 151 quantified metabolites. The GGM is much sparser than the correlation network, shows a modular structure with respect to metabolite classes, and is stable to the choice of samples in the data set. On the example of human fatty acid metabolism, we demonstrate for the first time that high partial correlation coefficients generally correspond to known metabolic reactions. This feature is evaluated both manually by investigating specific pairs of high-scoring metabolites, and then systematically on a literature-curated model of fatty acid synthesis and degradation. Our method detects many known reactions along with possibly novel pathway interactions, representing candidates for further experimental examination.

Conclusions

In summary, we demonstrate strong signatures of intracellular pathways in blood serum data, and provide a valuable tool for the unbiased reconstruction of metabolic reactions from large-scale metabolomics data sets.

Network inference from time-dependent Omics data

We provide a commented overview of the available databases for the systematic collection of pathway information and biological models essential for the interpretation of Omics data. Then, we present both the state of the art and the future challenges of network inference, a research area dealing with the deduction of reaction mechanisms from experimental Omics data. This approach represents one of the most challenging instances for making use of the huge amount of information gathered in the Omics era.

Reverse engineering of metabolic networks, a critical assessment

Inferring metabolic networks from metabolite concentration data is a central topic in systems biology. Mathematical techniques to extract information about the network from data have been proposed in the literature. This paper presents a critical assessment of the feasibility of reverse engineering of metabolic networks, illustrated with a selection of methods. Appropriate data are simulated to study the performance of four representative methods. An overview of sampling and measurement methods currently in use for generating time-resolved metabolomics data is given and contrasted with the needs of the discussed reverse engineering methods. The results of this assessment show that if full inference of a real-world metabolic network is the goal there is a large discrepancy between the requirements of reverse engineering of metabolic networks and contemporary measurement practice. Recommendations for improved time-resolved experimental designs are given.

Estimation of metabolic pathway systems from different data sources

Parameter estimation is the main bottleneck of metabolic pathway modelling. It may be addressed from the bottom up, using information on metabolites, enzymes and modulators, or from the top down, using metabolic time series data, which have become more prevalent in recent years. The authors propose here that it is useful to combine the two strategies and to complement time-series analysis with kinetic information. In particular, the authors investigate how the recent method of dynamic flux estimation (DFE) may be supplemented with other types of estimation. Using the glycolytic pathway in Lactococcus lactis as an illustration example, the authors demonstrate some strategies of such supplementation.

Developing optimal input design strategies in cancer systems biology with applications to microfluidic device engineering

Background

Mechanistic models are becoming more and more popular in Systems Biology; identification and control of models underlying biochemical pathways of interest in oncology is a primary goal in this field. Unfortunately the scarce availability of data still limits our understanding of the intrinsic characteristics of complex pathologies like cancer: acquiring information for a system understanding of complex reaction networks is time consuming and expensive. Stimulus response experiments (SRE) have been used to gain a deeper insight into the details of biochemical mechanisms underlying cell life and functioning. Optimisation of the input time-profile, however, still remains a major area of research due to the complexity of the problem and its relevance for the task of information retrieval in systems biology-related experiments.

Results

We have addressed the problem of quantifying the information associated to an experiment using the Fisher Information Matrix and we have proposed an optimal experimental design strategy based on evolutionary algorithm to cope with the problem of information gathering in Systems Biology. On the basis of the theoretical results obtained in the field of control systems theory, we have studied the dynamical properties of the signals to be used in cell stimulation. The results of this study have been used to develop a microfluidic device for the automation of the process of cell stimulation for system identification.

Conclusion

We have applied the proposed approach to the Epidermal Growth Factor Receptor pathway and we observed that it minimises the amount of parametric uncertainty associated to the identified model. A statistical framework based on Monte-Carlo estimations of the uncertainty ellipsoid confirmed the superiority of optimally designed experiments over canonical inputs. The proposed approach can be easily extended to multiobjective formulations that can also take advantage of identifiability analysis. Moreover, the availability of fully automated microfluidic platforms explicitly developed for the task of biochemical model identification will hopefully reduce the effects of the 'data rich-data poor' paradox in Systems Biology.

Optimal metabolic regulation using a constraint-based model

Regulation of metabolic enzymes plays a crucial role in the maintenance of metabolic homeostasis, and in the capacity of living systems to undergo physiological adaptation under multiple environmental conditions. Metabolic regulation is achieved through a complex interplay of transcriptional and post-transcriptional mechanisms, some of which have been experimentally characterized for specific pathways and organisms. Many of the details, however, including the values of most kinetic parameters, have proven difficult to elucidate. Hence, understanding the principles that underlie metabolic regulation strategies constitutes an ongoing challenge. In the context of genome-scale steady state models of metabolic networks, it has been shown that evolution may drive metabolic networks towards reaching computationally predictable optimal states, such as maximal growth capacity. Here we develop a new computational approach based on the hypothesis that the regulatory systems operating on metabolic networks have evolved towards an optimal architecture as well. Specifically, we hypothesize that the topology of metabolic regulation networks has been selected for optimally maintaining the system balanced around one or more steady states. Based on these hypotheses, we use methods related to flux balance analysis to construct a model of metabolic regulation based primarily on a metabolic network's topology, bypassing the requirement for the details of all kinetic parameters. This model predicts an optimal regulatory network of metabolic interactions that can resolve perturbations to a given steady state in a metabolic system. We explore the ability of the model to predict optimal regulatory responses in both a simple toy network and in a fragment of the well-described glycolysis pathway.

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.

Can complex cellular processes be governed by simple linear rules?

Complex living systems have shown remarkably well-orchestrated, self-organized, robust, and stable behavior under a wide range of perturbations. However, despite the recent generation of high-throughput experimental datasets, basic cellular processes such as division, differentiation, and apoptosis still remain elusive. One of the key reasons is the lack of understanding of the governing principles of complex living systems. Here, we have reviewed the success of perturbation-response approaches, where without the requirement of detailed in vivo physiological parameters, the analysis of temporal concentration or activation response unravels biological network features such as causal relationships of reactant species, regulatory motifs, etc. Our review shows that simple linear rules govern the response behavior of biological networks in an ensemble of cells. It is daunting to know why such simplicity could hold in a complex heterogeneous environment. Provided physical reasons can be explained for these phenomena, major advancement in the understanding of basic cellular processes could be achieved.

Linking high-resolution metabolic flux phenotypes and transcriptional regulation in yeast modulated by the global regulator Gcn4p

Genome sequencing dramatically increased our ability to understand cellular response to perturbation. Integrating system-wide measurements such as gene expression with networks of protein-protein interactions and transcription factor binding revealed critical insights into cellular behavior. However, the potential of systems biology approaches is limited by difficulties in integrating metabolic measurements across the functional levels of the cell despite their being most closely linked to cellular phenotype. To address this limitation, we developed a model-based approach to correlate mRNA and metabolic flux data that combines information from both interaction network models and flux determination models. We started by quantifying 5,764 mRNAs, 54 metabolites, and 83 experimental (13)C-based reaction fluxes in continuous cultures of yeast under stress in the absence or presence of global regulator Gcn4p. Although mRNA expression alone did not directly predict metabolic response, this correlation improved through incorporating a network-based model of amino acid biosynthesis (from r = 0.07 to 0.80 for mRNA-flux agreement). The model provides evidence of general biological principles: rewiring of metabolic flux (i.e., use of different reaction pathways) by transcriptional regulation and metabolite interaction density (i.e., level of pairwise metabolite-protein interactions) as a key biosynthetic control determinant. Furthermore, this model predicted flux rewiring in studies of follow-on transcriptional regulators that were experimentally validated with additional (13)C-based flux measurements. As a first step in linking metabolic control and genetic regulatory networks, this model underscores the importance of integrating diverse data types in large-scale cellular models. We anticipate that an integrated approach focusing on metabolic measurements will facilitate construction of more realistic models of cellular regulation for understanding diseases and constructing strains for industrial applications.

Identification of feedback loops embedded in cellular circuits by investigating non-causal impulse response components

Feedback circuits are crucial dynamic motifs which occur in many biomolecular regulatory networks. They play a pivotal role in the regulation and control of many important cellular processes such as gene transcription, signal transduction, and metabolism. In this study, we develop a novel computationally efficient method to identify feedback loops embedded in intracellular networks, which uses only time-series experimental data and requires no knowledge of the network structure. In the proposed approach, a non-parametric system identification technique, as well as a spectral factor analysis, is applied to derive a graphical criterion based on non-causal components of the system's impulse response. The appearance of non-causal components in the impulse response sequences arising from stochastic output perturbations is shown to imply the presence of underlying feedback connections within a linear network. In order to extend the approach to nonlinear networks, we linearize the intracellular networks about an equilibrium point, and then choose the magnitude of the output perturbations sufficiently small so that the resulting time-series responses remain close to the chosen equilibrium point. In this way, the impulse response sequences of the linearized system can be used to determine the presence or absence of feedback loops in the corresponding nonlinear network. The proposed method utilizes the time profile data from intracellular perturbation experiments and only requires the perturbability of output nodes. Most importantly, the method does not require any a priori knowledge of the system structure. For these reasons, the proposed approach is very well suited to identifying feedback loops in large-scale biomolecular networks. The effectiveness of the proposed method is illustrated via two examples: a synthetic network model with a negative feedback loop and a nonlinear caspase function model of apoptosis with a positive feedback loop.

Predicting novel features of toll-like receptor 3 signaling in macrophages

The Toll-like receptor (TLR) 3 plays a critical role in mammalian innate immune response against viral attacks by recognizing double-stranded RNA (dsRNA) or its synthetic analog polyinosinic-polycytidylic acid (poly (I∶C)). This leads to the activation of MAP kinases and NF-κB which results in the induction of type I interferons and proinflammatory cytokines to combat the viral infection. To understand the complex interplay of the various intracellular signaling molecules in the regulation of NF-κB and MAP kinases, we developed a computational TLR3 model based upon perturbation-response approach. We curated literature and databases to determine the TLR3 signaling topology specifically for murine macrophages. For initial model creation, we used wildtype temporal activation profiles of MAP kinases and NF-κB and, for model testing, used TRAF6 KO and TRADD KO data. From dynamic simulations we predict i) the existence of missing intermediary steps between extracellular poly (I∶C) stimulation and intracellular TLR3 binding, and ii) the presence of a novel pathway which is essential for JNK and p38, but not NF-κB, activation. Our work shows activation dynamics of signaling molecules can be used in conjunction with perturbation-response models to decipher novel signaling features of complicated immune pathways.

Efficient, sparse biological network determination

BACKGROUND

Determining the interaction topology of biological systems is a topic that currently attracts significant research interest. Typical models for such systems take the form of differential equations that involve polynomial and rational functions. Such nonlinear models make the problem of determining the connectivity of biochemical networks from time-series experimental data much harder. The use of linear dynamics and linearization techniques that have been proposed in the past can circumvent this, but the general problem of developing efficient algorithms for models that provide more accurate system descriptions remains open.

RESULTS

We present a network determination algorithm that can treat model descriptions with polynomial and rational functions and which does not make use of linearization. For this purpose, we make use of the observation that biochemical networks are in general 'sparse' and minimize the 1-norm of the decision variables (sum of weighted network connections) while constraints keep the error between data and the network dynamics small. The emphasis of our methodology is on determining the interconnection topology rather than the specific reaction constants and it takes into account the necessary properties that a chemical reaction network should have - something that techniques based on linearization can not. The problem can be formulated as a Linear Program, a convex optimization problem, for which efficient algorithms are available that can treat large data sets efficiently and uncertainties in data or model parameters.

CONCLUSION

The presented methodology is able to predict with accuracy and efficiency the connectivity structure of a chemical reaction network with mass action kinetics and of a gene regulatory network from simulation data even if the dynamics of these systems are non-polynomial (rational) and uncertainties in the data are taken into account. It also produces a network structure that can explain the real experimental data of L. lactis and is similar to the one found in the literature. Numerical methods based on Linear Programming can therefore help determine efficiently the network structure of biological systems from large data sets. The overall objective of this work is to provide methods to increase our understanding of complex biochemical systems, particularly through their interconnection and their non-equilibrium behavior.

Genetic network inference as a series of discrimination tasks

MOTIVATION

Genetic network inference methods based on sets of differential equations generally require a great deal of time, as the equations must be solved many times. To reduce the computational cost, researchers have proposed other methods for inferring genetic networks by solving sets of differential equations only a few times, or even without solving them at all. When we try to obtain reasonable network models using these methods, however, we must estimate the time derivatives of the gene expression levels with great precision. In this study, we propose a new method to overcome the drawbacks of inference methods based on sets of differential equations.

RESULTS

Our method infers genetic networks by obtaining classifiers capable of predicting the signs of the derivatives of the gene expression levels. For this purpose, we defined a genetic network inference problem as a series of discrimination tasks, then solved the defined series of discrimination tasks with a linear programming machine. Our experimental results demonstrated that the proposed method is capable of correctly inferring genetic networks, and doing so more than 500 times faster than the other inference methods based on sets of differential equations. Next, we applied our method to actual expression data of the bacterial SOS DNA repair system. And finally, we demonstrated that our approach relates to the inference method based on the S-system model. Though our method provides no estimation of the kinetic parameters, it should be useful for researchers interested only in the network structure of a target system.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Resonant response to temperature modulation for enzymatic dynamics characterization

We consider enzymes involved in a three-state Michaelis-Menten kinetics and submitted to well-chosen temperature modulations of small amplitude. From the first-order amplitudes of concentration oscillations, we design a response function that is maximum for targeted values of the chemical relaxation times. This resonant function can be used to screen a large set of enzymes and identify the one governed by the desired kinetics. The method gives access to all the dynamical parameters of the targeted enzyme without resorting to a fit. We show how to estimate the precision of this parameter determination and give some hints for experimental validation.

Learning biological networks: from modules to dynamics

Learning regulatory networks from genomics data is an important problem with applications spanning all of biology and biomedicine. Functional genomics projects offer a cost-effective means of greatly expanding the completeness of our regulatory models, and for some prokaryotic organisms they offer a means of learning accurate models that incorporate the majority of the genome. There are, however, several reasons to believe that regulatory network inference is beyond our current reach, such as (i) the combinatorics of the problem, (ii) factors we can't (or don't often) collect genome-wide measurements for and (iii) dynamics that elude cost-effective experimental designs. Recent works have demonstrated the ability to reconstruct large fractions of prokaryotic regulatory networks from compendiums of genomics data; they have also demonstrated that these global regulatory models can be used to predict the dynamics of the transcriptome. We review an overall strategy for the reconstruction of global networks based on these results in microbial systems.

Signaling flux redistribution at toll-like receptor pathway junctions

Various receptors on cell surface recognize specific extracellular molecules and trigger signal transduction altering gene expression in the nucleus. Gain or loss-of-function mutations of one molecule have shown to affect alternative signaling pathways with a poorly understood mechanism. In Toll-like receptor (TLR) 4 signaling, which branches into MyD88- and TRAM-dependent pathways upon lipopolysaccharide (LPS) stimulation, we investigated the gain or loss-of-function mutations of MyD88. We predict, using a computational model built on the perturbation-response approach and the law of mass conservation, that removal and addition of MyD88 in TLR4 activation, enhances and impairs, respectively, the alternative TRAM-dependent pathway through signaling flux redistribution (SFR) at pathway branches. To verify SFR, we treated MyD88-deficient macrophages with LPS and observed enhancement of TRAM-dependent pathway based on increased IRF3 phosphorylation and induction of Cxcl10 and Ifit2. Furthermore, increasing the amount of MyD88 in cultured cells showed decreased TRAM binding to TLR4. Investigating another TLR4 pathway junction, from TRIF to TRAF6, RIP1 and TBK1, the removal of MyD88-dependent TRAF6 increased expression of TRAM-dependent Cxcl10 and Ifit2. Thus, we demonstrate that SFR is a novel mechanism for enhanced activation of alternative pathways when molecules at pathway junctions are removed. Our data suggest that SFR may enlighten hitherto unexplainable intracellular signaling alterations in genetic diseases where gain or loss-of-function mutations are observed.

From the determination of complex reaction mechanisms to systems biology

This review presents several methods of determining complex chemical reaction mechanisms and their functions. One method is based on correlation functions of measured time series of concentrations of chemical species, another is on measurements of temporal responses of concentrations to various perturbations of arbitrary magnitude, the third deals with the analysis of oscillatory systems, and the fourth describes the use of genetic algorithms. All methods are applicable to chemical, biochemical, and biological reaction systems and to genetic networks. The methods depend on the design of appropriate experiments for the whole system and corresponding theories for interpretation that lead to information on the causal chemical connectivity of species, reaction pathways, reaction mechanisms, control centers in the system, and functions of the system. The first three methods require no assumption of a model or hypothesis, nor extensive calculations, unlike the interpretation of measurements made on a gene network at only one time. The methods offer advantageous approaches to systems biology.

The frequency dependence of osmo-adaptation in Saccharomyces cerevisiae

The propagation of information through signaling cascades spans a wide range of time scales, including the rapid ligand-receptor interaction and the much slower response of downstream gene expression. To determine which dynamic range dominates a response, we used periodic stimuli to measure the frequency dependence of signal transduction in the osmo-adaptation pathway of Saccharomyces cerevisiae. We applied system identification methods to infer a concise predictive model. We found that the dynamics of the osmo-adaptation response are dominated by a fast-acting negative feedback through the kinase Hog1 that does not require protein synthesis. After large osmotic shocks, an additional, much slower, negative feedback through gene expression allows cells to respond faster to future stimuli.

New surveyor tools for charting microbial metabolic maps

The computational reconstruction and analysis of cellular models of microbial metabolism is one of the great success stories of systems biology. The extent and quality of metabolic network reconstructions is, however, limited by the current state of biochemical knowledge. Can experimental high-throughput data be used to improve and expand network reconstructions to include unexplored areas of metabolism? Recent advances in experimental technology and analytical methods bring this aim an important step closer to realization. Data integration will play a particularly important part in exploiting the new experimental opportunities.

Function approximation approach to the inference of reduced NGnet models of genetic networks

BACKGROUND

The inference of a genetic network is a problem in which mutual interactions among genes are deduced using time-series of gene expression patterns. While a number of models have been proposed to describe genetic regulatory networks, this study focuses on a set of differential equations since it has the ability to model dynamic behavior of gene expression. When we use a set of differential equations to describe genetic networks, the inference problem can be defined as a function approximation problem. On the basis of this problem definition, we propose in this study a new method to infer reduced NGnet models of genetic networks.

RESULTS

Through numerical experiments on artificial genetic network inference problems, we demonstrated that our method has the ability to infer genetic networks correctly and it was faster than the other inference methods. We then applied the proposed method to actual expression data of the bacterial SOS DNA repair system, and succeeded in finding several reasonable regulations. When our method inferred the genetic network from the actual data, it required about 4.7 min on a single-CPU personal computer.

CONCLUSION

The proposed method has an ability to obtain reasonable networks with a short computational time. As a high performance computer is not always available at every laboratory, the short computational time of our method is a preferable feature. There does not seem to be a perfect model for the inference of genetic networks yet. Therefore, in order to extract reliable information from the observed gene expression data, we should infer genetic networks using multiple inference methods based on different models. Our approach could be used as one of the promising inference methods.

Negative autoregulation by FAS mediates robust fetal erythropoiesis

Tissue development is regulated by signaling networks that control developmental rate and determine ultimate tissue mass. Here we present a novel computational algorithm used to identify regulatory feedback and feedforward interactions between progenitors in developing erythroid tissue. The algorithm makes use of dynamic measurements of red cell progenitors between embryonic days 12 and 15 in the mouse. It selects for intercellular interactions that reproduce the erythroid developmental process and endow it with robustness to external perturbations. This analysis predicts that negative autoregulatory interactions arise between early erythroblasts of similar maturation stage. By studying embryos mutant for the death receptor FAS, or for its ligand, FASL, and by measuring the rate of FAS-mediated apoptosis in vivo, we show that FAS and FASL are pivotal negative regulators of fetal erythropoiesis, in the manner predicted by the computational model. We suggest that apoptosis in erythroid development mediates robust homeostasis regulating the number of red blood cells reaching maturity.

Consistency analysis of metabolic correlation networks

BACKGROUND

Metabolic correlation networks are derived from the covariance of metabolites in replicates of metabolomics experiments. They constitute an interesting intermediate between topology (i.e. the system's architecture defined by the set of reactions between metabolites) and dynamics (i.e. the metabolic concentrations observed as fluctuations around steady-state values in the metabolic network).

RESULTS

Here we analyze, how such a correlation network changes over time, and compare the relative positions of metabolites in the correlation networks with those in established metabolic networks derived from genome databases. We find that network similarity indeed decreases with an increasing time difference between these networks during a day/night course and, counter intuitively, that proximity of metabolites in the correlation network is no indicator of proximity of the metabolites in the metabolic network.

CONCLUSION

The organizing principles of correlation networks are distinct from those of metabolic reaction maps. Time courses of correlation networks may in the future prove an important data source for understanding these organizing principles.

Reconstructing biochemical pathways from time course data

Time series data on biochemical reactions reveal transient behavior, away from chemical equilibrium, and contain information on the dynamic interactions among reacting components. However, this information can be difficult to extract using conventional analysis techniques. We present a new method to infer biochemical pathway mechanisms from time course data using a global nonlinear modeling technique to identify the elementary reaction steps which constitute the pathway. The method involves the generation of a complete dictionary of polynomial basis functions based on the law of mass action. Using these basis functions, there are two approaches to model construction, namely the general to specific and the specific to general approach. We demonstrate that our new methodology reconstructs the chemical reaction steps and connectivity of the glycolytic pathway of Lactococcus lactis from time course experimental data.

Stochastic fluctuations in metabolic pathways

Fluctuations in the abundance of molecules in the living cell may affect its growth and well being. For regulatory molecules (e.g., signaling proteins or transcription factors), fluctuations in their expression can affect the levels of downstream targets in a network. Here, we develop an analytic framework to investigate the phenomenon of noise correlation in molecular networks. Specifically, we focus on the metabolic network, which is highly interlinked, and noise properties may constrain its structure and function. Motivated by the analogy between the dynamics of a linear metabolic pathway and that of the exactly soluble linear queuing network or, alternatively, a mass transfer system, we derive a plethora of results concerning fluctuations in the abundance of intermediate metabolites in various common motifs of the metabolic network. For all but one case examined, we find the steady-state fluctuation in different nodes of the pathways to be effectively uncorrelated. Consequently, fluctuations in enzyme levels only affect local properties and do not propagate elsewhere into metabolic networks, and intermediate metabolites can be freely shared by different reactions. Our approach may be applicable to study metabolic networks with more complex topologies or protein signaling networks that are governed by similar biochemical reactions. Possible implications for bioinformatic analysis of metabolomic data are discussed.

Numerical Matrices Method for nonlinear system identification and description of dynamics of biochemical reaction networks

A flexible Numerical Matrices Method (NMM) for nonlinear system identification has been developed based on a description of the dynamics of the system in terms of kinetic complexes. A set of related methods are presented that include increasing amounts of prior information about the reaction network structure, resulting in increased accuracy of the reconstructed rate constants. The NMM is based on an analytical least squares solution for a set of linear equations to determine the rate parameters. In the absence of prior information, all possible unimolecular and bimolecular reactions among the species in the system are considered, and the elements of a general kinetic matrix are determined. Inclusion of prior information is facilitated by formulation of the kinetic matrix in terms of a stoichiometry matrix or a more general set of representation matrices. A method for determination of the stoichiometry matrix beginning only with time-dependent concentration data is presented. In addition, we demonstrate that singularities that arise from linear dependencies among the species can be avoided by inclusion of data collected from a number of different initial states. The NMM provides a flexible set of tools for analysis of complex kinetic data, in particular for analysis of chemical and biochemical reaction networks.

Untangling the signalling wires

Mitogen-activated protein kinase (MAPK) cascades process myriads of stimuli, generating receptor-specific cellular outcomes. New work exploits emergent mathematics of network inference to reveal distinct feedback designs of the RAF/MEK/ERK cascade induced by two different growth factors. It shows that response specificity can arise from differential signal-induced wiring of overlapping protein networks.

Species connectivities and reaction mechanisms from neutral response experiments

We develop a new method for obtaining connectivity data for nonlinear reaction networks, based on linear response experiments. In our approach the linear response is not the result of an approximation procedure but is due to the appropriate design of the response experiments, that is (1) they are carried out with the preservation of constant values for the total (labeled plus unlabeled) input and output fluxes and (2) the labeled compounds obey a neutrality condition (i.e., they have practically the same kinetic and transport properties as the unlabeled compounds). Under these circumstances the linear response equations hold even though the kinetics of the process is highly nonlinear. On the basis of this linear response law, we develop a method for evaluating reaction connectivities in biochemical networks from stationary response experiments. Given a system in a stationary regime, a pulse of a labeled species is introduced (with conservation of the total flux) and then the response of all the species of the network is recorded. The mechanistic information is contained in a connectivity matrix, K, which can be evaluated from the response data by means of differential as well as integral methods. The approach does not require any prior knowledge of the reaction mechanism. We carried out a numerical study of the method, based on a two-step procedure. Starting from a known reaction mechanism, we generated response data sets, to which we add noise; then, we use the noisy data sets for retrieving the connectivity matrix. The calculations were done with two programs written in Mathematica: the urea cycle and the upper part of glycolysis are used as sample biochemical networks. Given enough computer power, there are no limitations concerning the number of species involved in the response experiments; on current desktop systems processing responses of teens of species would take a few hours. The method is limited by the occurrence of experimental errors: if experimental errors in the evaluation of fluxes are larger than 10%, the method may fail to reproduce the correct values of some elements of the connectivity matrix.

Cardiac system bioenergetics: metabolic basis of the Frank-Starling law

The fundamental principle of cardiac behaviour is described by the Frank-Starling law relating force of contraction during systole with end-diastolic volume. While both work and respiration rates increase linearly with imposed load, the basis of mechano-energetic coupling in heart muscle has remained a long-standing enigma. Here, we highlight advances made in understanding of complex cellular and molecular mechanisms that orchestrate coupling of mitochondrial oxidative phosphorylation with ATP utilization for muscle contraction. Cardiac system bioenergetics critically depends on an interrelated metabolic infrastructure regulating mitochondrial respiration and energy fluxes throughout cellular compartments. The data reviewed indicate the significance of two interrelated systems regulating mitochondrial respiration and energy fluxes in cells: (1) the creatine kinase, adenylate kinase and glycolytic pathways that communicate flux changes generated by cellular ATPases within structurally organized enzymatic modules and networks; and (2) a secondary system based on mitochondrial participation in cellular calcium cycle, which adjusts substrate oxidation and energy-transducing processes to meet increasing cellular energy demands. By conveying energetic signals to metabolic sensors, coupled phosphotransfer reactions provide a high-fidelity regulation of the excitation-contraction cycle. Such integration of energetics with calcium signalling systems provides the basis for 'metabolic pacing', synchronizing the cellular electrical and mechanical activities with energy supply processes.