Top-down analysis of temporal hierarchy in biochemical reaction networks

A data-driven approach for timescale decomposition of biochemical reaction networks

Understanding the dynamics of biological systems in evolving environments is a challenge due to their scale and complexity. Here, we present a computational framework for the timescale decomposition of biochemical reaction networks to distill essential patterns from their intricate dynamics. This approach identifies timescale hierarchies, concentration pools, and coherent structures from time-series data, providing a system-level description of reaction networks at physiologically important timescales. We apply this technique to kinetic models of hypothetical and biological pathways, validating it by reproducing analytically characterized or previously known concentration pools of these pathways. Moreover, by analyzing the timescale hierarchy of the glycolytic pathway, we elucidate the connections between the stoichiometric and dissipative structures of reaction networks and the temporal organization of coherent structures. Specifically, we show that glycolysis is a cofactor-driven pathway, the slowest dynamics of which are described by a balance between high-energy phosphate bond and redox trafficking. Overall, this approach provides more biologically interpretable characterizations of network dynamics than large-scale kinetic models, thus facilitating model reduction and personalized medicine applications. IMPORTANCE Complex interactions within interconnected biochemical reaction networks enable cellular responses to a wide range of unpredictable environmental perturbations. Understanding how biological functions arise from these intricate interactions has been a long-standing problem in biology. Here, we introduce a computational approach to dissect complex biological systems' dynamics in evolving environments. This approach characterizes the timescale hierarchies of complex reaction networks, offering a system-level understanding at physiologically relevant timescales. Analyzing various hypothetical and biological pathways, we show how stoichiometric properties shape the way energy is dissipated throughout reaction networks. Notably, we establish that glycolysis operates as a cofactor-driven pathway, where the slowest dynamics are governed by a balance between high-energy phosphate bonds and redox trafficking. This approach enhances our understanding of network dynamics and facilitates the development of reduced-order kinetic models with biologically interpretable components.

A data-driven approach for timescale decomposition of biochemical reaction networks

Understanding the dynamics of biological systems in evolving environments is a challenge due to their scale and complexity. Here, we present a computational framework for timescale decomposition of biochemical reaction networks to distill essential patterns from their intricate dynamics. This approach identifies timescale hierarchies, concentration pools, and coherent structures from time-series data, providing a system-level description of reaction networks at physiologically important timescales. We apply this technique to kinetic models of hypothetical and biological pathways, validating it by reproducing analytically characterized or previously known concentration pools of these pathways. Moreover, by analyzing the timescale hierarchy of the glycolytic pathway, we elucidate the connections between the stoichiometric and dissipative structures of reaction networks and the temporal organization of coherent structures. Specifically, we show that glycolysis is a cofactor driven pathway, the slowest dynamics of which are described by a balance between high-energy phosphate bond and redox trafficking. Overall, this approach provides more biologically interpretable characterizations of network dynamics than large-scale kinetic models, thus facilitating model reduction and personalized medicine applications.

Role of time scales and topology on the dynamics of complex networks

The interplay between time scales and structural properties of complex networks of nonlinear oscillators can generate many interesting phenomena, like amplitude death, cluster synchronization, frequency synchronization, etc. We study the emergence of such phenomena and their transitions by considering a complex network of dynamical systems in which a fraction of systems evolves on a slower time scale on the network. We report the transition to amplitude death for the whole network and the scaling near the transitions as the connectivity pattern changes. We also discuss the suppression and recovery of oscillations and the crossover behavior as the number of slow systems increases. By considering a scale free network of systems with multiple time scales, we study the role of heterogeneity in link structure on dynamical properties and the consequent critical behaviors. In this case with hubs made slow, our main results are the escape time statistics for loss of complete synchrony as the slowness spreads on the network and the self-organization of the whole network to a new frequency synchronized state. Our results have potential applications in biological, physical, and engineering networks consisting of heterogeneous oscillators.

Insights into Dynamic Network States Using Metabolomic Data

Metabolomic data is the youngest of the high-throughput data types; however, it is potentially one of the most informative, as it provides a direct, quantitative biochemical phenotype. There are a number of ways in which metabolomic data can be analyzed in systems biology; however, the thermodynamic and kinetic relevance of these data cannot be overstated. Genome-scale metabolic network reconstructions provide a natural context to incorporate metabolomic data in order to provide insight into the condition-specific kinetic characteristics of metabolic networks. Herein we discuss how metabolomic data can be incorporated into constraint-based models in a flexible framework that enables scaling from small pathways to cell-scale models, while being able to accommodate coarse-grained to more detailed, allosteric interactions, all using the well-known principle of mass action.

Topological and kinetic determinants of the modal matrices of dynamic models of metabolism

Large-scale kinetic models of metabolism are becoming increasingly comprehensive and accurate. A key challenge is to understand the biochemical basis of the dynamic properties of these models. Linear analysis methods are well-established as useful tools for characterizing the dynamic response of metabolic networks. Central to linear analysis methods are two key matrices: the Jacobian matrix (J) and the modal matrix (M-1) arising from its eigendecomposition. The modal matrix M-1 contains dynamically independent motions of the kinetic model near a reference state, and it is sparse in practice for metabolic networks. However, connecting the structure of M-1 to the kinetic properties of the underlying reactions is non-trivial. In this study, we analyze the relationship between J, M-1, and the kinetic properties of the underlying network for kinetic models of metabolism. Specifically, we describe the origin of mode sparsity structure based on features of the network stoichiometric matrix S and the reaction kinetic gradient matrix G. First, we show that due to the scaling of kinetic parameters in real networks, diagonal dominance occurs in a substantial fraction of the rows of J, resulting in simple modal structures with clear biological interpretations. Then, we show that more complicated modes originate from topologically-connected reactions that have similar reaction elasticities in G. These elasticities represent dynamic equilibrium balances within reactions and are key determinants of modal structure. The work presented should prove useful towards obtaining an understanding of the dynamics of kinetic models of metabolism, which are rooted in the network structure and the kinetic properties of reactions.

Mathematical modelling of microbes: metabolism, gene expression and growth

The growth of microorganisms involves the conversion of nutrients in the environment into biomass, mostly proteins and other macromolecules. This conversion is accomplished by networks of biochemical reactions cutting across cellular functions, such as metabolism, gene expression, transport and signalling. Mathematical modelling is a powerful tool for gaining an understanding of the functioning of this large and complex system and the role played by individual constituents and mechanisms. This requires models of microbial growth that provide an integrated view of the reaction networks and bridge the scale from individual reactions to the growth of a population. In this review, we derive a general framework for the kinetic modelling of microbial growth from basic hypotheses about the underlying reaction systems. Moreover, we show that several families of approximate models presented in the literature, notably flux balance models and coarse-grained whole-cell models, can be derived with the help of additional simplifying hypotheses. This perspective clearly brings out how apparently quite different modelling approaches are related on a deeper level, and suggests directions for further research.

Short relaxation times but long transient times in both simple and complex reaction networks

When relaxation towards an equilibrium or steady state is exponential at large times, one usually considers that the associated relaxation time τ, i.e. the inverse of the decay rate, is the longest characteristic time in the system. However, that need not be true, other times such as the lifetime of an infinitesimal perturbation can be much longer. In the present work, we demonstrate that this paradoxical property can arise even in quite simple systems such as a linear chain of reactions obeying mass action (MA) kinetics. By mathematical analysis of simple reaction networks, we pin-point the reason why the standard relaxation time does not provide relevant information on the potentially long transient times of typical infinitesimal perturbations. Overall, we consider four characteristic times and study their behaviour in both simple linear chains and in more complex reaction networks taken from the publicly available database ‘Biomodels’. In all these systems, whether involving MA rates, Michaelis–Menten reversible kinetics, or phenomenological laws for reaction rates, we find that the characteristic times corresponding to lifetimes of tracers and of concentration perturbations can be significantly longer than τ.

Time Hierarchies and Model Reduction in Canonical Non-linear Models

The time-scale hierarchies of a very general class of models in differential equations is analyzed. Classical methods for model reduction and time-scale analysis have been adapted to this formalism and a complementary method is proposed. A unified theoretical treatment shows how the structure of the system can be much better understood by inspection of two sets of singular values: one related to the stoichiometric structure of the system and another to its kinetics. The methods are exemplified first through a toy model, then a large synthetic network and finally with numeric simulations of three classical benchmark models of real biological systems.

Constructing kinetic models of metabolism at genome-scales: A review

Constraint-based modeling of biological networks (metabolism, transcription and signal transduction), although used successfully in many applications, suffer from specific limitations such as the lack of representation of metabolite concentrations and enzymatic regulation, which are necessary for a complete physiologically relevant model. Kinetic models conversely overcome these shortcomings and enable dynamic analysis of biological systems for enhanced in silico hypothesis generation. Nonetheless, kinetic models also have limitations for modeling at genome-scales chiefly due to: (i) model non-linearity; (ii) computational tractability; (iii) parameter identifiability; (iv) estimability; and (v) uncertainty. In order to support further development of kinetic models as viable alternatives to constraint-based models, this review presents a brief description of the existing obstacles towards building genome-scale kinetic models. Specific kinetic modeling frameworks capable of overcoming these obstacles are covered in this review. The tractability and physiological feasibility of these models are discussed with the objective of using available in vivo experimental observations to define the model parameter space. Among the different methods discussed, Monte Carlo kinetic models of metabolism stand out as potentially tractable methods to model genome scale networks while also addressing in vivo parameter uncertainty.

Bridging Mechanistic and Phenomenological Models of Complex Biological Systems

The inherent complexity of biological systems gives rise to complicated mechanistic models with a large number of parameters. On the other hand, the collective behavior of these systems can often be characterized by a relatively small number of phenomenological parameters. We use the Manifold Boundary Approximation Method (MBAM) as a tool for deriving simple phenomenological models from complicated mechanistic models. The resulting models are not black boxes, but remain expressed in terms of the microscopic parameters. In this way, we explicitly connect the macroscopic and microscopic descriptions, characterize the equivalence class of distinct systems exhibiting the same range of collective behavior, and identify the combinations of components that function as tunable control knobs for the behavior. We demonstrate the procedure for adaptation behavior exhibited by the EGFR pathway. From a 48 parameter mechanistic model, the system can be effectively described by a single adaptation parameter τ characterizing the ratio of time scales for the initial response and recovery time of the system which can in turn be expressed as a combination of microscopic reaction rates, Michaelis-Menten constants, and biochemical concentrations. The situation is not unlike modeling in physics in which microscopically complex processes can often be renormalized into simple phenomenological models with only a few effective parameters. The proposed method additionally provides a mechanistic explanation for non-universal features of the behavior.

Systems approach to excitation-energy and electron transfer reaction networks in photosystem II complex: model studies for chlorophyll a fluorescence induction kinetics

Photosystem II (PS II) is a protein complex which evolves oxygen and drives charge separation for photosynthesis employing electron and excitation-energy transfer processes over a wide timescale range from picoseconds to milliseconds. While the fluorescence emitted by the antenna pigments of this complex is known as an important indicator of the activity of photosynthesis, its interpretation was difficult because of the complexity of PS II. In this study, an extensive kinetic model which describes the complex and multi-timescale characteristics of PS II is analyzed through the use of the hierarchical coarse-graining method proposed in the authors׳ earlier work. In this coarse-grained analysis, the reaction center (RC) is described by two states, open and closed RCs, both of which consist of oxidized and neutral special pairs being in quasi-equilibrium states. Besides, the PS II model at millisecond scale with three-state RC, which was studied previously, could be derived by suitably adjusting the kinetic parameters of electron transfer between tyrosine and RC. Our novel coarse-grained model of PS II can appropriately explain the light-intensity dependent change of the characteristic patterns of fluorescence induction kinetics from O-J-I-P, which shows two inflection points, J and I, between initial point O and peak point P, to O-J-D-I-P, which shows a dip D between J and I inflection points.

Utilizing systems biology to unravel stomatal function and the hierarchies underpinning its control

Stomata control the concomitant exchange of CO2 and transpiration in land plants. While a constant supply of CO2 is need to maintain the rate of photosynthesis, the accompanying water losses must be tightly regulated to prevent dehydration and undesired metabolic changes. The factors affecting stomatal movement are directly coupled with the cellular networks of guard cells. Although the guard cell has been used as a model for characterization of signaling pathways, several important questions about its functioning remain elusive. Current modeling approaches describe the stomatal conductance in terms of relatively few easy-to-measure variables being unsuitable for in silico design of genetic manipulation strategies. Here, we argue that a system biology approach, combining modeling and high-throughput experiments, may be used to elucidate the mechanisms underlying stomata control and to determine targets for modulation of stomatal responses to environment. In support of our opinion, we review studies demonstrating how high-throughput approaches have provided a systems-view of guard cells. Finally, we emphasize the opportunities and challenges of genome-scale modeling and large-scale data integration for in silico manipulation of guard cell functions to improve crop yields, particularly under stress conditions which are of pertinence both to climate change and water use efficiency.

Designing Conservation Relations in Layered Synthetic Biomolecular Networks

In Synthetic Biology, biomolecular networks are designed and constructed to perform specified tasks. Design strategies for these networks tend to center on tuning the parameters of mathematical models to achieve a specified behavior, and implementing these parameters experimentally. This design strategy often assumes a fixed network structure that defines the possible behaviors, which may be too restrictive for our purposes. This paper investigates the extent to which the state space of a synthetic network can also be designed and shaped by parametric tuning. We exploit timescale separation to implement new, nonlinear, tunable conservation relations that hold for all times beyond a fast transient. We demonstrate an application of this design strategy by flexibly constraining the possible behaviors of a gene regulatory network through the design of fast protein interactions.

Model reduction by manifold boundaries

Understanding the collective behavior of complex systems from their basic components is a difficult yet fundamental problem in science. Existing model reduction techniques are either applicable under limited circumstances or produce "black boxes" disconnected from the microscopic physics. We propose a new approach by translating the model reduction problem for an arbitrary statistical model into a geometric problem of constructing a low-dimensional, submanifold approximation to a high-dimensional manifold. When models are overly complex, we use the observation that the model manifold is bounded with a hierarchy of widths and propose using the boundaries as submanifold approximations. We refer to this approach as the manifold boundary approximation method. We apply this method to several models, including a sum of exponentials, a dynamical systems model of protein signaling, and a generalized Ising model. By focusing on parameters rather than physical degrees of freedom, the approach unifies many other model reduction techniques, such as singular limits, equilibrium approximations, and the renormalization group, while expanding the domain of tractable models. The method produces a series of approximations that decrease the complexity of the model and reveal how microscopic parameters are systematically "compressed" into a few macroscopic degrees of freedom, effectively building a bridge between the microscopic and the macroscopic descriptions.

Network reconstruction of platelet metabolism identifies metabolic signature for aspirin resistance

Recently there has not been a systematic, objective assessment of the metabolic capabilities of the human platelet. A manually curated, functionally tested, and validated biochemical reaction network of platelet metabolism, iAT-PLT-636, was reconstructed using 33 proteomic datasets and 354 literature references. The network contains enzymes mapping to 403 diseases and 231 FDA approved drugs, alluding to an expansive scope of biochemical transformations that may affect or be affected by disease processes in multiple organ systems. The effect of aspirin (ASA) resistance on platelet metabolism was evaluated using constraint-based modeling, which revealed a redirection of glycolytic, fatty acid, and nucleotide metabolism reaction fluxes in order to accommodate eicosanoid synthesis and reactive oxygen species stress. These results were confirmed with independent proteomic data. The construction and availability of iAT-PLT-636 should stimulate further data-driven, systems analysis of platelet metabolism towards the understanding of pathophysiological conditions including, but not strictly limited to, coagulopathies.

Structure and dynamics of molecular networks: a novel paradigm of drug discovery: a comprehensive review

Despite considerable progress in genome- and proteome-based high-throughput screening methods and in rational drug design, the increase in approved drugs in the past decade did not match the increase of drug development costs. Network description and analysis not only give a systems-level understanding of drug action and disease complexity, but can also help to improve the efficiency of drug design. We give a comprehensive assessment of the analytical tools of network topology and dynamics. The state-of-the-art use of chemical similarity, protein structure, protein-protein interaction, signaling, genetic interaction and metabolic networks in the discovery of drug targets is summarized. We propose that network targeting follows two basic strategies. The "central hit strategy" selectively targets central nodes/edges of the flexible networks of infectious agents or cancer cells to kill them. The "network influence strategy" works against other diseases, where an efficient reconfiguration of rigid networks needs to be achieved by targeting the neighbors of central nodes/edges. It is shown how network techniques can help in the identification of single-target, edgetic, multi-target and allo-network drug target candidates. We review the recent boom in network methods helping hit identification, lead selection optimizing drug efficacy, as well as minimizing side-effects and drug toxicity. Successful network-based drug development strategies are shown through the examples of infections, cancer, metabolic diseases, neurodegenerative diseases and aging. Summarizing >1200 references we suggest an optimized protocol of network-aided drug development, and provide a list of systems-level hallmarks of drug quality. Finally, we highlight network-related drug development trends helping to achieve these hallmarks by a cohesive, global approach.

Dimensionality reduction of bistable biological systems

Time hierarchies, arising as a result of interactions between system's components, represent a ubiquitous property of dynamical biological systems. In addition, biological systems have been attributed switch-like properties modulating the response to various stimuli across different organisms and environmental conditions. Therefore, establishing the interplay between these features of system dynamics renders itself a challenging question of practical interest in biology. Existing methods are suitable for systems with one stable steady state employed as a well-defined reference. In such systems, the characterization of the time hierarchies has already been used for determining the components that contribute to the dynamics of biological systems. However, the application of these methods to bistable nonlinear systems is impeded due to their inherent dependence on the reference state, which in this case is no longer unique. Here, we extend the applicability of the reference-state analysis by proposing, analyzing, and applying a novel method, which allows investigation of the time hierarchies in systems exhibiting bistability. The proposed method is in turn used in identifying the components, other than reactions, which determine the systemic dynamical properties. We demonstrate that in biological systems of varying levels of complexity and spanning different biological levels, the method can be effectively employed for model simplification while ensuring preservation of qualitative dynamical properties (i.e., bistability). Finally, by establishing a connection between techniques from nonlinear dynamics and multivariate statistics, the proposed approach provides the basis for extending reference-based analysis to bistable systems.

Towards multiscale plant models: integrating cellular networks

One of the ambitions of 'crop systems biology' is to combine information from molecular biology with a broader view of plant development and growth. In the context of modeling, this calls for a multiscale perspective that focuses on the interplay between cellular and macroscopic studies. With this in mind, in this review we aim to draw attention to a panel of approaches that were developed in the context of systems biology and are used for analyzing and describing the behavior of cellular networks. Ultimately, insights obtained from these methods can be exploited to refine the description of plant processes, leading to integrated plant-cellular models.

Towards multiscale plant models: integrating cellular networks

One of the ambitions of 'crop systems biology' is to combine information from molecular biology with a broader view of plant development and growth. In the context of modeling, this calls for a multiscale perspective that focuses on the interplay between cellular and macroscopic studies. With this in mind, in this review we aim to draw attention to a panel of approaches that were developed in the context of systems biology and are used for analyzing and describing the behavior of cellular networks. Ultimately, insights obtained from these methods can be exploited to refine the description of plant processes, leading to integrated plant-cellular models.

Ion channels/transporters as epigenetic regulators? -a microRNA perspective

MicroRNA (miRNA) alterations in response to changes in an extracellular microenvironment have been observed and considered as one of the major mechanisms for epigenetic modifications of the cell. While enormous efforts have been made in the understanding of the role of miRNAs in regulating cellular responses to the microenvironment, the mechanistic insight into how extracellular signals can be transduced into miRNA alterations in cells is still lacking. Interestingly, recent studies have shown that ion channels/transporters, which are known to conduct or transport ions across the cell membrane, also exhibit changes in levels of expression and activities in response to changes of extracellular microenvironment. More importantly, alterations in expression and function of ion channels/transporters have been shown to result in changes in miRNAs that are known to change in response to alteration of the microenvironment. In this review, we aim to summarize the recent data demonstrating the ability of ion channels/transporters to transduce extracellular signals into miRNA changes and propose a potential link between cells and their microenvironment through ion channels/transporters. At the same time, we hope to provide new insights into epigenetic regulatory mechanisms underlying a number of physiological and pathological processes, including embryo development and cancer metastasis.

Simplification of biochemical models: a general approach based on the analysis of the impact of individual species and reactions on the systems dynamics

Background

Given the complex mechanisms underlying biochemical processes systems biology researchers tend to build ever increasing computational models. However, dealing with complex systems entails a variety of problems, e.g. difficult intuitive understanding, variety of time scales or non-identifiable parameters. Therefore, methods are needed that, at least semi-automatically, help to elucidate how the complexity of a model can be reduced such that important behavior is maintained and the predictive capacity of the model is increased. The results should be easily accessible and interpretable. In the best case such methods may also provide insight into fundamental biochemical mechanisms.

Results

We have developed a strategy based on the Computational Singular Perturbation (CSP) method which can be used to perform a "biochemically-driven" model reduction of even large and complex kinetic ODE systems. We provide an implementation of the original CSP algorithm in COPASI (a COmplex PAthway SImulator) and applied the strategy to two example models of different degree of complexity - a simple one-enzyme system and a full-scale model of yeast glycolysis.

Conclusion

The results show the usefulness of the method for model simplification purposes as well as for analyzing fundamental biochemical mechanisms. COPASI is freely available at http://www.copasi.org.

Dramatic reduction of dimensionality in large biochemical networks owing to strong pair correlations

Large multi-dimensionality of high-throughput datasets pertaining to cell signalling and gene regulation renders it difficult to extract mechanisms underlying the complex kinetics involving various biochemical compounds (e.g. proteins and lipids). Data-driven models often circumvent this difficulty by using pair correlations of the protein expression levels to produce a small number (fewer than 10) of principal components, each a linear combination of the concentrations, to successfully model how cells respond to different stimuli. However, it is not understood if this reduction is specific to a particular biological system or to nature of the stimuli used in these experiments. We study temporal changes in pair correlations, described by the covariance matrix, between concentrations of different molecular species that evolve following deterministic mass-action kinetics in large biologically relevant reaction networks and show that this dramatic reduction of dimensions (from hundreds to less than five) arises from the strong correlations between different species at any time and is insensitive to the form of the nonlinear interactions, network architecture, and to a wide range of values of rate constants and concentrations. We relate temporal changes in the eigenvalue spectrum of the covariance matrix to low-dimensional, local changes in directions of the system trajectory embedded in much larger dimensions using elementary differential geometry. We illustrate how to extract biologically relevant insights such as identifying significant timescales and groups of correlated chemical species from our analysis. Our work provides for the first time, to our knowledge, a theoretical underpinning for the successful experimental analysis and points to a way to extract mechanisms from large-scale high-throughput datasets.

Timescale analysis of rule-based biochemical reaction networks

The flow of information within a cell is governed by a series of protein-protein interactions that can be described as a reaction network. Mathematical models of biochemical reaction networks can be constructed by repetitively applying specific rules that define how reactants interact and what new species are formed on reaction. To aid in understanding the underlying biochemistry, timescale analysis is one method developed to prune the size of the reaction network. In this work, we extend the methods associated with timescale analysis to reaction rules instead of the species contained within the network. To illustrate this approach, we applied timescale analysis to a simple receptor-ligand binding model and a rule-based model of interleukin-12 (IL-12) signaling in naïve CD4+ T cells. The IL-12 signaling pathway includes multiple protein-protein interactions that collectively transmit information; however, the level of mechanistic detail sufficient to capture the observed dynamics has not been justified based on the available data. The analysis correctly predicted that reactions associated with Janus Kinase 2 and Tyrosine Kinase 2 binding to their corresponding receptor exist at a pseudo-equilibrium. By contrast, reactions associated with ligand binding and receptor turnover regulate cellular response to IL-12. An empirical Bayesian approach was used to estimate the uncertainty in the timescales. This approach complements existing rank- and flux-based methods that can be used to interrogate complex reaction networks. Ultimately, timescale analysis of rule-based models is a computational tool that can be used to reveal the biochemical steps that regulate signaling dynamics.

Graphical approach to model reduction for nonlinear biochemical networks

Model reduction is a central challenge to the development and analysis of multiscale physiology models. Advances in model reduction are needed not only for computational feasibility but also for obtaining conceptual insights from complex systems. Here, we introduce an intuitive graphical approach to model reduction based on phase plane analysis. Timescale separation is identified by the degree of hysteresis observed in phase-loops, which guides a “concentration-clamp” procedure for estimating explicit algebraic relationships between species equilibrating on fast timescales. The primary advantages of this approach over Jacobian-based timescale decomposition are that: 1) it incorporates nonlinear system dynamics, and 2) it can be easily visualized, even directly from experimental data. We tested this graphical model reduction approach using a 25-variable model of cardiac β₁-adrenergic signaling, obtaining 6- and 4-variable reduced models that retain good predictive capabilities even in response to new perturbations. These 6 signaling species appear to be optimal “kinetic biomarkers” of the overall β₁-adrenergic pathway. The 6-variable reduced model is well suited for integration into multiscale models of heart function, and more generally, this graphical model reduction approach is readily applicable to a variety of other complex biological systems.

Optimization of a blueprint for in vitro glycolysis by metabolic real-time analysis

Recruiting complex metabolic reaction networks for chemical synthesis has attracted considerable attention but frequently requires optimization of network composition and dynamics to reach sufficient productivity. As a design framework to predict optimal levels for all enzymes in the network is currently not available, state-of-the-art pathway optimization relies on high-throughput phenotype screening. We present here the development and application of a new in vitro real-time analysis method for the comprehensive investigation and rational programming of enzyme networks for synthetic tasks. We used this first to rationally and rapidly derive an optimal blueprint for the production of the fine chemical building block dihydroxyacetone phosphate (DHAP) via Escherichia coli's highly evolved glycolysis. Second, the method guided the three-step genetic implementation of the blueprint, yielding a synthetic operon with the predicted 2.5-fold-increased glycolytic flux toward DHAP. The new analytical setup drastically accelerates rational optimization of synthetic multienzyme networks.

Systems biology from micro-organisms to human metabolic diseases: the role of detailed kinetic models

Human metabolic diseases are typically network diseases. This holds not only for multifactorial diseases, such as metabolic syndrome or Type 2 diabetes, but even when a single gene defect is the primary cause, where the adaptive response of the entire network determines the severity of disease. The latter may differ between individuals carrying the same mutation. Understanding the adaptive responses of human metabolism naturally requires a systems biology approach. Modelling of metabolic pathways in micro-organisms and some mammalian tissues has yielded many insights, qualitative as well as quantitative, into their control and regulation. Yet, even for a well-known pathway such as glycolysis, precise predictions of metabolite dynamics from experimentally determined enzyme kinetics have been only moderately successful. In the present review, we compare kinetic models of glycolysis in three cell types (African trypanosomes, yeast and skeletal muscle), evaluate their predictive power and identify limitations in our understanding. Although each of these models has its own merits and shortcomings, they also share common features. For example, in each case independently measured enzyme kinetic parameters were used as input. Based on these 'lessons from glycolysis', we will discuss how to make best use of kinetic computer models to advance our understanding of human metabolic diseases.

A multiscale systems perspective on cancer, immunotherapy, and Interleukin-12

Monoclonal antibodies represent some of the most promising molecular targeted immunotherapies. However, understanding mechanisms by which tumors evade elimination by the immune system of the host presents a significant challenge for developing effective cancer immunotherapies. The interaction of cancer cells with the host is a complex process that is distributed across a variety of time and length scales. The time scales range from the dynamics of protein refolding (i.e., microseconds) to the dynamics of disease progression (i.e., years). The length scales span the farthest reaches of the human body (i.e., meters) down to the range of molecular interactions (i.e., nanometers). Limited ranges of time and length scales are used experimentally to observe and quantify changes in physiology due to cancer. Translating knowledge obtained from the limited scales observed experimentally to predict patient response is an essential prerequisite for the rational design of cancer immunotherapies that improve clinical outcomes. In studying multiscale systems, engineers use systems analysis and design to identify important components in a complex system and to test conceptual understanding of the integrated system behavior using simulation. The objective of this review is to summarize interactions between the tumor and cell-mediated immunity from a multiscale perspective. Interleukin-12 and its role in coordinating antibody-dependent cell-mediated cytotoxicity is used illustrate the different time and length scale that underpin cancer immunoediting. An underlying theme in this review is the potential role that simulation can play in translating knowledge across scales.

Task-oriented modular decomposition of biological networks: trigger mechanism in blood coagulation

Analysis of complex time-dependent biological networks is an important challenge in the current postgenomic era. We propose a middle-out approach for decomposition and analysis of complex time-dependent biological networks based on: 1), creation of a detailed mechanism-driven mathematical model of the network; 2), network response decomposition into several physiologically relevant subtasks; and 3), subsequent decomposition of the model, with the help of task-oriented necessity and sensitivity analysis into several modules that each control a single specific subtask, which is followed by further simplification employing temporal hierarchy reduction. The technique is tested and illustrated by studying blood coagulation. Five subtasks (threshold, triggering, control by blood flow velocity, spatial propagation, and localization), together with responsible modules, can be identified for the coagulation network. We show that the task of coagulation triggering is completely regulated by a two-step pathway containing a single positive feedback of factor V activation by thrombin. These theoretical predictions are experimentally confirmed by studies of fibrin generation in normal, factor V-, and factor VIII-deficient plasmas. The function of the factor V-dependent feedback is to minimize temporal and parametrical intervals of fibrin clot instability. We speculate that this pathway serves to lessen possibility of fibrin clot disruption by flow and subsequent thromboembolism.

A metabolic model of human erythrocytes: practical application of the E-Cell Simulation Environment

The human red blood cell (RBC) has long been used for modeling of complex biological networks, for elucidation of a wide variety of dynamic phenomena, and for understanding the fundamental topology of metabolic pathways. Here, we introduce our recent work on an RBC metabolic model using the E-Cell Simulation Environment. The model is sufficiently detailed to predict the temporal hypoxic response of each metabolite and, at the same time, successfully integrates modulation of metabolism and of the oxygen transporting capacity of hemoglobin. The model includes the mechanisms of RBC maintenance as a single cell system and the functioning of RBCs as components of a higher order system. Modeling of RBC metabolism is now approaching a fully mature stage of realistic predictions at the molecular level and will be useful for predicting conditions in biotechnological applications such as long-term cold storage of RBCs.

Mass action stoichiometric simulation models: incorporating kinetics and regulation into stoichiometric models

The ability to characterize biological dynamics is important for understanding the integrated molecular processes that underlie normal and abnormal cellular states. The availability of metabolomic data, in addition to new developments in the formal description of dynamic states of networks, has enabled a new data integration approach for building large-scale kinetic networks. We show that dynamic network models can be constructed in a scalable manner using metabolomic data mapped onto stoichiometric models, resulting in mass action stoichiometric simulation (MASS) models. Enzymes and their various functional states are represented explicitly as compounds, or nodes in a stoichiometric network, within this formalism. Analyses and simulations of MASS models explicitly show that regulatory enzymes can control dynamic states of networks in part by binding numerous metabolites at multiple sites. Thus, network functional states are reflected in the fractional states of a regulatory enzyme, such as the fraction of the total enzyme concentration that is in a catalytically active versus inactive state. The feasible construction of MASS models represents a practical means to increase the size, scope, and predictive capabilities of dynamic network models in cell and molecular biology.

Flux-concentration duality in dynamic nonequilibrium biological networks

The structure of dynamic states in biological networks is of fundamental importance in understanding their function. Considering the elementary reaction structure of reconstructed metabolic networks, we show how appreciation of a gradient matrix, G =dv/dx (where v is the vector of fluxes and x is the vector of concentrations), enables the formulation of dual Jacobian matrices. One is for concentrations, J(x) =S x G, and the other is for fluxes, J(v) =G x S. The fundamental properties of these two Jacobians and the underlying duality that relates them are delineated. We describe a generalized approach to decomposing reaction networks in terms of the thermodynamic and kinetic components in the context of the network structure. The thermodynamic and kinetic influences can be viewed in terms of direction-driver relationships in the network.

Using in silico models to simulate dual perturbation experiments: procedure development and interpretation of outcomes

Background

A growing number of realistic in silico models of metabolic functions are being formulated and can serve as 'dry lab' platforms to prototype and simulate experiments before they are performed. For example, dual perturbation experiments that vary both genetic and environmental parameters can readily be simulated in silico. Genetic and environmental perturbations were applied to a cell-scale model of the human erythrocyte and subsequently investigated.

Results

The resulting steady state fluxes and concentrations, as well as dynamic responses to the perturbations were analyzed, yielding two important conclusions: 1) that transporters are informative about the internal states (fluxes and concentrations) of a cell and, 2) that genetic variations can disrupt the natural sequence of dynamic interactions between network components. The former arises from adjustments in energy and redox states, while the latter is a result of shifting time scales in aggregate pool formation of metabolites. These two concepts are illustrated for glucose-6 phosphate dehydrogenase (G6PD) and pyruvate kinase (PK) in the human red blood cell.

Conclusion

Dual perturbation experiments in silico are much more informative for the characterization of functional states than single perturbations. Predictions from an experimentally validated cellular model of metabolism indicate that the measurement of cofactor precursor transport rates can inform the internal state of the cell when the external demands are altered or a causal genetic variation is introduced. Finally, genetic mutations that alter the clinical phenotype may also disrupt the 'natural' time scale hierarchy of interactions in the network.

Filling kinetic gaps: dynamic modeling of metabolism where detailed kinetic information is lacking

BACKGROUND

Integrative analysis between dynamical modeling of metabolic networks and data obtained from high throughput technology represents a worthy effort toward a holistic understanding of the link among phenotype and dynamical response. Even though the theoretical foundation for modeling metabolic network has been extensively treated elsewhere, the lack of kinetic information has limited the analysis in most of the cases. To overcome this constraint, we present and illustrate a new statistical approach that has two purposes: integrate high throughput data and survey the general dynamical mechanisms emerging for a slightly perturbed metabolic network.

METHODOLOGY/PRINCIPAL FINDINGS

This paper presents a statistic framework capable to study how and how fast the metabolites participating in a perturbed metabolic network reach a steady-state. Instead of requiring accurate kinetic information, this approach uses high throughput metabolome technology to define a feasible kinetic library, which constitutes the base for identifying, statistical and dynamical properties during the relaxation. For the sake of illustration we have applied this approach to the human Red blood cell metabolism (hRBC) and its capacity to predict temporal phenomena was evaluated. Remarkable, the main dynamical properties obtained from a detailed kinetic model in hRBC were recovered by our statistical approach. Furthermore, robust properties in time scale and metabolite organization were identify and one concluded that they are a consequence of the combined performance of redundancies and variability in metabolite participation.

CONCLUSIONS/SIGNIFICANCE

In this work we present an approach that integrates high throughput metabolome data to define the dynamic behavior of a slightly perturbed metabolic network where kinetic information is lacking. Having information of metabolite concentrations at steady-state, this method has significant relevance due its potential scope to analyze others genome scale metabolic reconstructions. Thus, I expect this approach will significantly contribute to explore the relationship between dynamic and physiology in other metabolic reconstructions, particularly those whose kinetic information is practically nulls. For instances, I envisage that this approach can be useful in genomic medicine or pharmacogenomics, where the estimation of time scales and the identification of metabolite organization may be crucial to characterize and identify (dis)functional stages.