Synergistic control of oscillations in the NF-B signalling pathway

Regulation of signal transduction by spatial parameters: a case in NF-κB oscillation

NF-κB is a transcription factor regulating expression of more than 500 genes, and its dysfunction leads to the autoimmune and inflammatory diseases. In malignant cancer cells, NF-κB is constitutively activated. Thus the elucidation of mechanisms for NF-κB regulation is important for the establishment of therapeutic treatment caused by incorrect NF-κB responses. Cytoplasmic NF-κB translocates to the nucleus by the application of extracellular stimuli such as cytokines. Nuclear NF-κB is known to oscillate with the cycle of 1.5-4.5 h, and it is thought that the oscillation pattern regulates the expression profiles of genes. In this review, first we briefly describe regulation mechanisms of NF-κB. Next, published computational simulations on the oscillation of NF-κB are summarised. There are at least 60 reports on the computational simulation and analysis of NF-κB oscillation. Third, the importance of a 'space' for the regulation of oscillation pattern of NF-κB is discussed, showing altered oscillation pattern by the change in spatial parameters such as diffusion coefficient, nuclear to cytoplasmic volume ratio (N/C ratio), and transport through nuclear membrane. Finally, simulations in a true intracellular space (TiCS), which is an intracellular 3D space reconstructed in a computer with organelles such as nucleus and mitochondria are discussed.

Role of Computational Modeling in Understanding Cell Cycle Oscillators

The periodic oscillations in the activity of the cell cycle regulatory program, drives the timely activation of key cell cycle events. Interesting dynamical systems, such as oscillators, have been investigated by various theoretical and computational modeling methods. Thanks to the insights achieved by these modeling efforts we have gained considerable insights about the underlying molecular regulatory networks that can drive cell cycle oscillations. Here we review the basic features and characteristics of biological oscillators, discussing from a computational modeling point of view their specific architectures and the current knowledge about the dynamics that the life evolution selected to drive cell cycle oscillations.

A method of ‘speed coefficients’ for biochemical model reduction applied to the NF-κB system

The relationship between components of biochemical network and the resulting dynamics of the overall system is a key focus of computational biology. However, as these networks and resulting mathematical models are inherently complex and non-linear, the understanding of this relationship becomes challenging. Among many approaches, model reduction methods provide an avenue to extract components responsible for the key dynamical features of the system. Unfortunately, these approaches often require intuition to apply. In this manuscript we propose a practical algorithm for the reduction of biochemical reaction systems using fast-slow asymptotics. This method allows the ranking of system variables according to how quickly they approach their momentary steady state, thus selecting the fastest for a steady state approximation. We applied this method to derive models of the Nuclear Factor kappa B network, a key regulator of the immune response that exhibits oscillatory dynamics. Analyses with respect to two specific solutions, which corresponded to different experimental conditions identified different components of the system that were responsible for the respective dynamics. This is an important demonstration of how reduction methods that provide approximations around a specific steady state, could be utilised in order to gain a better understanding of network topology in a broader context.

A simple model of NF-κB dynamics reproduces experimental observations

The mathematical modeling of the NF-κB oscillations has attracted considerable attention in recent times, but there is a lack of simple models in the literature that can capture the main features of the dynamics of this important transcription factor. For this reason we propose a simple model that summarizes the key steps of the NF-κB pathway. We show that the resulting 5-dimensional dynamical system can reproduce different phenomena observed in experiments. Our model can display smooth and spiky oscillations in the amount of nuclear NF-κB and can reproduce the variety of dynamics observed when different stimulations such as TNF-α and LPS are used. Furthermore we show that the model can be easily extended to reproduce the expression of early, intermediate and late genes upon stimulation. As a final example we show that our simple model can mimic the different transcriptional outputs observed when cells are treated with two different drugs leading to nuclear localization of NF-κB: Leptomycin B and Cycloheximide.

Systems biology and the integration of mechanistic explanation and mathematical explanation

The paper discusses how systems biology is working toward complex accounts that integrate explanation in terms of mechanisms and explanation by mathematical models-which some philosophers have viewed as rival models of explanation. Systems biology is an integrative approach, and it strongly relies on mathematical modeling. Philosophical accounts of mechanisms capture integrative in the sense of multilevel and multifield explanations, yet accounts of mechanistic explanation (as the analysis of a whole in terms of its structural parts and their qualitative interactions) have failed to address how a mathematical model could contribute to such explanations. I discuss how mathematical equations can be explanatorily relevant. Several cases from systems biology are discussed to illustrate the interplay between mechanistic research and mathematical modeling, and I point to questions about qualitative phenomena (rather than the explanation of quantitative details), where quantitative models are still indispensable to the explanation. Systems biology shows that a broader philosophical conception of mechanisms is needed, which takes into account functional-dynamical aspects, interaction in complex networks with feedback loops, system-wide functional properties such as distributed functionality and robustness, and a mechanism's ability to respond to perturbations (beyond its actual operation). I offer general conclusions for philosophical accounts of explanation.

Synergistic Synthetic Biology: Units in Concert

Synthetic biology aims at translating the methods and strategies from engineering into biology in order to streamline the design and construction of biological devices through standardized parts. Modular synthetic biology devices are designed by means of an adequate elimination of cross-talk that makes circuits orthogonal and specific. To that end, synthetic constructs need to be adequately optimized through in silico modeling by choosing the right complement of genetic parts and by experimental tuning through directed evolution and craftsmanship. In this review, we consider an additional and complementary tool available to the synthetic biologist for innovative design and successful construction of desired circuit functionalities: biological synergies. Synergy is a prevalent emergent property in biological systems that arises from the concerted action of multiple factors producing an amplification or cancelation effect compared with individual actions alone. Synergies appear in domains as diverse as those involved in chemical and protein activity, polypharmacology, and metabolic pathway complementarity. In conventional synthetic biology designs, synergistic cross-talk between parts and modules is generally attenuated in order to verify their orthogonality. Synergistic interactions, however, can induce emergent behavior that might prove useful for synthetic biology applications, like in functional circuit design, multi-drug treatment, or in sensing and delivery devices. Synergistic design principles are therefore complementary to those coming from orthogonal design and may provide added value to synthetic biology applications. The appropriate modeling, characterization, and design of synergies between biological parts and units will allow the discovery of yet unforeseeable, novel synthetic biology applications.

RECEPTOR-DEPENDENT SENSITIVITY OF NF-κB TO LOW PHYSIOLOGICAL LEVEL

In the NFκB signaling pathway, cells respond to different concentrations of the TNFα signal by means of NFκB transcription factors. Previous studies showed that most cells are activated under high-dose stimulations and NFκB activation results in oscillations in nuclear NFκB abundance. Here, by analyzing sensitivity gain for the response of the nuclear NFκB to the number of cell-surface receptors under low-dose stimulations, we show that changes in the receptor number can give rise to significant changes in the nonsaturation part of the dose–response curve, where the receptor activation rates are very sensitive to stimulations. In addition, the number of the activated receptors tends to increase in a large range of stimulation dose and can significantly influence the expression of the downstream genes. These results imply that the number of cell-surface receptors plays a role of information encoding like frequency or amplitude encoding described in previous studies.

Finding novel pharmaceuticals in the systems biology era using multiple effective drug targets, phenotypic screening and knowledge of transporters: where drug discovery went wrong and how to fix it

Despite the sequencing of the human genome, the rate of innovative and successful drug discovery in the pharmaceutical industry has continued to decrease. Leaving aside regulatory matters, the fundamental and interlinked intellectual issues proposed to be largely responsible for this are: (a) the move from 'function-first' to 'target-first' methods of screening and drug discovery; (b) the belief that successful drugs should and do interact solely with single, individual targets, despite natural evolution's selection for biochemical networks that are robust to individual parameter changes; (c) an over-reliance on the rule-of-5 to constrain biophysical and chemical properties of drug libraries; (d) the general abandoning of natural products that do not obey the rule-of-5; (e) an incorrect belief that drugs diffuse passively into (and presumably out of) cells across the bilayers portions of membranes, according to their lipophilicity; (f) a widespread failure to recognize the overwhelmingly important role of proteinaceous transporters, as well as their expression profiles, in determining drug distribution in and between different tissues and individual patients; and (g) the general failure to use engineering principles to model biology in parallel with performing 'wet' experiments, such that 'what if?' experiments can be performed in silico to assess the likely success of any strategy. These facts/ideas are illustrated with a reasonably extensive literature review. Success in turning round drug discovery consequently requires: (a) decent systems biology models of human biochemical networks; (b) the use of these (iteratively with experiments) to model how drugs need to interact with multiple targets to have substantive effects on the phenotype; (c) the adoption of polypharmacology and/or cocktails of drugs as a desirable goal in itself; (d) the incorporation of drug transporters into systems biology models, en route to full and multiscale systems biology models that incorporate drug absorption, distribution, metabolism and excretion; (e) a return to 'function-first' or phenotypic screening; and (f) novel methods for inferring modes of action by measuring the properties on system variables at all levels of the 'omes. Such a strategy offers the opportunity of achieving a state where we can hope to predict biological processes and the effect of pharmaceutical agents upon them. Consequently, this should both lower attrition rates and raise the rates of discovery of effective drugs substantially.

Exploiting genomic knowledge in optimising molecular breeding programmes: algorithms from evolutionary computing

Comparatively few studies have addressed directly the question of quantifying the benefits to be had from using molecular genetic markers in experimental breeding programmes (e.g. for improved crops and livestock), nor the question of which organisms should be mated with each other to best effect. We argue that this requires in silico modelling, an approach for which there is a large literature in the field of evolutionary computation (EC), but which has not really been applied in this way to experimental breeding programmes. EC seeks to optimise measurable outcomes (phenotypic fitnesses) by optimising in silico the mutation, recombination and selection regimes that are used. We review some of the approaches from EC, and compare experimentally, using a biologically relevant in silico landscape, some algorithms that have knowledge of where they are in the (genotypic) search space (G-algorithms) with some (albeit well-tuned ones) that do not (F-algorithms). For the present kinds of landscapes, F- and G-algorithms were broadly comparable in quality and effectiveness, although we recognise that the G-algorithms were not equipped with any ‘prior knowledge’ of epistatic pathway interactions. This use of algorithms based on machine learning has important implications for the optimisation of experimental breeding programmes in the post-genomic era when we shall potentially have access to the full genome sequence of every organism in a breeding population. The non-proprietary code that we have used is made freely available (via Supplementary information).

Roles of spatial parameters on the oscillation of nuclear NF-κB: computer simulations of a 3D spherical cell

Transcription factor NF-κB resides in the cytoplasm and translocates to the nucleus by application of extracellular stimuli. It is known that the nuclear NF-κB oscillates and different oscillation patterns lead to different gene expression. Nearly forty reports on modeling and simulation of nuclear NF-κB have been published to date. The computational models reported so far are temporal or two-dimensional, and the discussions on spatial parameters have not been involved or limited. Since spatial parameters in cancer cells such as nuclear to cytoplasmic volume (N/C) ratio are different from normal cells, it is important to understand the relationship between oscillation patterns and spatial parameters. Here we report simulations of a 3D computational model for the oscillation of nuclear NF-κB using A-Cell software. First, we found that the default biochemical kinetic constants used in the temporal model cannot replicate the experimentally observed oscillation in the 3D model. Thus, the default parameters should be changed in the 3D model. Second, spatial parameters such as N/C ratio, nuclear transport, diffusion coefficients, and the location of IκB synthesis were found to alter the oscillation pattern. Third, among them, larger N/C ratios resulted in persistent oscillation of nuclear NF-κB, and larger nuclear transport resulted in faster oscillation frequency. Our simulation results suggest that the changes in spatial parameters seen in cancer cells is one possible mechanism for alteration in the oscillation pattern of nuclear NF-κB and lead to the altered gene expression in these cells.

The emerging paradigm of network medicine in the study of human disease

The molecular pathways that govern human disease consist of molecular circuits that coalesce into complex, overlapping networks. These network pathways are presumably regulated in a coordinated fashion, but such regulation has been difficult to decipher using only reductionistic principles. The emerging paradigm of "network medicine" proposes to utilize insights garnered from network topology (eg, the static position of molecules in relation to their neighbors) as well as network dynamics (eg, the unique flux of information through the network) to understand better the pathogenic behavior of complex molecular interconnections that traditional methods fail to recognize. As methodologies evolve, network medicine has the potential to capture the molecular complexity of human disease while offering computational methods to discern how such complexity controls disease manifestations, prognosis, and therapy. This review introduces the fundamental concepts of network medicine and explores the feasibility and potential impact of network-based methods for predicting individual manifestations of human disease and designing rational therapies. Wherever possible, we emphasize the application of these principles to cardiovascular disease.

A methodology for global-sensitivity analysis of time-dependent outputs in systems biology modelling

One of the main challenges in the development of mathematical and computational models of biological systems is the precise estimation of parameter values. Understanding the effects of uncertainties in parameter values on model behaviour is crucial to the successful use of these models. Global sensitivity analysis (SA) can be used to quantify the variability in model predictions resulting from the uncertainty in multiple parameters and to shed light on the biological mechanisms driving system behaviour. We present a new methodology for global SA in systems biology which is computationally efficient and can be used to identify the key parameters and their interactions which drive the dynamic behaviour of a complex biological model. The approach combines functional principal component analysis with established global SA techniques. The methodology is applied to a model of the insulin signalling pathway, defects of which are a major cause of type 2 diabetes and a number of key features of the system are identified.

Scientific discovery as a combinatorial optimisation problem: how best to navigate the landscape of possible experiments?

A considerable number of areas of bioscience, including gene and drug discovery, metabolic engineering for the biotechnological improvement of organisms, and the processes of natural and directed evolution, are best viewed in terms of a ‘landscape’ representing a large search space of possible solutions or experiments populated by a considerably smaller number of actual solutions that then emerge. This is what makes these problems ‘hard’, but as such these are to be seen as combinatorial optimisation problems that are best attacked by heuristic methods known from that field. Such landscapes, which may also represent or include multiple objectives, are effectively modelled in silico, with modern active learning algorithms such as those based on Darwinian evolution providing guidance, using existing knowledge, as to what is the ‘best’ experiment to do next. An awareness, and the application, of these methods can thereby enhance the scientific discovery process considerably. This analysis fits comfortably with an emerging epistemology that sees scientific reasoning, the search for solutions, and scientific discovery as Bayesian processes.

Quantitative characterization and analysis of the dynamic NF-κB response in microglia

Background

Activation of the NF-κB transcription factor and its associated gene expression in microglia is a key component in the response to brain injury. Its activation is dynamic and is part of a network of biochemical species with multiple feedback regulatory mechanisms. Mathematical modeling, which has been instrumental for understanding the NF-κB response in other cell types, offers a valuable tool to investigate the regulation of NF-κB activation in microglia at a systems level.

Results

We quantify the dynamic response of NF-κB activation and activation of the upstream kinase IKK using ELISA measurements of a microglial cell line following treatment with the pro-inflammatory cytokine TNFα. A new mathematical model is developed based on these data sets using a modular procedure that exploits the feedback structure of the network. We show that the new model requires previously unmodeled dynamics involved in the stimulus-induced degradation of the inhibitor IκBα in order to properly describe microglial NF-κB activation in a statistically consistent manner. This suggests a more prominent role for the ubiquitin-proteasome system in regulating the activation of NF-κB to inflammatory stimuli. We also find that the introduction of nonlinearities in the kinetics of IKK activation and inactivation is essential for proper characterization of transient IKK activity and corresponds to known biological mechanisms. Numerical analyses of the model highlight key regulators of the microglial NF-κB response, as well as those governing IKK activation. Results illustrate the dynamic regulatory mechanisms and the robust yet fragile nature of the negative feedback regulated network.

Conclusions

We have developed a new mathematical model that incorporates previously unmodeled dynamics to characterize the dynamic response of the NF-κB signaling network in microglia. This model is the first of its kind for microglia and provides a tool for the quantitative, systems level study the dynamic cellular response to inflammatory stimuli.

Understanding dynamics using sensitivity analysis: caveat and solution

Background

Parametric sensitivity analysis (PSA) has become one of the most commonly used tools in computational systems biology, in which the sensitivity coefficients are used to study the parametric dependence of biological models. As many of these models describe dynamical behaviour of biological systems, the PSA has subsequently been used to elucidate important cellular processes that regulate this dynamics. However, in this paper, we show that the PSA coefficients are not suitable in inferring the mechanisms by which dynamical behaviour arises and in fact it can even lead to incorrect conclusions.

Results

A careful interpretation of parametric perturbations used in the PSA is presented here to explain the issue of using this analysis in inferring dynamics. In short, the PSA coefficients quantify the integrated change in the system behaviour due to persistent parametric perturbations, and thus the dynamical information of when a parameter perturbation matters is lost. To get around this issue, we present a new sensitivity analysis based on impulse perturbations on system parameters, which is named impulse parametric sensitivity analysis (iPSA). The inability of PSA and the efficacy of iPSA in revealing mechanistic information of a dynamical system are illustrated using two examples involving switch activation.

Conclusions

The interpretation of the PSA coefficients of dynamical systems should take into account the persistent nature of parametric perturbations involved in the derivation of this analysis. The application of PSA to identify the controlling mechanism of dynamical behaviour can be misleading. By using impulse perturbations, introduced at different times, the iPSA provides the necessary information to understand how dynamics is achieved, i.e. which parameters are essential and when they become important.

Minimally perturbing a gene regulatory network to avoid a disease phenotype: the glioma network as a test case

BACKGROUND

Mathematical modeling of biological networks is an essential part of Systems Biology. Developing and using such models in order to understand gene regulatory networks is a major challenge.

RESULTS

We present an algorithm that determines the smallest perturbations required for manipulating the dynamics of a network formulated as a Petri net, in order to cause or avoid a specified phenotype. By modifying McMillan's unfolding algorithm, we handle partial knowledge and reduce computation cost. The methodology is demonstrated on a glioma network. Out of the single gene perturbations, activation of glutathione S-transferase P (GSTP1) gene was by far the most effective in blocking the cancer phenotype. Among pairs of perturbations, NFkB and TGF-beta had the largest joint effect, in accordance with their role in the EMT process.

CONCLUSION

Our method allows perturbation analysis of regulatory networks and can overcome incomplete information. It can help in identifying drug targets and in prioritizing perturbation experiments.

Elucidation of functional consequences of signalling pathway interactions

BACKGROUND

A great deal of data has accumulated on signalling pathways. These large datasets are thought to contain much implicit information on their molecular structure, interaction and activity information, which provides a picture of intricate molecular networks believed to underlie biological functions. While tremendous advances have been made in trying to understand these systems, how information is transmitted within them is still poorly understood. This ever growing amount of data demands we adopt powerful computational techniques that will play a pivotal role in the conversion of mined data to knowledge, and in elucidating the topological and functional properties of protein - protein interactions.

RESULTS

A computational framework is presented which allows for the description of embedded networks, and identification of common shared components thought to assist in the transmission of information within the systems studied. By employing the graph theories of network biology - such as degree distribution, clustering coefficient, vertex betweenness and shortest path measures - topological features of protein-protein interactions for published datasets of the p53, nuclear factor kappa B (NF-kappaB) and G1/S phase of the cell cycle systems were ascertained. Highly ranked nodes which in some cases were identified as connecting proteins most likely responsible for propagation of transduction signals across the networks were determined. The functional consequences of these nodes in the context of their network environment were also determined. These findings highlight the usefulness of the framework in identifying possible combination or links as targets for therapeutic responses; and put forward the idea of using retrieved knowledge on the shared components in constructing better organised and structured models of signalling networks.

CONCLUSION

It is hoped that through the data mined reconstructed signal transduction networks, well developed models of the published data can be built which in the end would guide the prediction of new targets based on the pathway's environment for further analysis. Source code is available upon request.

A noisy paracrine signal determines the cellular NF-kappaB response to lipopolysaccharide

Nearly identical cells can exhibit substantially different responses to the same stimulus. We monitored the nuclear localization dynamics of nuclear factor kappaB (NF-kappaB) in single cells stimulated with tumor necrosis factor-alpha (TNF-alpha) and lipopolysaccharide (LPS). Cells stimulated with TNF-alpha have quantitative differences in NF-kappaB nuclear localization, whereas LPS-stimulated cells can be clustered into transient or persistent responders, representing two qualitatively different groups based on the NF-kappaB response. These distinct behaviors can be linked to a secondary paracrine signal secreted at low concentrations, such that not all cells undergo a second round of NF-kappaB activation. From our single-cell data, we built a computational model that captures cell variability, as well as population behaviors. Our findings show that mammalian cells can create "noisy" environments to produce diversified responses to stimuli.

Calibration of dynamic models of biological systems with KInfer

Methods for parameter estimation that are robust to experimental uncertainties and to stochastic and biological noise and that require a minimum of a priori input knowledge are of key importance in computational systems biology. The new method presented in this paper aims to ensure an inference model that deduces the rate constants of a system of biochemical reactions from experimentally measured time courses of reactants. This new method was applied to some challenging parameter estimation problems of nonlinear dynamic biological systems and was tested both on synthetic and real data. The synthetic case studies are the 12-state model of the SERCA pump and a model of a genetic network containing feedback loops of interaction between regulator and effector genes. The real case studies consist of a model of the reaction between the inhibitor kappaB kinase enzyme and its substrate in the signal transduction pathway of NF-kappaB, and a stiff model of the fermentation pathway of Lactococcus lactis.

Dynamical analysis of cellular networks based on the Green's function matrix

The complexity of cellular networks often limits human intuition in understanding functional regulations in a cell from static network diagrams. To this end, mathematical models of ordinary differential equations (ODEs) have commonly been used to simulate dynamical behavior of cellular networks, to which a quantitative model analysis can be applied in order to gain biological insights. In this paper, we introduce a dynamical analysis based on the use of Green's function matrix (GFM) as sensitivity coefficients with respect to initial concentrations. In contrast to the classical (parametric) sensitivity analysis, the GFM analysis gives a dynamical, molecule-by-molecule insight on how system behavior is accomplished and complementarily how (impulse) signal propagates through the network. The knowledge gained will have application from model reduction and validation to drug discovery research in identifying potential drug targets, studying drug efficacy and specificity, and optimizing drug dosing and timing. The efficacy of the method is demonstrated through applications to common network motifs and a Fas-induced programmed cell death model in Jurkat T cell line.

Pulsatile stimulation determines timing and specificity of NF-kappaB-dependent transcription

The nuclear factor kappaB (NF-kappaB) transcription factor regulates cellular stress responses and the immune response to infection. NF-kappaB activation results in oscillations in nuclear NF-kappaB abundance. To define the function of these oscillations, we treated cells with repeated short pulses of tumor necrosis factor-alpha at various intervals to mimic pulsatile inflammatory signals. At all pulse intervals that were analyzed, we observed synchronous cycles of NF-kappaB nuclear translocation. Lower frequency stimulations gave repeated full-amplitude translocations, whereas higher frequency pulses gave reduced translocation, indicating a failure to reset. Deterministic and stochastic mathematical models predicted how negative feedback loops regulate both the resetting of the system and cellular heterogeneity. Altering the stimulation intervals gave different patterns of NF-kappaB-dependent gene expression, which supports the idea that oscillation frequency has a functional role.

Iron behaving badly: inappropriate iron chelation as a major contributor to the aetiology of vascular and other progressive inflammatory and degenerative diseases

BACKGROUND

The production of peroxide and superoxide is an inevitable consequence of aerobic metabolism, and while these particular 'reactive oxygen species' (ROSs) can exhibit a number of biological effects, they are not of themselves excessively reactive and thus they are not especially damaging at physiological concentrations. However, their reactions with poorly liganded iron species can lead to the catalytic production of the very reactive and dangerous hydroxyl radical, which is exceptionally damaging, and a major cause of chronic inflammation.

REVIEW

We review the considerable and wide-ranging evidence for the involvement of this combination of (su)peroxide and poorly liganded iron in a large number of physiological and indeed pathological processes and inflammatory disorders, especially those involving the progressive degradation of cellular and organismal performance. These diseases share a great many similarities and thus might be considered to have a common cause (i.e. iron-catalysed free radical and especially hydroxyl radical generation).The studies reviewed include those focused on a series of cardiovascular, metabolic and neurological diseases, where iron can be found at the sites of plaques and lesions, as well as studies showing the significance of iron to aging and longevity. The effective chelation of iron by natural or synthetic ligands is thus of major physiological (and potentially therapeutic) importance. As systems properties, we need to recognise that physiological observables have multiple molecular causes, and studying them in isolation leads to inconsistent patterns of apparent causality when it is the simultaneous combination of multiple factors that is responsible.This explains, for instance, the decidedly mixed effects of antioxidants that have been observed, since in some circumstances (especially the presence of poorly liganded iron) molecules that are nominally antioxidants can actually act as pro-oxidants. The reduction of redox stress thus requires suitable levels of both antioxidants and effective iron chelators. Some polyphenolic antioxidants may serve both roles.Understanding the exact speciation and liganding of iron in all its states is thus crucial to separating its various pro- and anti-inflammatory activities. Redox stress, innate immunity and pro- (and some anti-)inflammatory cytokines are linked in particular via signalling pathways involving NF-kappaB and p38, with the oxidative roles of iron here seemingly involved upstream of the IkappaB kinase (IKK) reaction. In a number of cases it is possible to identify mechanisms by which ROSs and poorly liganded iron act synergistically and autocatalytically, leading to 'runaway' reactions that are hard to control unless one tackles multiple sites of action simultaneously. Some molecules such as statins and erythropoietin, not traditionally associated with anti-inflammatory activity, do indeed have 'pleiotropic' anti-inflammatory effects that may be of benefit here.

CONCLUSION

Overall we argue, by synthesising a widely dispersed literature, that the role of poorly liganded iron has been rather underappreciated in the past, and that in combination with peroxide and superoxide its activity underpins the behaviour of a great many physiological processes that degrade over time. Understanding these requires an integrative, systems-level approach that may lead to novel therapeutic targets.

Understanding NF-kappaB signaling via mathematical modeling

Mammalian inflammatory signaling, for which NF-kappaB is a principal transcription factor, is an exquisite example of how cellular signaling pathways can be regulated to produce different yet specific responses to different inflammatory insults. Mathematical models, tightly linked to experiment, have been instrumental in unraveling the forms of regulation in NF-kappaB signaling and their underlying molecular mechanisms. Our initial model of the IkappaB-NF-kappaB signaling module highlighted the role of negative feedback in the control of NF-kappaB temporal dynamics and gene expression. Subsequent studies sparked by this work have helped to characterize additional feedback loops, the input-output behavior of the module, crosstalk between multiple NF-kappaB-activating pathways, and NF-kappaB oscillations. We anticipate that computational techniques will enable further progress in the NF-kappaB field, and the signal transduction field in general, and we discuss potential upcoming developments.

Information-theoretic sensitivity analysis: a general method for credit assignment in complex networks

Most systems can be represented as networks that couple a series of nodes to each other via one or more edges, with typically unknown equations governing their quantitative behaviour. A major question then pertains to the importance of each of the elements that act as system inputs in determining the output(s). We show that any such system can be treated as a 'communication channel' for which the associations between inputs and outputs can be quantified via a decomposition of their mutual information into different components characterizing the main effect of individual inputs and their interactions. Unlike variance-based approaches, our novel methodology can easily accommodate correlated inputs.

Sensitivity analysis of a computational model of the IKK NF-kappaB IkappaBalpha A20 signal transduction network

The NF-kappaB signaling network plays an important role in many different compartments of the immune system during immune activation. Using a computational model of the NF-kappaB signaling network involving two negative regulators, IkappaBalpha and A20, we performed sensitivity analyses with three different sampling methods and present a ranking of the kinetic rate variables by the strength of their influence on the NF-kappaB signaling response. We also present a classification of temporal-response profiles of nuclear NF-kappaB concentration into six clusters, which can be regrouped to three biologically relevant clusters. Last, we constructed a reduced network of the IKK-NF-kappaB-IkappaBalpha-A20 signal transduction based on the ranking.

Single-cell time-lapse imaging of the dynamic control of NF-kappaB signalling

The transcription factor NF-kappaB (nuclear factor kappaB) regulates critical cellular processes including the inflammatory response, apoptosis and the cell cycle. Over the past 20 years many of the components of the NF-kappaB signalling pathway have been elucidated along with their functions. Recent research in this field has focused on the dynamic regulation and network control of this system. With key roles in so many important cellular processes, it is critical that NF-kappaB signalling is tightly regulated. Recently, single-cell imaging and mathematical modelling have identified that the timing of cellular responses may play an important role in the regulation of this pathway. p65/RelA (RelA) has been shown to translocate between the nucleus and cytoplasm with varying oscillatory patterns in different cell lines leading to differences in transcriptional outputs from NF-kappaB-regulated genes. Variations in the timing or persistence of these movements may control the maintenance and differential expression of NF-kappaB-regulated genes.

Oscillations in the immune system

Oscillations are surprisingly common in the immune system, both in its healthy state and in disease. The most famous example is that of periodic fevers caused by the malaria parasite. A number of hereditary disorders, which also cause periodic fevers, have also been known for a long time. Various reports of oscillations in cytokine concentrations following antigen challenge have been published over at least the past three decades. Oscillations can also occur at the intracellular level. Calcium oscillations following T-cell activation are familiar to all immunologists, and metabolic and reactive oxygen species oscillations in neutrophils have been well documented. More recently, oscillations in nuclear factor kappaB activity following stimulation by tumor necrosis factor alpha have received considerable publicity. However, despite all of these examples, oscillations in the immune system still tend to be considered mainly as pathological aberrations, and their causes and significance remained largely unknown. This is partly because of a lack of awareness within the immunological community of the appropriate theoretical frameworks for describing and analyzing such behavior. We provide an introduction to these frameworks and give a survey of the currently known oscillations that occur within the immune system.

Bridging the gap between in silico and cell-based analysis of the nuclear factor-kappaB signaling pathway by in vitro studies of IKK2

Previously, we have shown by sensitivity analysis, that the oscillatory behavior of nuclear factor (NF-kappaB) is coupled to free IkappaB kinase-2 (IKK2) and IkappaBalpha(IkappaBalpha), and that the phosphorylation of IkappaBalpha by IKK influences the amplitude of NF-kappaB oscillations. We have performed further analyses of the behavior of NF-kappaB and its signal transduction network to understand the dynamics of this system. A time lapse study of NF-kappaB translocation in 10,000 cells showed discernible oscillations in levels of nuclear NF-kappaB amongst cells when stimulated with interleukin (IL-1alpha), which suggests a small degree of synchronization amongst the cell population. When the kinetics for the phosphorylation of IkappaBalpha by IKK were measured, we found that the values for the affinity and catalytic efficiency of IKK2 for IkappaBalpha were dependent on assay conditions. The application of these kinetic parameters in our computational model of the NF-kappaB pathway resulted in significant differences in the oscillatory patterns of NF-kappaB depending on the rate constant value used. Hence, interpretation of in silico models should be made in the context of this uncertainty.

Oscillatory dynamics arising from competitive inhibition and multisite phosphorylation

There have been a growing number of observations of oscillating protein levels (p53 and NFkB) in eukaryotic signalling pathways. This has resulted in a renewed interest in the mechanism by which such oscillations might occur. Recent computational work has shown that a multisite phosphorylation mechanism such as that found in the MAPK cascade can theoretically exhibit bistability. The bistable behavior was shown to arise from sequestration and saturation mechanisms for the enzymes that catalyse the multisite phosphorylation cycle. These effects generate the positive feedback necessary for bistability. In this paper we describe two kinds of oscillatory dynamics which can occur in a network by which, both use such bistable multisite phosphorylated cycles. In the first example, the fully phosphorylated form of the phosphorylated cycle represses the production of the kinase, which carries out the phosphorylation of the unphosphorylated states of the cycle. The dynamics of this system leads to a relaxation oscillator. In the second example, we consider a cascade of two cycles, in which the fully phosphorylated form of the kinase, in the first cycle, phosphorylates the unphosphorylated forms in the second cycle. A feedback loop, by which the fully phosphorylated form of the second cycle inhibits the kinase step in the first cycle is also present. In this case we obtain a ring oscillator. Both these networks illustrate the versatility of the multisite bistable network.

Theodor Bücher Lecture. Metabolomics, modelling and machine learning in systems biology - towards an understanding of the languages of cells. Delivered on 3 July 2005 at the 30th FEBS Congress and the 9th IUBMB conference in Budapest

The newly emerging field of systems biology involves a judicious interplay between high-throughput 'wet' experimentation, computational modelling and technology development, coupled to the world of ideas and theory. This interplay involves iterative cycles, such that systems biology is not at all confined to hypothesis-dependent studies, with intelligent, principled, hypothesis-generating studies being of high importance and consequently very far from aimless fishing expeditions. I seek to illustrate each of these facets. Novel technology development in metabolomics can increase substantially the dynamic range and number of metabolites that one can detect, and these can be exploited as disease markers and in the consequent and principled generation of hypotheses that are consistent with the data and achieve this in a value-free manner. Much of classical biochemistry and signalling pathway analysis has concentrated on the analyses of changes in the concentrations of intermediates, with 'local' equations - such as that of Michaelis and Menten v=(Vmax x S)/(S+K m) - that describe individual steps being based solely on the instantaneous values of these concentrations. Recent work using single cells (that are not subject to the intellectually unsupportable averaging of the variable displayed by heterogeneous cells possessing nonlinear kinetics) has led to the recognition that some protein signalling pathways may encode their signals not (just) as concentrations (AM or amplitude-modulated in a radio analogy) but via changes in the dynamics of those concentrations (the signals are FM or frequency-modulated). This contributes in principle to a straightforward solution of the crosstalk problem, leads to a profound reassessment of how to understand the downstream effects of dynamic changes in the concentrations of elements in these pathways, and stresses the role of signal processing (and not merely the intermediates) in biological signalling. It is this signal processing that lies at the heart of understanding the languages of cells. The resolution of many of the modern and postgenomic problems of biochemistry requires the development of a myriad of new technologies (and maybe a new culture), and thus regular input from the physical sciences, engineering, mathematics and computer science. One solution, that we are adopting in the Manchester Interdisciplinary Biocentre (http://www.mib.ac.uk/) and the Manchester Centre for Integrative Systems Biology (http://www.mcisb.org/), is thus to colocate individuals with the necessary combinations of skills. Novel disciplines that require such an integrative approach continue to emerge. These include fields such as chemical genomics, synthetic biology, distributed computational environments for biological data and modelling, single cell diagnostics/bionanotechnology, and computational linguistics/text mining.

Insights into the behaviour of systems biology models from dynamic sensitivity and identifiability analysis: a case study of an NF-κB signalling pathway

Mathematical modelling offers a variety of useful techniques to help in understanding the intrinsic behaviour of complex signal transduction networks. From the system engineering point of view, the dynamics of metabolic and signal transduction models can always be described by nonlinear ordinary differential equations (ODEs) following mass balance principles. Based on the state-space formulation, many methods from the area of automatic control can conveniently be applied to the modelling, analysis and design of cell networks. In the present study, dynamic sensitivity analysis is performed on a model of the IkappaB-NF-kappaB signal pathway system. Univariate analysis of the Euclidean-form overall sensitivities shows that only 8 out of the 64 parameters in the model have major influence on the nuclear NF-kappaB oscillations. The sensitivity matrix is then used to address correlation analysis, identifiability assessment and measurement set selection within the framework of least squares estimation and multivariate analysis. It is shown that certain pairs of parameters are exactly or highly correlated to each other in terms of their effects on the measured variables. The experimental design strategy provides guidance on which proteins should best be considered for measurement such that the unknown parameters can be estimated with the best statistical precision. The whole analysis scheme we describe provides efficient parameter estimation techniques for complex cell networks.