Properties of switch-like bioregulatory networks studied by simulation of the hypoxia response control system

Generic algebraic conditions for the occurrence of switch-like behavior of a chemical kinetic system of the hypoxia pathway

Weakly reversible chemical reaction networks with zero deficiency associated with mass-action kinetics admit, within each positive stoichiometric compatibility class, one positive steady state which is locally asymptotically stable and this irrespective of the values of the kinetics constants. Networks which do not enjoy these structural properties potentially exhibit more diverse dynamical behaviors. In this article, we consider a chemical reaction network associated with mass-action kinetics which is not weakly reversible and has a deficiency larger than one. The chemical reactions are at most bimolecular, but inflow and outflow reactions are present. Our results are as follows. We establish the existence of positive steady-state solutions and obtain their analytic expressions in the concentration space and in convex coordinates. We show that the system fulfills necessary conditions for a saddle-node and for a bifurcation into a saddle and a node. We apply a constructive approach to obtain a set of numerical values for the state variables and kinetic parameters, not reported previously, such that the reduced Jacobian is characterized by a zero eigenvalue with all other eigenvalues having negative real parts. The bifurcation diagram confirms the presence of the switch-like behavior.

Development of a Smart Portable Hypoxic Chamber with Accurate Sensing, Control and Visualization of In Vitro Cell Culture for Replication of Cancer Microenvironment

Clinical resistance towards treatment is a major concern in cancer therapy. This is due to in vitro studies lacking essential microenvironmental aspects. Tumor-hypoxia is an important pathophysiological phenomenon in numerous malignant tumors. Various studies have shown the importance of a hypoxic microenvironment (HME) in cancer drug resistance and its effects on cellular signaling and metabolism pathways. Most drugs fail in transition from a laboratory to clinical trials because of the variability in the testing microenvironment conditions. It is, thus, very crucial that research work needs to replicate these conditions in vitro to test the drugs and/or drug carriers for cancer therapy. Previous works have used a portable hypoxia chamber to reduce the cell microenvironment to hypoxic conditions. These techniques lack reliability and consistency due to a lack of control and visualization. In this research, we developed a smart portable hypoxia chamber that could accurately control the oxygen inside the portable chamber and have a global visualization. The proposed hypoxia chamber provided ease of use with the ranges of 1% to 20% oxygen with increments of 0.5%, as well as reproducibility and accuracy. The chamber displayed great precision on reaching the set oxygen limit and a high stability in maintaining that set level of oxygen compared to the uncontrolled setup for extended durations (24 h). For instance, at a 2% oxygen level, our automated system maintained this level over 1400 min, whereas the oxygen level fluctuated up to 4.5% in the conventional hypoxic chamber. We have also demonstrated the pitfalls of uncontrolled and non-visualized hypoxia chamber setup and the dire need for our system. The hypoxia-induced factor (HIF-1α) expression in cancer cell lines was tested and compared between the conventional hypoxia setup and our automated hypoxia chamber. We observed that there was a twofold increase in HIF-1α expression in the automated controlled chamber compared to the conventional device. The device also provided real-time sensing, visualization and control of the chamber conditions, which could aid in complex in vitro studies.

A structural analysis of the hypoxia response network

Background

The hypoxia-inducible factor-1 (HIF-1) signaling pathway is an important topic in high-altitude medicine. Network analysis is a novel method for integrating information on different aspects and levels of biological networks. However, this method has not been used in research on the HIF-1 signaling pathway network. To introduce this method into HIF-1-related research fields and verify its feasibility and effectiveness, we used a network analytical method to explore the structural attributes of the HIF-1 signaling pathway network.

Methods

First, we analyzed the overall network of the HIF-1 signaling pathway using information retrieved from the Kyoto Encyclopedia of Genes and Genomes (KEGG). We performed topology analysis, centrality analysis, and subgroup analysis of the network. Then, we analyzed the core network based on the overall network analysis. We analyzed the properties of the topology, the bow-tie structure, and the structural complexity of the core network.

Results

We obtained topological structure diagrams and quantitative indicators of the overall and core networks of the HIF-1 signaling pathway. For the structure diagrams, we generated topology diagrams of the network and the bow-tie structure of the core network. As quantitative indicators, we identified topology, centrality, subgroups, the bow-tie structure, and structural complexity. The topology indicators were the number of nodes, the number of lines, the network diameter, and the network density. The centrality indicators were the degree, closeness, and betweenness. The cohesive subgroup indicator was the components of the network. The bow-tie structure indicators included the core, input, and tendril-like structures. The structural complexity indicators included a power-law fitting model and its scale parameter.

Conclusions

The core network could be extracted based on the subgroup analysis of the overall network of the HIF-1 signaling pathway. The critical elements of the network could be identified in the centrality analysis. The results of the study show the feasibility and effectiveness of the network analytical method used to explore the network properties of the HIF-1 signaling pathway and provide support for further research.

Cycling hypoxia selects for constitutive HIF stabilization

Tumors experience temporal and spatial fluctuations in oxygenation. Hypoxia inducible transcription factors (HIF-α) respond to low levels of oxygen and induce re-supply oxygen. HIF-α stabilization is typically facultative, induced by hypoxia and reduced by normoxia. In some cancers, HIF-α stabilization becomes constitutive under normoxia. We develop a mathematical model that predicts how fluctuating oxygenation affects HIF-α stabilization and impacts net cell proliferation by balancing the base growth rate, the proliferative cost of HIF-α expression, and the mortality from not expressing HIF-α during hypoxia. We compare optimal net cell proliferation rate between facultative and constitutive HIF-α regulation in environments with different oxygen profiles. We find that that facultative HIF-α regulation promotes greater net cell proliferation than constitutive regulation with stochastic or slow periodicity in oxygenation. However, cell fitness is nearly identical for both HIF-α regulation strategies under rapid periodic oxygenation fluctuations. The model thus indicates that cells constitutively expressing HIF-α may be at a selective advantage when the cost of expression is low. In cancer, this condition is known as pseudohypoxia or the “Warburg Effect”. We conclude that rapid and regular cycling of oxygenation levels selects for pseudohypoxia, and that this is consistent with the ecological theory of optimal defense.

HACE1 blocks HIF1α accumulation under hypoxia in a RAC1 dependent manner

Uncovering the mechanisms that underpin how tumor cells adapt to microenvironmental stress is essential to better understand cancer progression. The HACE1 (HECT domain and ankyrin repeat-containing E3 ubiquitin-protein ligase) gene is a tumor suppressor that inhibits the growth, invasive capacity, and metastasis of cancer cells. However, the direct regulatory pathways whereby HACE1 confers this tumor-suppressive effect remain to be fully elucidated. In this report, we establish a link between HACE1 and the major stress factor, hypoxia-inducible factor 1 alpha (HIF1α). We find that HACE1 blocks the accumulation of HIF1α during cellular hypoxia through decreased protein stability. This property is dependent on HACE1 E3 ligase activity and loss of Ras-related C3 botulinum toxin substrate 1 (RAC1), an established target of HACE1 mediated ubiquitinylation and degradation. In vivo, genetic deletion of Rac1 reversed the increased HIF1α expression observed in Hace1^-/- mice in murine KRas^G12D-driven lung tumors. An inverse relationship was observed between HACE1 and HIF1α levels in tumors compared to patient-matched normal kidney tissues, highlighting the potential pathophysiological significance of our findings. Together, our data uncover a previously unrecognized function for the HACE1 tumor suppressor in blocking HIF1α accumulation under hypoxia in a RAC1-dependent manner.

Orchestration of lincRNA-p21 and miR-155 in Modulating the Adaptive Dynamics of HIF-1α

Hypoxia-inducible factor-1 (HIF-1) is the key regulator of cellular adaptive response to hypoxia. Accumulating evidence shows that HIF-1 induces some non-coding RNAs (ncRNAs) including lncRNAs and miRNAs to modulate its own activity, enclosing several feedback loops. How the two classes of ncRNAs are orchestrated in the HIF-1-dependent adaptive response to hypoxia is poorly understood. By selecting lincRNA-p21 and miR-155 as the representatives, we develop an integrated model of the HIF-1 network comprising interlinked positive and negative feedback loops to clarify the interplay between the two ncRNAs in the hypoxic response. By numerical simulations, we find that coordination of lincRNA-p21 and miR-155 shapes the adaptive dynamics of HIF-1α: lincRNA-p21 induction in the early phase stimulates the upregulation of HIF-1α via stabilizing it, while miR-155 induction in the late phase promotes the recovery of HIF-1α via enhancing the degradation of its mRNA. Moreover, HIF-1α-induced PHD2 plays an auxiliary role in the decline of HIF-1α. In addition, lincRNA-p21 and miR-155 modulate each other via regulating HIF-1α activity. Together, lincRNA-p21 and miR-155 coordinate in modulating HIF-1α dynamics, and our work may shed light on the role for ncRNAs in the cellular adaptation to hypoxia.

Investigations of the underlying mechanisms of HIF-1α and CITED2 binding to TAZ1

The TAZ1 domain of CREB binding protein is crucial for transcriptional regulation and recognizes multiple targets. The interactions between TAZ1 and its specific targets are related to the cellular hypoxic negative feedback regulation. Previous experiments reported that one of the TAZ1 targets, CITED2, is an efficient competitor of another target, HIF-1α. Here, by developing the structure-based models of TAZ1 complexes, we have uncovered the underlying mechanisms of the competitions between the two intrinsic disordered proteins (IDPs) HIF-1α and CITED2 binding to TAZ1. Our results support the experimental hypothesis on the competition mechanisms and the apparent affinity. Furthermore, the simulations locate the dominant position of forming TAZ1-CITED2 complex in both thermodynamics and kinetics. For thermodynamics, TAZ1-CITED2 is the lowest basin located on the free energy surface of binding in the ternary system. For kinetics, the results suggest that CITED2 binds to TAZ1 faster than HIF-1α. In addition, the analysis of contact map and Φ values is important for guiding further experimental studies to understand the biomolecular functions of IDPs.

Mathematical model of hypoxia and tumor signaling interplay reveals the importance of hypoxia and cell-to-cell variability in tumor growth inhibition

Background

Human tumor is a complex tissue with multiple heterogeneous hypoxic regions and significant cell-to-cell variability. Due to the complexity of the disease, the explanation of why anticancer therapies fail cannot be attributed to intrinsic or acquired drug resistance alone. Furthermore, there are inconsistent reports of hypoxia-induced kinase activities in different cancer cell-lines, where increase, decreases, or no change has been observed. Thus, we asked, why are there widely contrasting results in kinase activity under hypoxia in different cancer cell-lines and how does hypoxia play a role in anti-cancer drug sensitivity?

Results

We took a modeling approach to address these questions by analyzing the model simulation to explain why hypoxia driven signals can have dissimilar impact on tumor growth and alter the efficacy of anti-cancer drugs. Repeated simulations with varying concentrations of biomolecules followed by decision tree analysis reveal that the highly differential effects among heterogeneous subpopulation of tumor cells could be governed by varying concentrations of just a few key biomolecules. These biomolecules include activated serine/threonine-specific protein kinases (pRAF), mitogen-activated protein kinase kinase (pMEK), protein kinase B (pAkt), or phosphoinositide-4,5-bisphosphate 3-kinase (pPI3K). Additionally, the ratio of activated extracellular signal-regulated kinases (pERK) or pAkt to its respective total was a key factor in determining the sensitivity of pERK or pAkt to hypoxia.

Conclusion

This work offers a mechanistic insight into how hypoxia can affect the efficacy of anti-cancer drug that targets tumor signaling and provides a framework to identify the types of tumor cells that are either sensitive or resistant to anti-cancer therapy.

Interleukin-15 Signaling in HIF-1α Regulation in Natural Killer Cells, Insights Through Mathematical Models

Natural killer (NK) cells belong to the first line of host defense against infection and cancer. Cytokines, including interleukin-15 (IL-15), critically regulate NK cell activity, resulting in recognition and direct killing of transformed and infected target cells. NK cells have to adapt and respond in inflamed and often hypoxic areas. Cellular stabilization and accumulation of the transcription factor hypoxia-inducible factor-1α (HIF-1α) is a key mechanism of the cellular hypoxia response. At the same time, HIF-1α plays a critical role in both innate and adaptive immunity. While the HIF-1α hydroxylation and degradation pathway has been recently described with the help of mathematical methods, less is known concerning the mechanistic mathematical description of processes regulating the levels of HIF-1α mRNA and protein. In this work we combine mathematical modeling with experimental laboratory analysis and examine the dynamic relationship between HIF-1α mRNA, HIF-1α protein, and IL-15-mediated upstream signaling events in NK cells from human blood. We propose a system of non-linear ordinary differential equations with positive and negative feedback loops for describing the complex interplay of HIF-1α regulators. The experimental design is optimized with the help of mathematical methods, and numerical optimization techniques yield reliable parameter estimates. The mathematical model allows for the investigation and prediction of HIF-1α stabilization under different inflammatory conditions and provides a better understanding of mechanisms mediating cellular enrichment of HIF-1α. Thanks to the combination of in vitro experimental data and in silico predictions we identified the mammalian target of rapamycin (mTOR), the nuclear factor-κB (NF-κB), and the signal transducer and activator of transcription 3 (STAT3) as central regulators of HIF-1α accumulation. We hypothesize that the regulatory pathway proposed here for NK cells can be extended to other types of immune cells. Understanding the molecular mechanisms involved in the dynamic regulation of the HIF-1α pathway in immune cells is of central importance to the immune cell function and could be a promising strategy in the design of treatments for human inflammatory diseases and cancer.

Acute vs. Chronic vs. Cyclic Hypoxia: Their Differential Dynamics, Molecular Mechanisms, and Effects on Tumor Progression

Hypoxia has been shown to increase the aggressiveness and severity of tumor progression. Along with chronic and acute hypoxic regions, solid tumors contain regions of cycling hypoxia (also called intermittent hypoxia or IH). Cyclic hypoxia is mimicked in vitro and in vivo by periodic exposure to cycles of hypoxia and reoxygenation (H-R cycles). Compared to chronic hypoxia, cyclic hypoxia has been shown to augment various hallmarks of cancer to a greater extent: angiogenesis, immune evasion, metastasis, survival etc. Cycling hypoxia has also been shown to be the major contributing factor in increasing the risk of cancer in obstructive sleep apnea (OSA) patients. Here, we first compare and contrast the effects of acute, chronic and intermittent hypoxia in terms of molecular pathways activated and the cellular processes affected. We highlight the underlying complexity of these differential effects and emphasize the need to investigate various combinations of factors impacting cellular adaptation to hypoxia: total duration of hypoxia, concentration of oxygen (O2), and the presence of and frequency of H-R cycles. Finally, we summarize the effects of cycling hypoxia on various hallmarks of cancer highlighting their dependence on the abovementioned factors. We conclude with a call for an integrative and rigorous analysis of the effects of varying extents and durations of hypoxia on cells, including tools such as mechanism-based mathematical modelling and microfluidic setups.

Mathematical Model for Tissue-Level Hypoxic Response in Microfluidic Environment

Availability of essential species like oxygen is critical in shaping the dynamics of tumor growth. When the intracellular oxygen level falls below normal, it initiates major cascades in cellular dynamics leading to tumor cell survival. In a cellular block with cells growing away from the blood vessel, the scenario can be aggravated for the cells further inside the block. In this study, the dynamics of intracellular species inside a colony of tumor cells are investigated by varying the cell-block thickness and cell types in a microfluidic cell culture device. The oxygen transport across the cell block is modeled through diffusion, while ascorbate (AS) transport from the extracellular medium is addressed by a concentration-dependent uptake model. The extracellular and intracellular descriptions were coupled through the consumption and traffic of species from the microchannel to the cell block. Our model shows that the onset of hypoxia is possible in HeLa cell within minutes depending on the cell location, although the nutrient supply inside the channel is maintained in normoxic levels. This eventually leads to total oxygen deprivation inside the cell block in the extreme case, representing the development of a necrotic core that maintains a dynamic balance with growing cells and scarce supply. The numerical model reveals that species concentration and hypoxic response are different for HeLa and HelaS3 cells. Results also indicate that the long-term hypoxic response from a microfluidic cellular block stays within 5% of the values of a tissue with the basal layer. The hybrid model can be very useful in designing microfluidic experiments to satisfactorily predict the tissue-level response in cancer research.

Hypersensitive termination of the hypoxic response by a disordered protein switch

The cellular response to hypoxia is critical for cell survival and is fine-tuned to allow cells to recover from hypoxic stress and adapt to heterogeneous or fluctuating oxygen levels^1,2. The hypoxic response is mediated by the α subunit of the transcription factor HIF-1 (HIF-1α)³, which interacts via its intrinsically disordered C-terminal transactivation domain with the TAZ1 (CH1) domain of the general transcriptional coactivators CBP and p300 to control transcription of critical adaptive genes^4–6. One such gene is CITED2, a negative feedback regulator that attenuates HIF transcriptional activity by competing for TAZ1 binding through its own disordered transactivation domain^7–9. Little is known about the molecular mechanism by which CITED2 displaces the tightly bound HIF-1α from their common cellular target. The HIF-1α and CITED2 transactivation domains bind to TAZ1 through helical motifs that flank a conserved LP(Q/E)L sequence that is essential for negative feedback regulation^5,6,8,9. We show that CITED2 displaces HIF-1α by forming a transient ternary complex with TAZ1 and HIF-1α and competing for a shared binding site via its LPEL motif, thus promoting a conformational change in TAZ1 that increases the rate of HIF-1α dissociation. Through allosteric enhancement of HIF-1α release, CITED2 activates a highly responsive negative feedback circuit that rapidly and efficiently attenuates the hypoxic response, even at modest CITED2 concentrations. This hypersensitive regulatory switch is entirely dependent on the unique flexibility and binding properties of these intrinsically disordered proteins and exemplifies a likely common strategy used by the cell to respond rapidly to environmental signals.

Transcriptional and Post-Transcriptional Regulation of Thrombospondin-1 Expression: A Computational Model

Hypoxia is an important physiological stress signal that drives angiogenesis, the formation of new blood vessels. Besides an increase in the production of pro-angiogenic signals such as vascular endothelial growth factor (VEGF), hypoxia also stimulates the production of anti-angiogenic signals. Thrombospondin-1 (TSP-1) is one of the anti-angiogenic factors whose synthesis is driven by hypoxia. Cellular synthesis of TSP-1 is tightly regulated by different intermediate biomolecules including proteins that interact with hypoxia-inducible factors (HIFs), transcription factors that are activated by receptor and intracellular signaling, and microRNAs which are small non-coding RNA molecules that function in post-transcriptional modification of gene expression. Here we present a computational model that describes the mechanistic interactions between intracellular biomolecules and cooperation between signaling pathways that together make up the complex network of TSP-1 regulation both at the transcriptional and post-transcriptional level. Assisted by the model, we conduct in silico experiments to compare the efficacy of different therapeutic strategies designed to modulate TSP-1 synthesis in conditions that simulate tumor and peripheral arterial disease microenvironment. We conclude that TSP-1 production in endothelial cells depends on not only the availability of certain growth factors but also the fine-tuned signaling cascades that are initiated by hypoxia.

Stochastic Petri Net Modeling of Hypoxia Pathway Predicts a Novel Incoherent Feed-Forward Loop Controlling SDF-1 Expression in Acute Kidney Injury

Homing of stem cells to the sites of injury is crucial for tissue regeneration. Stromal derived factor 1 (SDF-1) is among the most important chemokines recruiting these cells. Unexpectedly, our previous experimental data on mouse models of acute kidney injury showed that SDF-1 has a declining trend following ischemic kidney insult. To describe this unforeseen observation, a stochastic Petri net model of SDF-1 regulation in the hypoxia pathway was constructed based on main related components extracted from literature. Using this strategy, predictions regarding the underlying mechanisms of SDF-1 kinetics are generated and a novel incoherent feed forward loop regulating SDF-1 expression is proposed. The computational approach suggested here can be exploited to propose novel therapies for debilitating disorders such as kidney injury.

Computational Model of MicroRNA Control of HIF-VEGF Pathway: Insights into the Pathophysiology of Ischemic Vascular Disease and Cancer

HRMs (hypoxia-responsive miRNAs) are a specific group of microRNAs that are regulated by hypoxia. Recent studies revealed that several HRMs including let-7 family miRNAs were highly induced in response to HIF (hypoxia-inducible factor) stabilization in hypoxia, and they potently participated in angiogenesis by targeting AGO1 (argonaute 1) and upregulating VEGF (vascular endothelial growth factor). Here we constructed a novel computational model of microRNA control of HIF-VEGF pathway in endothelial cells to quantitatively investigate the role of HRMs in modulating the cellular adaptation to hypoxia. The model parameters were optimized and the simulations based on these parameters were validated against several published in vitro experimental data. To advance the mechanistic understanding of oxygen sensing in hypoxia, we demonstrated that the rate of HIF-1α nuclear import substantially influences its stabilization and the formation of HIF-1 transcription factor complex. We described the biological feedback loops involving let-7 and AGO1 in which the impact of external perturbations were minimized; as a pair of master regulators when low oxygen tension was sensed, they coordinated the critical process of VEGF desuppression in a controlled manner. Prompted by the model-motivated discoveries, we proposed and assessed novel pathway-specific therapeutics that modulate angiogenesis by adjusting VEGF synthesis in tumor and ischemic cardiovascular disease. Through simulations that capture the complex interactions between miRNAs and miRNA-processing molecules, this model explores an innovative perspective about the distinctive yet integrated roles of different miRNAs in angiogenesis, and it will help future research to elucidate the dysregulated miRNA profiles found in cancer and various cardiovascular diseases.

Cells living in a hypoxic environment secrete signals to stimulate new blood vessel growth, a process termed angiogenesis, to acquire more oxygen and nutrients. Hypoxia-inducible factor 1 (HIF-1) accumulates in hypoxia and expedites the release of pro-angiogenic cytokines such as vascular endothelial growth factor (VEGF), a prime inducer of angiogenesis. The intermediate signaling events connecting HIF-1 and VEGF are tightly controlled by microRNAs (miRs), which are endogenous, non-coding RNA molecules and powerful regulators in cancer and cardiovascular disease. Given the importance of angiogenesis in tumor development and post-ischemia reperfusion, it holds great basic research and therapeutic value to investigate how miRs modulate intracellular VEGF synthesis to control angiogenesis in hypoxia. We present a computational model that details the interactions between miRs and other key molecules which make up different hierarchies in HIF-miR-VEGF pathway. Based on simulation analysis, new potential therapies are introduced and tested in silico, from which the strategies that most effectively reduce VEGF synthesis in cancer, or enhance VEGF release in ischemic vascular disease are identified. We conclude that in hypoxia different miRs work consonantly to fine-tune the cellular adaptations; when a master miR alters its expression, dynamics of other miRs vary accordingly which together contribute to aberrant RNA/protein profiles observed in the pathophysiology of multiple diseases.

Modeling dioxygenase enzyme kinetics in familial paraganglioma

Hypoxia inducible factors (HIFs) play vital roles in cellular maintenance of oxygen homeostasis. These transcription factors are responsible for the expression of genes involved in angiogenesis, metabolism, and cell proliferation. Here, we generate a detailed mathematical model for the enzyme kinetics of α-ketoglutarate-dependent HIF prolyl 4-hydroxylase domain (PHD) dioxygenases to simulate our in vitro data showing synergistic PHD inhibition by succinate and hypoxia in experimental models of succinate dehydrogenase loss, which phenocopy familial paraganglioma. Our mathematical model confirms the inhibitory synergy of succinate and hypoxia under physiologically-relevant conditions. In agreement with our experimental data, the model predicts that HIF1α is not stabilized under atmospheric oxygen concentrations, as observed. Further, the model confirms that addition of α-ketoglutarate can reverse PHD inhibition by succinate and hypoxia in SDH-deficient cells.

Role of compartmentalization on HiF-1α degradation dynamics during changing oxygen conditions: a computational approach

HiF-1α is the central protein driving the cellular response to hypoxia. Its accumulation in cancer cells is linked to the appearance of chemoresistant and aggressive tumor phenotypes. As a consequence, understanding the regulation of HiF-1α dynamics is a major issue to design new anti-cancer therapies. In this paper, we propose a model of the hypoxia pathway, involving HiF-1α and its inhibitor pVHL. Based on data from the literature, we made the hypothesis that the regulation of HiF-1α involves two compartments (nucleus and cytoplasm) and a constitutive shuttle of the pVHL protein between them. We first show that this model captures correctly the main features of HiF-1α dynamics, including the bi-exponential degradation profile in normoxia, the kinetics of induction in hypoxia, and the switch-like accumulation. Second, we simulated the effects of a hypoxia/reoxygenation event, and show that it generates a strong instability of HiF-1α. The protein concentration rapidly increases 3 hours after the reoxygenation, and exhibits an oscillating pattern. This effect vanishes if we do not consider compartmentalization of HiF-1α. This result can explain various counter-intuitive observations about the specific molecular and cellular response to the reoxygenation process. Third, we simulated the HiF-1α dynamics in the tumor case. We considered different types of mutations associated with tumorigenesis, and we compared their consequences on HiF-1α dynamics. Then, we tested different therapeutics strategies. We show that a therapeutic decrease of HiF-1α nuclear level is not always correlated with an attenuation of reoxygenation-induced instabilities. Thus, it appears that the design of anti-HiF-1α therapies have to take into account these two aspects to maximize their efficiency.

Design and analysis of a Petri net model of the Von Hippel-Lindau (VHL) tumor suppressor interaction network

Von Hippel-Lindau (VHL) syndrome is a hereditary condition predisposing to the development of different cancer forms, related to germline inactivation of the homonymous tumor suppressor pVHL. The best characterized function of pVHL is the ubiquitination dependent degradation of Hypoxia Inducible Factor (HIF) via the proteasome. It is also involved in several cellular pathways acting as a molecular hub and interacting with more than 200 different proteins. Molecular details of pVHL plasticity remain in large part unknown. Here, we present a novel manually curated Petri Net (PN) model of the main pVHL functional pathways. The model was built using functional information derived from the literature. It includes all major pVHL functions and is able to credibly reproduce VHL syndrome at the molecular level. The reliability of the PN model also allowed in silico knockout experiments, driven by previous model analysis. Interestingly, PN analysis suggests that the variability of different VHL manifestations is correlated with the concomitant inactivation of different metabolic pathways.

Tight control of hypoxia-inducible factor-α transient dynamics is essential for cell survival in hypoxia

Intracellular signaling involving hypoxia-inducible factor (HIF) controls the adaptive responses to hypoxia. There is a growing body of evidence demonstrating that intracellular signals encode temporal information. Thus, the dynamics of protein levels, as well as protein quantity and/or localization, impacts on cell fate. We hypothesized that such temporal encoding has a role in HIF signaling and cell fate decisions triggered by hypoxic conditions. Using live cell imaging in a controlled oxygen environment, we observed transient 3-h pulses of HIF-1α and -2α expression under continuous hypoxia. We postulated that the well described prolyl hydroxylase (PHD) oxygen sensors and HIF negative feedback regulators could be the origin of the pulsatile HIF dynamics. We used iterative mathematical modeling and experimental analysis to scrutinize which parameter of the PHD feedback could control HIF timing and we probed for the functional redundancy between the three main PHD proteins. We identified PHD2 as the main PHD responsible for HIF peak duration. We then demonstrated that this has important consequences, because the transient nature of the HIF pulse prevents cell death by avoiding transcription of p53-dependent pro-apoptotic genes. We have further shown the importance of considering HIF dynamics for coupling mathematical models by using a described HIF-p53 mathematical model. Our results indicate that the tight control of HIF transient dynamics has important functional consequences on the cross-talk with key signaling pathways controlling cell survival, which is likely to impact on HIF targeting strategies for hypoxia-associated diseases such as tumor progression and ischemia.

Hypoxia-inducible factor (HIF) network: insights from mathematical models

Oxygen is a crucial molecule for cellular function. When oxygen demand exceeds supply, the oxygen sensing pathway centred on the hypoxia inducible factor (HIF) is switched on and promotes adaptation to hypoxia by up-regulating genes involved in angiogenesis, erythropoiesis and glycolysis. The regulation of HIF is tightly modulated through intricate regulatory mechanisms. Notably, its protein stability is controlled by the oxygen sensing prolyl hydroxylase domain (PHD) enzymes and its transcriptional activity is controlled by the asparaginyl hydroxylase FIH (factor inhibiting HIF-1).To probe the complexity of hypoxia-induced HIF signalling, efforts in mathematical modelling of the pathway have been underway for around a decade. In this paper, we review the existing mathematical models developed to describe and explain specific behaviours of the HIF pathway and how they have contributed new insights into our understanding of the network. Topics for modelling included the switch-like response to decreased oxygen gradient, the role of micro environmental factors, the regulation by FIH and the temporal dynamics of the HIF response. We will also discuss the technical aspects, extent and limitations of these models. Recently, HIF pathway has been implicated in other disease contexts such as hypoxic inflammation and cancer through crosstalking with pathways like NFκB and mTOR. We will examine how future mathematical modelling and simulation of interlinked networks can aid in understanding HIF behaviour in complex pathophysiological situations. Ultimately this would allow the identification of new pharmacological targets in different disease settings.

A dynamic model of the hypoxia-inducible factor 1α (HIF-1α) network

Activation of the hypoxia-inducible factor (HIF) pathway is a critical step in the transcriptional response to hypoxia. Although many of the key proteins involved have been characterised, the dynamics of their interactions in generating this response remain unclear. In the present study, we have generated a comprehensive mathematical model of the HIF-1α pathway based on core validated components and dynamic experimental data, and confirm the previously described connections within the predicted network topology. Our model confirms previous work demonstrating that the steps leading to optimal HIF-1α transcriptional activity require sequential inhibition of both prolyl- and asparaginyl-hydroxylases. We predict from our model (and confirm experimentally) that there is residual activity of the asparaginyl-hydroxylase FIH (factor inhibiting HIF) at low oxygen tension. Furthermore, silencing FIH under conditions where prolyl-hydroxylases are inhibited results in increased HIF-1α transcriptional activity, but paradoxically decreases HIF-1α stability. Using a core module of the HIF network and mathematical proof supported by experimental data, we propose that asparaginyl hydroxylation confers a degree of resistance upon HIF-1α to proteosomal degradation. Thus, through in vitro experimental data and in silico predictions, we provide a comprehensive model of the dynamic regulation of HIF-1α transcriptional activity by hydroxylases and use its predictive and adaptive properties to explain counter-intuitive biological observations.

Regulation of SREBP during hypoxia requires Ofd1-mediated control of both DNA binding and degradation

The prolyl hydroxylase Ofd1 enables yeast cells to adapt to hypoxia by regulating the DNA binding and degradation of the hypoxic transcription factor Sre1N. These two regulatory functions are inseparable in vivo. A mathematical model of the Ofd1 system is used to show that both functions are necessary for Ofd1 to work as observed.

Cells adapt to changes in ambient oxygen by changing their gene expression patterns. In fission yeast, the sterol regulatory element–binding protein Sre1 is proteolytically cleaved under low oxygen, and its N-terminal segment (Sre1N) serves as a hypoxic transcription factor. When oxygen is present, the prolyl hydroxylase Ofd1 down-regulates Sre1N activity in two ways: first, by inhibiting its binding to DNA, and second, by accelerating its degradation. Here we use a mathematical model to assess what each of these two regulatory functions contributes to the hypoxic response of the cell. By disabling individual regulatory functions in the model, which would be difficult in vivo, we found that the Ofd1 function of inhibiting Sre1N binding to DNA is essential for oxygen-dependent Sre1N regulation. The other Ofd1 function of accelerating Sre1N degradation is necessary for the yeast to quickly turn off its hypoxic response when oxygen is restored. In addition, the model predicts that increased Ofd1 production at low oxygen plays an important role in the hypoxic response, and the model indicates that the Ofd1 binding partner Nro1 tunes the response to oxygen. This model quantifies our understanding of a novel oxygen-sensing mechanism that is widely conserved.

Molecular mechanisms of chronic intermittent hypoxia and hypertension

Obstructive sleep apnea (OSA) is characterized by episodes of repeated airway obstruction resulting in cessation (apnea) or reduction (hypopnea) in airflow during sleep. These events lead to intermittent hypoxia and hypercapnia, sleep fragmentation, and changes in intrathoracic pressure, and are associated with a marked surge in sympathetic activity and an abrupt increase in blood pressure. Blood pressure remains elevated during wakefulness despite the absence of obstructive events resulting in a high prevalence of hypertension in patients with OSA. There is substantial evidence that suggests that chronic intermittent hypoxia (CIH) leads to sustained sympathoexcitation during the day and changes in vasculature resulting in hypertension in patients with OSA. Mechanisms of sympathoexcitation include augmentation of peripheral chemoreflex sensitivity and a direct effect on central sites of sympathetic regulation. Interestingly, the vascular changes that occur with CIH have been ascribed to the same molecules that have been implicated in the augmented sympathetic tone in CIH. This review will discuss the hypothesized molecular mechanisms involved in the development of hypertension with CIH, will build a conceptual model for the development of hypertension following CIH, and will propose a systems biology approach in further elucidating the relationship between CIH and the development of hypertension.

Identification of genes expressed in juvenile Haliotis rufescens in response to different copper concentrations in the north of Chile under controlled conditions

This study reports molecular markers potentially associated with resistance or sensitivity to the impact of copper in juvenile red abalone, Haliotis rufescens, in the north of Chile under experimental conditions. Genomic analysis was made applying subtractive hybridization libraries (SSH) to identify genes up-and down regulated during cooper exposure in abalone over periods of 12 and 168 h exposed to 2.5 and 10 μg/L of Cu(+2). Results obtained from the SSH library revealed 368 different sequences regulated by copper, that correspond to eight major physiological functions. The validation of these sequences obtained by SSH as well as their expression kinetics were made by PCR in real time on 14 potential genes regulated by metal stress. This study provides information for the characterization of potential genomic markers that may be used in future environmental monitoring and to investigate new mechanisms of stress to copper in this commercially important marine species.

A formal MIM specification and tools for the common exchange of MIM diagrams: an XML-Based format, an API, and a validation method

Background

The Molecular Interaction Map (MIM) notation offers a standard set of symbols and rules on their usage for the depiction of cellular signaling network diagrams. Such diagrams are essential for disseminating biological information in a concise manner. A lack of software tools for the notation restricts wider usage of the notation. Development of software is facilitated by a more detailed specification regarding software requirements than has previously existed for the MIM notation.

Results

A formal implementation of the MIM notation was developed based on a core set of previously defined glyphs. This implementation provides a detailed specification of the properties of the elements of the MIM notation. Building upon this specification, a machine-readable format is provided as a standardized mechanism for the storage and exchange of MIM diagrams. This new format is accompanied by a Java-based application programming interface to help software developers to integrate MIM support into software projects. A validation mechanism is also provided to determine whether MIM datasets are in accordance with syntax rules provided by the new specification.

Conclusions

The work presented here provides key foundational components to promote software development for the MIM notation. These components will speed up the development of interoperable tools supporting the MIM notation and will aid in the translation of data stored in MIM diagrams to other standardized formats. Several projects utilizing this implementation of the notation are outlined herein. The MIM specification is available as an additional file to this publication. Source code, libraries, documentation, and examples are available at http://discover.nci.nih.gov/mim.

Computational models of VEGF-associated angiogenic processes in cancer

Tumour angiogenesis allows a growing mass of cancer cells to overcome oxygen diffusion limitation and to increase cell survival. The growth of capillaries from pre-existing blood vessels is the result of numerous signalling cascades involving different molecules and of cellular events involving multiple cell and tissue types. Computational models offer insight into the mechanisms governing angiogenesis and provide quantitative information on parameters difficult to assess by experiments alone. In this article, we summarize results from computational models of tumour angiogenic processes with a focus on the molecular-detailed vascular endothelial growth factor-associated models that have been developed in our laboratory, spanning multiple scales from the molecular to whole body.

Systems biology of pro-angiogenic therapies targeting the VEGF system

Vascular endothelial growth factor (VEGF) is a family of cytokines for which the dysregulation of expression is involved in many diseases; for some, excess VEGF causes pathological hypervascularization, while for others VEGF-induced vascular remodeling may alleviate ischemia and/or hypoxia. Anti-angiogenic therapies attacking the VEGF pathway have begun to live up to their promise for treatment of certain cancers and of age-related macular degeneration. However, the corollary is not yet true: in coronary artery disease and peripheral artery disease, clinical trials of pro-angiogenic VEGF delivery have not, so far, proven successful. The VEGF and VEGF-receptor system is complex, with at least five ligand genes, some encoding multiple protein isoforms and five receptor genes. A systems biology approach for designing pro-angiogenic therapies, using a combination of quantitative experimental approaches and detailed computational models, is essential to deal with this complexity and to understand the effects of drugs targeting the system. This approach allows us to learn from unsuccessful clinical trials and to design and test novel single therapeutics or combinations of therapeutics. Among the parameters that can be varied in order to determine optimal strategy are dosage, timing of multiple doses, route of administration, and the molecular target.

Hypoxia-dependent sequestration of an oxygen sensor by a widespread structural motif can shape the hypoxic response--a predictive kinetic model

Background

The activity of the heterodimeric transcription factor hypoxia inducible factor (HIF) is regulated by the post-translational, oxygen-dependent hydroxylation of its α-subunit by members of the prolyl hydroxylase domain (PHD or EGLN)-family and by factor inhibiting HIF (FIH). PHD-dependent hydroxylation targets HIFα for rapid proteasomal degradation; FIH-catalysed asparaginyl-hydroxylation of the C-terminal transactivation domain (CAD) of HIFα suppresses the CAD-dependent subset of the extensive transcriptional responses induced by HIF. FIH can also hydroxylate ankyrin-repeat domain (ARD) proteins, a large group of proteins which are functionally unrelated but share common structural features. Competition by ARD proteins for FIH is hypothesised to affect FIH activity towards HIFα; however the extent of this competition and its effect on the HIF-dependent hypoxic response are unknown.

Results

To analyse if and in which way the FIH/ARD protein interaction affects HIF-activity, we created a rate equation model. Our model predicts that an oxygen-regulated sequestration of FIH by ARD proteins significantly shapes the input/output characteristics of the HIF system. The FIH/ARD protein interaction is predicted to create an oxygen threshold for HIFα CAD-hydroxylation and to significantly sharpen the signal/response curves, which not only focuses HIFα CAD-hydroxylation into a defined range of oxygen tensions, but also makes the response ultrasensitive to varying oxygen tensions. Our model further suggests that the hydroxylation status of the ARD protein pool can encode the strength and the duration of a hypoxic episode, which may allow cells to memorise these features for a certain time period after reoxygenation.

Conclusions

The FIH/ARD protein interaction has the potential to contribute to oxygen-range finding, can sensitise the response to changes in oxygen levels, and can provide a memory of the strength and the duration of a hypoxic episode. These emergent properties are predicted to significantly shape the characteristics of HIF activity in animal cells. We argue that the FIH/ARD interaction should be taken into account in studies of the effect of pharmacological inhibition of the HIF-hydroxylases and propose that the interaction of a signalling sensor with a large group of proteins might be a general mechanism for the regulation of signalling pathways.

Predicted functions of MdmX in fine-tuning the response of p53 to DNA damage

Tumor suppressor protein p53 is regulated by two structurally homologous proteins, Mdm2 and MdmX. In contrast to Mdm2, MdmX lacks ubiquitin ligase activity. Although the essential interactions of MdmX are known, it is not clear how they function to regulate p53. The regulation of tumor suppressor p53 by Mdm2 and MdmX in response to DNA damage was investigated by mathematical modeling of a simplified network. The simplified network model was derived from a detailed molecular interaction map (MIM) that exhibited four coherent DNA damage response pathways. The results suggest that MdmX may amplify or stabilize DNA damage-induced p53 responses via non-enzymatic interactions. Transient effects of MdmX are mediated by reservoirs of p53∶MdmX and Mdm2∶MdmX heterodimers, with MdmX buffering the concentrations of p53 and/or Mdm2. A survey of kinetic parameter space disclosed regions of switch-like behavior stemming from such reservoir-based transients. During an early response to DNA damage, MdmX positively or negatively regulated p53 activity, depending on the level of Mdm2; this led to amplification of p53 activity and switch-like response. During a late response to DNA damage, MdmX could dampen oscillations of p53 activity. A possible role of MdmX may be to dampen such oscillations that otherwise could produce erratic cell behavior. Our study suggests how MdmX may participate in the response of p53 to DNA damage either by increasing dependency of p53 on Mdm2 or by dampening oscillations of p53 activity and presents a model for experimental investigation.

A Molecular Interaction Map (MIM) akin to a circuit diagram of an electric device can give a comprehensive view of cellular processes and help understand complex protein functions in cells. To this end, we generated a MIM focused on the p53-Mdm2-MdmX network proteins and performed computer simulations to help understand how Mdm2 and MdmX may regulate p53. Proper regulation of p53 is important for cell survival: elevated levels of p53 can lead to cell death, and decreased levels of p53 can lead to cancer. Mdm2 and MdmX are structurally homologous proteins that regulate p53. Mdm2 negatively regulates p53 by degradation, but MdmX regulation of p53 is not well understood. Recently, Mdm2 and MdmX have been recognized as potential cancer therapeutic targets. In an effort to better understand how MdmX can alter the p53 activity under various conditions, we used mathematical models based on the MIM network to generate hypotheses that can be tested by experiments. Our simulations suggest that MdmX may increase the dependency of p53 on Mdm2 or dampen p53 oscillations during DNA damage response.

Structural analysis to determine the core of hypoxia response network

The advent of sophisticated molecular biology techniques allows to deduce the structure of complex biological networks. However, networks tend to be huge and impose computational challenges on traditional mathematical analysis due to their high dimension and lack of reliable kinetic data. To overcome this problem, complex biological networks are decomposed into modules that are assumed to capture essential aspects of the full network's dynamics. The question that begs for an answer is how to identify the core that is representative of a network's dynamics, its function and robustness. One of the powerful methods to probe into the structure of a network is Petri net analysis. Petri nets support network visualization and execution. They are also equipped with sound mathematical and formal reasoning based on which a network can be decomposed into modules. The structural analysis provides insight into the robustness and facilitates the identification of fragile nodes. The application of these techniques to a previously proposed hypoxia control network reveals three functional modules responsible for degrading the hypoxia-inducible factor (HIF). Interestingly, the structural analysis identifies superfluous network parts and suggests that the reversibility of the reactions are not important for the essential functionality. The core network is determined to be the union of the three reduced individual modules. The structural analysis results are confirmed by numerical integration of the differential equations induced by the individual modules as well as their composition. The structural analysis leads also to a coarse network structure highlighting the structural principles inherent in the three functional modules. Importantly, our analysis identifies the fragile node in this robust network without which the switch-like behavior is shown to be completely absent.

A systems biology perspective on Nrf2-mediated antioxidant response

Cells in vivo are constantly exposed to reactive oxygen species (ROS) generated endogenously and exogenously. To defend against the deleterious consequences of ROS, cells contain multiple antioxidant enzymes expressed in various cellular compartments to scavenge these toxic species. Under oxidative stresses, these antioxidant enzymes are upregulated to restore redox homeostasis. Such an adaptive response results from the activation of a redox-sensitive gene regulatory network mediated by nuclear factor E2-related factor 2. To more completely understand how the redox control system is designed by nature to meet homeostatic goals, we have examined the network from a systems perspective using engineering approaches. As with man-made control devices, the redox control system can be decomposed into distinct functional modules, including transducer, controller, actuator, and plant. Cells achieve specific performance objectives by utilizing nested feedback loops, feedforward control, and ultrasensitive signaling motifs, etc. Given that endogenously generated ROS are also used as signaling molecules, our analysis suggests a novel mode of action to explain oxidative stress-induced pathological conditions and diseases. Specifically, by adaptively upregulating antioxidant enzymes, oxidative stress may inadvertently attenuate ROS signals that mediate physiological processes, resulting in aberrations of cellular functions and adverse consequences. Lastly, by simultaneously considering the two competing cellular tasks-adaptive antioxidant defense and ROS signaling-we re-examine the premise that dietary antioxidant supplements is generally beneficial to human health. Our analysis highlights some possible adverse effects of these widely consumed antioxidants.

Multiscale models of angiogenesis

Vascular disease, cancer, stroke, neurodegeneration, diabetes, inflammation, asthma, obesity, arthritis--the list of conditions that involve angiogenesis reads like main chapters in a book on pathology. Angiogenesis, the growth of capillaries from preexisting vessels, also occurs in normal physiology, in response to exercise or in the process of wound healing.Why and when is angiogenesis prevalent? What controls the process? How can we intelligently control it? These are the key questions driving researchers in fields as diverse as cell biology, oncology, cardiology, neurology, biomathematics, systems biology, and biomedical engineering. As bioengineers, we approach angiogenesis as a complex, interconnected system of events occurring in sequence and in parallel, on multiple levels, triggered by a main stimulus, e.g., hypoxia.

Gene regulation in response to graded hypoxia: the non-redundant roles of the oxygen sensors PHD and FIH in the HIF pathway

Hypoxia Inducible Factor (HIF), being the master protein involved in adaptation to low pO(2), plays a major role in many physiological and pathological phenomena: development, inflammation, ischemia and cancer. Prolyl hydroxylase (PHD) and factor inhibiting HIF (FIH) are the two oxygen sensors that regulate the HIF pathway. Here we model the regulatory dynamics in an oxygen gradient by a system of differential equations. A part of the work consists in a qualitative analysis, driven independently of the values of the parameters, which explains the non-redundant functional roles of FIH and PHD. In a second part, we use biological experiments to fit the model in a physiologically relevant context and run simulations. Simulation results are confronted with success to independent biological experiments. The combination of biological data and mathematical analysis stresses that FIH is a fine modulator determining whether a given gene should be induced in mildly or in strongly hypoxic areas. Moreover it gives access to other functional predictions that are not directly accessible by pure experiments, for instance the stoichiometry of prolyl-hydroxylation on HIF, and the switch-like properties of the system.

AVAILABILITY

an interactive simulation interface is available at http://sdi.ljad.free.fr/spip.php?article111.

Systems biology of vascular endothelial growth factors

Several cytokine families have roles in the development, maintenance, and remodeling of the microcirculation. Of these, the vascular endothelial growth factor (VEGF) family is one of the best studied and one of the most complex. Five VEGF ligand genes and five cell-surface receptor genes are known in the human, and each of these may be transcribed as multiple splice isoforms to generate an extensive family of proteins, many of which are subject to further proteolytic processing. Using the VEGF family as an example, we describe the current knowledge of growth-factor expression, processing, and transport in vivo. Experimental studies and computational simulations are being used to measure and predict the activity of these molecules, and we describe avenues of research that seek to fill the remaining gaps in our understanding of VEGF family behavior.

Identification of differentially expressed genes of the Pacific oyster Crassostrea gigas exposed to prolonged thermal stress

Groups of oysters (Crassostrea gigas) were exposed to 25 degrees C for 24 days (controls to 13 degrees C) to explore the biochemical and molecular pathways affected by prolonged thermal stress. This temperature is 4 degrees C above the summer seawater temperature encountered in western Brittany, France where the animals were collected. Suppression subtractive hybridization was used to identify specific up- and downregulated genes in gill and mantle tissues after 7-10 and 24 days of exposure. The resulting libraries contain 858 different sequences that potentially represent highly expressed genes in thermally stressed oysters. Expression of 17 genes identified in these libraries was studied using real-time PCR in gills and mantle at different time points over the course of the thermal stress. Differential gene expression levels were much higher in gills than in the mantle, showing that gills are more sensitive to thermal stress. Expression of most transcripts (mainly heat shock proteins and genes involved in cellular homeostasis) showed a high and rapid increase at 3-7 days of exposure, followed by a decrease at 14 days, and a second, less-pronounced increase at 17-24 days. A slow-down in protein synthesis occurred after 24 days of thermal stress.

Pathway switching explains the sharp response characteristic of hypoxia response network

Hypoxia induces the expression of genes that alter metabolism through the hypoxia-inducible factor (HIF). A theoretical model based on differential equations of the hypoxia response network has been previously proposed in which a sharp response to changes in oxygen concentration was observed but not quantitatively explained. That model consisted of reactions involving 23 molecular species among which the concentrations of HIF and oxygen were linked through a complex set of reactions. In this paper, we analyze this previous model using a combination of mathematical tools to draw out the key components of the network and explain quantitatively how they contribute to the sharp oxygen response. We find that the switch-like behavior is due to pathway-switching wherein HIF degrades rapidly under normoxia in one pathway, while the other pathway accumulates HIF to trigger downstream genes under hypoxia. The analytic technique is potentially useful in studying larger biomedical networks.

A complex biomolecular network utilizes different pathways to perform different functions. However, the interactions within the network are typically so complicated that the pathway structure is usually hidden. By some mathematical techniques, the pathways can be identified and possibly decoupled, whereby the insightful details of the network can be exposed. As an example, we study in this paper the hypoxia response network that manifests a dramatic switch-like behavior for certain sets of rate constants: a slight change of the oxygen concentration close to a critical value will lead to distinct reaction patterns. By a technique called extreme pathway analysis, the network is decoupled into three major and some minor pathways. Flux distribution among these pathways can thus be measured by integrating the ordinary differential equations for any given set of rate constants. For the sets of rate constants where the switch-like behavior is observed, we found that such a behavior is due to the switching of flux between two of the three major pathways.

Accelerated search for biomolecular network models to interpret high-throughput experimental data

BACKGROUND

The functions of human cells are carried out by biomolecular networks, which include proteins, genes, and regulatory sites within DNA that encode and control protein expression. Models of biomolecular network structure and dynamics can be inferred from high-throughput measurements of gene and protein expression. We build on our previously developed fuzzy logic method for bridging quantitative and qualitative biological data to address the challenges of noisy, low resolution high-throughput measurements, i.e., from gene expression microarrays. We employ an evolutionary search algorithm to accelerate the search for hypothetical fuzzy biomolecular network models consistent with a biological data set. We also develop a method to estimate the probability of a potential network model fitting a set of data by chance. The resulting metric provides an estimate of both model quality and dataset quality, identifying data that are too noisy to identify meaningful correlations between the measured variables.

RESULTS

Optimal parameters for the evolutionary search were identified based on artificial data, and the algorithm showed scalable and consistent performance for as many as 150 variables. The method was tested on previously published human cell cycle gene expression microarray data sets. The evolutionary search method was found to converge to the results of exhaustive search. The randomized evolutionary search was able to converge on a set of similar best-fitting network models on different training data sets after 30 generations running 30 models per generation. Consistent results were found regardless of which of the published data sets were used to train or verify the quantitative predictions of the best-fitting models for cell cycle gene dynamics.

CONCLUSION

Our results demonstrate the capability of scalable evolutionary search for fuzzy network models to address the problem of inferring models based on complex, noisy biomolecular data sets. This approach yields multiple alternative models that are consistent with the data, yielding a constrained set of hypotheses that can be used to optimally design subsequent experiments.

A computational model of intracellular oxygen sensing by hypoxia-inducible factor HIF1 alpha

Hypoxia-inducible factor-1, HIF1, transcriptionally activates over 200 genes vital for cell homeostasis and angiogenesis. We developed a computational model to gain a detailed quantitative understanding of how HIF1 acts to sense oxygen and respond to hypoxia. The model consists of kinetic equations describing the intracellular variation of 17 compounds, including HIF1, iron, prolyl hydroxylase, oxygen, ascorbate, 2-oxoglutarate, von Hippel Lindau protein and associated complexes. We tested an existing hypothesis of a switch-like change in HIF1 expression in response to a gradual decrease in O2 concentration. Our model predicts that depending on the molecular environment, such as intracellular iron levels, the hypoxic response varies considerably. We show HIF1-activated cellular responses can be divided into two categories: a steep, switch-like response to O2 and a gradual one. Discovery of this dual response prompted comparison of two therapeutic strategies, ascorbate and iron supplementation, and prolyl hydroxylase targeting, to predict under what microenvironments either effectively increases HIF1alpha hydroxylation. Results provide crucial insight into the effects of iron and prolyl hydroxylase on oxygen sensing. The model advances quantitative molecular level understanding of HIF1 pathways--an endeavor that will help elucidate the diverse responses to hypoxia found in cancer, ischemia and exercise.

Depicting combinatorial complexity with the molecular interaction map notation

To help us understand how bioregulatory networks operate, we need a standard notation for diagrams analogous to electronic circuit diagrams. Such diagrams must surmount the difficulties posed by complex patterns of protein modifications and multiprotein complexes. To meet that challenge, we have designed the molecular interaction map (MIM) notation (http://discover.nci.nih.gov/mim/). Here we show the advantages of the MIM notation for three important types of diagrams: (1) explicit diagrams that define specific pathway models for computer simulation; (2) heuristic maps that organize the available information about molecular interactions and encompass the possible processes or pathways; and (3) diagrams of combinatorially complex models. We focus on signaling from the epidermal growth factor receptor family (EGFR, ErbB), a network that reflects the major challenges of representing in a compact manner the combinatorial complexity of multimolecular complexes. By comparing MIMs with other diagrams of this network that have recently been published, we show the utility of the MIM notation. These comparisons may help cell and systems biologists adopt a graphical language that is unambiguous and generally understood.

Chk2 molecular interaction map and rationale for Chk2 inhibitors

To organize the rapidly accumulating information on bioregulatory networks related to the histone gamma-H2AX-ATM-Chk2-p53-Mdm2 pathways in concise and unambiguous diagrams, we used the molecular interaction map notation (http://discover.nci.nih.gov/min). Molecular interaction maps are particularly useful for networks that include protein-protein binding and posttranslational modifications (e.g., phosphorylation). Both are important for nearly all of the proteins involved in DNA double-strand break signaling. Visualizing the regulatory circuits underlying cellular signaling may help identify key regulatory reactions and defects that can serve as targets for anticancer drugs.

Molecular interaction maps of bioregulatory networks: a general rubric for systems biology

A standard for bioregulatory network diagrams is urgently needed in the same way that circuit diagrams are needed in electronics. Several graphical notations have been proposed, but none has become standard. We have prepared many detailed bioregulatory network diagrams using the molecular interaction map (MIM) notation, and we now feel confident that it is suitable as a standard. Here, we describe the MIM notation formally and discuss its merits relative to alternative proposals. We show by simple examples how to denote all of the molecular interactions commonly found in bioregulatory networks. There are two forms of MIM diagrams. "Heuristic" MIMs present the repertoire of interactions possible for molecules that are colocalized in time and place. "Explicit" MIMs define particular models (derived from heuristic MIMs) for computer simulation. We show also how pathways or processes can be highlighted on a canonical heuristic MIM. Drawing a MIM diagram, adhering to the rules of notation, imposes a logical discipline that sharpens one's understanding of the structure and function of a network.

Molecular interaction map of the p53 and Mdm2 logic elements, which control the Off-On switch of p53 in response to DNA damage

The molecular network that controls responses to genotoxic stress is centered at p53 and Mdm2. Recent findings have shown this network to be more complex than previously envisioned. Using a notation specifically designed for circuit diagram-like representations of bioregulatory networks, we have prepared an updated molecular interaction map of the immediate connections of p53 and Mdm2, which are described as logic elements of the network. We use the map as the basis for a comprehensive review of current concepts of signal processing by these logic elements (an interactive version of the maps-eMIMs can be examined at ). We also used molecular interaction maps to propose a p53 Off-On switch in response to DNA damage.