The core control system of intracellular iron homeostasis: a mathematical model

Joint inference of physiological network and survival analysis identifies factors associated with aging rate

We describe methodology for joint reconstruction of physiological-survival networks from observational data capable of identifying key survival-associated variables, inferring a minimal physiological network structure, and bridging this network to the Gompertzian survival layer. Using synthetic network structures, we show that the method is capable of identifying aging variables in cohorts as small as 5,000 participants. Applying the methodology to the observational human cohort, we find that interleukin-6, vascular calcification, and red-blood distribution width are strong predictors of baseline fitness. More important, we find that red blood cell counts, kidney function, and phosphate level are directly linked to the Gompertzian aging rate. Our model therefore enables discovery of processes directly linked to the aging rate of our species. We further show that this epidemiological framework can be applied as a causal inference engine to simulate the effects of interventions on physiology and longevity.

Cyclic attractors of nonexpanding q-ary networks

Discrete dynamical systems in which model components take on categorical values have been successfully applied to biological networks to study their global dynamic behavior. Boolean models in particular have been used extensively. However, multi-state models have also emerged as effective computational tools for the analysis of complex mechanisms underlying biological networks. Models in which variables assume more than two discrete states provide greater resolution, but this scheme introduces discontinuities. In particular, variables can increase or decrease by more than one unit in one time step. This can be corrected, without changing fixed points of the system, by applying an additional rule to each local activation function. On the other hand, if one is interested in cyclic attractors of their system, then this rule can potentially introduce new cyclic attractors that were not observed previously. This article makes some advancements in understanding the state space dynamics of multi-state network models with synchronous, sequential, or block-sequential update schedules and establishes conditions under which no new cyclic attractors are added to networks when the additional rule is applied. Our analytical results have the potential to be incorporated into modeling software and aid researchers in their analyses of biological multi-state networks.

A computational model for prediction of ferritin and haemoglobin levels in blood donors

Blood donors are at risk of iron deficiency anaemia. While this risk is decreased through ferritin-based deferral, ideally ferritin monitoring should also aid in optimising donation frequencies. We extended an existing model of haemoglobin (Hb) synthesis with iron homeostasis and validated the model on a cohort of 300 new donors whose ferritin levels were measured from stored blood samples collected over a 2-year period. We then used the donor's gender, body weight, height, and baseline Hb and ferritin levels to predict subsequent Hb and ferritin levels. The prediction error was within measurement variability in 88% of Hb level predictions and 64% of ferritin level predictions. A sensitivity analysis of the model revealed that baseline ferritin level was the most important in predicting future ferritin levels. Finally, we used the model to calculate the annual donation frequency at which donors would keep their ferritin level >15 ng/ml when measured after donating for 2 years. The mean annual donation frequency would then be 1.9 for women and 4.1 for men. The computational model, requiring baseline values only, can predict future Hb and ferritin levels remarkably well. This enables determination of optimal donation frequencies for individual donors at the start of their donation career.

A mathematical model of iron import and trafficking in wild-type and Mrs3/4ΔΔ yeast cells

Background

Iron plays crucial roles in the metabolism of eukaryotic cells. Much iron is trafficked into mitochondria where it is used for iron-sulfur cluster assembly and heme biosynthesis. A yeast strain in which Mrs3/4, the high-affinity iron importers on the mitochondrial inner membrane, are deleted exhibits a slow-growth phenotype when grown under iron-deficient conditions. However, these cells grow at WT rates under iron-sufficient conditions. The object of this study was to develop a mathematical model that could explain this recovery on the molecular level.

Results

A multi-tiered strategy was used to solve an ordinary-differential-equations-based mathematical model of iron import, trafficking, and regulation in growing Saccharomyces cerevisiae cells. At the simplest level of modeling, all iron in the cell was presumed to be a single species and the cell was considered to be a single homogeneous volume. Optimized parameters associated with the rate of iron import and the rate of dilution due to cell growth were determined. At the next level of complexity, the cell was divided into three regions, including cytosol, mitochondria, and vacuoles, each of which was presumed to contain a single form of iron. Optimized parameters associated with import into these regions were determined. At the final level of complexity, nine components were assumed within the same three cellular regions. Parameters obtained at simpler levels of complexity were used to help solve the more complex versions of the model; this was advantageous because the data used for solving the simpler model variants were more reliable and complete relative to those required for the more complex variants. The optimized full-complexity model simulated the observed phenotype of WT and Mrs3/4ΔΔ cells with acceptable fidelity, and the model exhibited some predictive power.

Conclusions

The developed model highlights the importance of an Fe^II mitochondrial pool and the necessary exclusion of O₂ in the mitochondrial matrix for eukaryotic iron-sulfur cluster metabolism. Similar multi-tiered strategies could be used for any micronutrient in which concentrations and metabolic forms have been determined in different organelles within a growing eukaryotic cell.

Electronic supplementary material

The online version of this article (10.1186/s12918-019-0702-2) contains supplementary material, which is available to authorized users.

No effects without causes: the Iron Dysregulation and Dormant Microbes hypothesis for chronic, inflammatory diseases

Since the successful conquest of many acute, communicable (infectious) diseases through the use of vaccines and antibiotics, the currently most prevalent diseases are chronic and progressive in nature, and are all accompanied by inflammation. These diseases include neurodegenerative (e.g. Alzheimer's, Parkinson's), vascular (e.g. atherosclerosis, pre-eclampsia, type 2 diabetes) and autoimmune (e.g. rheumatoid arthritis and multiple sclerosis) diseases that may appear to have little in common. In fact they all share significant features, in particular chronic inflammation and its attendant inflammatory cytokines. Such effects do not happen without underlying and initially 'external' causes, and it is of interest to seek these causes. Taking a systems approach, we argue that these causes include (i) stress-induced iron dysregulation, and (ii) its ability to awaken dormant, non-replicating microbes with which the host has become infected. Other external causes may be dietary. Such microbes are capable of shedding small, but functionally significant amounts of highly inflammagenic molecules such as lipopolysaccharide and lipoteichoic acid. Sequelae include significant coagulopathies, not least the recently discovered amyloidogenic clotting of blood, leading to cell death and the release of further inflammagens. The extensive evidence discussed here implies, as was found with ulcers, that almost all chronic, infectious diseases do in fact harbour a microbial component. What differs is simply the microbes and the anatomical location from and at which they exert damage. This analysis offers novel avenues for diagnosis and treatment.

Trace Elements and Healthcare: A Bioinformatics Perspective

Biological trace elements are essential for human health. Imbalance in trace element metabolism and homeostasis may play an important role in a variety of diseases and disorders. While the majority of previous researches focused on experimental verification of genes involved in trace element metabolism and those encoding trace element-dependent proteins, bioinformatics study on trace elements is relatively rare and still at the starting stage. This chapter offers an overview of recent progress in bioinformatics analyses of trace element utilization, metabolism, and function, especially comparative genomics of several important metals. The relationship between individual elements and several diseases based on recent large-scale systematic studies such as genome-wide association studies and case-control studies is discussed. Lastly, developments of ionomics and its recent application in human health are also introduced.

Activated Oncogenic Pathway Modifies Iron Network in Breast Epithelial Cells: A Dynamic Modeling Perspective

Dysregulation of iron metabolism in cancer is well documented and it has been suggested that there is interdependence between excess iron and increased cancer incidence and progression. In an effort to better understand the linkages between iron metabolism and breast cancer, a predictive mathematical model of an expanded iron homeostasis pathway was constructed that includes species involved in iron utilization, oxidative stress response and oncogenic pathways. The model leads to three predictions. The first is that overexpression of iron regulatory protein 2 (IRP2) recapitulates many aspects of the alterations in free iron and iron-related proteins in cancer cells without affecting the oxidative stress response or the oncogenic pathways included in the model. This prediction was validated by experimentation. The second prediction is that iron-related proteins are dramatically affected by mitochondrial ferritin overexpression. This prediction was validated by results in the pertinent literature not used for model construction. The third prediction is that oncogenic Ras pathways contribute to altered iron homeostasis in cancer cells. This prediction was validated by a combination of simulation experiments of Ras overexpression and catalase knockout in conjunction with the literature. The model successfully captures key aspects of iron metabolism in breast cancer cells and provides a framework upon which more detailed models can be built.

Iron is required for cellular metabolism and growth, but can be toxic due to its ability to cause high oxidative stress and consequently DNA damage. To prevent damage, all organisms that require iron have developed mechanisms to tightly control iron levels. Dysregulation of iron metabolism is detrimental and can contribute to a wide range of diseases, including cancer. This paper presents a predictive mathematical model of iron regulation linked to iron utilization, oxidative stress, and the oncogenic response specific to normal breast epithelial cells. The model uses a discrete modeling framework to generate novel biological hypotheses for an investigation of how normal breast cells become malignant cells, capturing a breast cancer phenotype of iron homeostasis through overexpression and knockout simulations. The new biology discovered is (1) IRP2 overexpression alters the iron homeostasis pathway in breast cells, without affecting the oxidative stress response or oncogenic pathways, (2) an activated oncogenic pathway disrupts iron regulation in breast cancer cells.

Analysis of a dynamic model of guard cell signaling reveals the stability of signal propagation

BACKGROUND

Analyzing the long-term behaviors (attractors) of dynamic models of biological systems can provide valuable insight into biological phenotypes and their stability. In this paper we identify the allowed long-term behaviors of a multi-level, 70-node dynamic model of the stomatal opening process in plants.

RESULTS

We start by reducing the model's huge state space. We first reduce unregulated nodes and simple mediator nodes, then simplify the regulatory functions of selected nodes while keeping the model consistent with experimental observations. We perform attractor analysis on the resulting 32-node reduced model by two methods: 1. converting it into a Boolean model, then applying two attractor-finding algorithms; 2. theoretical analysis of the regulatory functions. We further demonstrate the robustness of signal propagation by showing that a large percentage of single-node knockouts does not affect the stomatal opening level.

CONCLUSIONS

Combining both methods with analysis of perturbation scenarios, we conclude that all nodes except two in the reduced model have a single attractor; and only two nodes can admit oscillations. The multistability or oscillations of these four nodes do not affect the stomatal opening level in any situation. This conclusion applies to the original model as well in all the biologically meaningful cases. In addition, the stomatal opening level is resilient against single-node knockouts. Thus, we conclude that the complex structure of this signal transduction network provides multiple information propagation pathways while not allowing extensive multistability or oscillations, resulting in robust signal propagation. Our innovative combination of methods offers a promising way to analyze multi-level models.

A Dormant Microbial Component in the Development of Preeclampsia

Preeclampsia (PE) is a complex, multisystem disorder that remains a leading cause of morbidity and mortality in pregnancy. Four main classes of dysregulation accompany PE and are widely considered to contribute to its severity. These are abnormal trophoblast invasion of the placenta, anti-angiogenic responses, oxidative stress, and inflammation. What is lacking, however, is an explanation of how these themselves are caused. We here develop the unifying idea, and the considerable evidence for it, that the originating cause of PE (and of the four classes of dysregulation) is, in fact, microbial infection, that most such microbes are dormant and hence resist detection by conventional (replication-dependent) microbiology, and that by occasional resuscitation and growth it is they that are responsible for all the observable sequelae, including the continuing, chronic inflammation. In particular, bacterial products such as lipopolysaccharide (LPS), also known as endotoxin, are well known as highly inflammagenic and stimulate an innate (and possibly trained) immune response that exacerbates the inflammation further. The known need of microbes for free iron can explain the iron dysregulation that accompanies PE. We describe the main routes of infection (gut, oral, and urinary tract infection) and the regularly observed presence of microbes in placental and other tissues in PE. Every known proteomic biomarker of "preeclampsia" that we assessed has, in fact, also been shown to be raised in response to infection. An infectious component to PE fulfills the Bradford Hill criteria for ascribing a disease to an environmental cause and suggests a number of treatments, some of which have, in fact, been shown to be successful. PE was classically referred to as endotoxemia or toxemia of pregnancy, and it is ironic that it seems that LPS and other microbial endotoxins really are involved. Overall, the recognition of an infectious component in the etiology of PE mirrors that for ulcers and other diseases that were previously considered to lack one.

Metabolomics and systems pharmacology: why and how to model the human metabolic network for drug discovery

Metabolism represents the 'sharp end' of systems biology, because changes in metabolite concentrations are necessarily amplified relative to changes in the transcriptome, proteome and enzyme activities, which can be modulated by drugs. To understand such behaviour, we therefore need (and increasingly have) reliable consensus (community) models of the human metabolic network that include the important transporters. Small molecule 'drug' transporters are in fact metabolite transporters, because drugs bear structural similarities to metabolites known from the network reconstructions and from measurements of the metabolome. Recon2 represents the present state-of-the-art human metabolic network reconstruction; it can predict inter alia: (i) the effects of inborn errors of metabolism; (ii) which metabolites are exometabolites, and (iii) how metabolism varies between tissues and cellular compartments. However, even these qualitative network models are not yet complete. As our understanding improves so do we recognise more clearly the need for a systems (poly)pharmacology.

A systems biology approach to iron metabolism

Iron is critical to the survival of almost all living organisms. However, inappropriately low or high levels of iron are detrimental and contribute to a wide range of diseases. Recent advances in the study of iron metabolism have revealed multiple intricate pathways that are essential to the maintenance of iron homeostasis. Further, iron regulation involves processes at several scales, ranging from the subcellular to the organismal. This complexity makes a systems biology approach crucial, with its enabling technology of computational models based on a mathematical description of regulatory systems. Systems biology may represent a new strategy for understanding imbalances in iron metabolism and their underlying causes.

A computational model of liver iron metabolism

Iron is essential for all known life due to its redox properties; however, these same properties can also lead to its toxicity in overload through the production of reactive oxygen species. Robust systemic and cellular control are required to maintain safe levels of iron, and the liver seems to be where this regulation is mainly located. Iron misregulation is implicated in many diseases, and as our understanding of iron metabolism improves, the list of iron-related disorders grows. Recent developments have resulted in greater knowledge of the fate of iron in the body and have led to a detailed map of its metabolism; however, a quantitative understanding at the systems level of how its components interact to produce tight regulation remains elusive. A mechanistic computational model of human liver iron metabolism, which includes the core regulatory components, is presented here. It was constructed based on known mechanisms of regulation and on their kinetic properties, obtained from several publications. The model was then quantitatively validated by comparing its results with previously published physiological data, and it is able to reproduce multiple experimental findings. A time course simulation following an oral dose of iron was compared to a clinical time course study and the simulation was found to recreate the dynamics and time scale of the systems response to iron challenge. A disease state simulation of haemochromatosis was created by altering a single reaction parameter that mimics a human haemochromatosis gene (HFE) mutation. The simulation provides a quantitative understanding of the liver iron overload that arises in this disease. This model supports and supplements understanding of the role of the liver as an iron sensor and provides a framework for further modelling, including simulations to identify valuable drug targets and design of experiments to improve further our knowledge of this system.

Iron is an essential nutrient required for healthy life but, in excess, is the cause of debilitating and even fatal conditions. The most common genetic disorder in humans caused by a mutation, haemochromatosis, results in an iron overload in the liver. Indeed, the liver plays a central role in the regulation of iron. Recently, an increasing amount of detail has been discovered about molecules related to iron metabolism, but an understanding of how they work together and regulate iron levels (in healthy people) or fail to do it (in disease) is still missing. We present a mathematical model of the regulation of liver iron metabolism that provides explanations of its dynamics and allows further hypotheses to be formulated and later tested in experiments. Importantly, the model reproduces accurately the healthy liver iron homeostasis and simulates haemochromatosis, showing how the causative mutation leads to iron overload. We investigate how best to control iron regulation and identified reactions that can be targets of new medicines to treat iron overload. The model provides a virtual laboratory for investigating iron metabolism and improves understanding of the method by which the liver senses and controls iron levels.

An analysis of a 'community-driven' reconstruction of the human metabolic network

Following a strategy similar to that used in baker's yeast (Herrgård et al. Nat Biotechnol 26:1155-1160, 2008). A consensus yeast metabolic network obtained from a community approach to systems biology (Herrgård et al. 2008; Dobson et al. BMC Syst Biol 4:145, 2010). Further developments towards a genome-scale metabolic model of yeast (Dobson et al. 2010; Heavner et al. BMC Syst Biol 6:55, 2012). Yeast 5-an expanded reconstruction of the Saccharomyces cerevisiae metabolic network (Heavner et al. 2012) and in Salmonella typhimurium (Thiele et al. BMC Syst Biol 5:8, 2011). A community effort towards a knowledge-base and mathematical model of the human pathogen Salmonellatyphimurium LT2 (Thiele et al. 2011), a recent paper (Thiele et al. Nat Biotechnol 31:419-425, 2013). A community-driven global reconstruction of human metabolism (Thiele et al. 2013) described a much improved 'community consensus' reconstruction of the human metabolic network, called Recon 2, and the authors (that include the present ones) have made it freely available via a database at http://humanmetabolism.org/ and in SBML format at Biomodels (http://identifiers.org/biomodels.db/MODEL1109130000). This short analysis summarises the main findings, and suggests some approaches that will be able to exploit the availability of this model to advantage.

Application of circuit simulation method for differential modeling of TIM-2 iron uptake and metabolism in mouse kidney cells

Circuit simulation is a powerful methodology to generate differential mathematical models. Due to its highly accurate modeling capability, circuit simulation can be used to investigate interactions between the parts and processes of a cellular system. Circuit simulation has become a core technology for the field of electrical engineering, but its application in biology has not yet been fully realized. As a case study for evaluating the more advanced features of a circuit simulation tool called Advanced Design System (ADS), we collected and modeled laboratory data for iron metabolism in mouse kidney cells for a H ferritin (HFt) receptor, T cell immunoglobulin and mucin domain-2 (TIM-2). The internal controlling parameters of TIM-2 associated iron metabolism were extracted and the ratios of iron movement among cellular compartments were quantified by ADS. The differential model processed by circuit simulation demonstrated a capability to identify variables and predict outcomes that could not be readily measured by in vitro experiments. For example, an initial rate of uptake of iron-loaded HFt (Fe-HFt) was 2.17 pmol per million cells. TIM-2 binding probability with Fe-HFt was 16.6%. An average of 8.5 min was required for the complex of TIM-2 and Fe-HFt to form an endosome. The endosome containing HFt lasted roughly 2 h. At the end of endocytosis, about 28% HFt remained intact and the rest was degraded. Iron released from degraded HFt was in the labile iron pool (LIP) and stimulated the generation of endogenous HFt for new storage. Both experimental data and the model showed that TIM-2 was not involved in the process of iron export. The extracted internal controlling parameters successfully captured the complexity of TIM-2 pathway and the use of circuit simulation-based modeling across a wider range of cellular systems is the next step for validating the significance and utility of this method.

Iron and cancer: more ore to be mined

Iron is an essential nutrient that facilitates cell proliferation and growth. However, iron also has the capacity to engage in redox cycling and free radical formation. Therefore, iron can contribute to both tumour initiation and tumour growth; recent work has also shown that iron has a role in the tumour microenvironment and in metastasis. Pathways of iron acquisition, efflux, storage and regulation are all perturbed in cancer, suggesting that reprogramming of iron metabolism is a central aspect of tumour cell survival. Signalling through hypoxia-inducible factor (HIF) and WNT pathways may contribute to altered iron metabolism in cancer. Targeting iron metabolic pathways may provide new tools for cancer prognosis and therapy.

Cellular iron metabolism in prognosis and therapy of breast cancer

Despite many recent advances, breast cancer remains a clinical challenge. Current issues include improving prognostic evaluation and increasing therapeutic options for women whose tumors are refractory to current frontline therapies. Iron metabolism is frequently disrupted in breast cancer, and may offer an opportunity to address these challenges. Iron enhances breast tumor initiation, growth and metastases. Iron may contribute to breast tumor initiation by promoting redox cycling of estrogen metabolites. Up-regulation of iron import and down-regulation of iron export may enable breast cancer cells to acquire and retain excess iron. Alterations in iron metabolism in macrophages and other cells of the tumor microenvironment may also foster breast tumor growth. Expression of iron metabolic genes in breast tumors is predictive of breast cancer prognosis. Iron chelators and other strategies designed to limit iron may have therapeutic value in breast cancer. The dependence of breast cancer on iron presents rich opportunities for improved prognostic evaluation and therapeutic intervention.