SBMLBioModels: B - C

Genome-scale metabolic reconstructions provide a biologically meaningful mechanistic basis for the genotype-phenotype relationship. The global human metabolic network, termed Recon 1, has recently been reconstructed allowing the systems analysis of human metabolic physiology and pathology. Utilizing high-throughput data, Recon 1 has recently been tailored to different cells and tissues, including the liver, kidney, brain, and alveolar macrophage. These models have shown utility in the study of systems medicine. However, no integrated analysis between human tissues has been done.To describe tissue-specific functions, Recon 1 was tailored to describe metabolism in three human cells: adipocytes, hepatocytes, and myocytes. These cell-specific networks were manually curated and validated based on known cellular metabolic functions. To study intercellular interactions, a novel multi-tissue type modeling approach was developed to integrate the metabolic functions for the three cell types, and subsequently used to simulate known integrated metabolic cycles. In addition, the multi-tissue model was used to study diabetes: a pathology with systemic properties. High-throughput data was integrated with the network to determine differential metabolic activity between obese and type II obese gastric bypass patients in a whole-body context.The multi-tissue type modeling approach presented provides a platform to study integrated metabolic states. As more cell and tissue-specific models are released, it is critical to develop a framework in which to study their interdependencies. link: http://identifiers.org/pubmed/22041191

Genome-scale metabolic reconstructions provide a biologically meaningful mechanistic basis for the genotype-phenotype relationship. The global human metabolic network, termed Recon 1, has recently been reconstructed allowing the systems analysis of human metabolic physiology and pathology. Utilizing high-throughput data, Recon 1 has recently been tailored to different cells and tissues, including the liver, kidney, brain, and alveolar macrophage. These models have shown utility in the study of systems medicine. However, no integrated analysis between human tissues has been done.To describe tissue-specific functions, Recon 1 was tailored to describe metabolism in three human cells: adipocytes, hepatocytes, and myocytes. These cell-specific networks were manually curated and validated based on known cellular metabolic functions. To study intercellular interactions, a novel multi-tissue type modeling approach was developed to integrate the metabolic functions for the three cell types, and subsequently used to simulate known integrated metabolic cycles. In addition, the multi-tissue model was used to study diabetes: a pathology with systemic properties. High-throughput data was integrated with the network to determine differential metabolic activity between obese and type II obese gastric bypass patients in a whole-body context.The multi-tissue type modeling approach presented provides a platform to study integrated metabolic states. As more cell and tissue-specific models are released, it is critical to develop a framework in which to study their interdependencies. link: http://identifiers.org/pubmed/22041191

Genome-scale metabolic reconstructions provide a biologically meaningful mechanistic basis for the genotype-phenotype relationship. The global human metabolic network, termed Recon 1, has recently been reconstructed allowing the systems analysis of human metabolic physiology and pathology. Utilizing high-throughput data, Recon 1 has recently been tailored to different cells and tissues, including the liver, kidney, brain, and alveolar macrophage. These models have shown utility in the study of systems medicine. However, no integrated analysis between human tissues has been done.To describe tissue-specific functions, Recon 1 was tailored to describe metabolism in three human cells: adipocytes, hepatocytes, and myocytes. These cell-specific networks were manually curated and validated based on known cellular metabolic functions. To study intercellular interactions, a novel multi-tissue type modeling approach was developed to integrate the metabolic functions for the three cell types, and subsequently used to simulate known integrated metabolic cycles. In addition, the multi-tissue model was used to study diabetes: a pathology with systemic properties. High-throughput data was integrated with the network to determine differential metabolic activity between obese and type II obese gastric bypass patients in a whole-body context.The multi-tissue type modeling approach presented provides a platform to study integrated metabolic states. As more cell and tissue-specific models are released, it is critical to develop a framework in which to study their interdependencies. link: http://identifiers.org/pubmed/22041191

Genome-scale metabolic reconstructions provide a biologically meaningful mechanistic basis for the genotype-phenotype relationship. The global human metabolic network, termed Recon 1, has recently been reconstructed allowing the systems analysis of human metabolic physiology and pathology. Utilizing high-throughput data, Recon 1 has recently been tailored to different cells and tissues, including the liver, kidney, brain, and alveolar macrophage. These models have shown utility in the study of systems medicine. However, no integrated analysis between human tissues has been done.To describe tissue-specific functions, Recon 1 was tailored to describe metabolism in three human cells: adipocytes, hepatocytes, and myocytes. These cell-specific networks were manually curated and validated based on known cellular metabolic functions. To study intercellular interactions, a novel multi-tissue type modeling approach was developed to integrate the metabolic functions for the three cell types, and subsequently used to simulate known integrated metabolic cycles. In addition, the multi-tissue model was used to study diabetes: a pathology with systemic properties. High-throughput data was integrated with the network to determine differential metabolic activity between obese and type II obese gastric bypass patients in a whole-body context.The multi-tissue type modeling approach presented provides a platform to study integrated metabolic states. As more cell and tissue-specific models are released, it is critical to develop a framework in which to study their interdependencies. link: http://identifiers.org/pubmed/22041191

In order to choose optimal personalized anticancer treatments, transcriptomic data should be analyzed within the frame of biological networks. The best known human biological network (in terms of the interactions between its different components) is metabolism. Cancer cells have been known to have specific metabolic features for a long time and currently there is a growing interest in characterizing new cancer specific metabolic hallmarks. In this article it is presented a method to find personalized therapeutic windows using RNA-seq data and Genome Scale Metabolic Models. This method is implemented in the python library, pyTARG. Our predictions showed that the most anticancer selective (affecting 27 out of 34 considered cancer cell lines and only 1 out of 6 healthy mesenchymal stem cell lines) single metabolic reactions are those involved in cholesterol biosynthesis. Excluding cholesterol biosynthesis, all the considered cell lines can be selectively affected by targeting different combinations (from 1 to 5 reactions) of only 18 metabolic reactions, which suggests that a small subset of drugs or siRNAs combined in patient specific manners could be at the core of metabolism based personalized treatments. link: http://identifiers.org/doi/10.18632/oncotarget.24805

Intracellular Ca(2+) oscillations are commonly observed in a large number of cell types in response to stimulation by an extracellular agonist. In most cell types the mechanism of regular spiking is well understood and models based on Ca(2+)-induced Ca(2+) release (CICR) can account for many experimental observations. However, cells do not always exhibit simple Ca(2+) oscillations. In response to given agonists, some cells show more complex behaviour in the form of bursting, i.e. trains of Ca(2+) spikes separated by silent phases. Here we develop several theoretical models, based on physiologically plausible assumptions, that could account for complex intracellular Ca(2+) oscillations. The models are all based on one- or two-pool models based on CICR. We extend these models by (i) considering the inhibition of the Ca(2+)-release channel on a unique intracellular store at high cytosolic Ca(2+) concentrations, (ii) taking into account the Ca(2+)-activated degradation of inositol 1,4,5-trisphosphate (IP(3)), or (iii) considering explicity the evolution of the Ca(2+) concentration in two different pools, one sensitive and the other one insensitive to IP(3). Besides simple periodic oscillations, these three models can all account for more complex oscillatory behaviour in the form of bursting. Moreover, the model that takes the kinetics of IP(3) into account shows chaotic behaviour. link: http://identifiers.org/pubmed/17029867

Intracellular Ca(2+) oscillations are commonly observed in a large number of cell types in response to stimulation by an extracellular agonist. In most cell types the mechanism of regular spiking is well understood and models based on Ca(2+)-induced Ca(2+) release (CICR) can account for many experimental observations. However, cells do not always exhibit simple Ca(2+) oscillations. In response to given agonists, some cells show more complex behaviour in the form of bursting, i.e. trains of Ca(2+) spikes separated by silent phases. Here we develop several theoretical models, based on physiologically plausible assumptions, that could account for complex intracellular Ca(2+) oscillations. The models are all based on one- or two-pool models based on CICR. We extend these models by (i) considering the inhibition of the Ca(2+)-release channel on a unique intracellular store at high cytosolic Ca(2+) concentrations, (ii) taking into account the Ca(2+)-activated degradation of inositol 1,4,5-trisphosphate (IP(3)), or (iii) considering explicity the evolution of the Ca(2+) concentration in two different pools, one sensitive and the other one insensitive to IP(3). Besides simple periodic oscillations, these three models can all account for more complex oscillatory behaviour in the form of bursting. Moreover, the model that takes the kinetics of IP(3) into account shows chaotic behaviour. link: http://identifiers.org/pubmed/17029867

Intracellular Ca(2+) oscillations are commonly observed in a large number of cell types in response to stimulation by an extracellular agonist. In most cell types the mechanism of regular spiking is well understood and models based on Ca(2+)-induced Ca(2+) release (CICR) can account for many experimental observations. However, cells do not always exhibit simple Ca(2+) oscillations. In response to given agonists, some cells show more complex behaviour in the form of bursting, i.e. trains of Ca(2+) spikes separated by silent phases. Here we develop several theoretical models, based on physiologically plausible assumptions, that could account for complex intracellular Ca(2+) oscillations. The models are all based on one- or two-pool models based on CICR. We extend these models by (i) considering the inhibition of the Ca(2+)-release channel on a unique intracellular store at high cytosolic Ca(2+) concentrations, (ii) taking into account the Ca(2+)-activated degradation of inositol 1,4,5-trisphosphate (IP(3)), or (iii) considering explicity the evolution of the Ca(2+) concentration in two different pools, one sensitive and the other one insensitive to IP(3). Besides simple periodic oscillations, these three models can all account for more complex oscillatory behaviour in the form of bursting. Moreover, the model that takes the kinetics of IP(3) into account shows chaotic behaviour. link: http://identifiers.org/pubmed/17029867

Crosstalk mechanisms have not been studied as thoroughly as individual signaling pathways. We exploit experimental and computational approaches to reveal how a concordant interplay between the insulin and epidermal growth factor (EGF) signaling networks can potentiate mitogenic signaling. In HEK293 cells, insulin is a poor activator of the Ras/ERK (extracellular signal-regulated kinase) cascade, yet it enhances ERK activation by low EGF doses. We find that major crosstalk mechanisms that amplify ERK signaling are localized upstream of Ras and at the Ras/Raf level. Computational modeling unveils how critical network nodes, the adaptor proteins GAB1 and insulin receptor substrate (IRS), Src kinase, and phosphatase SHP2, convert insulin-induced increase in the phosphatidylinositol-3,4,5-triphosphate (PIP(3)) concentration into enhanced Ras/ERK activity. The model predicts and experiments confirm that insulin-induced amplification of mitogenic signaling is abolished by disrupting PIP(3)-mediated positive feedback via GAB1 and IRS. We demonstrate that GAB1 behaves as a non-linear amplifier of mitogenic responses and insulin endows EGF signaling with robustness to GAB1 suppression. Our results show the feasibility of using computational models to identify key target combinations and predict complex cellular responses to a mixture of external cues. link: http://identifiers.org/pubmed/19357636

Heterotrimeric G protein signaling is regulated by signaling modules composed of heterotrimeric G proteins, active G protein-coupled receptors (Rs), which activate G proteins, and GTPase-activating proteins (GAPs), which deactivate G proteins. We term these modules GTPase-cycle modules. The local concentrations of these proteins are spatially regulated between plasma membrane microdomains and between the plasma membrane and cytosol, but no data or models are available that quantitatively explain the effect of such regulation on signaling. We present a computational model of the GTPase-cycle module that predicts that the interplay of local G protein, R, and GAP concentrations gives rise to 16 distinct signaling regimes and numerous intermediate signaling phenomena. The regimes suggest alternative modes of the GTPase-cycle module that occur based on defined local concentrations of the component proteins. In one mode, signaling occurs while G protein and receptor are unclustered and GAP eliminates signaling; in another, G protein and receptor are clustered and GAP can rapidly modulate signaling but does not eliminate it. Experimental data from multiple GTPase-cycle modules is interpreted in light of these predictions. The latter mode explains previously paradoxical data in which GAP does not alter maximal current amplitude of G protein-activated ion channels, but hastens signaling. The predictions indicate how variations in local concentrations of the component proteins create GTPase-cycle modules with distinctive phenotypes. They provide a quantitative framework for investigating how regulation of local concentrations of components of the GTPase-cycle module affects signaling. link: http://identifiers.org/pubmed/15520372

Streptomyces are filamentous soil bacteria that produce more than half of the known microbial antibiotics. We present the first genome-scale metabolic model of a representative of this group–Streptomyces coelicolor A3(2). The metabolism reconstruction was based on annotated genes, physiological and biochemical information. The stoichiometric model includes 819 biochemical conversions and 152 transport reactions, accounting for a total of 971 reactions. Of the reactions in the network, 700 are unique, while the rest are iso-reactions. The network comprises 500 metabolites. A total of 711 open reading frames (ORFs) were included in the model, which corresponds to 13% of the ORFs with assigned function in the S. coelicolor A3(2) genome. In a comparative analysis with the Streptomyces avermitilis genome, we showed that the metabolic genes are highly conserved between these species and therefore the model is suitable for use with other Streptomycetes. Flux balance analysis was applied for studies of the reconstructed metabolic network and to assess its metabolic capabilities for growth and polyketides production. The model predictions of wild-type and mutants' growth on different carbon and nitrogen sources agreed with the experimental data in most cases. We estimated the impact of each reaction knockout on the growth of the in silico strain on 62 carbon sources and two nitrogen sources, thereby identifying the "core" of the essential reactions. We also illustrated how reconstruction of a metabolic network at the genome level can be used to fill gaps in genome annotation. link: http://identifiers.org/pubmed/15930493

We consider a three-state model comprising tumor cells, effector cells, and tumor-detecting cells under the influence of noises. It is demonstrated that inevitable stochastic forces existing in all three cell species are able to suppress tumor cell growth completely. Whereas the deterministic model does not reveal a stable tumor-free state, the auto-correlated noise combined with cross-correlation functions can either lead to tumor-dormant states, tumor progression, as well as to an elimination of tumor cells. The auto-correlation function exhibits a finite correlation time τ, while the cross-correlation functions shows a white-noise behavior. The evolution of each of the three kinds of cells leads to a multiplicative noise coupling. The model is investigated by means of a multivariate Fokker-Planck equation for small τ. The different behavior of the system is, above all, determined by the variation of the correlation time and the strength of the cross-correlation between tumor and tumor-detecting cells. The theoretical model is based on a biological background discussed in detail, and the results are tested using realistic parameters from experimental observations. link: http://identifiers.org/pubmed/21929038

Drug resistance (DR) is a phenomenon characterized by the tolerance of a disease to pharmaceutical treatment. In cancer patients, DR is one of the main challenges that limit the therapeutic potential of the existing treatments. Therefore, overcoming DR by restoring the sensitivity of cancer cells would be greatly beneficial. In this context, mathematical modeling can be used to provide novel therapeutic strategies that maximize the efficiency of anti-cancer agents and potentially overcome DR. In this paper, we present a new multiscale model devoted to the interaction of potential treatments with multiple myeloma (MM) development. In this model, MM cells are represented as individual objects that move, divide, and die by apoptosis. The fate of each cell depends on intracellular and extracellular regulation, as well as the administered treatment. The model is used to explore the combined effects of a tyrosine-kinase inhibitor (TKI) with a pentose phosphate pathway (PPP) inhibitor. We use numerical simulations to tailor effective and safe treatment regimens that may eradicate the MM tumors. The model suggests that an interval for the daily dose of the PPP inhibitor can maximize the responsiveness of MM cells to the treatment with TKIs. Then, it demonstrates that the combination of high-dose pulsatile TKI treatment with high-dose daily PPP inhibitor therapy can potentially eradicate the tumor.The predictions of numerical simulations using such a model can be considered as testable hypotheses in future pre-clinical experiments and clinical studies. link: http://identifiers.org/pubmed/31809782

Brands2002 - Monosaccharide-casein systems

A kinetic model of the Maillard reaction occurring in heated monosaccharide-casein system.

This model is described in the article: Kinetic modeling of reactions in heated monosaccharide-casein systems., Brands CM, van Boekel MA,Journal of Agricultural and Food Chemistry. 2002, 50(23):6725-6739

Abstract: In the present study, a kinetic model of the Maillard reaction occurring in heated monosaccharide-casein systems was proposed. Its parameters, the reaction rate constants, were estimated via multiresponse modeling. The determinant criterion was used as the statistical fit criterion instead of the familiar least squares to avoid statistical problems. The kinetic model was extensively tested by varying the reaction conditions. Different sugars (glucose, fructose, galactose, and tagatose) were studied regarding their effect on the reaction kinetics. This study has shown the power of multiresponse modeling for the unraveling of complicated reaction routes as occur in the Maillard reaction. The iterative process of proposing a model, confronting it with experiments, and criticizing the model was passed through four times to arrive at a model that was largely consistent with all results obtained. A striking difference was found between aldose and ketose sugars as suggested by the modeling results: not the ketoses themselves but only their reaction products were found to be reactive in the Maillard reaction.

This model is hosted on BioModels Database and identified by MODEL8177704759.

To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models.

To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedicated to the public domain worldwide. Please refer to CC0 Public Domain Dedication for more information.

Insulin and other hormones control target cells through a network of signal-mediating molecules. Such networks are extremely complex due to multiple feedback loops in combination with redundancy, shared signal mediators, and cross-talk between signal pathways. We present a novel framework that integrates experimental work and mathematical modeling to quantitatively characterize the role and relation between co-existing submechanisms in complex signaling networks. The approach is independent of knowing or uniquely estimating model parameters because it only relies on (i) rejections and (ii) core predictions (uniquely identified properties in unidentifiable models). The power of our approach is demonstrated through numerous iterations between experiments, model-based data analyses, and theoretical predictions to characterize the relative role of co-existing feedbacks governing insulin signaling. We examined phosphorylation of the insulin receptor and insulin receptor substrate-1 and endocytosis of the receptor in response to various different experimental perturbations in primary human adipocytes. The analysis revealed that receptor endocytosis is necessary for two identified feedback mechanisms involving mass and information transfer, respectively. Experimental findings indicate that interfering with the feedback may substantially increase overall signaling strength, suggesting novel therapeutic targets for insulin resistance and type 2 diabetes. Because the central observations are present in other signaling networks, our results may indicate a general mechanism in hormonal control. link: http://identifiers.org/pubmed/20421297

Because understanding of the inventory, connectivity and dynamics of the components characterizing the process of coagulation is relatively mature, it has become an attractive target for physiochemical modeling. Such models can potentially improve the design of therapeutics. The prothrombinase complex (composed of the protease factor (F)Xa and its cofactor FVa) plays a central role in this network as the main producer of thrombin, which catalyses both the activation of platelets and the conversion of fibrinogen to fibrin, the main substances of a clot. A key negative feedback loop that prevents clot propagation beyond the site of injury is the thrombin-dependent generation of activated protein C (APC), an enzyme that inactivates FVa, thus neutralizing the prothrombinase complex. APC inactivation of FVa is complex, involving the production of partially active intermediates and "protection" of FVa from APC by both FXa and prothrombin. An empirically validated mathematical model of this process would be useful in advancing the predictive capacity of comprehensive models of coagulation.A model of human APC inactivation of prothrombinase was constructed in a stepwise fashion by analyzing time courses of FVa inactivation in empirical reaction systems with increasing number of interacting components and generating corresponding model constructs of each reaction system. Reaction mechanisms, rate constants and equilibrium constants informing these model constructs were initially derived from various research groups reporting on APC inactivation of FVa in isolation, or in the presence of FXa or prothrombin. Model predictions were assessed against empirical data measuring the appearance and disappearance of multiple FVa degradation intermediates as well as prothrombinase activity changes, with plasma proteins derived from multiple preparations. Our work integrates previously published findings and through the cooperative analysis of in vitro experiments and mathematical constructs we are able to produce a final validated model that includes 24 chemical reactions and interactions with 14 unique rate constants which describe the flux in concentrations of 24 species.This study highlights the complexity of the inactivation process and provides a module of equations describing the Protein C pathway that can be integrated into existing comprehensive mathematical models describing tissue factor initiated coagulation. link: http://identifiers.org/pubmed/22607732

We have developed a computer program that simulates the intracellular reactions mediating the rapid (nonadaptive) chemotactic response of Escherichia coli bacteria to the attractant aspartate and the repellent Ni2+ ions. The model is built from modular units representing the molecular components involved, which are each assigned a known value of intracellular concentration and enzymatic rate constant wherever possible. The components are linked into a network of coupled biochemical reactions based on a compilation of widely accepted mechanisms but incorporating several novel features. The computer motor shows the same pattern of runs, tumbles and pauses seen in actual bacteria and responds in the same way as living bacteria to sudden changes in concentration of aspartate or Ni2+. The simulated network accurately reproduces the phenotype of more than 30 mutants in which components of the chemotactic pathway are deleted and/or expressed in excess amounts and shows a rapidity of response to a step change in aspartate concentration similar to living bacteria. Discrepancies between the simulation and real bacteria in the phenotype of certain mutants and in the gain of the chemotactic response to aspartate suggest the existence of additional as yet unidentified interactions in the in vivo signal processing pathway. link: http://identifiers.org/pubmed/8334303

The chemotactic response of bacteria is mediated by complexes containing two molecules each of a transmembrane receptor and the intracellular signaling proteins CheA and CheW. Mutants in which one or the other of the proteins of this complex are absent, inactive, or expressed at elevated amounts show altered chemotactic behavior and the phenotypes are difficult to interpret for some overexpression mutants. We have examined the possibility that these unexpected phenotypes might arise from the binding steps that lead to active complex formation. A limited genetic algorithm was used to search for sets of binding reactions and associated binding constants expected to give mutant phenotypes in accord with experimental data. Different sets of binding equilibria and different assumptions about the activity of particular receptor complexes were tried. Computer analysis demonstrated that it is possible to obtain sets of binding equilibria consistent with the observed phenotypes and provided a simple explanation for these phenotypes in terms of the distribution of active and inactive complexes formed under various conditions. Optimization methods of this kind offer a unique way to analyze reactions taking place inside living cells based on behavioral data. link: http://identifiers.org/pubmed/8573792

Studies in animals and humans suggest that the diurnal pattern in plasma melatonin levels is due to the hormone's rates of synthesis, circulatory infusion and clearance, circadian control of synthesis onset and offset, environmental lighting conditions, and error in the melatonin immunoassay. A two-dimensional linear differential equation model of the hormone is formulated and is used to analyze plasma melatonin levels in 18 normal healthy male subjects during a constant routine. Recently developed Bayesian statistical procedures are used to incorporate correctly the magnitude of the immunoassay error into the analysis. The estimated parameters [median (range)] were clearance half-life of 23.67 (14.79-59.93) min, synthesis onset time of 2206 (1940-0029), synthesis offset time of 0621 (0246-0817), and maximum N-acetyltransferase activity of 7.17(2.34-17.93) pmol x l(-1) x min(-1). All were in good agreement with values from previous reports. The difference between synthesis offset time and the phase of the core temperature minimum was 1 h 15 min (-4 h 38 min-2 h 43 min). The correlation between synthesis onset and the dim light melatonin onset was 0.93. Our model provides a more physiologically plausible estimate of the melatonin synthesis onset time than that given by the dim light melatonin onset and the first reliable means of estimating the phase of synthesis offset. Our analysis shows that the circadian and pharmacokinetics parameters of melatonin can be reliably estimated from a single model. link: http://identifiers.org/pubmed/9124558

The inherent complexity of cellular signaling networks and their importance to a wide range of cellular functions necessitates the development of modeling methods that can be applied toward making predictions and highlighting the appropriate experiments to test our understanding of how these systems are designed and function. We use methods of statistical mechanics to extract useful predictions for complex cellular signaling networks. A key difficulty with signaling models is that, while significant effort is being made to experimentally measure the rate constants for individual steps in these networks, many of the parameters required to describe their behavior remain unknown or at best represent estimates. To establish the usefulness of our approach, we have applied our methods toward modeling the nerve growth factor (NGF)-induced differentiation of neuronal cells. In particular, we study the actions of NGF and mitogenic epidermal growth factor (EGF) in rat pheochromocytoma (PC12) cells. Through a network of intermediate signaling proteins, each of these growth factors stimulates extracellular regulated kinase (Erk) phosphorylation with distinct dynamical profiles. Using our modeling approach, we are able to predict the influence of specific signaling modules in determining the integrated cellular response to the two growth factors. Our methods also raise some interesting insights into the design and possible evolution of cellular systems, highlighting an inherent property of these systems that we call 'sloppiness.' link: http://identifiers.org/pubmed/16204838

Metabolism is one of the best studied fields of biochemistry, but its regulation involves processes on many different levels, some of which are still not understood well enough to allow for quantitative modeling and prediction. Glycolysis in yeast is a good example: although high-quality quantitative data are available, well-established mathematical models typically only cover direct regulation of the involved enzymes by metabolite binding. The effect of various metabolites on the enzyme kinetics is summarized in carefully developed mathematical formulae. However, this approach implicitly assumes that the enzyme concentrations themselves are constant, thus neglecting other regulatory levels–e.g. transcriptional and translational regulation–involved in the regulation of enzyme activities. It is believed, however, that different experimental conditions result in different enzyme activities regulated by the above mechanisms. Detailed modeling of all regulatory levels is still out of reach since some of the necessary data–e.g. quantitative large scale enzyme concentration data sets–are lacking or rare. Nevertheless, a viable approach is to include the regulation of enzyme concentrations into an established model and to investigate whether this improves the predictive capabilities. Proteome data are usually hard to obtain, but levels of mRNA transcripts may be used instead as clues for changes in enzyme concentrations. Here we investigate whether including mRNA data into an established model of yeast glycolysis allows to predict the steady state metabolic concentrations for different experimental conditions. To this end, we modified an established ODE model for the glycolytic pathway of yeast to include changes of enzyme concentrations. Presumable changes were inferred from mRNA transcript level measurement data. We investigate how this approach can be used to predict metabolite concentrations for steady-state yeast cultures at five different oxygen levels ranging from anaerobic to fully aerobic conditions. We were partly able to reproduce the experimental data and present a number of changes that were necessary to improve the modeling result. link: http://identifiers.org/pubmed/19425118

Ammonium assimilation in Escherichia coli is regulated through multiple mechanisms (metabolic, signal transduction leading to covalent modification, transcription, and translation), which (in-)directly affect the activities of its two ammonium-assimilating enzymes, i.e. glutamine synthetase (GS) and glutamate dehydrogenase (GDH). Much is known about the kinetic properties of the components of the regulatory network that these enzymes are part of, but the ways in which, and the extents to which the network leads to subtle and quasi-intelligent regulation are unappreciated. To determine whether our present knowledge of the interactions between and the kinetic properties of the components of this network is complete - to the extent that when integrated in a kinetic model it suffices to calculate observed physiological behaviour - we now construct a kinetic model of this network, based on all of the kinetic data on the components that is available in the literature. We use this model to analyse regulation of ammonium assimilation at various carbon statuses for cells that have adapted to low and high ammonium concentrations. We show how a sudden increase in ammonium availability brings about a rapid redirection of the ammonium assimilation flux from GS/glutamate synthase (GOGAT) to GDH. The extent of redistribution depends on the nitrogen and carbon status of the cell. We develop a method to quantify the relative importance of the various regulators in the network. We find the importance is shared among regulators. We confirm that the adenylylation state of GS is the major regulator but that a total of 40% of the regulation is mediated by ADP (22%), glutamate (10%), glutamine (7%) and ATP (1%). The total steady-state ammonium assimilation flux is remarkably robust against changes in the ammonium concentration, but the fluxes through GS and GDH are completely nonrobust. Gene expression of GOGAT above a threshold value makes expression of GS under ammonium-limited conditions, and of GDH under glucose-limited conditions, sufficient for ammonium assimilation. link: http://identifiers.org/pubmed/15819889

The underlying cause of thrombosis in a large protein C (PC) deficient Vermont kindred appears to be multicausal and not explained by PC deficiency alone. We evaluated the contribution of coagulation factors to thrombin generation in this population utilizing a mathematical model that incorporates a mechanistic description of the PC pathway. Thrombin generation profiles for each individual were generated with and without the contribution of the PC pathway. Parameters that describe thrombin generation: maximum level (MaxL) and rate (MaxR), their respective times (TMaxL, TMaxR), area under the curve (AUC) and clotting time (CT) were examined in individuals ± PC mutation, ± prothrombin G20210A polymorphism and ± thrombosis history (DVT or PE). This family (n = 364) is shifted towards greater thrombin generation relative to the mean physiologic control. When this family was analyzed with the PC pathway, our results showed that: carriers of the PC mutation (n = 81) had higher MaxL and MaxR and greater AUC (all p<0.001) than non-carriers (n = 283); and individuals with a DVT and/or PE history (n = 13) had higher MaxL (p = 0.005) and greater AUC (p<0.001) than individuals without a thrombosis history (n = 351). These differences were further stratified by gender, with women in all categories generating more thrombin than males. These results show that all individuals within this family with or without PC deficiency have an increased baseline procoagulant potential reflective of increased thrombin generation. In addition, variations within the plasma composition of each individual can further segregate out increased procoagulant phenotypes, with gender-associated plasma compositional differences playing a large role. link: http://identifiers.org/pubmed/22984498

Type 2 diabetes originates in an expanding adipose tissue that for unknown reasons becomes insulin resistant. Insulin resistance reflects impairments in insulin signaling, but mechanisms involved are unclear because current research is fragmented. We report a systems level mechanistic understanding of insulin resistance, using systems wide and internally consistent data from human adipocytes. Based on quantitative steady-state and dynamic time course data on signaling intermediaries, normally and in diabetes, we developed a dynamic mathematical model of insulin signaling. The model structure and parameters are identical in the normal and diabetic states of the model, except for three parameters that change in diabetes: (i) reduced concentration of insulin receptor, (ii) reduced concentration of insulin-regulated glucose transporter GLUT4, and (iii) changed feedback from mammalian target of rapamycin in complex with raptor (mTORC1). Modeling reveals that at the core of insulin resistance in human adipocytes is attenuation of a positive feedback from mTORC1 to the insulin receptor substrate-1, which explains reduced sensitivity and signal strength throughout the signaling network. Model simulations with inhibition of mTORC1 are comparable with experimental data on inhibition of mTORC1 using rapamycin in human adipocytes. We demonstrate the potential of the model for identification of drug targets, e.g. increasing the feedback restores insulin signaling, both at the cellular level and, using a multilevel model, at the whole body level. Our findings suggest that insulin resistance in an expanded adipose tissue results from cell growth restriction to prevent cell necrosis. link: http://identifiers.org/pubmed/23400783

Type 2 diabetes originates in an expanding adipose tissue that for unknown reasons becomes insulin resistant. Insulin resistance reflects impairments in insulin signaling, but mechanisms involved are unclear because current research is fragmented. We report a systems level mechanistic understanding of insulin resistance, using systems wide and internally consistent data from human adipocytes. Based on quantitative steady-state and dynamic time course data on signaling intermediaries, normally and in diabetes, we developed a dynamic mathematical model of insulin signaling. The model structure and parameters are identical in the normal and diabetic states of the model, except for three parameters that change in diabetes: (i) reduced concentration of insulin receptor, (ii) reduced concentration of insulin-regulated glucose transporter GLUT4, and (iii) changed feedback from mammalian target of rapamycin in complex with raptor (mTORC1). Modeling reveals that at the core of insulin resistance in human adipocytes is attenuation of a positive feedback from mTORC1 to the insulin receptor substrate-1, which explains reduced sensitivity and signal strength throughout the signaling network. Model simulations with inhibition of mTORC1 are comparable with experimental data on inhibition of mTORC1 using rapamycin in human adipocytes. We demonstrate the potential of the model for identification of drug targets, e.g. increasing the feedback restores insulin signaling, both at the cellular level and, using a multilevel model, at the whole body level. Our findings suggest that insulin resistance in an expanded adipose tissue results from cell growth restriction to prevent cell necrosis. link: http://identifiers.org/pubmed/23400783

BACKGROUND: The individual character of pharmacokinetics is of great importance in the risk assessment of new drug leads in pharmacological research. Amongst others, it is severely influenced by the properties and inter-individual variability of the enzymes and transporters of the drug detoxification system of the liver. Predicting individual drug biotransformation capacity requires quantitative and detailed models. RESULTS: In this contribution we present the de novo deterministic modeling of atorvastatin biotransformation based on comprehensive published knowledge on involved metabolic and transport pathways as well as physicochemical properties. The model was evaluated on primary human hepatocytes and parameter identifiability analysis was performed under multiple experimental constraints. Dynamic simulations of atorvastatin biotransformation considering the inter-individual variability of the two major involved enzymes CYP3A4 and UGT1A3 based on quantitative protein expression data in a large human liver bank (n = 150) highlighted the variability in the individual biotransformation profiles and therefore also points to the individuality of pharmacokinetics. CONCLUSIONS: A dynamic model for the biotransformation of atorvastatin has been developed using quantitative metabolite measurements in primary human hepatocytes. The model comprises kinetics for transport processes and metabolic enzymes as well as population liver expression data allowing us to assess the impact of inter-individual variability of concentrations of key proteins. Application of computational tools for parameter sensitivity analysis enabled us to considerably improve the validity of the model and to create a consistent framework for precise computer-aided simulations in toxicology. link: http://identifiers.org/pubmed/21548957

The size of a cell sets the scale for all biochemical processes within it, thereby affecting cellular fitness and survival. Hence, cell size needs to be kept within certain limits and relatively constant over multiple generations. However, how cells measure their size and use this information to regulate growth and division remains controversial. Here, we present two mechanistic mathematical models of the budding yeast (S. cerevisiae) cell cycle to investigate competing hypotheses on size control: inhibitor dilution and titration of nuclear sites. Our results suggest that an inhibitor-dilution mechanism, in which cell growth dilutes the transcriptional inhibitor Whi5 against the constant activator Cln3, can facilitate size homeostasis. This is achieved by utilising a positive feedback loop to establish a fixed size threshold for the START transition, which efficiently couples cell growth to cell cycle progression. Yet, we show that inhibitor dilution cannot reproduce the size of mutants that alter the cell’s overall ploidy and WHI5 gene copy number. By contrast, size control through titration of Cln3 against a constant number of genomic binding sites for the transcription factor SBF recapitulates both size homeostasis and the size of these mutant strains. Moreover, this model produces an imperfect ‘sizer’ behaviour in G1 and a ‘timer’ in S/G2/M, which combine to yield an ‘adder’ over the whole cell cycle; an observation recently made in experiments. Hence, our model connects these phenomenological data with the molecular details of the cell cycle, providing a systems-level perspective of budding yeast size control. link: http://identifiers.org/doi/10.1371/journal.pcbi.1006548

Adaptation of the cellular metabolism to varying external conditions is brought about by regulated changes in the activity of enzymes and transporters. Hormone-dependent reversible enzyme phosphorylation and concentration changes of reactants and allosteric effectors are the major types of rapid kinetic enzyme regulation, whereas on longer time scales changes in protein abundance may also become operative. Here, we used a comprehensive mathematical model of the hepatic glucose metabolism of rat hepatocytes to decipher the relative importance of different regulatory modes and their mutual interdependencies in the hepatic control of plasma glucose homeostasis.Model simulations reveal significant differences in the capability of liver metabolism to counteract variations of plasma glucose in different physiological settings (starvation, ad libitum nutrient supply, diabetes). Changes in enzyme abundances adjust the metabolic output to the anticipated physiological demand but may turn into a regulatory disadvantage if sudden unexpected changes of the external conditions occur. Allosteric and hormonal control of enzyme activities allow the liver to assume a broad range of metabolic states and may even fully reverse flux changes resulting from changes of enzyme abundances alone. Metabolic control analysis reveals that control of the hepatic glucose metabolism is mainly exerted by enzymes alone, which are differently controlled by alterations in enzyme abundance, reversible phosphorylation, and allosteric effects.In hepatic glucose metabolism, regulation of enzyme activities by changes of reactants, allosteric effects, and reversible phosphorylation is equally important as changes in protein abundance of key regulatory enzymes. link: http://identifiers.org/pubmed/26935066

Thrombin is an enzyme that is generated in both vascular and non-vascular systems. In blood coagulation, a fundamental process in all species, thrombin induces the formation of a fibrin clot. A dynamical model of thrombin generation in the presence of lipid surfaces is presented. This model also includes the self-regulating thrombin feedback reactions, the thrombomodulin-protein C-protein S inhibitory system, tissue factor pathway inhibitor (TFPI), and the inhibitor, antithrombin (AT). The dynamics of this complex system were found to be highly lipid dependent, as would be expected from experimental studies. Simulations of this model indicate that a threshold lipid level is required to generate physiologically relevant amounts of thrombin. The dependence of the onset, the peak levels, and the duration of thrombin generation on lipid was saturable. The lipid concentration affects the way in which the inhibitors modulate thrombin production. A novel feature of this model is the inclusion of the dynamical protein C pathway, initiated by thrombin feedback. This inhibitory system exerts its effects on the lipid surface, where its substrates are formed. The maximum impact of TFPI occurs at intermediate vesicle concentrations. Inhibition by AT is only indirectly affected by the lipid since AT irreversibly binds only to solution phase proteins. In a system with normal plasma concentrations of the proteins involved in thrombin formation, the combination of these three inhibitors is sufficient both to effectively stop thrombin generation prior to the exhaustion of its precursor, prothrombin, and to inhibit all thrombin formed. This model can be used to predict thrombin generation under extreme lipid conditions that are difficult to implement experimentally and to examine thrombin generation in non-vascular systems. link: http://identifiers.org/pubmed/12974500

A mathematical model is constructed to study thrombin production in human ovarian follicular fluid. The model results show that the amount of thrombin that can be produced in ovarian follicular fluid is much lower than that in blood plasma, failing to reach the level required for fibrin formation, and thereby supporting the hypothesis that in follicular fluid thrombin functions to initiate cellular activities via intracellular signalling receptors. It is also concluded that the absence of the amplification pathway to thrombin production in follicular fluid is a major factor in restricting the amount of thrombin that can be produced. Titration of the initial concentrations of the various reactants in the model lead to predictions for the amount of tissue factor and phospholipid that is required to maintain thrombin production in the follicle, as well as to the conclusion that tissue factor pathway inhibitor has little effect on the time that thrombin generation is sustained. Numerical experiments to determine the effect of factor V, which is at a much reduced level in follicular fluid compared to plasma, and thrombomodulin, illustrate the importance for further experimental work to determine values for several parameters that have yet to be reported in the literature. link: http://identifiers.org/pubmed/16838084

A mathematical model is constructed to study thrombin production in human ovarian follicular fluid. The model results show that the amount of thrombin that can be produced in ovarian follicular fluid is much lower than that in blood plasma, failing to reach the level required for fibrin formation, and thereby supporting the hypothesis that in follicular fluid thrombin functions to initiate cellular activities via intracellular signalling receptors. It is also concluded that the absence of the amplification pathway to thrombin production in follicular fluid is a major factor in restricting the amount of thrombin that can be produced. Titration of the initial concentrations of the various reactants in the model lead to predictions for the amount of tissue factor and phospholipid that is required to maintain thrombin production in the follicle, as well as to the conclusion that tissue factor pathway inhibitor has little effect on the time that thrombin generation is sustained. Numerical experiments to determine the effect of factor V, which is at a much reduced level in follicular fluid compared to plasma, and thrombomodulin, illustrate the importance for further experimental work to determine values for several parameters that have yet to be reported in the literature. link: http://identifiers.org/pubmed/16838084

Rivaroxaban is an oral, direct Factor Xa inhibitor approved in the European Union and several other countries for the prevention of venous thromboembolism in adult patients undergoing elective hip or knee replacement surgery and is in advanced clinical development for the treatment of thromboembolic disorders. Its mechanism of action is antithrombin independent and differs from that of other anticoagulants, such as warfarin (a vitamin K antagonist), enoxaparin (an indirect thrombin/Factor Xa inhibitor) and dabigatran (a direct thrombin inhibitor). A blood coagulation computer model has been developed, based on several published models and preclinical and clinical data. Unlike previous models, the current model takes into account both the intrinsic and extrinsic pathways of the coagulation cascade, and possesses some unique features, including a blood flow component and a portfolio of drug action mechanisms. This study aimed to use the model to compare the mechanism of action of rivaroxaban with that of warfarin, and to evaluate the efficacy and safety of different rivaroxaban doses with other anticoagulants included in the model. Rather than reproducing known standard clinical measurements, such as the prothrombin time and activated partial thromboplastin time clotting tests, the anticoagulant benchmarking was based on a simulation of physiologically plausible clotting scenarios. Compared with warfarin, rivaroxaban showed a favourable sensitivity for tissue factor concentration inducing clotting, and a steep concentration-effect relationship, rapidly flattening towards higher inhibitor concentrations, both suggesting a broad therapeutic window. The predicted dosing window is highly accordant with the final dose recommendation based upon extensive clinical studies. link: http://identifiers.org/pubmed/21526168

The long-lasting anticoagulant effect of vitamin K antagonists can be problematic in cases of adverse drug reactions or when patients are switched to another anticoagulant therapy. The objective of this study was to examine in silico the anticoagulant effect of rivaroxaban, an oral, direct Factor Xa inhibitor, combined with the residual effect of discontinued warfarin. Our simulations were based on the recommended anticoagulant dosing regimen for stroke prevention in patients with atrial fibrillation. The effects of the combination of discontinued warfarin plus rivaroxaban were simulated using an extended version of a previously validated blood coagulation computer model. A strong synergistic effect of the two distinct mechanisms of action was observed in the first 2-3 days after warfarin discontinuation; thereafter, the effect was close to additive. Nomograms for the introduction of rivaroxaban therapy after warfarin discontinuation were derived for Caucasian and Japanese patients using safety and efficacy criteria described previously, together with the coagulation model. The findings of our study provide a mechanistic pharmacologic rationale for dosing schedules during the therapy switch from warfarin to rivaroxaban and support the switching strategies as outlined in the Summary of Product Characteristics and Prescribing Information for rivaroxaban. link: http://identifiers.org/pubmed/25426077

According to receptor theory, the effect of a ligand depends on the amount of agonist-receptor complex. Therefore, changes in receptor abundance should have quantitative effects. However, the response to pheromone in Saccharomyces cerevisiae is robust (unaltered) to increases or reductions in the abundance of the G-protein-coupled receptor (GPCR), Ste2, responding instead to the fraction of occupied receptor. We found experimentally that this robustness originates during G-protein activation. We developed a complete mathematical model of this step, which suggested the ability to compute fractional occupancy depends on the physical interaction between the inhibitory regulator of G-protein signaling (RGS), Sst2, and the receptor. Accordingly, replacing Sst2 by the heterologous hsRGS4, incapable of interacting with the receptor, abolished robustness. Conversely, forcing hsRGS4:Ste2 interaction restored robustness. Taken together with other results of our work, we conclude that this GPCR pathway computes fractional occupancy because ligand-bound GPCR-RGS complexes stimulate signaling while unoccupied complexes actively inhibit it. In eukaryotes, many RGSs bind to specific GPCRs, suggesting these complexes with opposing activities also detect fraction occupancy by a ratiometric measurement. Such complexes operate as push-pull devices, which we have recently described. link: http://identifiers.org/pubmed/28034910

According to receptor theory, the effect of a ligand depends on the amount of agonist-receptor complex. Therefore, changes in receptor abundance should have quantitative effects. However, the response to pheromone in Saccharomyces cerevisiae is robust (unaltered) to increases or reductions in the abundance of the G-protein-coupled receptor (GPCR), Ste2, responding instead to the fraction of occupied receptor. We found experimentally that this robustness originates during G-protein activation. We developed a complete mathematical model of this step, which suggested the ability to compute fractional occupancy depends on the physical interaction between the inhibitory regulator of G-protein signaling (RGS), Sst2, and the receptor. Accordingly, replacing Sst2 by the heterologous hsRGS4, incapable of interacting with the receptor, abolished robustness. Conversely, forcing hsRGS4:Ste2 interaction restored robustness. Taken together with other results of our work, we conclude that this GPCR pathway computes fractional occupancy because ligand-bound GPCR-RGS complexes stimulate signaling while unoccupied complexes actively inhibit it. In eukaryotes, many RGSs bind to specific GPCRs, suggesting these complexes with opposing activities also detect fraction occupancy by a ratiometric measurement. Such complexes operate as push-pull devices, which we have recently described. link: http://identifiers.org/pubmed/28034910

The presence of activation peptides (AP) of the vitamin K-dependent proteins in the phlebotomy blood of human subjects suggests that active serine proteases may circulate in blood as well. The goal of the current study was to evaluate the influence of trace amounts of key coagulation proteases on tissue factor-independent thrombin generation using three models of coagulation. With procoagulants and select coagulation inhibitors at mean physiological concentrations, concentrations of factor IXa, factor Xa, and thrombin were set either equal to those of their AP or to values that would result based upon the rates of AP/enzyme generation and steady state enzyme inhibition. In the latter case, numerical simulation predicts that sufficient thrombin to produce a solid clot would be generated in approximately 2 min. Empirical data from the synthetic plasma suggest clotting times of 3-5 min, which are similar to that observed in contact pathway-inhibited whole blood (4.3 min) initiated with the same concentrations of factors IXa and Xa and thrombin. Numerical simulations performed with the concentrations of two of the enzymes held constant and one varied suggest that the presence of any pair of enzymes is sufficient to yield rapid clot formation. Modeling of states (numerical simulation and whole blood) where only one circulating protease is present at steady state concentration shows significant thrombin generation only for factor IXa. The addition of factor Xa and thrombin has little effect (if any) on thrombin generation induced by factor IXa alone. These data indicate that 1) concentrations of active coagulation enzymes circulating in vivo are significantly lower than can be predicted from the concentrations of their AP, and 2) expected trace amounts of factor IXa can trigger thrombin generation in the absence of tissue factor. link: http://identifiers.org/pubmed/15039440

A network of oscillatory bursting neurons with excitatory coupling is hypothesized to define the primary kernel for respiratory rhythm generation in the pre-Bötzinger complex (pre-BötC) in mammals. Two minimal models of these neurons are proposed. In model 1, bursting arises via fast activation and slow inactivation of a persistent Na+ current INaP-h. In model 2, bursting arises via a fast-activating persistent Na+ current INaP and slow activation of a K+ current IKS. In both models, action potentials are generated via fast Na+ and K+ currents. The two models have few differences in parameters to facilitate a rigorous comparison of the two different burst-generating mechanisms. Both models are consistent with many of the dynamic features of electrophysiological recordings from pre-BötC oscillatory bursting neurons in vitro, including voltage-dependent activity modes (silence, bursting, and beating), a voltage-dependent burst frequency that can vary from 0.05 to >1 Hz, and a decaying spike frequency during bursting. These results are robust and persist across a wide range of parameter values for both models. However, the dynamics of model 1 are more consistent with experimental data in that the burst duration decreases as the baseline membrane potential is depolarized and the model has a relatively flat membrane potential trajectory during the interburst interval. We propose several experimental tests to demonstrate the validity of either model and to differentiate between the two mechanisms. link: http://identifiers.org/pubmed/10400966

Boolean approaches and extensions thereof are becoming increasingly popular to model signaling and regulatory networks, including those controlling cell differentiation, pattern formation and embryonic development. Here, we describe a logical modeling framework relying on three steps: the delineation of a regulatory graph, the specification of multilevel components, and the encoding of Boolean rules specifying the behavior of model components depending on the levels or activities of their regulators. Referring to a non-deterministic, asynchronous updating scheme, we present several complementary methods and tools enabling the computation of stable activity patterns, the verification of the reachability of such patterns, as well as the generation of mean temporal evolution curves and the computation of the probabilities to reach distinct activity patterns. We apply this logical framework to the regulatory network controlling T lymphocyte specification. This process involves cross-regulations between specific T cell regulatory factors and factors driving alternative differentiation pathways, which remain accessible during the early steps of thymocyte development. Many transcription factors needed for T cell specification are required in other hematopoietic differentiation pathways and are combined in a fine-tuned, time-dependent fashion to achieve T cell commitment. Using the software GINsim, we integrated current knowledge into a dynamical model, which recapitulates the main developmental steps from early progenitors entering the thymus up to T cell commitment, as well as the impact of various documented environmental and genetic perturbations. Our model analysis further enabled the identification of several knowledge gaps. The model, software and whole analysis workflow are provided in computer-readable and executable form to ensure reproducibility and ease extensions. link: http://identifiers.org/pubmed/32450961

The prescription drug epidemic in the United States has gained attention in recent years. Vicodin, along with its generic version, is the country's mostly widely prescribed pain reliever, and it contains a narcotic component that can lead to physical and chemical dependency. The majority of Vicodin abusers were first introduced via prescription, unlike other drugs which are often experienced for the first time due to experimentation. Most abusers report obtaining their supply from a prescription, either their own or someone else's. Although the problem with prescription drug abuse is well known, there is no standard method of addressing the problem. To better understand how to do this, we develop and analyze a mathematical model of Vicodin use and abuse, considering only those patients who were initially prescribed the drug. Through global sensitivity analysis, we show that focusing efforts on abuse prevention rather than treatment has greater success at reducing the population of Vicodin abusers. Our results demonstrate that relying solely on rehabilitation and other treatment programs is not enough to combat the prescription drug problem in the United States. We anticipate that implementing preventative measures in both prescribers and patients will reduce the number of Vicodin abusers. link: http://identifiers.org/pubmed/31513802

Immediately following fertilization, the fruit fly embryo undergoes 13 rapid, synchronous, syncytial nuclear division cycles driven by maternal genes and proteins. During these mitotic cycles, there are barely detectable oscillations in the total level of B-type cyclins. In this paper, we propose a dynamical model for the molecular events underlying these early nuclear division cycles in Drosophila. The model distinguishes nuclear and cytoplasmic compartments of the embryo and permits exploration of a variety of rules for protein transport between the compartments. Numerical simulations reproduce the main features of wild-type mitotic cycles: patterns of protein accumulation and degradation, lengthening of later cycles, and arrest in interphase 14. The model is consistent with mutations that introduce subtle changes in the number of mitotic cycles before interphase arrest. Bifurcation analysis of the differential equations reveals the dependence of mitotic oscillations on cycle number, and how this dependence is altered by mutations. The model can be used to predict the phenotypes of novel mutations and effective ranges of the unmeasured rate constants and transport coefficients in the proposed mechanism. link: http://identifiers.org/pubmed/17667953

We present, here, a detailed and curated map of molecular interactions taking place in the regulation of the cell cycle by the retinoblastoma protein (RB/RB1). Deregulations and/or mutations in this pathway are observed in most human cancers. The map was created using Systems Biology Graphical Notation language with the help of CellDesigner 3.5 software and converted into BioPAX 2.0 pathway description format. In the current state the map contains 78 proteins, 176 genes, 99 protein complexes, 208 distinct chemical species and 165 chemical reactions. Overall, the map recapitulates biological facts from approximately 350 publications annotated in the diagram. The network contains more details about RB/E2F interaction network than existing large-scale pathway databases. Structural analysis of the interaction network revealed a modular organization of the network, which was used to elaborate a more summarized, higher-level representation of RB/E2F network. The simplification of complex networks opens the road for creating realistic computational models of this regulatory pathway. link: http://identifiers.org/pubmed/18319725

Cytokines such as TNF and FASL can trigger death or survival depending on cell lines and cellular conditions. The mechanistic details of how a cell chooses among these cell fates are still unclear. The understanding of these processes is important since they are altered in many diseases, including cancer and AIDS. Using a discrete modelling formalism, we present a mathematical model of cell fate decision recapitulating and integrating the most consistent facts extracted from the literature. This model provides a generic high-level view of the interplays between NFkappaB pro-survival pathway, RIP1-dependent necrosis, and the apoptosis pathway in response to death receptor-mediated signals. Wild type simulations demonstrate robust segregation of cellular responses to receptor engagement. Model simulations recapitulate documented phenotypes of protein knockdowns and enable the prediction of the effects of novel knockdowns. In silico experiments simulate the outcomes following ligand removal at different stages, and suggest experimental approaches to further validate and specialise the model for particular cell types. We also propose a reduced conceptual model implementing the logic of the decision process. This analysis gives specific predictions regarding cross-talks between the three pathways, as well as the transient role of RIP1 protein in necrosis, and confirms the phenotypes of novel perturbations. Our wild type and mutant simulations provide novel insights to restore apoptosis in defective cells. The model analysis expands our understanding of how cell fate decision is made. Moreover, our current model can be used to assess contradictory or controversial data from the literature. Ultimately, it constitutes a valuable reasoning tool to delineate novel experiments. link: http://identifiers.org/pubmed/20221256

Computational studies of biological networks can help to identify components and wirings responsible for observed phenotypes. However, studying stochastic networks controlling many biological processes is challenging. Similar to Schrödinger's equation in quantum mechanics, the chemical master equation (CME) provides a basic framework for understanding stochastic networks. However, except for simple problems, the CME cannot be solved analytically. Here we use a method called discrete chemical master equation (dCME) to compute directly the full steady-state probability landscape of the lysogeny maintenance network in phage lambda from its CME. Results show that wild-type phage lambda can maintain a constant level of repressor over a wide range of repressor degradation rate and is stable against UV irradiation, ensuring heritability of the lysogenic state. Furthermore, it can switch efficiently to the lytic state once repressor degradation increases past a high threshold by a small amount. We find that beyond bistability and nonlinear dimerization, cooperativity between repressors bound to O(R)1 and O(R)2 is required for stable and heritable epigenetic state of lysogeny that can switch efficiently. Mutants of phage lambda lack stability and do not possess a high threshold. Instead, they are leaky and respond to gradual changes in degradation rate. Our computation faithfully reproduces the hair triggers for UV-induced lysis observed in mutants and the limitation in robustness against mutations. The landscape approach computed from dCME is general and can be applied to study broad issues in systems biology. link: http://identifiers.org/pubmed/20937911

The newly characterized interleukin (IL)-21 plays a central role in the transition from innate immunity to adaptive immunity and shows substantial tumor regression in mice. IL-21 is now developed as a cancer immunotherapeutic drug, but conditions for efficacious therapy, and the conflicting immunostimulatory and immunoinhibitory influence of the cytokine, are yet to be defined. We studied the effects of IL-21 on tumor eradication in a mathematical model focusing on natural killer (NK) cell-mediated and CD8+ T-cell-mediated lysis of tumor cells. Model parameters were estimated using results in tumor-bearing mice treated with IL-21 via cytokine gene therapy (CGT), hydrodynamics-based gene delivery (HGD), or standard interval dosing (SID). Our model accurately retrieved experimental growth dynamics in the nonimmunogenic B16 melanoma and the immunogenic MethA and MCA205 fibrosarcomas, showing a strong dependence of the NK-cell/CD8+ T-cell balance on tumor immunogenicity. Moreover, in melanoma, simulations of CGT-like dosing regimens, dynamically determined according to tumor mass changes, resulted in efficient disease elimination. In contrast, in fibrosarcoma, such a strategy was not superior to that of fixed dosing regimens, HGD or SID. Our model supports clinical use of IL-21 as a potent stimulator of cellular immunity against cancer, and suggests selecting the immunotherapy strategy according to tumor immunogenicity. Nonimmunogenic tumors, but not highly immunogenic tumors, should be controlled by IL-21 dosing, which depends on tumor mass at the time of administration. This method imitates, yet amplifies, the natural anticancer immune response rather than accelerates only one of the response arms in an unbalanced manner. link: http://identifiers.org/pubmed/16849579

Cancer cells utilize large amounts of ATP to sustain growth, relying primarily on non-oxidative, fermentative pathways for its production. In many types of cancers this leads, even in the presence of oxygen, to the secretion of carbon equivalents (usually in the form of lactate) in the cell’s surroundings, a feature known as the Warburg effect. While the molecular basis of this phenomenon are still to be elucidated, it is clear that the spilling of energy resources contributes to creating a peculiar microenvironment for tumors, possibly characterized by a degree of toxicity. This suggests that mechanisms for recycling the fermentation products (e.g. a lactate shuttle) may be active, effectively inducing a mutually beneficial metabolic coupling between aberrant and non-aberrant cells. Here we analyze this scenario through a large-scale in silico metabolic model of interacting human cells. By going beyond the cell-autonomous description, we show that elementary physico-chemical constraints indeed favor the establishment of such a coupling under very broad conditions. The characterization we obtained by tuning the aberrant cell’s demand for ATP, amino-acids and fatty acids and/or the imbalance in nutrient partitioning provides quantitative support to the idea that synergistic multi-cell effects play a central role in cancer sustainment. link: http://identifiers.org/doi/10.1038/srep11880

The well-known Kirschner-Panetta model for tumour-immune System interplay [Kirschner, D., Panetta, J.C., 1998. Modelling immunotherapy of the tumour-immune interaction. J. Math. Biol. 37 (3), 235-252] reproduces a number of features of this essential interaction, but it excludes the possibility of tumour suppression by the immune system in the absence of therapy. Here we present a hybrid-stochastic version of that model. In this new framework, we show that in reality the model is also able to reproduce the suppression, through stochastic extinction after the first spike of an oscillation. link: http://identifiers.org/pubmed/20580640

Differentiation of CD4+ T cells into effector or regulatory phenotypes is tightly controlled by the cytokine milieu, complex intracellular signaling networks and numerous transcriptional regulators. We combined experimental approaches and computational modeling to investigate the mechanisms controlling differentiation and plasticity of CD4+ T cells in the gut of mice. Our computational model encompasses the major intracellular pathways involved in CD4+ T cell differentiation into T helper 1 (Th1), Th2, Th17 and induced regulatory T cells (iTreg). Our modeling efforts predicted a critical role for peroxisome proliferator-activated receptor gamma (PPARγ) in modulating plasticity between Th17 and iTreg cells. PPARγ regulates differentiation, activation and cytokine production, thereby controlling the induction of effector and regulatory responses, and is a promising therapeutic target for dysregulated immune responses and inflammation. Our modeling efforts predict that following PPARγ activation, Th17 cells undergo phenotype switch and become iTreg cells. This prediction was validated by results of adoptive transfer studies showing an increase of colonic iTreg and a decrease of Th17 cells in the gut mucosa of mice with colitis following pharmacological activation of PPARγ. Deletion of PPARγ in CD4+ T cells impaired mucosal iTreg and enhanced colitogenic Th17 responses in mice with CD4+ T cell-induced colitis. Thus, for the first time we provide novel molecular evidence in vivo demonstrating that PPARγ in addition to regulating CD4+ T cell differentiation also plays a major role controlling Th17 and iTreg plasticity in the gut mucosa. link: http://identifiers.org/pubmed/23592971

T helper (Th) cells play a major role in the immune response and pathology at the gastric mucosa during Helicobacter pylori infection. There is a limited mechanistic understanding regarding the contributions of CD4+ T cell subsets to gastritis development during H. pylori colonization. We used two computational approaches: ordinary differential equation (ODE)-based and agent-based modeling (ABM) to study the mechanisms underlying cellular immune responses to H. pylori and how CD4+ T cell subsets influenced initiation, progression and outcome of disease. To calibrate the model, in vivo experimentation was performed by infecting C57BL/6 mice intragastrically with H. pylori and assaying immune cell subsets in the stomach and gastric lymph nodes (GLN) on days 0, 7, 14, 30 and 60 post-infection. Our computational model reproduced the dynamics of effector and regulatory pathways in the gastric lamina propria (LP) in silico. Simulation results show the induction of a Th17 response and a dominant Th1 response, together with a regulatory response characterized by high levels of mucosal Treg) cells. We also investigated the potential role of peroxisome proliferator-activated receptor γ (PPARγ) activation on the modulation of host responses to H. pylori by using loss-of-function approaches. Specifically, in silico results showed a predominance of Th1 and Th17 cells in the stomach of the cell-specific PPARγ knockout system when compared to the wild-type simulation. Spatio-temporal, object-oriented ABM approaches suggested similar dynamics in induction of host responses showing analogous T cell distributions to ODE modeling and facilitated tracking lesion formation. In addition, sensitivity analysis predicted a crucial contribution of Th1 and Th17 effector responses as mediators of histopathological changes in the gastric mucosa during chronic stages of infection, which were experimentally validated in mice. These integrated immunoinformatics approaches characterized the induction of mucosal effector and regulatory pathways controlled by PPARγ during H. pylori infection affecting disease outcomes. link: http://identifiers.org/doi/10.1371/journal.pone.0073365