SBMLBioModels: A - B

In order for the cell's genome to be passed intact from one generation to the next, the events of the cell cycle (DNA replication, mitosis, cell division) must be executed in the correct order, despite the considerable molecular noise inherent in any protein-based regulatory system residing in the small confines of a eukaryotic cell. To assess the effects of molecular fluctuations on cell-cycle progression in budding yeast cells, we have constructed a new model of the regulation of Cln- and Clb-dependent kinases, based on multisite phosphorylation of their target proteins and on positive and negative feedback loops involving the kinases themselves. To account for the significant role of noise in the transcription and translation steps of gene expression, the model includes mRNAs as well as proteins. The model equations are simulated deterministically and stochastically to reveal the bistable switching behavior on which proper cell-cycle progression depends and to show that this behavior is robust to the level of molecular noise expected in yeast-sized cells (approximately 50 fL volume). The model gives a quantitatively accurate account of the variability observed in the G1-S transition in budding yeast, which is governed by an underlying sizer+timer control system. link: http://identifiers.org/pubmed/20739927

Eukaryotic cell proliferation involves DNA replication, a tightly regulated process mediated by a multitude of protein factors. In budding yeast, the initiation of replication is facilitated by the heterohexameric origin recognition complex (ORC). ORC binds to specific origins of replication and then serves as a scaffold for the recruitment of other factors such as Cdt1, Cdc6, the Mcm2-7 complex, Cdc45 and the Dbf4-Cdc7 kinase complex. While many of the mechanisms controlling these associations are well documented, mathematical models are needed to explore the network's dynamic behaviour. We have developed an ordinary differential equation-based model of the protein-protein interaction network describing replication initiation.The model was validated against quantified levels of protein factors over a range of cell cycle timepoints. Using chromatin extracts from synchronized Saccharomyces cerevisiae cell cultures, we were able to monitor the in vivo fluctuations of several of the aforementioned proteins, with additional data obtained from the literature. The model behaviour conforms to perturbation trials previously reported in the literature, and accurately predicts the results of our own knockdown experiments. Furthermore, we successfully incorporated our replication initiation model into an established model of the entire yeast cell cycle, thus providing a comprehensive description of these processes.This study establishes a robust model of the processes driving DNA replication initiation. The model was validated against observed cell concentrations of the driving factors, and characterizes the interactions between factors implicated in eukaryotic DNA replication. Finally, this model can serve as a guide in efforts to generate a comprehensive model of the mammalian cell cycle in order to explore cancer-related phenotypes. link: http://identifiers.org/pubmed/22738223

CD4 T cells play a fundamental role in the adaptive immune response including the stimulation of cytotoxic lymphocytes (CTLs). Human immunodeficiency virus (HIV) which infects and kills CD4 T cells causes progressive failure of the immune system. However, HIV particles are also reproduced by the infected CD4 T cells. Therefore, during HIV infection, infected and healthy CD4 T cells act in opposition to each other, reproducing virus particles and activating and stimulating cellular immune responses, respectively. In this investigation, we develop and analyze a simple system of four ordinary differential equations that accounts for these two opposing roles of CD4 T cells. The model illustrates the importance of the CTL immune response during the asymptomatic stage of HIV infection. In addition, the solution behavior exhibits the two stages of infection, asymptomatic and final AIDS stages. In the model, a weak immune response results in a short asymptomatic stage and faster development of AIDS, whereas a strong immune response illustrates the long asymptomatic stage. A model with a latent stage for infected CD4 T cells is also investigated and compared numerically with the original model. The model shows that strong stimulation of CTLs by CD4 T cells is necessary to prevent progression to the AIDS stage. link: http://identifiers.org/doi/10.1016/j.apm.2019.05.028

Despite large cell-to-cell variations in the concentrations of individual signaling proteins, cells transmit signals correctly. This phenomenon raises the question of what signaling systems do to prevent a predicted high failure rate. Here we combine quantitative modeling, RNA interference, and targeted selective reaction monitoring (SRM) mass spectrometry, and we show for the ubiquitous and fundamental calcium signaling system that cells monitor cytosolic and endoplasmic reticulum (ER) Ca(2+) levels and adjust in parallel the concentrations of the store-operated Ca(2+) influx mediator stromal interaction molecule (STIM), the plasma membrane Ca(2+) pump plasma membrane Ca-ATPase (PMCA), and the ER Ca(2+) pump sarco/ER Ca(2+)-ATPase (SERCA). Model calculations show that this combined parallel regulation in protein expression levels effectively stabilizes basal cytosolic and ER Ca(2+) levels and preserves receptor signaling. Our results demonstrate that, rather than directly controlling the relative level of signaling proteins in a forward regulation strategy, cells prevent transmission failure by sensing the state of the signaling pathway and using multiple parallel adaptive feedbacks. link: http://identifiers.org/pubmed/21844332

Despite large cell-to-cell variations in the concentrations of individual signaling proteins, cells transmit signals correctly. This phenomenon raises the question of what signaling systems do to prevent a predicted high failure rate. Here we combine quantitative modeling, RNA interference, and targeted selective reaction monitoring (SRM) mass spectrometry, and we show for the ubiquitous and fundamental calcium signaling system that cells monitor cytosolic and endoplasmic reticulum (ER) Ca(2+) levels and adjust in parallel the concentrations of the store-operated Ca(2+) influx mediator stromal interaction molecule (STIM), the plasma membrane Ca(2+) pump plasma membrane Ca-ATPase (PMCA), and the ER Ca(2+) pump sarco/ER Ca(2+)-ATPase (SERCA). Model calculations show that this combined parallel regulation in protein expression levels effectively stabilizes basal cytosolic and ER Ca(2+) levels and preserves receptor signaling. Our results demonstrate that, rather than directly controlling the relative level of signaling proteins in a forward regulation strategy, cells prevent transmission failure by sensing the state of the signaling pathway and using multiple parallel adaptive feedbacks. link: http://identifiers.org/pubmed/21844332

Despite improvements in cancer therapy and treatments, tumor recurrence is a common event in cancer patients. One explanation of recurrence is that cancer therapy focuses on treatment of tumor cells and does not eradicate cancer stem cells (CSCs). CSCs are postulated to behave similar to normal stem cells in that their role is to maintain homeostasis. That is, when the population of tumor cells is reduced or depleted by treatment, CSCs will repopulate the tumor, causing recurrence. In this paper, we study the application of the CSC Hypothesis to the treatment of glioblastoma multiforme by immunotherapy. We extend the work of Kogan et al. (2008) to incorporate the dynamics of CSCs, prove the existence of a recurrence state, and provide an analysis of possible cancerous states and their dependence on treatment levels. link: http://identifiers.org/pubmed/27022405

Not many models of mammalian cell cycle system exist due to its complexity. Some models are too complex and hard to understand, while some others are too simple and not comprehensive enough. Moreover, some essential aspects, such as the response of G1-S and G2-M checkpoints to DNA damage as well as the growth factor signalling, have not been investigated from a systems point of view in current mammalian cell cycle models. To address these issues, we bring a holistic perspective to cell cycle by mathematically modelling it as a complex system consisting of important sub-systems that interact with each other. This retains the functionality of the system and provides a clearer interpretation to the processes within it while reducing the complexity in comprehending these processes. To achieve this, we first update a published ODE mathematical model of cell cycle with current knowledge. Then the part of the mathematical model relevant to each sub-system is shown separately in conjunction with a diagram of the sub-system as part of this representation. The model sub-systems are Growth Factor, DNA damage, G1-S, and G2-M checkpoint signalling. To further simplify the model and better explore the function of sub-systems, they are further divided into modules. Here we also add important new modules of: chk-related rapid cell cycle arrest, p53 modules expanded to seamlessly integrate with the rapid arrest module, Tyrosine phosphatase modules that activate CycCdk complexes and play a crucial role in rapid and delay arrest at both G1-S and G2-M, Tyrosine Kinase module that is important for inactivating nuclear transport of CycBcdk1 through Wee1 to resist M phase entry, Plk1-Related module that is crucial in activating Tyrosine phosphatases and inactivating Tyrosine kinase, and APC-Related module to show steps in CycB degradation. This multi-level systems approach incorporating all known aspects of cell cycle allowed us to (i) study, through dynamic simulation of an ODE model, comprehensive details of cell cycle dynamics under normal and DNA damage conditions revealing the role and value of the added new modules and elements, (ii) assess, through a global sensitivity analysis, the most influential sub-systems, modules and parameters on system response, such as G1-S and G2-M transitions, and (iii) probe deeply into the relationship between DNA damage and cell cycle progression and test the biological evidence that G1-S is relatively inefficient in arresting damaged cells compared to G2-M checkpoint. To perform sensitivity analysis, Self-Organizing Map with Correlation Coefficient Analysis (SOMCCA) is developed which shows that Growth Factor and G1-S Checkpoint sub-systems and 13 parameters in the modules within them are crucial for G1-S and G2-M transitions. To study the relative efficiency of DNA damage checkpoints, a Checkpoint Efficiency Evaluator (CEE) is developed based on perturbation studies and statistical Type II error. Accordingly, cell cycle is about 96% efficient in arresting damaged cells with G2-M checkpoint being more efficient than G1-S. Further, both checkpoint systems are near perfect (98.6%) in passing healthy cells. Thus this study has shown the efficacy of the proposed systems approach to gain a better understanding of different aspects of mammalian cell cycle system separately and as an integrated system that will also be useful in investigating targeted therapy in future cancer treatments. link: http://identifiers.org/pubmed/28647496

The kinetics of binding L-arginine and three alternative substrates (homoarginine, N-methylarginine, and N-hydroxyarginine) to neuronal nitric oxide synthase (nNOS) were characterized by conventional and stopped-flow spectroscopy. Because binding these substrates has only a small effect on the light absorbance spectrum of tetrahydrobiopterin-saturated nNOS, their binding was monitored by following displacement of imidazole, which displays a significant change in Soret absorbance from 427 to 398 nm. Rates of spectral change upon mixing Im-nNOS with increasing amounts of substrates were obtained and found to be monophasic in all cases. For each substrate, a plot of the apparent rate versus substrate concentration showed saturation at the higher concentrations. K(-)(1), k(2), k(-)(2), and the apparent dissociation constant were derived for each substrate from the kinetic data. The dissociation constants mostly agreed with those calculated from equilibrium spectral data obtained by titrating Im-nNOS with each substrate. We conclude that nNOS follows a two-step, reversible mechanism of substrate binding in which there is a rapid equilibrium between Im-nNOS and the substrate S followed by a slower isomerization process to generate nNOS'-S: Im-nNOS + S if Im-nNOS-S if nNOS'-S + Im. All four substrates followed this general mechanism, but differences in their kinetic values were significant and may contribute to their varying capacities to support NO synthesis. link: http://identifiers.org/pubmed/10493814

The kinetics of binding L-arginine and three alternative substrates (homoarginine, N-methylarginine, and N-hydroxyarginine) to neuronal nitric oxide synthase (nNOS) were characterized by conventional and stopped-flow spectroscopy. Because binding these substrates has only a small effect on the light absorbance spectrum of tetrahydrobiopterin-saturated nNOS, their binding was monitored by following displacement of imidazole, which displays a significant change in Soret absorbance from 427 to 398 nm. Rates of spectral change upon mixing Im-nNOS with increasing amounts of substrates were obtained and found to be monophasic in all cases. For each substrate, a plot of the apparent rate versus substrate concentration showed saturation at the higher concentrations. K(-)(1), k(2), k(-)(2), and the apparent dissociation constant were derived for each substrate from the kinetic data. The dissociation constants mostly agreed with those calculated from equilibrium spectral data obtained by titrating Im-nNOS with each substrate. We conclude that nNOS follows a two-step, reversible mechanism of substrate binding in which there is a rapid equilibrium between Im-nNOS and the substrate S followed by a slower isomerization process to generate nNOS'-S: Im-nNOS + S if Im-nNOS-S if nNOS'-S + Im. All four substrates followed this general mechanism, but differences in their kinetic values were significant and may contribute to their varying capacities to support NO synthesis. link: http://identifiers.org/pubmed/10493814

The kinetics of binding L-arginine and three alternative substrates (homoarginine, N-methylarginine, and N-hydroxyarginine) to neuronal nitric oxide synthase (nNOS) were characterized by conventional and stopped-flow spectroscopy. Because binding these substrates has only a small effect on the light absorbance spectrum of tetrahydrobiopterin-saturated nNOS, their binding was monitored by following displacement of imidazole, which displays a significant change in Soret absorbance from 427 to 398 nm. Rates of spectral change upon mixing Im-nNOS with increasing amounts of substrates were obtained and found to be monophasic in all cases. For each substrate, a plot of the apparent rate versus substrate concentration showed saturation at the higher concentrations. K(-)(1), k(2), k(-)(2), and the apparent dissociation constant were derived for each substrate from the kinetic data. The dissociation constants mostly agreed with those calculated from equilibrium spectral data obtained by titrating Im-nNOS with each substrate. We conclude that nNOS follows a two-step, reversible mechanism of substrate binding in which there is a rapid equilibrium between Im-nNOS and the substrate S followed by a slower isomerization process to generate nNOS'-S: Im-nNOS + S if Im-nNOS-S if nNOS'-S + Im. All four substrates followed this general mechanism, but differences in their kinetic values were significant and may contribute to their varying capacities to support NO synthesis. link: http://identifiers.org/pubmed/10493814

The kinetics of binding L-arginine and three alternative substrates (homoarginine, N-methylarginine, and N-hydroxyarginine) to neuronal nitric oxide synthase (nNOS) were characterized by conventional and stopped-flow spectroscopy. Because binding these substrates has only a small effect on the light absorbance spectrum of tetrahydrobiopterin-saturated nNOS, their binding was monitored by following displacement of imidazole, which displays a significant change in Soret absorbance from 427 to 398 nm. Rates of spectral change upon mixing Im-nNOS with increasing amounts of substrates were obtained and found to be monophasic in all cases. For each substrate, a plot of the apparent rate versus substrate concentration showed saturation at the higher concentrations. K(-)(1), k(2), k(-)(2), and the apparent dissociation constant were derived for each substrate from the kinetic data. The dissociation constants mostly agreed with those calculated from equilibrium spectral data obtained by titrating Im-nNOS with each substrate. We conclude that nNOS follows a two-step, reversible mechanism of substrate binding in which there is a rapid equilibrium between Im-nNOS and the substrate S followed by a slower isomerization process to generate nNOS'-S: Im-nNOS + S if Im-nNOS-S if nNOS'-S + Im. All four substrates followed this general mechanism, but differences in their kinetic values were significant and may contribute to their varying capacities to support NO synthesis. link: http://identifiers.org/pubmed/10493814

Salmonella are closely related to commensal Escherichia coli but have gained virulence factors enabling them to behave as enteric pathogens. Less well studied are the similarities and differences that exist between the metabolic properties of these organisms that may contribute toward niche adaptation of Salmonella pathogens. To address this, we have constructed a genome scale Salmonella metabolic model (iMA945). The model comprises 945 open reading frames or genes, 1964 reactions, and 1036 metabolites. There was significant overlap with genes present in E. coli MG1655 model iAF1260. In silico growth predictions were simulated using the model on different carbon, nitrogen, phosphorous, and sulfur sources. These were compared with substrate utilization data gathered from high throughput phenotyping microarrays revealing good agreement. Of the compounds tested, the majority were utilizable by both Salmonella and E. coli. Nevertheless a number of differences were identified both between Salmonella and E. coli and also within the Salmonella strains included. These differences provide valuable insight into differences between a commensal and a closely related pathogen and within different pathogenic strains opening new avenues for future explorations. link: http://identifiers.org/pubmed/19690172

Kinetic models of metabolism require detailed knowledge of kinetic parameters. However, due to measurement errors or lack of data this knowledge is often uncertain. The model of glycolysis in the parasitic protozoan Trypanosoma brucei is a particularly well analysed example of a quantitative metabolic model, but so far it has been studied with a fixed set of parameters only. Here we evaluate the effect of parameter uncertainty. In order to define probability distributions for each parameter, information about the experimental sources and confidence intervals for all parameters were collected. We created a wiki-based website dedicated to the detailed documentation of this information: the SilicoTryp wiki (http://silicotryp.ibls.gla.ac.uk/wiki/Glycolysis). Using information collected in the wiki, we then assigned probability distributions to all parameters of the model. This allowed us to sample sets of alternative models, accurately representing our degree of uncertainty. Some properties of the model, such as the repartition of the glycolytic flux between the glycerol and pyruvate producing branches, are robust to these uncertainties. However, our analysis also allowed us to identify fragilities of the model leading to the accumulation of 3-phosphoglycerate and/or pyruvate. The analysis of the control coefficients revealed the importance of taking into account the uncertainties about the parameters, as the ranking of the reactions can be greatly affected. This work will now form the basis for a comprehensive Bayesian analysis and extension of the model considering alternative topologies. link: http://identifiers.org/pubmed/22379410

Thrombotic disorders can lead to uncontrolled thrombin generation and clot formation within the circulatory system leading to vascular thrombosis. Direct inhibitors of thrombin have been developed and tested in clinical trials for the treatment of a variety of these thrombotic disorders. The bleeding complications observed during these trials have raised questions about their clinical use. The development of a computer-based model of coagulation using the kinetic rates of individual reactions and concentrations of the constituents involved in each reaction within blood has made it possible to study coagulation pathologies in silico. We present an extension of our initial model of coagulation to include several specific thrombin inhibitors. Using this model we have studied the effect of a variety of inhibitors on thrombin generation and compared these results with the clinically observed data. The data suggest that numerical models will be useful in predicting the effectiveness of inhibitors of coagulation. link: http://identifiers.org/pubmed/12871372

Time-dependent light input is an important feature of computational models of the circadian clock. However, publicly available models encoded in standard representations such as the Systems Biology Markup Language (SBML) either do not encode this input or use different mechanisms to do so, which hinders reproducibility of published results as well as model reuse. The authors describe here a numerically continuous function suitable for use in SBML for models of circadian rhythms forced by periodic light-dark cycles. The Input Signal Step Function (ISSF) is broadly applicable to encoding experimental manipulations, such as drug treatments, temperature changes, or inducible transgene expression, which may be transient, periodic, or mixed. It is highly configurable and is able to reproduce a wide range of waveforms. The authors have implemented this function in SBML and demonstrated its ability to modify the behavior of publicly available models to accurately reproduce published results. The implementation of ISSF allows standard simulation software to reproduce specialized circadian protocols, such as the phase-response curve. To facilitate the reuse of this function in public models, the authors have developed software to configure its behavior without any specialist knowledge of SBML. A community-standard approach to represent the inputs that entrain circadian clock models could particularly facilitate research in chronobiology. link: http://identifiers.org/pubmed/22855577

In higher plants, the amino acid phenylalanine is a substrate of both primary and secondary metabolic pathways. The primary pathway that consumes phenylalanine, protein biosynthesis, is essential for the viability of all cells. Meanwhile, the secondary pathways are not necessary for the survival of individual cells, but benefit of the plant as a whole. Here we focus on the monolignol pathway, a secondary metabolic pathway in the cytosol that rapidly consumes phenylalanine to produce the precursors of lignin during wood formation. In planta monolignol biosynthesis involves a series of seemingly redundant steps wherein shikimate, a precursor of phenylalanine synthesized in the plastid, is transiently ligated to the main substrate of the pathway. However, shikimate is not catalytically involved in the reactions of the monolignol pathway, and is only needed for pathway enzymes to recognize their main substrates. After some steps the shikimate moiety is removed unaltered, and the main substrate continues along the pathway. It has been suggested that this portion of the monolignol pathway fulfills a regulatory role in the following way. Low phenylalanine concentrations (viz. availability) correlate with low shikimate concentrations. When shikimate concentratios are low, flux into the monolignol pathway will be limited by means of the steps requiring shikimate. Thus, when the concentration of phenylalanine is low it will be reserved for protein biosynthesis. Here we employ a theoretical approach to test this hypothesis. Simplified versions of plant phenylalanine metabolism are modelled as systems of ordinary differential equations. Our analysis shows that the seemingly redundant steps can be sufficient for the prioritization of protein biosynthesis over the monolignol pathway when the availability of phenylalanine is low, depending on system parameters. Thus, the phenylalanine precursor shikimate may signal low phenylalanine availability to secondary pathways. Because our models have been abstracted from plant phenylalanine metabolism, this mechanism of metabolic signalling, which we call the Precursor Shutoff Valve (PSV), may also be present in other biochemical networks comprised of two pathways that share a common substrate. link: http://identifiers.org/pubmed/30412698

This is a mathematical study about tumor growth from a different perspective, with the aim of predicting and/or controlling the disease. The focus is on the effect and interaction of tumor cell with immune and drug. This paper presents a mathematical model of immune response and a cycle phase specific drug using a system of ordinary differential equations. Stability analysis is used to produce stability regions for various values of certain parameters during mitosis. The stability region of the graph shows that the curve splits the tumor decay and growth regions in the absence of immune response. However, when immune response is present, the tumor growth region is decreased. When drugs are considered in the system, the stability region remains unchanged as the system with the presence of immune response but the population of tumor cells at interphase and metaphase is reduced with percentage differences of 1.27 and 1.53 respectively. The combination of immunity and drug to fight cancer provides a better method to reduce tumor population compared to immunity alone. link: http://identifiers.org/doi/10.11113/jt.v79.9791

Combined virotherapy and immunotherapy has been emergingas a promising and effective cancer treatment for some time.Intratumoural injections of an oncolytic virus instigate an immunereaction in the host, resulting in an influx of immune cells tothe tumour site. Through combining an oncolytic viral vector withimmunostimulatory cytokines an additional antitumour immuneresponse can be initiated, whereby immune cells induce apoptosisin both uninfected and virus infected tumour cells. We developa mathematical model to reproduce the experimental results fortumour growth under treatment with an oncolytic adenovirus co-expressing the immunostimulatory cytokines interleukin 12 (IL-12)and granulocyte-monocyte colony stimulating factor (GM-CSF). Byexploring heterogeneity in the immune cell stimulation by thetreatment, we find a subset of the parameter space for the immunecell induced apoptosis rate, in which the treatment will be lesseffective in a short time period. Therefore, we believe the bivariatenature of treatment outcome, whereby tumours are either completelyeradicated or grow unbounded, can be explained by heterogeneity inthis immune characteristic. Furthermore, the model highlights theapparent presence of negative feedback in the helper T cell and APCstimulation dynamics, when IL-12 and GM-CSF are co-expressed asopposed to individually expressed by the viral vector. link: http://identifiers.org/doi/10.1080/23737867.2018.1438216

The cancer stem cell hypothesis has gained currency in recent times but concerns remain about its scientific foundations because of significant gaps that exist between research findings and comprehensive knowledge about cancer stem cells (CSCs). In this light, a mathematical model that considers hematopoietic dynamics in the diseased state of the bone marrow and peripheral blood is proposed and used to address findings about CSCs. The ensuing model, resulting from a modification and refinement of a recent model, develops out of the position that mathematical models of CSC development, that are few at this time, are needed to provide insightful underpinnings for biomedical findings about CSCs as the CSC idea gains traction. Accordingly, the mathematical challenges brought on by the model that mirror general challenges in dealing with nonlinear phenomena are discussed and placed in context. The proposed model describes the logical occurrence of discrete time delays, that by themselves present mathematical challenges, in the evolving cell populations under consideration. Under the challenging circumstances, the steady state properties of the model system of delay differential equations are obtained, analyzed, and the resulting mathematical predictions arising therefrom are interpreted and placed within the framework of findings regarding CSCs. Simulations of the model are carried out by considering various parameter scenarios that reflect different experimental situations involving disease evolution in human hosts. Model analyses and simulations suggest that the emergence of the cancer stem cell population alongside other malignant cells engenders higher dimensions of complexity in the evolution of malignancy in the bone marrow and peripheral blood at the expense of healthy hematopoietic development. The model predicts the evolution of an aberrant environment in which the malignant population particularly in the bone marrow shows tendencies of reaching an uncontrollable equilibrium state. Essentially, the model shows that a structural relationship exists between CSCs and non-stem malignant cells that confers on CSCs the role of temporally enhancing and stimulating the expansion of non-stem malignant cells while also benefitting from increases in their own population and these CSCs may be the main protagonists that drive the ultimate evolution of the uncontrollable equilibrium state of such malignant cells and these may have implications for treatment. link: http://identifiers.org/pubmed/30296448

The model reproduces the time profiles of p27, E2F and aE/cdk2 as depicted in Figure 5 c of the paper. Model was simulated on MathSBML.

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Li C, Donizelli M, Rodriguez N, Dharuri H, Endler L, Chelliah V, Li L, He E, Henry A, Stefan MI, Snoep JL, Hucka M, Le Novère N, Laibe C (2010) BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst Biol., 4:92.

HIV infection leads to two cell fates, the viral productive state or viral latency (a reversible non-productive state). HIV latency is relevant because infected active CD4+ T-lymphocytes can reach a resting memory state in which the provirus remains silent for long periods of time. Despite experimental and theoretical efforts, the causal molecular mechanisms responsible for HIV latency are only partially understood. Studies have determined that HIV latency is influenced by the innate immune response carried out by cell restriction factors that inhibit the postintegration steps in the virus replication cycle. In this study, we present a mathematical study that combines deterministic and stochastic approaches to analyze the interactions between HIV proteins and the innate immune response. Using wide ranges of parameter values, we observed the following: (1) a phenomenological description of the viral productive and latent cell phenotypes is obtained by bistable and bimodal dynamics, (2) biochemical noise reduces the probability that an infected cell adopts the latent state, (3) the effects of the innate immune response enhance the HIV latency state, (4) the conditions of the cell before infection affect the latent phenotype, i.e., the existing expression of cell restriction factors propitiates HIV latency, and existing expression of HIV proteins reduces HIV latency. link: http://identifiers.org/pubmed/24997239

Background: Mathematical models are used to gain an integrative understanding of biochemical processes and networks. Commonly the models are based on deterministic ordinary differential equations. When molecular counts are low, stochastic formalisms like Monte Carlo simulations are more appropriate and well established. However, compared to the wealth of computational methods used to fit and analyze deterministic models, there is only little available to quantify the exactness of the fit of stochastic models compared to experimental data or to analyze different aspects of the modeling results. Results: Here, we developed a method to fit stochastic simulations to experimental high-throughput data, meaning data that exhibits distributions. The method uses a comparison of the probability density functions that are computed based on Monte Carlo simulations and the experimental data. Multiple parameter values are iteratively evaluated using optimization routines. The method improves its performance by selecting parameters values after comparing the similitude between the deterministic stability of the system and the modes in the experimental data distribution. As a case study we fitted a model of the IRF7 gene expression circuit to time-course experimental data obtained by flow cytometry. IRF7 shows bimodal dynamics upon IFN stimulation. This dynamics occurs due to the switching between active and basal states of the IRF7 promoter. However, the exact molecular mechanisms responsible for the bimodality of IRF7 is not fully understood. Conclusions: Our results allow us to conclude that the activation of the IRF7 promoter by the combination of IRF7 and ISGF3 is sufficient to explain the observed bimodal dynamics. link: http://identifiers.org/doi/10.1186/s12918-017-0406-4

Background: Mathematical models are used to gain an integrative understanding of biochemical processes and networks. Commonly the models are based on deterministic ordinary differential equations. When molecular counts are low, stochastic formalisms like Monte Carlo simulations are more appropriate and well established. However, compared to the wealth of computational methods used to fit and analyze deterministic models, there is only little available to quantify the exactness of the fit of stochastic models compared to experimental data or to analyze different aspects of the modeling results. Results: Here, we developed a method to fit stochastic simulations to experimental high-throughput data, meaning data that exhibits distributions. The method uses a comparison of the probability density functions that are computed based on Monte Carlo simulations and the experimental data. Multiple parameter values are iteratively evaluated using optimization routines. The method improves its performance by selecting parameters values after comparing the similitude between the deterministic stability of the system and the modes in the experimental data distribution. As a case study we fitted a model of the IRF7 gene expression circuit to time-course experimental data obtained by flow cytometry. IRF7 shows bimodal dynamics upon IFN stimulation. This dynamics occurs due to the switching between active and basal states of the IRF7 promoter. However, the exact molecular mechanisms responsible for the bimodality of IRF7 is not fully understood. Conclusions: Our results allow us to conclude that the activation of the IRF7 promoter by the combination of IRF7 and ISGF3 is sufficient to explain the observed bimodal dynamics. link: http://identifiers.org/doi/10.1186/s12918-017-0406-4

Rice straw is a major crop residue which is burnt in many countries, creating significant air pollution. Thus, alternative routes for disposal of rice straw are needed. Biotechnological treatment of rice straw hydrolysate has potential to convert this agriculture waste into valuable biofuel(s) and platform chemicals. Geobacillus thermoglucosidasius is a thermophile with properties specially suited for use as a biocatalyst in lignocellulosic bioprocesses, such as high optimal temperature and tolerance to high levels of ethanol. However, the capabilities of Geobacillus thermoglucosidasius to utilize sugars in rice straw hydrolysate for making bioethanol and other platform chemicals have not been fully explored. In this work, we have created a genome scale metabolic model (denoted iGT736) of the organism containing 736 gene products, 1159 reactions and 1163 metabolites. The model was validated both by purely theoretical approaches and by comparing the behaviour of the model to previously published experimental results. The model was then used to determine the yields of a variety of platform chemicals from glucose and xylose — two primary sugars in rice straw hydrolysate. A comparison with results from a model of Escherichia coli shows that Geobacillus thermoglucosidasius is capable of producing a wider range of products, and that for the products also produced by Escherichia coli, the yields are comparable. We also discuss strategies to utilise arabinose, a minor component of rice straw hydrolysate, and propose additional reactions to lead to the synthesis of xylitol, not currently produced by Geobacillus thermoglucosidasius. Our results provide additional motivation for the current exploration of the industrial potential of Geobacillus thermoglucosidasius and we make our model publicly available to aid the development of metabolic engineering strategies for this organism. link: http://identifiers.org/doi/10.1016/j.jbiotec.2017.03.031

Molecular interaction networks establish all cell biological processes. The networks are under intensive research that is facilitated by new high-throughput measurement techniques for the detection, quantification, and characterization of molecules and their physical interactions. For the common model organism yeast Saccharomyces cerevisiae, public databases store a significant part of the accumulated information and, on the way to better understanding of the cellular processes, there is a need to integrate this information into a consistent reconstruction of the molecular interaction network. This work presents and validates RefRec, the most comprehensive molecular interaction network reconstruction currently available for yeast. The reconstruction integrates protein synthesis pathways, a metabolic network, and a protein-protein interaction network from major biological databases. The core of the reconstruction is based on a reference object approach in which genes, transcripts, and proteins are identified using their primary sequences. This enables their unambiguous identification and non-redundant integration. The obtained total number of different molecular species and their connecting interactions is approximately 67,000. In order to demonstrate the capacity of RefRec for functional predictions, it was used for simulating the gene knockout damage propagation in the molecular interaction network in approximately 590,000 experimentally validated mutant strains. Based on the simulation results, a statistical classifier was subsequently able to correctly predict the viability of most of the strains. The results also showed that the usage of different types of molecular species in the reconstruction is important for accurate phenotype prediction. In general, the findings demonstrate the benefits of global reconstructions of molecular interaction networks. With all the molecular species and their physical interactions explicitly modeled, our reconstruction is able to serve as a valuable resource in additional analyses involving objects from multiple molecular -omes. For that purpose, RefRec is freely available in the Systems Biology Markup Language format. link: http://identifiers.org/pubmed/20498836

Stimulus reinforcement strengthens learning. Intervals between reinforcement affect both the kind of learning that occurs and the amount of learning. Stimuli spaced by a few minutes result in more effective learning than when massed together. There are several synaptic correlates of repeated stimuli, such as different kinds of plasticity and the amplitude of synaptic change. Here we study the role of signalling pathways in the synapse on this selectivity for spaced stimuli. Using the in vitro hippocampal slice technique we monitored long-term potentiation (LTP) amplitude in CA1 for repeated 100-Hz, 1-s tetani. We observe the highest LTP levels when the inter-tetanus interval is 5-10 min. We tested biochemical activity in the slice following the same stimuli, and found that extracellular signal-regulated kinase type II (ERKII) but not CaMKII exhibits a peak at about 10 min. When calcium influx into the slice is buffered using AM-ester calcium dyes, amplitude of the physiological and biochemical response is reduced, but the timing is not shifted. We have previously used computer simulations of synaptic signalling to predict such temporal tuning from signalling pathways. In the current study we consider feedback and feedforward models that exhibit temporal tuning consistent with our experiments. We find that a model incorporating post-stimulus build-up of PKM zeta acting upstream of mitogen-activated protein kinase is sufficient to explain the observed temporal tuning. On the basis of these combined experimental and modelling results we propose that the dynamics of PKM activation and ERKII signalling may provide a mechanism for functionally important forms of synaptic pattern selectivity. link: http://identifiers.org/pubmed/15548210

Stimulus reinforcement strengthens learning. Intervals between reinforcement affect both the kind of learning that occurs and the amount of learning. Stimuli spaced by a few minutes result in more effective learning than when massed together. There are several synaptic correlates of repeated stimuli, such as different kinds of plasticity and the amplitude of synaptic change. Here we study the role of signalling pathways in the synapse on this selectivity for spaced stimuli. Using the in vitro hippocampal slice technique we monitored long-term potentiation (LTP) amplitude in CA1 for repeated 100-Hz, 1-s tetani. We observe the highest LTP levels when the inter-tetanus interval is 5-10 min. We tested biochemical activity in the slice following the same stimuli, and found that extracellular signal-regulated kinase type II (ERKII) but not CaMKII exhibits a peak at about 10 min. When calcium influx into the slice is buffered using AM-ester calcium dyes, amplitude of the physiological and biochemical response is reduced, but the timing is not shifted. We have previously used computer simulations of synaptic signalling to predict such temporal tuning from signalling pathways. In the current study we consider feedback and feedforward models that exhibit temporal tuning consistent with our experiments. We find that a model incorporating post-stimulus build-up of PKM zeta acting upstream of mitogen-activated protein kinase is sufficient to explain the observed temporal tuning. On the basis of these combined experimental and modelling results we propose that the dynamics of PKM activation and ERKII signalling may provide a mechanism for functionally important forms of synaptic pattern selectivity. link: http://identifiers.org/pubmed/15548210

Stimulus reinforcement strengthens learning. Intervals between reinforcement affect both the kind of learning that occurs and the amount of learning. Stimuli spaced by a few minutes result in more effective learning than when massed together. There are several synaptic correlates of repeated stimuli, such as different kinds of plasticity and the amplitude of synaptic change. Here we study the role of signalling pathways in the synapse on this selectivity for spaced stimuli. Using the in vitro hippocampal slice technique we monitored long-term potentiation (LTP) amplitude in CA1 for repeated 100-Hz, 1-s tetani. We observe the highest LTP levels when the inter-tetanus interval is 5-10 min. We tested biochemical activity in the slice following the same stimuli, and found that extracellular signal-regulated kinase type II (ERKII) but not CaMKII exhibits a peak at about 10 min. When calcium influx into the slice is buffered using AM-ester calcium dyes, amplitude of the physiological and biochemical response is reduced, but the timing is not shifted. We have previously used computer simulations of synaptic signalling to predict such temporal tuning from signalling pathways. In the current study we consider feedback and feedforward models that exhibit temporal tuning consistent with our experiments. We find that a model incorporating post-stimulus build-up of PKM zeta acting upstream of mitogen-activated protein kinase is sufficient to explain the observed temporal tuning. On the basis of these combined experimental and modelling results we propose that the dynamics of PKM activation and ERKII signalling may provide a mechanism for functionally important forms of synaptic pattern selectivity. link: http://identifiers.org/pubmed/15548210

Strong inputs to neurons trigger complex biochemical events leading to synaptic plasticity. These biochemical events occur at many spatial scales, ranging from submicron dendritic spines to signals that propagate hundreds of microns from dendrites to the nucleus. ERKII is an important signaling molecule that is involved in many aspects of plasticity, including local excitability, communication with the nucleus, and control of local protein synthesis. We observed that ERKII activation spreads long distances in apical dendrites of stimulated hippocampal CA1 pyramidal neurons. We combined experiments and models to show that this >100 mum spread was too large to be explained by biochemical reaction-diffusion effects. We show that two modes of calcium entry along the dendrite contribute to the extensive activation of ERKII. We predict the occurrence of feedback between biophysical events resulting in calcium entry, and biochemical events resulting in ERKII activation. This feedback causes a switch-like propagation of ERKII activation, coupled with enhanced electrical excitability, along the apical dendrite. We propose that this propagating switch forms zones on dendrites in which plasticity is facilitated. link: http://identifiers.org/pubmed/19404460

Strong inputs to neurons trigger complex biochemical events leading to synaptic plasticity. These biochemical events occur at many spatial scales, ranging from submicron dendritic spines to signals that propagate hundreds of microns from dendrites to the nucleus. ERKII is an important signaling molecule that is involved in many aspects of plasticity, including local excitability, communication with the nucleus, and control of local protein synthesis. We observed that ERKII activation spreads long distances in apical dendrites of stimulated hippocampal CA1 pyramidal neurons. We combined experiments and models to show that this >100 mum spread was too large to be explained by biochemical reaction-diffusion effects. We show that two modes of calcium entry along the dendrite contribute to the extensive activation of ERKII. We predict the occurrence of feedback between biophysical events resulting in calcium entry, and biochemical events resulting in ERKII activation. This feedback causes a switch-like propagation of ERKII activation, coupled with enhanced electrical excitability, along the apical dendrite. We propose that this propagating switch forms zones on dendrites in which plasticity is facilitated. link: http://identifiers.org/pubmed/19404460

A striking and defining feature of circadian clocks is the small variation in period over a physiological range of temperatures. This is referred to as temperature compensation, although recent work has suggested that the variation observed is a specific, adaptive control of period. Moreover, given that many biological rate constants have a Q(10) of around 2, it is remarkable that such clocks remain rhythmic under significant temperature changes. We introduce a new mathematical model for the Neurospora crassa circadian network incorporating experimental work showing that temperature alters the balance of translation between a short and long form of the FREQUENCY (FRQ) protein. This is used to discuss period control and functionality for the Neurospora system. The model reproduces a broad range of key experimental data on temperature dependence and rhythmicity, both in wild-type and mutant strains. We present a simple mechanism utilising the presence of the FRQ isoforms (isoform switching) by which period control could have evolved, and argue that this regulatory structure may also increase the temperature range where the clock is robustly rhythmic. link: http://identifiers.org/pubmed/18277380

A striking and defining feature of circadian clocks is the small variation in period over a physiological range of temperatures. This is referred to as temperature compensation, although recent work has suggested that the variation observed is a specific, adaptive control of period. Moreover, given that many biological rate constants have a Q(10) of around 2, it is remarkable that such clocks remain rhythmic under significant temperature changes. We introduce a new mathematical model for the Neurospora crassa circadian network incorporating experimental work showing that temperature alters the balance of translation between a short and long form of the FREQUENCY (FRQ) protein. This is used to discuss period control and functionality for the Neurospora system. The model reproduces a broad range of key experimental data on temperature dependence and rhythmicity, both in wild-type and mutant strains. We present a simple mechanism utilising the presence of the FRQ isoforms (isoform switching) by which period control could have evolved, and argue that this regulatory structure may also increase the temperature range where the clock is robustly rhythmic. link: http://identifiers.org/pubmed/18277380

Non-invasive measurements of pH have shown that both tumour and normal cells have intracellular pH (pHi) that lies on the alkaline side of neutrality (7.1-7.2). However, extracellular pH (pHe) is reported to be more acidic in some tumours compared to normal tissues. Many cellular processes and therapeutic agents are known to be tightly pH dependent which makes the study of intracellular pH regulation of paramount importance. We develop a mathematical model that examines the role of various membrane-based ion transporters in tumour pH regulation, in particular, with a focus on the interplay between lactate and H(+) ions and whether the lactate/H(+) symporter activity is sufficient to give rise to the observed reversed pH gradient that is seen is some tumours. Using linear stability analysis and numerical methods, we are able to gain a clear understanding of the relationship between lactate and H(+) ions. We extend this analysis using perturbation techniques to specifically examine a rapid change in H(+)-ion concentrations relative to variations in lactate. We then perform a parameter sensitivity analysis to explore solution robustness to parameter variations. An important result from our study is that a reversed pH gradient is possible in our system but for unrealistic parameter estimates-pointing to the possible involvement of other mechanisms in cellular pH gradient reversal, for example acidic vesicles, lysosomes, golgi and endosomes. link: http://identifiers.org/pubmed/23340437

The transition from exponential to stationary phase in Streptomyces coelicolor is accompanied by a major metabolic switch and results in a strong activation of secondary metabolism. Here we have explored the underlying reorganization of the metabolome by combining computational predictions based on constraint-based modeling and detailed transcriptomics time course observations.We reconstructed the stoichiometric matrix of S. coelicolor, including the major antibiotic biosynthesis pathways, and performed flux balance analysis to predict flux changes that occur when the cell switches from biomass to antibiotic production. We defined the model input based on observed fermenter culture data and used a dynamically varying objective function to represent the metabolic switch. The predicted fluxes of many genes show highly significant correlation to the time series of the corresponding gene expression data. Individual mispredictions identify novel links between antibiotic production and primary metabolism.Our results show the usefulness of constraint-based modeling for providing a detailed interpretation of time course gene expression data. link: http://identifiers.org/pubmed/20338070

Apoptosis in response to TRAIL or TNF requires the activation of initiator caspases, which then activate the effector caspases that dismantle cells and cause death. However, little is known about the dynamics and regulatory logic linking initiators and effectors. Using a combination of live-cell reporters, flow cytometry, and immunoblotting, we find that initiator caspases are active during the long and variable delay that precedes mitochondrial outer membrane permeabilization (MOMP) and effector caspase activation. When combined with a mathematical model of core apoptosis pathways, experimental perturbation of regulatory links between initiator and effector caspases reveals that XIAP and proteasome-dependent degradation of effector caspases are important in restraining activity during the pre-MOMP delay. We identify conditions in which restraint is impaired, creating a physiologically indeterminate state of partial cell death with the potential to generate genomic instability. Together, these findings provide a quantitative picture of caspase regulatory networks and their failure modes. link: http://identifiers.org/pubmed/18406323

A mathematical model of glycolysis in bloodstream form Trypanosoma brucei was developed previously on the basis of all available enzyme kinetic data (Bakker, B. M., Michels, P. A. M., Opperdoes, F. R., and Westerhoff, H. V. (1997) J. Biol. Chem. 272, 3207-3215). The model predicted correctly the fluxes and cellular metabolite concentrations as measured in non-growing trypanosomes and the major contribution to the flux control exerted by the plasma membrane glucose transporter. Surprisingly, a large overcapacity was predicted for hexokinase (HXK), phosphofructokinase (PFK), and pyruvate kinase (PYK). Here, we present our further analysis of the control of glycolytic flux in bloodstream form T. brucei. First, the model was optimized and extended with recent information about the kinetics of enzymes and their activities as measured in lysates of in vitro cultured growing trypanosomes. Second, the concentrations of five glycolytic enzymes (HXK, PFK, phosphoglycerate mutase, enolase, and PYK) in trypanosomes were changed by RNA interference. The effects of the knockdown of these enzymes on the growth, activities, and levels of various enzymes and glycolytic flux were studied and compared with model predictions. Data thus obtained support the conclusion from the in silico analysis that HXK, PFK, and PYK are in excess, albeit less than predicted. Interestingly, depletion of PFK and enolase had an effect on the activity (but not, or to a lesser extent, expression) of some other glycolytic enzymes. Enzymes located both in the glycosomes (the peroxisome-like organelles harboring the first seven enzymes of the glycolytic pathway of trypanosomes) and in the cytosol were affected. These data suggest the existence of novel regulatory mechanisms operating in trypanosome glycolysis. link: http://identifiers.org/pubmed/15955817

The class of immunosuppressive lymphocytes known as regulatory T cells (Tregs) has been identified as a key component in preventing autoimmune diseases. Although Tregs have been incorporated previously in mathematical models of autoimmunity, we take a novel approach which emphasizes the importance of professional antigen presenting cells (pAPCs). We examine three possible mechanisms of Treg action (each in isolation) through ordinary differential equation (ODE) models. The immune response against a particular autoantigen is suppressed both by Tregs specific for that antigen and by Tregs of arbitrary specificities, through their action on either maturing or already mature pAPCs or on autoreactive effector T cells. In this deterministic approach, we find that qualitative long-term behaviour is predicted by the basic reproductive ratio R(0) for each system. When R(0)<1, only the trivial equilibrium exists and is stable; when R(0)>1, this equilibrium loses its stability and a stable non-trivial equilibrium appears. We interpret the absence of self-damaging populations at the trivial equilibrium to imply a state of self-tolerance, and their presence at the non-trivial equilibrium to imply a state of chronic autoimmunity. Irrespective of mechanism, our model predicts that Tregs specific for the autoantigen in question play no role in the system's qualitative long-term behaviour, but have quantitative effects that could potentially reduce an autoimmune response to sub-clinical levels. Our results also suggest an important role for Tregs of arbitrary specificities in modulating the qualitative outcome. A stochastic treatment of the same model demonstrates that the probability of developing a chronic autoimmune response increases with the initial exposure to self antigen or autoreactive effector T cells. The three different mechanisms we consider, while leading to a number of similar predictions, also exhibit key differences in both transient dynamics (ODE approach) and the probability of chronic autoimmunity (stochastic approach). link: http://identifiers.org/pubmed/20195912

The class of immunosuppressive lymphocytes known as regulatory T cells (Tregs) has been identified as a key component in preventing autoimmune diseases. Although Tregs have been incorporated previously in mathematical models of autoimmunity, we take a novel approach which emphasizes the importance of professional antigen presenting cells (pAPCs). We examine three possible mechanisms of Treg action (each in isolation) through ordinary differential equation (ODE) models. The immune response against a particular autoantigen is suppressed both by Tregs specific for that antigen and by Tregs of arbitrary specificities, through their action on either maturing or already mature pAPCs or on autoreactive effector T cells. In this deterministic approach, we find that qualitative long-term behaviour is predicted by the basic reproductive ratio R(0) for each system. When R(0)<1, only the trivial equilibrium exists and is stable; when R(0)>1, this equilibrium loses its stability and a stable non-trivial equilibrium appears. We interpret the absence of self-damaging populations at the trivial equilibrium to imply a state of self-tolerance, and their presence at the non-trivial equilibrium to imply a state of chronic autoimmunity. Irrespective of mechanism, our model predicts that Tregs specific for the autoantigen in question play no role in the system's qualitative long-term behaviour, but have quantitative effects that could potentially reduce an autoimmune response to sub-clinical levels. Our results also suggest an important role for Tregs of arbitrary specificities in modulating the qualitative outcome. A stochastic treatment of the same model demonstrates that the probability of developing a chronic autoimmune response increases with the initial exposure to self antigen or autoreactive effector T cells. The three different mechanisms we consider, while leading to a number of similar predictions, also exhibit key differences in both transient dynamics (ODE approach) and the probability of chronic autoimmunity (stochastic approach). link: http://identifiers.org/pubmed/20195912

The molecular oscillator of the mammalian circadian clock consists in a dynamical network of genes and proteins whose main regulatory mechanisms occur at the transcriptional level. From a dynamical point of view, the mechanisms leading to an oscillatory solution with an orderly protein peak expression and a clear day/night phase distinction remain unclear. Our goal is to identify the essential interactions needed to generate phase opposition between the activating CLOCK:BMAL1 and the repressing PER:CRY complexes and to better distinguish these two main clock molecular phases relating to rest/activity and fast/feeding cycles. To do this, we develop a transcription-based mathematical model centered on linear combinations of the clock controlled elements (CCEs): E-box, R-box and D-box. Each CCE is responsive to activators and repressors. After model calibration with single-cell data, we explore entrainment and period tuning via interplay with metabolism. Variation of the PER degradation rate γp, relating to the tau mutation, results in asymmetric changes in the duration of the different clock molecular phases. Time spent at the state of high PER/PER:CRY decreases with γp, while time spent at the state of high BMAL1 and CRY1, both proteins with activity in promoting insulin sensitivity, remains constant. This result suggests a possible mechanism behind the altered metabolism of tau mutation animals. Furthermore, we expose the clock system to two regulatory inputs, one relating to the fast/feeding cycle and the other to the light-dependent synchronization signaling. We observe the phase difference between these signals to also affect the relative duration of molecular clock states. Simulated circadian misalignment, known to correlate with insulin resistance, leads to decreased duration of BMAL1 expression. Our results reveal a possible mechanism for clock-controlled metabolic homeostasis, whereby the circadian clock controls the relative duration of different molecular (and metabolic) states in response to signaling inputs. link: http://identifiers.org/pubmed/31539528

Human cancers display intra-tumor heterogeneity in many phenotypic features, such as expression of cell surface receptors, growth, and angiogenic, proliferative, and immunogenic factors, which represent obstacles to a successful immune response. In this paper, we propose a nonlinear mathematical model of cancer immunosurveillance that takes into account some of these features based on cell-mediated immune responses. The model describes phenomena that are seen in vivo, such as tumor dormancy, robustness, immunoselection over tumor heterogeneity (also called "cancer immunoediting") and strong sensitivity to initial conditions in the composition of tumor microenvironment. The results framework has as common element the tumor as an attractor for abnormal cells. Bifurcation analysis give us as tumor attractors fixed-points, limit cycles and chaotic attractors, the latter emerging from period-doubling cascade displaying Feigenbaum's universality. Finally, we simulated both elimination and escape tumor scenarios by means of a stochastic version of the model according to the Doob-Gillespie algorithm. link: http://identifiers.org/pubmed/30930063

This paper develops a mathematical model for the feedback control of glucose regulation in the healthy human being and is based on the work of Sorensen (1985). The proposed model serves as a starting point for modeling type II diabetes. Four agents - glucose and the three hormones insulin, glucagon, and incretins - are assumed to have an effect on glucose metabolism. By letting compartments represent anatomical organs, the model has a close resemblance to a real human body. Mass balance equations that account for blood flows, exchange between compartments, and metabolic sinks and sources are written, and these result in simultaneous differential equations that are solved numerically. The metabolic sinks and sources - removing or adding glucose, insulin, glucagon, and incretins - describe physiological processes in the body. These processes function as feedback control systems and have nonlinear behaviors. The results of simulations performed for three different clinical test types indicate that the model is successful in simulating intravenous glucose, oral glucose, and meals containing mainly carbohydrates link: http://identifiers.org/doi/10.1109/CDC.2006.377192

This paper develops a mathematical model for the feedback control of glucose regulation in the healthy human being and is based on the work of Sorensen (1985). The proposed model serves as a starting point for modeling type II diabetes. Four agents - glucose and the three hormones insulin, glucagon, and incretins - are assumed to have an effect on glucose metabolism. By letting compartments represent anatomical organs, the model has a close resemblance to a real human body. Mass balance equations that account for blood flows, exchange between compartments, and metabolic sinks and sources are written, and these result in simultaneous differential equations that are solved numerically. The metabolic sinks and sources - removing or adding glucose, insulin, glucagon, and incretins - describe physiological processes in the body. These processes function as feedback control systems and have nonlinear behaviors. The results of simulations performed for three different clinical test types indicate that the model is successful in simulating intravenous glucose, oral glucose, and meals containing mainly carbohydrates link: http://identifiers.org/doi/10.1109/CDC.2006.377192

The genome of living organisms is constantly exposed to several damaging agents that induce different types of DNA lesions, leading to cellular malfunctioning and onset of many diseases. To maintain genome stability, cells developed various repair and tolerance systems to counteract the effects of DNA damage. Here we focus on Post Replication Repair (PRR), the pathway involved in the bypass of DNA lesions induced by sunlight exposure and UV radiation. PRR acts through two different mechanisms, activated by mono- and poly-ubiquitylation of the DNA sliding clamp, called Proliferating Cell Nuclear Antigen (PCNA).We developed a novel protocol to measure the time-course ratios between mono-, di- and tri-ubiquitylated PCNA isoforms on a single western blot, which were used as the wet readout for PRR events in wild type and mutant S. cerevisiae cells exposed to acute UV radiation doses. Stochastic simulations of PCNA ubiquitylation dynamics, performed by exploiting a novel mechanistic model of PRR, well fitted the experimental data at low UV doses, but evidenced divergent behaviors at high UV doses, thus driving the design of further experiments to verify new hypothesis on the functioning of PRR. The model predicted the existence of a UV dose threshold for the proper functioning of the PRR model, and highlighted an overlapping effect of Nucleotide Excision Repair (the pathway effectively responsible to clean the genome from UV lesions) on the dynamics of PCNA ubiquitylation in different phases of the cell cycle. In addition, we showed that ubiquitin concentration can affect the rate of PCNA ubiquitylation in PRR, offering a possible explanation to the DNA damage sensitivity of yeast strains lacking deubiquitylating enzymes.We exploited an in vivo and in silico combinational approach to analyze for the first time in a Systems Biology context the events of PCNA ubiquitylation occurring in PRR in budding yeast cells. Our findings highlighted an intricate functional crosstalk between PRR and other events controlling genome stability, and evidenced that PRR is more complicated and still far less characterized than previously thought. link: http://identifiers.org/pubmed/23514624

Multiple interacting mechanisms control the formation and dissolution of clots to maintain blood in a state of delicate balance. In addition to a myriad of biochemical reactions, rheological factors also play a crucial role in modulating the response of blood to external stimuli. To date, a comprehensive model for clot formation and dissolution, that takes into account the biochemical, medical and rheological factors, has not been put into place, the existing models emphasizing either one or the other of the factors. In this paper, after discussing the various biochemical, physiologic and rheological factors at some length, we develop a model for clot formation and dissolution that incorporates many of the relevant crucial factors that have a bearing on the problem. The model, though just a first step towards understanding a complex phenomenon, goes further than previous models in integrating the biochemical, physiologic and rheological factors that come into play. link: http://identifiers.org/doi/10.1080/10273660412331317415

The release of the genome sequences of two strains of Aspergillus niger has allowed systems-level investigations of this important microbial cell factory. To this end, tools for doing data integration of multi-ome data are necessary, and especially interesting in the context of metabolism. On the basis of an A. niger bibliome survey, we present the largest model reconstruction of a metabolic network reported for a fungal species. The reconstructed gapless metabolic network is based on the reportings of 371 articles and comprises 1190 biochemically unique reactions and 871 ORFs. Inclusion of isoenzymes increases the total number of reactions to 2240. A graphical map of the metabolic network is presented. All levels of the reconstruction process were based on manual curation. From the reconstructed metabolic network, a mathematical model was constructed and validated with data on yields, fluxes and transcription. The presented metabolic network and map are useful tools for examining systemwide data in a metabolic context. Results from the validated model show a great potential for expanding the use of A. niger as a high-yield production platform. link: http://identifiers.org/pubmed/18364712

The chronic Philadelphia-negative myeloproliferative neoplasms (MPNs) are acquired stem cell neoplasms which ultimately may transform to acute myelogenous leukemia. Most recently, chronic inflammation has been described as an important factor for the development and progression of MPNs in the biological continuum from early cancer stage to the advanced myelofibrosis stage, the MPNs being described as "A Human Inflammation Model for Cancer Development". This novel concept has been built upon clinical, experimental, genomic, immunological and not least epidemiological studies. Only a few studies have described the development of MPNs by mathematical models, and none have addressed the role of inflammation for clonal evolution and disease progression. Herein, we aim at using mathematical modelling to substantiate the concept of chronic inflammation as an important trigger and driver of MPNs.The basics of the model describe the proliferation from stem cells to mature cells including mutations of healthy stem cells to become malignant stem cells. We include a simple inflammatory coupling coping with cell death and affecting the basic model beneath. First, we describe the system without feedbacks or regulatory interactions. Next, we introduce inflammatory feedback into the system. Finally, we include other feedbacks and regulatory interactions forming the inflammatory-MPN model. Using mathematical modeling, we add further proof to the concept that chronic inflammation may be both a trigger of clonal evolution and an important driving force for MPN disease progression. Our findings support intervention at the earliest stage of cancer development to target the malignant clone and dampen concomitant inflammation. link: http://identifiers.org/pubmed/28859112

Immunotherapies are important methods for controlling and curing malignant tumors. Based on recent observations that many tumors have been immuno-selected to evade recognition by the traditional cytotoxic T lymphocytes, we propose mathematical models of tumor-CD4+-cytokine interactions to investigate the role of CD4+ on tumor regression. Treatments of either CD4+ or cytokine are applied to study their effectiveness. It is found that doses of treatments are critical in determining the fate of the tumor, and tumor cells can be eliminated completely if doses of cytokine are large. Bistability is observed in models with either of the treatment strategies, which signifies that a careful planning of the treatment strategy is necessary for achieving a satisfactory outcome. link: http://identifiers.org/doi/10.1002/mma.3370

Various intracellular bacterial symbionts that provide their host with essential nutrients have much-reduced genomes, attributed largely to genomic decay and relaxed selection. To obtain quantitative estimates of the metabolic function of these bacteria, we reconstructed genome- and transcriptome-informed metabolic models of three xylem-feeding insects that bear two bacterial symbionts with complementary metabolic functions: a primary symbiont, Sulcia, that has codiversified with the insects, and a coprimary symbiont of distinct taxonomic origin and with different degrees of genome reduction in each insect species (Hodgkinia in a cicada, Baumannia in a sharpshooter, and Sodalis in a spittlebug). Our simulations reveal extensive bidirectional flux of multiple metabolites between each symbiont and the host, but near-complete metabolic segregation (i.e., near absence of metabolic cross-feeding) between the two symbionts, a likely mode of host control over symbiont metabolism. Genome reduction of the symbionts is associated with an increased number of host metabolic inputs to the symbiont and also reduced metabolic cost to the host. In particular, Sulcia and Hodgkinia with genomes of ≤0.3 Mb are calculated to recycle ∼30 to 80% of host-derived nitrogen to essential amino acids returned to the host, while Baumannia and Sodalis with genomes of ≥0.6 Mb recycle 10 to 15% of host nitrogen. We hypothesize that genome reduction of symbionts may be driven by selection for increased host control and reduced host costs, as well as by the stochastic process of genomic decay and relaxed selection.IMPORTANCE Current understanding of many animal-microbial symbioses involving unculturable bacterial symbionts with much-reduced genomes derives almost entirely from nonquantitative inferences from genome data. To overcome this limitation, we reconstructed multipartner metabolic models that quantify both the metabolic fluxes within and between three xylem-feeding insects and their bacterial symbionts. This revealed near-complete metabolic segregation between cooccurring bacterial symbionts, despite extensive metabolite exchange between each symbiont and the host, suggestive of strict host controls over the metabolism of its symbionts. We extended the model analysis to investigate metabolic costs. The positive relationship between symbiont genome size and the metabolic cost incurred by the host points to fitness benefits to the host of bearing symbionts with small genomes. The multicompartment metabolic models developed here can be applied to other symbioses that are not readily tractable to experimental approaches. link: http://identifiers.org/pubmed/30254121

Various intracellular bacterial symbionts that provide their host with essential nutrients have much-reduced genomes, attributed largely to genomic decay and relaxed selection. To obtain quantitative estimates of the metabolic function of these bacteria, we reconstructed genome- and transcriptome-informed metabolic models of three xylem-feeding insects that bear two bacterial symbionts with complementary metabolic functions: a primary symbiont, Sulcia, that has codiversified with the insects, and a coprimary symbiont of distinct taxonomic origin and with different degrees of genome reduction in each insect species (Hodgkinia in a cicada, Baumannia in a sharpshooter, and Sodalis in a spittlebug). Our simulations reveal extensive bidirectional flux of multiple metabolites between each symbiont and the host, but near-complete metabolic segregation (i.e., near absence of metabolic cross-feeding) between the two symbionts, a likely mode of host control over symbiont metabolism. Genome reduction of the symbionts is associated with an increased number of host metabolic inputs to the symbiont and also reduced metabolic cost to the host. In particular, Sulcia and Hodgkinia with genomes of ≤0.3 Mb are calculated to recycle ∼30 to 80% of host-derived nitrogen to essential amino acids returned to the host, while Baumannia and Sodalis with genomes of ≥0.6 Mb recycle 10 to 15% of host nitrogen. We hypothesize that genome reduction of symbionts may be driven by selection for increased host control and reduced host costs, as well as by the stochastic process of genomic decay and relaxed selection.IMPORTANCE Current understanding of many animal-microbial symbioses involving unculturable bacterial symbionts with much-reduced genomes derives almost entirely from nonquantitative inferences from genome data. To overcome this limitation, we reconstructed multipartner metabolic models that quantify both the metabolic fluxes within and between three xylem-feeding insects and their bacterial symbionts. This revealed near-complete metabolic segregation between cooccurring bacterial symbionts, despite extensive metabolite exchange between each symbiont and the host, suggestive of strict host controls over the metabolism of its symbionts. We extended the model analysis to investigate metabolic costs. The positive relationship between symbiont genome size and the metabolic cost incurred by the host points to fitness benefits to the host of bearing symbionts with small genomes. The multicompartment metabolic models developed here can be applied to other symbioses that are not readily tractable to experimental approaches. link: http://identifiers.org/pubmed/30254121

Various intracellular bacterial symbionts that provide their host with essential nutrients have much-reduced genomes, attributed largely to genomic decay and relaxed selection. To obtain quantitative estimates of the metabolic function of these bacteria, we reconstructed genome- and transcriptome-informed metabolic models of three xylem-feeding insects that bear two bacterial symbionts with complementary metabolic functions: a primary symbiont, Sulcia, that has codiversified with the insects, and a coprimary symbiont of distinct taxonomic origin and with different degrees of genome reduction in each insect species (Hodgkinia in a cicada, Baumannia in a sharpshooter, and Sodalis in a spittlebug). Our simulations reveal extensive bidirectional flux of multiple metabolites between each symbiont and the host, but near-complete metabolic segregation (i.e., near absence of metabolic cross-feeding) between the two symbionts, a likely mode of host control over symbiont metabolism. Genome reduction of the symbionts is associated with an increased number of host metabolic inputs to the symbiont and also reduced metabolic cost to the host. In particular, Sulcia and Hodgkinia with genomes of ≤0.3 Mb are calculated to recycle ∼30 to 80% of host-derived nitrogen to essential amino acids returned to the host, while Baumannia and Sodalis with genomes of ≥0.6 Mb recycle 10 to 15% of host nitrogen. We hypothesize that genome reduction of symbionts may be driven by selection for increased host control and reduced host costs, as well as by the stochastic process of genomic decay and relaxed selection.IMPORTANCE Current understanding of many animal-microbial symbioses involving unculturable bacterial symbionts with much-reduced genomes derives almost entirely from nonquantitative inferences from genome data. To overcome this limitation, we reconstructed multipartner metabolic models that quantify both the metabolic fluxes within and between three xylem-feeding insects and their bacterial symbionts. This revealed near-complete metabolic segregation between cooccurring bacterial symbionts, despite extensive metabolite exchange between each symbiont and the host, suggestive of strict host controls over the metabolism of its symbionts. We extended the model analysis to investigate metabolic costs. The positive relationship between symbiont genome size and the metabolic cost incurred by the host points to fitness benefits to the host of bearing symbionts with small genomes. The multicompartment metabolic models developed here can be applied to other symbioses that are not readily tractable to experimental approaches. link: http://identifiers.org/pubmed/30254121

Insects feeding on the nutrient-poor diet of xylem plant sap generally bear two microbial symbionts that are localized to different organs (bacteriomes) and provide complementary sets of essential amino acids (EAAs). Here, we investigate the metabolic basis for the apparent paradox that xylem-feeding insects are under intense selection for metabolic efficiency but incur the cost of maintaining two symbionts for functions mediated by one symbiont in other associations. Using stable isotope analysis of central carbon metabolism and metabolic modeling, we provide evidence that the bacteriomes of the spittlebug Clastoptera proteus display high rates of aerobic glycolysis, with syntrophic splitting of glucose oxidation. Specifically, our data suggest that one bacteriome (containing the bacterium Sulcia, which synthesizes seven EAAs) predominantly processes glucose glycolytically, producing pyruvate and lactate, and the exported pyruvate and lactate is assimilated by the second bacteriome (containing the bacterium Zinderia, which synthesizes three energetically costly EAAs) and channeled through the TCA cycle for energy generation by oxidative phosphorylation. We, furthermore, calculate that this metabolic arrangement supports the high ATP demand in Zinderia bacteriomes for Zinderia-mediated synthesis of energy-intensive EAAs. We predict that metabolite cross-feeding among host cells may be widespread in animal–microbe symbioses utilizing low-nutrient diets. link: http://identifiers.org/doi/10.1038/s41396-020-0661-z

Insects feeding on the nutrient-poor diet of xylem plant sap generally bear two microbial symbionts that are localized to different organs (bacteriomes) and provide complementary sets of essential amino acids (EAAs). Here, we investigate the metabolic basis for the apparent paradox that xylem-feeding insects are under intense selection for metabolic efficiency but incur the cost of maintaining two symbionts for functions mediated by one symbiont in other associations. Using stable isotope analysis of central carbon metabolism and metabolic modeling, we provide evidence that the bacteriomes of the spittlebug Clastoptera proteus display high rates of aerobic glycolysis, with syntrophic splitting of glucose oxidation. Specifically, our data suggest that one bacteriome (containing the bacterium Sulcia, which synthesizes seven EAAs) predominantly processes glucose glycolytically, producing pyruvate and lactate, and the exported pyruvate and lactate is assimilated by the second bacteriome (containing the bacterium Zinderia, which synthesizes three energetically costly EAAs) and channeled through the TCA cycle for energy generation by oxidative phosphorylation. We, furthermore, calculate that this metabolic arrangement supports the high ATP demand in Zinderia bacteriomes for Zinderia-mediated synthesis of energy-intensive EAAs. We predict that metabolite cross-feeding among host cells may be widespread in animal–microbe symbioses utilizing low-nutrient diets. link: http://identifiers.org/doi/10.1038/s41396-020-0661-z

Insects feeding on the nutrient-poor diet of xylem plant sap generally bear two microbial symbionts that are localized to different organs (bacteriomes) and provide complementary sets of essential amino acids (EAAs). Here, we investigate the metabolic basis for the apparent paradox that xylem-feeding insects are under intense selection for metabolic efficiency but incur the cost of maintaining two symbionts for functions mediated by one symbiont in other associations. Using stable isotope analysis of central carbon metabolism and metabolic modeling, we provide evidence that the bacteriomes of the spittlebug Clastoptera proteus display high rates of aerobic glycolysis, with syntrophic splitting of glucose oxidation. Specifically, our data suggest that one bacteriome (containing the bacterium Sulcia, which synthesizes seven EAAs) predominantly processes glucose glycolytically, producing pyruvate and lactate, and the exported pyruvate and lactate is assimilated by the second bacteriome (containing the bacterium Zinderia, which synthesizes three energetically costly EAAs) and channeled through the TCA cycle for energy generation by oxidative phosphorylation. We, furthermore, calculate that this metabolic arrangement supports the high ATP demand in Zinderia bacteriomes for Zinderia-mediated synthesis of energy-intensive EAAs. We predict that metabolite cross-feeding among host cells may be widespread in animal–microbe symbioses utilizing low-nutrient diets. link: http://identifiers.org/doi/10.1038/s41396-020-0661-z

An important goal for many nutrition-based microbiome studies is to identify the metabolic function of microbes in complex microbial communities and their impact on host physiology. This research can be confounded by poorly understood effects of community composition and host diet on the metabolic traits of individual taxa. Here, we investigated these multiway interactions by constructing and analyzing metabolic models comprising every combination of five bacterial members of the <i>Drosophila</i> gut microbiome (from single taxa to the five-member community of <i>Acetobacter</i> and <i>Lactobacillus</i> species) under three nutrient regimes. We show that the metabolic function of <i>Drosophila</i> gut bacteria is dynamic, influenced by community composition, and responsive to dietary modulation. Furthermore, we show that ecological interactions such as competition and mutualism identified from the growth patterns of gut bacteria are underlain by a diversity of metabolic interactions, and show that the bacteria tend to compete for amino acids and B vitamins more frequently than for carbon sources. Our results reveal that, in addition to fermentation products such as acetate, intermediates of the tricarboxylic acid (TCA) cycle, including 2-oxoglutarate and succinate, are produced at high flux and cross-fed between bacterial taxa, suggesting important roles for TCA cycle intermediates in modulating <i>Drosophila</i> gut microbe interactions and the potential to influence host traits. These metabolic models provide specific predictions of the patterns of ecological and metabolic interactions among gut bacteria under different nutrient regimes, with potentially important consequences for overall community metabolic function and nutritional interactions with the host.<b>IMPORTANCE</b> <i>Drosophila</i> is an important model for microbiome research partly because of the low complexity of its mostly culturable gut microbiota. Our current understanding of how <i>Drosophila</i> interacts with its gut microbes and how these interactions influence host traits derives almost entirely from empirical studies that focus on individual microbial taxa or classes of metabolites. These studies have failed to capture fully the complexity of metabolic interactions that occur between host and microbe. To overcome this limitation, we reconstructed and analyzed 31 metabolic models for every combination of the five principal bacterial taxa in the gut microbiome of <i>Drosophila</i> This revealed that metabolic interactions between <i>Drosophila</i> gut bacterial taxa are highly dynamic and influenced by cooccurring bacteria and nutrient availability. Our results generate testable hypotheses about among-microbe ecological interactions in the <i>Drosophila</i> gut and the diversity of metabolites available to influence host traits. link: http://identifiers.org/pubmed/33947801

An important goal for many nutrition-based microbiome studies is to identify the metabolic function of microbes in complex microbial communities and their impact on host physiology. This research can be confounded by poorly understood effects of community composition and host diet on the metabolic traits of individual taxa. Here, we investigated these multiway interactions by constructing and analyzing metabolic models comprising every combination of five bacterial members of the <i>Drosophila</i> gut microbiome (from single taxa to the five-member community of <i>Acetobacter</i> and <i>Lactobacillus</i> species) under three nutrient regimes. We show that the metabolic function of <i>Drosophila</i> gut bacteria is dynamic, influenced by community composition, and responsive to dietary modulation. Furthermore, we show that ecological interactions such as competition and mutualism identified from the growth patterns of gut bacteria are underlain by a diversity of metabolic interactions, and show that the bacteria tend to compete for amino acids and B vitamins more frequently than for carbon sources. Our results reveal that, in addition to fermentation products such as acetate, intermediates of the tricarboxylic acid (TCA) cycle, including 2-oxoglutarate and succinate, are produced at high flux and cross-fed between bacterial taxa, suggesting important roles for TCA cycle intermediates in modulating <i>Drosophila</i> gut microbe interactions and the potential to influence host traits. These metabolic models provide specific predictions of the patterns of ecological and metabolic interactions among gut bacteria under different nutrient regimes, with potentially important consequences for overall community metabolic function and nutritional interactions with the host.<b>IMPORTANCE</b> <i>Drosophila</i> is an important model for microbiome research partly because of the low complexity of its mostly culturable gut microbiota. Our current understanding of how <i>Drosophila</i> interacts with its gut microbes and how these interactions influence host traits derives almost entirely from empirical studies that focus on individual microbial taxa or classes of metabolites. These studies have failed to capture fully the complexity of metabolic interactions that occur between host and microbe. To overcome this limitation, we reconstructed and analyzed 31 metabolic models for every combination of the five principal bacterial taxa in the gut microbiome of <i>Drosophila</i> This revealed that metabolic interactions between <i>Drosophila</i> gut bacterial taxa are highly dynamic and influenced by cooccurring bacteria and nutrient availability. Our results generate testable hypotheses about among-microbe ecological interactions in the <i>Drosophila</i> gut and the diversity of metabolites available to influence host traits. link: http://identifiers.org/pubmed/33947801

An important goal for many nutrition-based microbiome studies is to identify the metabolic function of microbes in complex microbial communities and their impact on host physiology. This research can be confounded by poorly understood effects of community composition and host diet on the metabolic traits of individual taxa. Here, we investigated these multiway interactions by constructing and analyzing metabolic models comprising every combination of five bacterial members of the <i>Drosophila</i> gut microbiome (from single taxa to the five-member community of <i>Acetobacter</i> and <i>Lactobacillus</i> species) under three nutrient regimes. We show that the metabolic function of <i>Drosophila</i> gut bacteria is dynamic, influenced by community composition, and responsive to dietary modulation. Furthermore, we show that ecological interactions such as competition and mutualism identified from the growth patterns of gut bacteria are underlain by a diversity of metabolic interactions, and show that the bacteria tend to compete for amino acids and B vitamins more frequently than for carbon sources. Our results reveal that, in addition to fermentation products such as acetate, intermediates of the tricarboxylic acid (TCA) cycle, including 2-oxoglutarate and succinate, are produced at high flux and cross-fed between bacterial taxa, suggesting important roles for TCA cycle intermediates in modulating <i>Drosophila</i> gut microbe interactions and the potential to influence host traits. These metabolic models provide specific predictions of the patterns of ecological and metabolic interactions among gut bacteria under different nutrient regimes, with potentially important consequences for overall community metabolic function and nutritional interactions with the host.<b>IMPORTANCE</b> <i>Drosophila</i> is an important model for microbiome research partly because of the low complexity of its mostly culturable gut microbiota. Our current understanding of how <i>Drosophila</i> interacts with its gut microbes and how these interactions influence host traits derives almost entirely from empirical studies that focus on individual microbial taxa or classes of metabolites. These studies have failed to capture fully the complexity of metabolic interactions that occur between host and microbe. To overcome this limitation, we reconstructed and analyzed 31 metabolic models for every combination of the five principal bacterial taxa in the gut microbiome of <i>Drosophila</i> This revealed that metabolic interactions between <i>Drosophila</i> gut bacterial taxa are highly dynamic and influenced by cooccurring bacteria and nutrient availability. Our results generate testable hypotheses about among-microbe ecological interactions in the <i>Drosophila</i> gut and the diversity of metabolites available to influence host traits. link: http://identifiers.org/pubmed/33947801

An important goal for many nutrition-based microbiome studies is to identify the metabolic function of microbes in complex microbial communities and their impact on host physiology. This research can be confounded by poorly understood effects of community composition and host diet on the metabolic traits of individual taxa. Here, we investigated these multiway interactions by constructing and analyzing metabolic models comprising every combination of five bacterial members of the <i>Drosophila</i> gut microbiome (from single taxa to the five-member community of <i>Acetobacter</i> and <i>Lactobacillus</i> species) under three nutrient regimes. We show that the metabolic function of <i>Drosophila</i> gut bacteria is dynamic, influenced by community composition, and responsive to dietary modulation. Furthermore, we show that ecological interactions such as competition and mutualism identified from the growth patterns of gut bacteria are underlain by a diversity of metabolic interactions, and show that the bacteria tend to compete for amino acids and B vitamins more frequently than for carbon sources. Our results reveal that, in addition to fermentation products such as acetate, intermediates of the tricarboxylic acid (TCA) cycle, including 2-oxoglutarate and succinate, are produced at high flux and cross-fed between bacterial taxa, suggesting important roles for TCA cycle intermediates in modulating <i>Drosophila</i> gut microbe interactions and the potential to influence host traits. These metabolic models provide specific predictions of the patterns of ecological and metabolic interactions among gut bacteria under different nutrient regimes, with potentially important consequences for overall community metabolic function and nutritional interactions with the host.<b>IMPORTANCE</b> <i>Drosophila</i> is an important model for microbiome research partly because of the low complexity of its mostly culturable gut microbiota. Our current understanding of how <i>Drosophila</i> interacts with its gut microbes and how these interactions influence host traits derives almost entirely from empirical studies that focus on individual microbial taxa or classes of metabolites. These studies have failed to capture fully the complexity of metabolic interactions that occur between host and microbe. To overcome this limitation, we reconstructed and analyzed 31 metabolic models for every combination of the five principal bacterial taxa in the gut microbiome of <i>Drosophila</i> This revealed that metabolic interactions between <i>Drosophila</i> gut bacterial taxa are highly dynamic and influenced by cooccurring bacteria and nutrient availability. Our results generate testable hypotheses about among-microbe ecological interactions in the <i>Drosophila</i> gut and the diversity of metabolites available to influence host traits. link: http://identifiers.org/pubmed/33947801

An important goal for many nutrition-based microbiome studies is to identify the metabolic function of microbes in complex microbial communities and their impact on host physiology. This research can be confounded by poorly understood effects of community composition and host diet on the metabolic traits of individual taxa. Here, we investigated these multiway interactions by constructing and analyzing metabolic models comprising every combination of five bacterial members of the <i>Drosophila</i> gut microbiome (from single taxa to the five-member community of <i>Acetobacter</i> and <i>Lactobacillus</i> species) under three nutrient regimes. We show that the metabolic function of <i>Drosophila</i> gut bacteria is dynamic, influenced by community composition, and responsive to dietary modulation. Furthermore, we show that ecological interactions such as competition and mutualism identified from the growth patterns of gut bacteria are underlain by a diversity of metabolic interactions, and show that the bacteria tend to compete for amino acids and B vitamins more frequently than for carbon sources. Our results reveal that, in addition to fermentation products such as acetate, intermediates of the tricarboxylic acid (TCA) cycle, including 2-oxoglutarate and succinate, are produced at high flux and cross-fed between bacterial taxa, suggesting important roles for TCA cycle intermediates in modulating <i>Drosophila</i> gut microbe interactions and the potential to influence host traits. These metabolic models provide specific predictions of the patterns of ecological and metabolic interactions among gut bacteria under different nutrient regimes, with potentially important consequences for overall community metabolic function and nutritional interactions with the host.<b>IMPORTANCE</b> <i>Drosophila</i> is an important model for microbiome research partly because of the low complexity of its mostly culturable gut microbiota. Our current understanding of how <i>Drosophila</i> interacts with its gut microbes and how these interactions influence host traits derives almost entirely from empirical studies that focus on individual microbial taxa or classes of metabolites. These studies have failed to capture fully the complexity of metabolic interactions that occur between host and microbe. To overcome this limitation, we reconstructed and analyzed 31 metabolic models for every combination of the five principal bacterial taxa in the gut microbiome of <i>Drosophila</i> This revealed that metabolic interactions between <i>Drosophila</i> gut bacterial taxa are highly dynamic and influenced by cooccurring bacteria and nutrient availability. Our results generate testable hypotheses about among-microbe ecological interactions in the <i>Drosophila</i> gut and the diversity of metabolites available to influence host traits. link: http://identifiers.org/pubmed/33947801

BACKGROUND: Escherichia coli is a model prokaryote, an important pathogen, and a key organism for industrial biotechnology. E. coli W (ATCC 9637), one of four strains designated as safe for laboratory purposes, has not been sequenced. E. coli W is a fast-growing strain and is the only safe strain that can utilize sucrose as a carbon source. Lifecycle analysis has demonstrated that sucrose from sugarcane is a preferred carbon source for industrial bioprocesses. RESULTS: We have sequenced and annotated the genome of E. coli W. The chromosome is 4,900,968 bp and encodes 4,764 ORFs. Two plasmids, pRK1 (102,536 bp) and pRK2 (5,360 bp), are also present. W has unique features relative to other sequenced laboratory strains (K-12, B and Crooks): it has a larger genome and belongs to phylogroup B1 rather than A. W also grows on a much broader range of carbon sources than does K-12. A genome-scale reconstruction was developed and validated in order to interrogate metabolic properties. CONCLUSIONS: The genome of W is more similar to commensal and pathogenic B1 strains than phylogroup A strains, and therefore has greater utility for comparative analyses with these strains. W should therefore be the strain of choice, or 'type strain' for group B1 comparative analyses. The genome annotation and tools created here are expected to allow further utilization and development of E. coli W as an industrial organism for sucrose-based bioprocesses. Refinements in our E. coli metabolic reconstruction allow it to more accurately define E. coli metabolism relative to previous models. link: http://identifiers.org/pubmed/21208457

In this paper a mathematical model is presented that describes growth, immune escape, and siRNA treatment of tumors. The model consists of a system of nonlinear, ordinary differential equations describing tumor cells and immune effectors, as well as the immuno-stimulatory and suppressive cytokines IL-2 and TGF-β. TGF-β suppresses the immune system by inhibiting the activation of effector cells and reducing tumor antigen expression. It also stimulates tumor growth by promoting angiogenesis, explaining the inclusion of an angiogenic switch mechanism for TGF-β activity. The model predicts that increasing the rate of TGF-β production for reasonable values of tumor antigenicity enhances tumor growth and its ability to escape host detection. The model is then extended to include siRNA treatment which suppresses TGF-β production by targeting the mRNA that codes for TGF-β, thereby reducing the presence and effect of TGF-β in tumor cells. Comparison of tumor response to multiple injections of siRNA with behavior of untreated tumors demonstrates the effectiveness of this proposed treatment strategy. A second administration method, continuous infusion, is included to contrast the ideal outcome of siRNA treatment. The model's results predict conditions under which siRNA treatment can be successful in returning an aggressive, TGF-β producing tumor to its passive, non-immune evading state. link: http://identifiers.org/doi/10.3934/dcdsb.2004.4.39

The Calvin-Benson cycle (CBC) provides the precursors for biomass synthesis necessary for plant growth. The dynamic behavior and yield of the CBC depend on the environmental conditions and regulation of the cellular state. Accurate quantitative models hold the promise of identifying the key determinants of the tightly regulated CBC function and their effects on the responses in future climates. We provide an integrative analysis of the largest compendium of existing models for photosynthetic processes. Based on the proposed ranking, our framework facilitates the discovery of best-performing models with regard to metabolomics data and of candidates for metabolic engineering. link: http://identifiers.org/pubmed/22001849

The Calvin-Benson cycle (CBC) provides the precursors for biomass synthesis necessary for plant growth. The dynamic behavior and yield of the CBC depend on the environmental conditions and regulation of the cellular state. Accurate quantitative models hold the promise of identifying the key determinants of the tightly regulated CBC function and their effects on the responses in future climates. We provide an integrative analysis of the largest compendium of existing models for photosynthetic processes. Based on the proposed ranking, our framework facilitates the discovery of best-performing models with regard to metabolomics data and of candidates for metabolic engineering. link: http://identifiers.org/pubmed/22001849

The Calvin-Benson cycle (CBC) provides the precursors for biomass synthesis necessary for plant growth. The dynamic behavior and yield of the CBC depend on the environmental conditions and regulation of the cellular state. Accurate quantitative models hold the promise of identifying the key determinants of the tightly regulated CBC function and their effects on the responses in future climates. We provide an integrative analysis of the largest compendium of existing models for photosynthetic processes. Based on the proposed ranking, our framework facilitates the discovery of best-performing models with regard to metabolomics data and of candidates for metabolic engineering. link: http://identifiers.org/pubmed/22001849

The Calvin-Benson cycle (CBC) provides the precursors for biomass synthesis necessary for plant growth. The dynamic behavior and yield of the CBC depend on the environmental conditions and regulation of the cellular state. Accurate quantitative models hold the promise of identifying the key determinants of the tightly regulated CBC function and their effects on the responses in future climates. We provide an integrative analysis of the largest compendium of existing models for photosynthetic processes. Based on the proposed ranking, our framework facilitates the discovery of best-performing models with regard to metabolomics data and of candidates for metabolic engineering. link: http://identifiers.org/pubmed/22001849

The Calvin-Benson cycle (CBC) provides the precursors for biomass synthesis necessary for plant growth. The dynamic behavior and yield of the CBC depend on the environmental conditions and regulation of the cellular state. Accurate quantitative models hold the promise of identifying the key determinants of the tightly regulated CBC function and their effects on the responses in future climates. We provide an integrative analysis of the largest compendium of existing models for photosynthetic processes. Based on the proposed ranking, our framework facilitates the discovery of best-performing models with regard to metabolomics data and of candidates for metabolic engineering. link: http://identifiers.org/pubmed/22001849

The Calvin-Benson cycle (CBC) provides the precursors for biomass synthesis necessary for plant growth. The dynamic behavior and yield of the CBC depend on the environmental conditions and regulation of the cellular state. Accurate quantitative models hold the promise of identifying the key determinants of the tightly regulated CBC function and their effects on the responses in future climates. We provide an integrative analysis of the largest compendium of existing models for photosynthetic processes. Based on the proposed ranking, our framework facilitates the discovery of best-performing models with regard to metabolomics data and of candidates for metabolic engineering. link: http://identifiers.org/pubmed/22001849

The Calvin-Benson cycle (CBC) provides the precursors for biomass synthesis necessary for plant growth. The dynamic behavior and yield of the CBC depend on the environmental conditions and regulation of the cellular state. Accurate quantitative models hold the promise of identifying the key determinants of the tightly regulated CBC function and their effects on the responses in future climates. We provide an integrative analysis of the largest compendium of existing models for photosynthetic processes. Based on the proposed ranking, our framework facilitates the discovery of best-performing models with regard to metabolomics data and of candidates for metabolic engineering. link: http://identifiers.org/pubmed/22001849

The Calvin-Benson cycle (CBC) provides the precursors for biomass synthesis necessary for plant growth. The dynamic behavior and yield of the CBC depend on the environmental conditions and regulation of the cellular state. Accurate quantitative models hold the promise of identifying the key determinants of the tightly regulated CBC function and their effects on the responses in future climates. We provide an integrative analysis of the largest compendium of existing models for photosynthetic processes. Based on the proposed ranking, our framework facilitates the discovery of best-performing models with regard to metabolomics data and of candidates for metabolic engineering. link: http://identifiers.org/pubmed/22001849

The Calvin-Benson cycle (CBC) provides the precursors for biomass synthesis necessary for plant growth. The dynamic behavior and yield of the CBC depend on the environmental conditions and regulation of the cellular state. Accurate quantitative models hold the promise of identifying the key determinants of the tightly regulated CBC function and their effects on the responses in future climates. We provide an integrative analysis of the largest compendium of existing models for photosynthetic processes. Based on the proposed ranking, our framework facilitates the discovery of best-performing models with regard to metabolomics data and of candidates for metabolic engineering. link: http://identifiers.org/pubmed/22001849

The Calvin-Benson cycle (CBC) provides the precursors for biomass synthesis necessary for plant growth. The dynamic behavior and yield of the CBC depend on the environmental conditions and regulation of the cellular state. Accurate quantitative models hold the promise of identifying the key determinants of the tightly regulated CBC function and their effects on the responses in future climates. We provide an integrative analysis of the largest compendium of existing models for photosynthetic processes. Based on the proposed ranking, our framework facilitates the discovery of best-performing models with regard to metabolomics data and of candidates for metabolic engineering. link: http://identifiers.org/pubmed/22001849

The Calvin-Benson cycle (CBC) provides the precursors for biomass synthesis necessary for plant growth. The dynamic behavior and yield of the CBC depend on the environmental conditions and regulation of the cellular state. Accurate quantitative models hold the promise of identifying the key determinants of the tightly regulated CBC function and their effects on the responses in future climates. We provide an integrative analysis of the largest compendium of existing models for photosynthetic processes. Based on the proposed ranking, our framework facilitates the discovery of best-performing models with regard to metabolomics data and of candidates for metabolic engineering. link: http://identifiers.org/pubmed/22001849

The nuclear factor kappaB (NF-kappaB) transcription factor regulates cellular stress responses and the immune response to infection. NF-kappaB activation results in oscillations in nuclear NF-kappaB abundance. To define the function of these oscillations, we treated cells with repeated short pulses of tumor necrosis factor-alpha at various intervals to mimic pulsatile inflammatory signals. At all pulse intervals that were analyzed, we observed synchronous cycles of NF-kappaB nuclear translocation. Lower frequency stimulations gave repeated full-amplitude translocations, whereas higher frequency pulses gave reduced translocation, indicating a failure to reset. Deterministic and stochastic mathematical models predicted how negative feedback loops regulate both the resetting of the system and cellular heterogeneity. Altering the stimulation intervals gave different patterns of NF-kappaB-dependent gene expression, which supports the idea that oscillation frequency has a functional role. link: http://identifiers.org/pubmed/19359585

Slow and discontinuous wave conduction through nonuniform junctions in cardiac tissues is generally considered unsafe and proarrythmogenic. However, the relationships between tissue structure, wave conduction velocity, and safety at such junctions are unknown. We have developed a structurally and electrophysiologically detailed model of the canine Purkinje-ventricular junction (PVJ) and varied its heterogeneity parameters to determine such relationships. We show that neither very fast nor very slow conduction is safe, and there exists an optimal velocity that provides the maximum safety factor for conduction through the junction. The resultant conduction time delay across the PVJ is a natural consequence of the electrophysiological and morphological differences between the Purkinje fiber and ventricular tissue. The delay allows the PVJ to accumulate and pass sufficient charge to excite the adjacent ventricular tissue, but is not long enough for the source-to-load mismatch at the junction to be enhanced over time. The observed relationships between the conduction velocity and safety factor can provide new insights into optimal conditions for wave propagation through nonuniform junctions between various cardiac tissues. link: http://identifiers.org/pubmed/19580741

Experimental evidence suggests that regional differences in action potential (AP) morphology can provide a substrate for initiation and maintenance of reentrant arrhythmias in the right atrium (RA), but the relationships between the complex electrophysiological and anatomical organization of the RA and the genesis of reentry are unclear. In this study, a biophysically detailed three-dimensional computer model of the right atrial tissue was constructed to study the role of tissue heterogeneity and anisotropy in arrhythmogenesis. The model of Lindblad et al. for a rabbit atrial cell was modified to incorporate experimental data on regional differences in several ionic currents (primarily, I(Na), I(CaL), I(K1), I(to), and I(sus)) between the crista terminalis and pectinate muscle cells. The modified model was validated by its ability to reproduce the AP properties measured experimentally. The anatomical model of the rabbit RA (including tissue geometry and fiber orientation) was based on a recent histological reconstruction. Simulations with the resultant electrophysiologically and anatomically detailed three-dimensional model show that complex organization of the RA tissue causes breakdown of regular AP conduction patterns at high pacing rates (>11.75 Hz): as the AP in the crista terminalis cells is longer, and electrotonic coupling transverse to fibers of the crista terminalis is weak, high-frequency pacing at the border between the crista terminalis and pectinate muscles results in a unidirectional conduction block toward the crista terminalis and generation of reentry. Contributions of the tissue heterogeneity and anisotropy to reentry initiation mechanisms are quantified by measuring action potential duration (APD) gradients at the border between the crista terminalis and pectinate muscles: the APD gradients are high in areas where both heterogeneity and anisotropy are high, such that intrinsic APD differences are not diminished by electrotonic interactions. Thus, our detailed computer model reconstructs complex electrical activity in the RA, and provides new insights into the mechanisms of transition from focal atrial tachycardia into reentry. link: http://identifiers.org/pubmed/19186122

Exploiting signaling pathways for the purpose of controlling cell function entails identifying and manipulating the information content of intracellular signals. As in the case of the ubiquitously expressed, eukaryotic mitogen-activated protein kinase (MAPK) signaling pathway, this information content partly resides in the signals' dynamical properties. Here, we utilize a mathematical model to examine mechanisms that govern MAPK pathway dynamics, particularly the role of putative negative feedback mechanisms in generating complete signal adaptation, a term referring to the reset of a signal to prestimulation levels. In addition to yielding adaptation of its direct target, feedback mechanisms implemented in our model also indirectly assist in the adaptation of signaling components downstream of the target under certain conditions. In fact, model predictions identify conditions yielding ultra-desensitization of signals in which complete adaptation of target and downstream signals culminates even while stimulus recognition (i.e., receptor-ligand binding) continues to increase. Moreover, the rate at which signal decays can follow first-order kinetics with respect to signal intensity, so that signal adaptation is achieved in the same amount of time regardless of signal intensity or ligand dose. All of these features are consistent with experimental findings recently obtained for the Chinese hamster ovary (CHO) cell lines (Asthagiri et al., J. Biol. Chem. 1999, 274, 27119-27127). Our model further predicts that although downstream effects are independent of whether an enzyme or adaptor protein is targeted by negative feedback, adaptor-targeted feedback can "back-propagate" effects upstream of the target, specifically resulting in increased steady-state upstream signal. Consequently, where these upstream components serve as nodes within a signaling network, feedback can transfer signaling through these nodes into alternate pathways, thereby promoting the sort of signaling cross-talk that is becoming more widely appreciated. link: http://identifiers.org/pubmed/11312698

A simplified mathematical model of cell metabolism describing ion pump, glycolysis and adenylate metabolism was developed and investigated in order to clarify the functional role of the adenylate metabolism system in human erythrocytes. The adenylate metabolism system was shown to be able to function as a specific regulatory system stabilizing intracellular ion concentration and, hence, erythrocyte volume under changes in the permeability of cell membrane. This stabilization is provided via an increase in adenylate pool in association with ATPases rate elevation. Proper regulation of adenylate pool size might be achieved even in the case when AMP synthesis rate remains constant and only AMP degradation rate varies. The best stabilization of intracellular ion concentration in the model is attained when the rate of AMP destruction is directly proportional to ATP concentration and is inversely proportional to AMP concentration. An optimal rate of adenylate metabolism in erythrocytes ranges from several tenths of a percent to several percent of the glycolytic flux. An increase in this rate results in deterioration of cell metabolism stability. Decrease in the rate of adenylate metabolism makes the functioning of this metabolic system inefficient, because the time necessary to achieve stabilization of intracellular ion concentration becomes comparable with erythrocyte life span. link: http://identifiers.org/pubmed/8733433

In order to improve the interpretation of functional neuroimaging data, we implemented a mathematical model of the coupling between membrane ionic currents, energy metabolism (i.e., ATP regeneration via phosphocreatine buffer effect, glycolysis, and mitochondrial respiration), blood-brain barrier exchanges, and hemodynamics. Various hypotheses were tested for the variation of the cerebral metabolic rate of oxygen (CMRO(2)): (H1) the CMRO(2) remains at its baseline level; (H2) the CMRO(2) is enhanced as soon as the cerebral blood flow (CBF) increases; (H3) the CMRO(2) increase depends on intracellular oxygen and pyruvate concentrations, and intracellular ATP/ADP ratio; (H4) in addition to hypothesis H3, the CMRO(2) progressively increases, due to the action of a second messenger. A good agreement with experimental data from magnetic resonance imaging and spectroscopy (MRI and MRS) was obtained when we simulated sustained and repetitive activation protocols using hypotheses (H3) or (H4), rather than hypotheses (H1) or (H2). Furthermore, by studying the effect of the variation of some physiologically important parameters on the time course of the modeled blood-oxygenation-level-dependent (BOLD) signal, we were able to formulate hypotheses about the physiological or biochemical significance of functional magnetic resonance data, especially the poststimulus undershoot and the baseline drift. link: http://identifiers.org/pubmed/12414257

Understanding cerebral energy metabolism in neurons and astrocytes is necessary for the interpretation of functional brain imaging data. It has been suggested that astrocytes can provide lactate as an energy fuel to neurons, a process referred to as astrocyte-neuron lactate shuttle (ANLS). Some authors challenged this hypothesis, defending the classical view that glucose is the major energy substrate of neurons, at rest as well as in response to a stimulation. To test the ANLS hypothesis from a theoretical point of view, we developed a mathematical model of compartmentalized energy metabolism between neurons and astrocytes, adopting hypotheses highly unfavorable to ANLS. Simulation results can be divided between two groups, depending on the relative neuron versus astrocyte stimulation. If this ratio is low, ANLS is observed during all the stimulus and poststimulus periods (continuous ANLS), but a high ratio induces ANLS only at the beginning of the stimulus and during the poststimulus period (triphasic behavior). Finally, our results show that current experimental data on lactate kinetics are compatible with the ANLS hypothesis, and that it is essential to assess the neuronal and astrocytic NADH/NAD+ ratio changes to test the ANLS hypothesis. link: http://identifiers.org/pubmed/15931164

Fluid-phase endocytosis (pinocytosis) kinetics were studied inDictyostelium discoideum amoebae from the axenic strain Ax-2 that exhibits high rates of fluid-phase endocytosis when cultured in liquid nutrient media. Fluorescein-labelled dextran (FITC-dextran) was used as a marker in continuous uptake- and in pulse-chase exocytosis experiments. In the latter case, efflux of the marker was monitored on cells loaded for short periods of time and resuspended in marker-free medium. A multicompartmental model was developed which describes satisfactorily fluid-phase endocytosis kinetics. In particular, it accounts correctly for the extended latency period before exocytosis in pulse-chase experiments and it suggests the existence of some sorts of maturation stages in the pathway. link: http://identifiers.org/doi/10.1007/BF00713556

Fluid-phase endocytosis (pinocytosis) kinetics were studied inDictyostelium discoideum amoebae from the axenic strain Ax-2 that exhibits high rates of fluid-phase endocytosis when cultured in liquid nutrient media. Fluorescein-labelled dextran (FITC-dextran) was used as a marker in continuous uptake- and in pulse-chase exocytosis experiments. In the latter case, efflux of the marker was monitored on cells loaded for short periods of time and resuspended in marker-free medium. A multicompartmental model was developed which describes satisfactorily fluid-phase endocytosis kinetics. In particular, it accounts correctly for the extended latency period before exocytosis in pulse-chase experiments and it suggests the existence of some sorts of maturation stages in the pathway. link: http://identifiers.org/doi/10.1007/BF00713556

Under favorable conditions, many proteins can assemble into macroscopically large aggregates such as the amyloid fibrils that are associated with Alzheimer's, Parkinson's, and other neurological and systemic diseases. The overall process of protein aggregation is characterized by initial lag time during which no detectable aggregation occurs in the solution and by maximal aggregation rate at which the dissolved protein converts into aggregates. In this study, the correlation between the lag time and the maximal rate of protein aggregation is analyzed. It is found that the product of these two quantities depends on a single numerical parameter, the kinetic index of the curve quantifying the time evolution of the fraction of protein aggregated. As this index depends relatively little on the conditions and/or system studied, our finding provides insight into why for many experiments the values of the product of the lag time and the maximal aggregation rate are often equal or quite close to each other. It is shown how the kinetic index is related to a basic kinetic parameter of a recently proposed theory of protein aggregation. link: http://identifiers.org/pubmed/20602358

Multiple myeloma is a hematologic malignancy associated with the development of a destructive osteolytic bone disease.Mathematical models are developed for normal bone remodeling and for the dysregulated bone remodeling that occurs in myeloma bone disease. The models examine the critical signaling between osteoclasts (bone resorption) and osteoblasts (bone formation). The interactions of osteoclasts and osteoblasts are modeled as a system of differential equations for these cell populations, which exhibit stable oscillations in the normal case and unstable oscillations in the myeloma case. In the case of untreated myeloma, osteoclasts increase and osteoblasts decrease, with net bone loss as the tumor grows. The therapeutic effects of targeting both myeloma cells and cells of the bone marrow microenvironment on these dynamics are examined.The current model accurately reflects myeloma bone disease and illustrates how treatment approaches may be investigated using such computational approaches.This article was reviewed by Ariosto Silva and Mark P. Little. link: http://identifiers.org/pubmed/20406449

Multiple myeloma is a hematologic malignancy associated with the development of a destructive osteolytic bone disease.Mathematical models are developed for normal bone remodeling and for the dysregulated bone remodeling that occurs in myeloma bone disease. The models examine the critical signaling between osteoclasts (bone resorption) and osteoblasts (bone formation). The interactions of osteoclasts and osteoblasts are modeled as a system of differential equations for these cell populations, which exhibit stable oscillations in the normal case and unstable oscillations in the myeloma case. In the case of untreated myeloma, osteoclasts increase and osteoblasts decrease, with net bone loss as the tumor grows. The therapeutic effects of targeting both myeloma cells and cells of the bone marrow microenvironment on these dynamics are examined.The current model accurately reflects myeloma bone disease and illustrates how treatment approaches may be investigated using such computational approaches.This article was reviewed by Ariosto Silva and Mark P. Little. link: http://identifiers.org/pubmed/20406449

Multiple myeloma is a hematologic malignancy associated with the development of a destructive osteolytic bone disease.Mathematical models are developed for normal bone remodeling and for the dysregulated bone remodeling that occurs in myeloma bone disease. The models examine the critical signaling between osteoclasts (bone resorption) and osteoblasts (bone formation). The interactions of osteoclasts and osteoblasts are modeled as a system of differential equations for these cell populations, which exhibit stable oscillations in the normal case and unstable oscillations in the myeloma case. In the case of untreated myeloma, osteoclasts increase and osteoblasts decrease, with net bone loss as the tumor grows. The therapeutic effects of targeting both myeloma cells and cells of the bone marrow microenvironment on these dynamics are examined.The current model accurately reflects myeloma bone disease and illustrates how treatment approaches may be investigated using such computational approaches.This article was reviewed by Ariosto Silva and Mark P. Little. link: http://identifiers.org/pubmed/20406449

BACKGROUND: Neisseria meningitidis is a human pathogen that can infect diverse sites within the human host. The major diseases caused by N. meningitidis are responsible for death and disability, especially in young infants. In general, most of the recent work on N. meningitidis focuses on potential antigens and their functions, immunogenicity, and pathogenicity mechanisms. Very little work has been carried out on Neisseria primary metabolism over the past 25 years. RESULTS: Using the genomic database of N. meningitidis serogroup B together with biochemical and physiological information in the literature we constructed a genome-scale flux model for the primary metabolism of N. meningitidis. The validity of a simplified metabolic network derived from the genome-scale metabolic network was checked using flux-balance analysis in chemostat cultures. Several useful predictions were obtained from in silico experiments, including substrate preference. A minimal medium for growth of N. meningitidis was designed and tested successfully in batch and chemostat cultures. CONCLUSION: The verified metabolic model describes the primary metabolism of N. meningitidis in a chemostat in steady state. The genome-scale model is valuable because it offers a framework to study N. meningitidis metabolism as a whole, or certain aspects of it, and it can also be used for the purpose of vaccine process development (for example, the design of growth media). The flux distribution of the main metabolic pathways (that is, the pentose phosphate pathway and the Entner-Douderoff pathway) indicates that the major part of pyruvate (69%) is synthesized through the ED-cleavage, a finding that is in good agreement with literature. link: http://identifiers.org/pubmed/17617894

The objective of this study was to create a clinically applicable mathematical model of immunotherapy for cancer and use it to explore differences between successful and unsuccessful treatment scenarios. The simplified predator-prey model includes four lumped parameters: tumor growth rate, g; immune cell killing efficiency, k; immune cell signaling factor, λ; and immune cell half-life decay, μ. The predator-prey equations as functions of time, t, for normalized tumor cell numbers, y, (the prey) and immunocyte numbers, ×, (the predators) are: dy/dt = gy - kx and dx/dt = λxy - μx. A parameter estimation procedure that capitalizes on available clinical data and the timing of clinically observable phenomena gives mid-range benchmarks for parameters representing the unstable equilibrium case in which the tumor neither grows nor shrinks. Departure from this equilibrium results in oscillations in tumor cell numbers and in many cases complete elimination of the tumor. Several paradoxical phenomena are predicted, including increasing tumor cell numbers prior to a population crash, apparent cure with late recurrence, one or more cycles of tumor growth prior to eventual tumor elimination, and improved tumor killing with initially weaker immune parameters or smaller initial populations of immune cells. The model and the parameter estimation techniques are easily adapted to various human cancers that evoke an immune response. They may help clinicians understand and predict certain strange and unexpected effects in the world of tumor immunity and lead to the design of clinical trials to test improved treatment protocols for patients. link: http://identifiers.org/pubmed/22432059

Cellular signal transduction is governed by multiple feedback mechanisms to elicit robust cellular decisions. The specific contributions of individual feedback regulators, however, remain unclear. Based on extensive time-resolved data sets in primary erythroid progenitor cells, we established a dynamic pathway model to dissect the roles of the two transcriptional negative feedback regulators of the suppressor of cytokine signaling (SOCS) family, CIS and SOCS3, in JAK2/STAT5 signaling. Facilitated by the model, we calculated the STAT5 response for experimentally unobservable Epo concentrations and provide a quantitative link between cell survival and the integrated response of STAT5 in the nucleus. Model predictions show that the two feedbacks CIS and SOCS3 are most effective at different ligand concentration ranges due to their distinct inhibitory mechanisms. This divided function of dual feedback regulation enables control of STAT5 responses for Epo concentrations that can vary 1000-fold in vivo. Our modeling approach reveals dose-dependent feedback control as key property to regulate STAT5-mediated survival decisions over a broad range of ligand concentrations. link: http://identifiers.org/pubmed/21772264

Cellular signal transduction is governed by multiple feedback mechanisms to elicit robust cellular decisions. The specific contributions of individual feedback regulators, however, remain unclear. Based on extensive time-resolved data sets in primary erythroid progenitor cells, we established a dynamic pathway model to dissect the roles of the two transcriptional negative feedback regulators of the suppressor of cytokine signaling (SOCS) family, CIS and SOCS3, in JAK2/STAT5 signaling. Facilitated by the model, we calculated the STAT5 response for experimentally unobservable Epo concentrations and provide a quantitative link between cell survival and the integrated response of STAT5 in the nucleus. Model predictions show that the two feedbacks CIS and SOCS3 are most effective at different ligand concentration ranges due to their distinct inhibitory mechanisms. This divided function of dual feedback regulation enables control of STAT5 responses for Epo concentrations that can vary 1000-fold in vivo. Our modeling approach reveals dose-dependent feedback control as key property to regulate STAT5-mediated survival decisions over a broad range of ligand concentrations. link: http://identifiers.org/pubmed/21772264

BACKGROUND:Oral administration of drugs is convenient and shows good compliance but it can be affected by many factors in the gastrointestinal (GI) system. Consumption of food is one of the major factors affecting the GI system and consequently the absorption of drugs. The aim of this study was to develop a mechanistic GI absorption model for explaining the effect of food on fenofibrate pharmacokinetics (PK), focusing on the food type and calorie content. METHODS:Clinical data from a fenofibrate PK study involving three different conditions (fasting, standard meals and high-fat meals) were used. The model was developed by nonlinear mixed effect modeling method. Both linear and nonlinear effects were evaluated to explain the impact of food intake on drug absorption. Similarly, to explain changes in gastric emptying time for the drug due to food effects was evaluated. RESULTS:The gastric emptying rate increased by 61.7% during the first 6.94 h after food consumption. Increased calories in the duodenum increased the absorption rate constant of the drug in fed conditions (standard meal = 16.5%, high-fat meal = 21.8%) compared with fasted condition. The final model displayed good prediction power and precision. CONCLUSIONS:A mechanistic GI absorption model for quantitatively evaluating the effects of food on fenofibrate absorption was successfully developed, and acceptable parameters were obtained. The mechanism-based PK model of fenofibrate can quantify the effects of food on drug absorption by food type and calorie content. link: http://identifiers.org/pubmed/29370865

The circadian rhythms influence the metabolic activity from molecular level to tissue, organ, and host level. Disruption of the circadian rhythms manifests to the host's health as metabolic syndromes, including obesity, diabetes, and elevated plasma glucose, eventually leading to cardiovascular diseases. Therefore, it is imperative to understand the mechanism behind the relationship between circadian rhythms and metabolism. To start answering this question, we propose a semimechanistic mathematical model to study the effect of circadian disruption on hepatic gluconeogenesis in humans. Our model takes the light-dark cycle and feeding-fasting cycle as two environmental inputs that entrain the metabolic activity in the liver. The model was validated by comparison with data from mice and rat experimental studies. Formal sensitivity and uncertainty analyses were conducted to elaborate on the driving forces for hepatic gluconeogenesis. Furthermore, simulating the impact of Clock gene knockout suggests that modification to the local pathways tied most closely to the feeding-fasting rhythms may be the most efficient way to restore the disrupted glucose metabolism in liver. link: http://identifiers.org/pubmed/29351477

We propose a mathematical model for mitochondria-dependent apoptosis, in which kinetic cooperativity in formation of the apoptosome is a key element ensuring bistability. We examine the role of Bax and Bcl-2 synthesis and degradation rates, as well as the number of mitochondrial permeability transition pores (MPTPs), on the cell response to apoptotic stimuli. Our analysis suggests that cooperative apoptosome formation is a mechanism for inducing bistability, much more robust than that induced by other mechanisms, such as inhibition of caspase-3 by the inhibitor of apoptosis (IAP). Simulations predict a pathological state in which cells will exhibit a monostable cell survival if Bax degradation rate is above a threshold value, or if Bax expression rate is below a threshold value. Otherwise, cell death or survival occur depending on initial caspase-3 levels. We show that high expression rates of Bcl-2 can counteract the effects of Bax. Our simulations also demonstrate a monostable (pathological) apoptotic response if the number of MPTPs exceeds a threshold value. This study supports our contention, based on mathematical modeling, that cooperativity in apoptosome formation is critically important for determining the healthy responses to apoptotic stimuli, and helps define the roles of Bax, Bcl-2, and MPTP vis-à-vis apoptosome formation. link: http://identifiers.org/pubmed/16339882

Despite the establishment of the important role of nitric oxide (NO) on apoptosis, a molecular-level understanding of the origin of its dichotomous pro- and anti-apoptotic effects has been elusive. We propose a new mathematical model for simulating the effects of nitric oxide (NO) on apoptosis. The new model integrates mitochondria-dependent apoptotic pathways with NO-related reactions, to gain insights into the regulatory effect of the reactive NO species N(2)O(3), non-heme iron nitrosyl species (FeL(n)NO), and peroxynitrite (ONOO(-)). The biochemical pathways of apoptosis coupled with NO-related reactions are described by ordinary differential equations using mass-action kinetics. In the absence of NO, the model predicts either cell survival or apoptosis (a bistable behavior) with shifts in the onset time of apoptotic response depending on the strength of extracellular stimuli. Computations demonstrate that the relative concentrations of anti- and pro-apoptotic reactive NO species, and their interplay with glutathione, determine the net anti- or pro-apoptotic effects at long time points. Interestingly, transient effects on apoptosis are also observed in these simulations, the duration of which may reach up to hours, despite the eventual convergence to an anti-apoptotic state. Our computations point to the importance of precise timing of NO production and external stimulation in determining the eventual pro- or anti-apoptotic role of NO. link: http://identifiers.org/pubmed/18509469

Despite the establishment of the important role of nitric oxide (NO) on apoptosis, a molecular-level understanding of the origin of its dichotomous pro- and anti-apoptotic effects has been elusive. We propose a new mathematical model for simulating the effects of nitric oxide (NO) on apoptosis. The new model integrates mitochondria-dependent apoptotic pathways with NO-related reactions, to gain insights into the regulatory effect of the reactive NO species N(2)O(3), non-heme iron nitrosyl species (FeL(n)NO), and peroxynitrite (ONOO(-)). The biochemical pathways of apoptosis coupled with NO-related reactions are described by ordinary differential equations using mass-action kinetics. In the absence of NO, the model predicts either cell survival or apoptosis (a bistable behavior) with shifts in the onset time of apoptotic response depending on the strength of extracellular stimuli. Computations demonstrate that the relative concentrations of anti- and pro-apoptotic reactive NO species, and their interplay with glutathione, determine the net anti- or pro-apoptotic effects at long time points. Interestingly, transient effects on apoptosis are also observed in these simulations, the duration of which may reach up to hours, despite the eventual convergence to an anti-apoptotic state. Our computations point to the importance of precise timing of NO production and external stimulation in determining the eventual pro- or anti-apoptotic role of NO. link: http://identifiers.org/pubmed/18509469

We propose a mathematical model for the regulation of the G1-phase of the mammalian cell cycle taking into account interactions of cyclin D/cdk4, cyclin E/cdk2, Rb and E2F. Mathematical analysis of this model predicts that a change in the proliferative status in response to a change in concentrations of serum growth factors will exhibit the property of hysteresis: the concentration of growth factors required to induce proliferation is higher than the concentration required to maintain proliferation. We experimentally confirmed this prediction in mouse embryonic fibroblasts in vitro. In agreement with the mathematical model, this indicates that changes in proliferative mode caused by small changes in concentrations of growth factors are not easily reversible. Based on this study, we discuss the importance of proliferation hysteresis for cell cycle regulation. link: http://identifiers.org/pubmed/12695688

The Edmonston vaccine strain of measles virus has potent and selective activity against a wide range of tumors. Tumor cells infected by this virus or genetically modified strains express viral proteins that allow them to fuse with neighboring cells to form syncytia that ultimately die. Moreover, infected cells may produce new virus particles that proceed to infect additional tumor cells. We present a model of tumor and virus interactions based on established biology and with proper accounting of the free virus population. The range of model parameters is estimated by fitting to available experimental data. The stability of equilibrium states corresponding to complete tumor eradication, therapy failure and partial tumor reduction is discussed. We use numerical simulations to explore conditions for which the model predicts successful therapy and tumor eradication. The model exhibits damped, as well as stable oscillations in a range of parameter values. These oscillatory states are organized by a Hopf bifurcation. link: http://identifiers.org/pubmed/18316099

Rheumatoid arthritis (RA) is a chronic inflammatory disease preferentially affecting the joints and leading, if untreated, to progressive joint damage and disability. Cytokines, a group of small inducible proteins, which act as intercellular messengers, are key regulators of the inflammation that characterizes RA. They can be classified into pro-inflammatory and anti-inflammatory groups. Numerous cytokines have been implicated in the regulation of RA with complex up and down regulatory interactions. This paper considers a two-variable model for the interactions between pro-inflammatory and anti-inflammatory cytokines, and demonstrates that mathematical modelling may be used to investigate the involvement of cytokines in the disease process. The model displays a range of possible behaviours, such as bistability and oscillations, which are strongly reminiscent of the behaviour of RA e.g. genetic susceptibility and remitting-relapsing disease. We also show that the dose regimen as well as the dose level are important factors in RA treatments. link: http://identifiers.org/pubmed/23002057

Rheumatoid arthritis (RA) is a chronic inflammatory disease preferentially affecting the joints and leading, if untreated, to progressive joint damage and disability. Cytokines, a group of small inducible proteins, which act as intercellular messengers, are key regulators of the inflammation that characterizes RA. They can be classified into pro-inflammatory and anti-inflammatory groups. Numerous cytokines have been implicated in the regulation of RA with complex up and down regulatory interactions. This paper considers a two-variable model for the interactions between pro-inflammatory and anti-inflammatory cytokines, and demonstrates that mathematical modelling may be used to investigate the involvement of cytokines in the disease process. The model displays a range of possible behaviours, such as bistability and oscillations, which are strongly reminiscent of the behaviour of RA e.g. genetic susceptibility and remitting-relapsing disease. We also show that the dose regimen as well as the dose level are important factors in RA treatments. link: http://identifiers.org/pubmed/23002057

Osteoarthritis (OA) is a degenerative disease which causes pain and stiffness in joints. OA progresses through excessive degradation of joint cartilage, eventually leading to significant joint degeneration and loss of function. Cytokines, a group of cell signalling proteins, present in raised concentrations in OA joints, can be classified into pro-inflammatory and anti-inflammatory groups. They mediate cartilage degradation through several mechanisms, primarily the up-regulation of matrix metalloproteinases (MMPs), a group of collagen-degrading enzymes. In this paper we show that the interactions of cytokines within cartilage have a crucial role to play in OA progression and treatment. We develop a four-variable ordinary differential equation model for the interactions between pro- and anti-inflammatory cytokines, MMPs and fibronectin fragments (Fn-fs), a by-product of cartilage degradation and up-regulator of cytokines. We show that the model has four classes of dynamic behaviour: homoeostasis, bistable inflammation, tristable inflammation and persistent inflammation. We show that positive and negative feedbacks controlling cytokine production rates can determine either a pre-disposition to OA or initiation of OA. Further, we show that manipulation of cytokine, MMP and Fn-fs levels can be used to treat OA, but we suggest that multiple treatment targets may be essential to halt or slow disease progression. link: http://identifiers.org/pubmed/28213682

Plants depend on the signalling of the phytohormone auxin for their development and for responding to environmental perturbations. The associated biomolecular signalling network involves a negative feedback on Aux/IAA proteins which mediate the influence of auxin (the signal) on the auxin response factor (ARF) transcription factors (the drivers of the response). To probe the role of this feedback, we consider alternative in silico signalling networks implementing different operating principles. By a comparative analysis, we find that the presence of a negative feedback allows the system to have a far larger sensitivity in its dynamical response to auxin and that this sensitivity does not prevent the system from being highly resilient. Given this insight, we build a new biomolecular signalling model for quantitatively describing such Aux/IAA and ARF responses. link: http://identifiers.org/pubmed/29410878