SBMLBioModels: M - N

Network of signaling proteins and functional interaction between the infected cell and the leishmanial parasite, though are not well understood, may be deciphered computationally by reconstructing the immune signaling network. As we all know signaling pathways are well-known abstractions that explain the mechanisms whereby cells respond to signals, collections of pathways form networks, and interactions between pathways in a network, known as cross-talk, enables further complex signaling behaviours. In silico perturbations can help identify sensitive crosstalk points in the network which can be pharmacologically tested. In this study, we have developed a model for immune signaling cascade in leishmaniasis and based upon the interaction analysis obtained through simulation, we have developed a model network, between four signaling pathways i.e., CD14, epidermal growth factor (EGF), tumor necrotic factor (TNF) and PI3 K mediated signaling. Principal component analysis of the signaling network showed that EGF and TNF pathways can be potent pharmacological targets to curb leishmaniasis. The approach is illustrated with a proposed workable model of epidermal growth factor receptor (EGFR) that modulates the immune response. EGFR signaling represents a critical junction between inflammation related signal and potent cell regulation machinery that modulates the expression of cytokines. link: http://identifiers.org/pubmed/24432155

The goal of palliative cancer chemotherapy treatment is to prolong survival and improve quality of life when tumour eradication is not feasible. Chemotherapy protocol design is considered in this context using a simple, robust, model of advanced tumour growth with Gompertzian dynamics, taking into account the effects of drug resistance. It is predicted that reduced chemotherapy protocols can readily lead to improved survival times due to the effects of competition between resistant and sensitive tumour cells. Very early palliation is also predicted to quickly yield near total tumour resistance and thus decrease survival duration. Finally, our simulations indicate that failed curative attempts using dose densification, a common protocol escalation strategy, can reduce survival times. link: http://identifiers.org/pubmed/19135065

Living organisms perform and control complex behaviours by using webs of chemical reactions organized in precise networks. This powerful system concept, which is at the very core of biology, has recently become a new foundation for bioengineering. Remarkably, however, it is still extremely difficult to rationally create such network architectures in artificial, non-living and well-controlled settings. We introduce here a method for such a purpose, on the basis of standard DNA biochemistry. This approach is demonstrated by assembling de novo an efficient chemical oscillator: we encode the wiring of the corresponding network in the sequence of small DNA templates and obtain the predicted dynamics. Our results show that the rational cascading of standard elements opens the possibility to implement complex behaviours in vitro. Because of the simple and well-controlled environment, the corresponding chemical network is easily amenable to quantitative mathematical analysis. These synthetic systems may thus accelerate our understanding of the underlying principles of biological dynamic modules. link: http://identifiers.org/pubmed/21283142

BACKGROUND: Synechocystis sp. PCC6803 is a cyanobacterium considered as a candidate photo-biological production platform–an attractive cell factory capable of using CO2 and light as carbon and energy source, respectively. In order to enable efficient use of metabolic potential of Synechocystis sp. PCC6803, it is of importance to develop tools for uncovering stoichiometric and regulatory principles in the Synechocystis metabolic network. RESULTS: We report the most comprehensive metabolic model of Synechocystis sp. PCC6803 available, iSyn669, which includes 882 reactions, associated with 669 genes, and 790 metabolites. The model includes a detailed biomass equation which encompasses elementary building blocks that are needed for cell growth, as well as a detailed stoichiometric representation of photosynthesis. We demonstrate applicability of iSyn669 for stoichiometric analysis by simulating three physiologically relevant growth conditions of Synechocystis sp. PCC6803, and through in silico metabolic engineering simulations that allowed identification of a set of gene knock-out candidates towards enhanced succinate production. Gene essentiality and hydrogen production potential have also been assessed. Furthermore, iSyn669 was used as a transcriptomic data integration scaffold and thereby we found metabolic hot-spots around which gene regulation is dominant during light-shifting growth regimes. CONCLUSIONS: iSyn669 provides a platform for facilitating the development of cyanobacteria as microbial cell factories. link: http://identifiers.org/pubmed/21083885

We use a modeling and simulation approach to carry out an in silico analysis of the metabolic pathways involving arginine as a precursor of nitric oxide or polyamines in aorta endothelial cells. Our model predicts conditions of physiological steady state, as well as the response of the system to changes in the control parameter, external arginine concentration. Metabolic flux control analysis allowed us to predict the values of flux control coefficients for all the transporters and enzymes included in the model. This analysis fulfills the flux control coefficient summation theorem and shows that both the low affinity transporter and arginase share the control of the fluxes through these metabolic pathways. link: http://identifiers.org/pubmed/17520329

In this paper, we propose and analyse a mathematical model for chronic myelogenous leukemia (CML), a cancer of the blood. We model the interaction between naive T cells, effector T cells, and CML cancer cells in the body, using a system of ordinary differential equations which gives rates of change of the three cell populations. One of the difficulties in modeling CML is the scarcity of experimental data which can be used to estimate parameters values. To compensate for the resulting uncertainties, we use Latin hypercube sampling (LHS) on large ranges of possible parameter values in our analysis. A major goal of this work is the determination of parameters which play a critical role in remission or clearance of the cancer in the model. Our analysis examines 12 parameters, and identifies two of these, the growth and death rates of CML, as critical to the outcome of the system. Our results indicate that the most promising research avenues for treatments of CML should be those that affect these two significant parameters (CML growth and death rates), while altering the other parameters should have little effect on the outcome. link: http://identifiers.org/pubmed/15038986

In this paper, we propose and analyse a mathematical model for chronic myelogenous leukemia (CML), a cancer of the blood. We model the interaction between naive T cells, effector T cells, and CML cancer cells in the body, using a system of ordinary differential equations which gives rates of change of the three cell populations. One of the difficulties in modeling CML is the scarcity of experimental data which can be used to estimate parameters values. To compensate for the resulting uncertainties, we use Latin hypercube sampling (LHS) on large ranges of possible parameter values in our analysis. A major goal of this work is the determination of parameters which play a critical role in remission or clearance of the cancer in the model. Our analysis examines 12 parameters, and identifies two of these, the growth and death rates of CML, as critical to the outcome of the system. Our results indicate that the most promising research avenues for treatments of CML should be those that affect these two significant parameters (CML growth and death rates), while altering the other parameters should have little effect on the outcome. link: http://identifiers.org/pubmed/15038986

Loss of proteostasis and cellular senescence are key hallmarks of aging, but direct cause-effect relationships are not well understood. We show that most yeast cells arrest in G1 before death with low nuclear levels of Cln3, a key G1 cyclin extremely sensitive to chaperone status. Chaperone availability is seriously compromised in aged cells, and the G1 arrest coincides with massive aggregation of a metastable chaperone-activity reporter. Moreover, G1-cyclin overexpression increases lifespan in a chaperone-dependent manner. As a key prediction of a model integrating autocatalytic protein aggregation and a minimal Start network, enforced protein aggregation causes a severe reduction in lifespan, an effect that is greatly alleviated by increased expression of specific chaperones or cyclin Cln3. Overall, our data show that proteostasis breakdown, by compromising chaperone activity and G1-cyclin function, causes an irreversible arrest in G1, configuring a molecular pathway postulating proteostasis decay as a key contributing effector of cell senescence. link: http://identifiers.org/pubmed/31518229

Cardiovascular disease (CVD) is the leading cause of morbidity and mortality in the UK. This condition becomes increasingly prevalent during ageing; 34.1% and 29.8% of males and females respectively, over 75 years of age have an underlying cardiovascular problem. The dysregulation of cholesterol metabolism is inextricably correlated with cardiovascular health and for this reason low density lipoprotein cholesterol (LDL-C) and high density lipoprotein cholesterol (HDL-C) are routinely used as biomarkers of CVD risk. The aim of this work was to use mathematical modelling to explore how cholesterol metabolism is affected by the ageing process. To do this we updated a previously published whole-body mathematical model of cholesterol metabolism to include an additional 96 mechanisms that are fundamental to this biological system. Additional mechanisms were added to cholesterol absorption, cholesterol synthesis, reverse cholesterol transport (RCT), bile acid synthesis, and their enterohepatic circulation. The sensitivity of the model was explored by the use of both local and global parameter scans. In addition, acute cholesterol feeding was used to explore the effectiveness of the regulatory mechanisms which are responsible for maintaining whole-body cholesterol balance. It was found that our model behaves as a hypo-responder to cholesterol feeding, while both the hepatic and intestinal pools of cholesterol increased significantly. The model was also used to explore the effects of ageing in tandem with three different cholesterol ester transfer protein (CETP) genotypes. Ageing in the presence of an atheroprotective CETP genotype, conferring low CETP activity, resulted in a 0.6% increase in LDL-C. In comparison, ageing with a genotype reflective of high CETP activity, resulted in a 1.6% increase in LDL-C. Thus, the model has illustrated the importance of CETP genotypes such as I405V, and their potential role in healthy ageing. link: http://identifiers.org/pubmed/27157786

Cellular systems are generally robust against fluctuations of intracellular parameters such as gene expression level. However, little is known about expression limits of genes required to halt cellular systems. In this study, using the fission yeast Schizosaccharomyces pombe, we developed a genetic 'tug-of-war' (gTOW) method to assess the overexpression limit of certain genes. Using gTOW, we determined copy number limits for 31 cell-cycle regulators; the limits varied from 1 to >100. Comparison with orthologs of the budding yeast Saccharomyces cerevisiae suggested the presence of a conserved fragile core in the eukaryotic cell cycle. Robustness profiles of networks regulating cytokinesis in both yeasts (septation-initiation network (SIN) and mitotic exit network (MEN)) were quite different, probably reflecting differences in their physiologic functions. Fragility in the regulation of GTPase spg1 was due to dosage imbalance against GTPase-activating protein (GAP) byr4. Using the gTOW data, we modified a mathematical model and successfully reproduced the robustness of the S. pombe cell cycle with the model. link: http://identifiers.org/pubmed/22146300

Barnacle muscle fibers subjected to constant current stimulation produce a variety of types of oscillatory behavior when the internal medium contains the Ca++ chelator EGTA. Oscillations are abolished if Ca++ is removed from the external medium, or if the K+ conductance is blocked. Available voltage-clamp data indicate that the cell's active conductance systems are exceptionally simple. Given the complexity of barnacle fiber voltage behavior, this seems paradoxical. This paper presents an analysis of the possible modes of behavior available to a system of two noninactivating conductance mechanisms, and indicates a good correspondence to the types of behavior exhibited by barnacle fiber. The differential equations of a simple equivalent circuit for the fiber are dealt with by means of some of the mathematical techniques of nonlinear mechanics. General features of the system are (a) a propensity to produce damped or sustained oscillations over a rather broad parameter range, and (b) considerable latitude in the shape of the oscillatory potentials. It is concluded that for cells subject to changeable parameters (either from cell to cell or with time during cellular activity), a system dominated by two noninactivating conductances can exhibit varied oscillatory and bistable behavior. link: http://identifiers.org/pubmed/7260316

Barnacle muscle fibers subjected to constant current stimulation produce a variety of types of oscillatory behavior when the internal medium contains the Ca++ chelator EGTA. Oscillations are abolished if Ca++ is removed from the external medium, or if the K+ conductance is blocked. Available voltage-clamp data indicate that the cell's active conductance systems are exceptionally simple. Given the complexity of barnacle fiber voltage behavior, this seems paradoxical. This paper presents an analysis of the possible modes of behavior available to a system of two noninactivating conductance mechanisms, and indicates a good correspondence to the types of behavior exhibited by barnacle fiber. The differential equations of a simple equivalent circuit for the fiber are dealt with by means of some of the mathematical techniques of nonlinear mechanics. General features of the system are (a) a propensity to produce damped or sustained oscillations over a rather broad parameter range, and (b) considerable latitude in the shape of the oscillatory potentials. It is concluded that for cells subject to changeable parameters (either from cell to cell or with time during cellular activity), a system dominated by two noninactivating conductances can exhibit varied oscillatory and bistable behavior. link: http://identifiers.org/pubmed/7260316

Eukaryotic cell cycle progression is controlled by the ordered action of cyclin-dependent kinases, activation of which occurs through the binding of the cyclin to the Cdk followed by phosphorylation of a conserved threonine in the T-loop of the Cdk by Cdk-activating kinase (CAK). Despite our understanding of the structural changes, which occur upon Cdk/cyclin formation and activation, little is known about the dynamics of the molecular events involved. We have characterized the mechanism of Cdk2/cyclin A complex formation and activation at the molecular and dynamic level by rapid kinetics and demonstrate here that it is a two-step process. The first step involves the rapid association between the PSTAIRE helix of Cdk2 and helices 3 and 5 of the cyclin to yield an intermediate complex in which the threonine in the T-loop is not accessible for phosphorylation. Additional contacts between the C-lobe of the Cdk and the N-terminal helix of the cyclin then induce the isomerization of the Cdk into a fully mature form by promoting the exposure of the T-loop for phosphorylation by CAK and the formation of the substrate binding site. This conformational change is selective for the cyclin partner. link: http://identifiers.org/pubmed/11959850

The aggregation of proteins has been hypothesized to be an underlying cause of many neurological disorders including Alzheimer's, Parkinson's, and Huntington's diseases; protein aggregation is also important to normal life function in cases such as G to F-actin, glutamate dehydrogenase, and tubulin and flagella formation. For this reason, the underlying mechanism of protein aggregation, and accompanying kinetic models for protein nucleation and growth (growth also being called elongation, polymerization, or fibrillation in the literature), have been investigated for more than 50 years. As a way to concisely present the key prior literature in the protein aggregation area, Table 1 in the main text summarizes 23 papers by 10 groups of authors that provide 5 basic classes of mechanisms for protein aggregation over the period from 1959 to 2007. However, and despite this major prior effort, still lacking are both (i) anything approaching a consensus mechanism (or mechanisms), and (ii) a generally useful, and thus widely used, simplest/"Ockham's razor" kinetic model and associated equations that can be routinely employed to analyze a broader range of protein aggregation kinetic data. Herein we demonstrate that the 1997 Finke-Watzky (F-W) 2-step mechanism of slow continuous nucleation, A –> B (rate constant k1), followed by typically fast, autocatalytic surface growth, A + B –> 2B (rate constant k2), is able to quantitatively account for the kinetic curves from all 14 representative data sets of neurological protein aggregation found by a literature search (the prion literature was largely excluded for the purposes of this study in order provide some limit to the resultant literature that was covered). The F-W model is able to deconvolute the desired nucleation, k1, and growth, k2, rate constants from those 14 data sets obtained by four different physical methods, for three different proteins, and in nine different labs. The fits are generally good, and in many cases excellent, with R2 values >or=0.98 in all cases. As such, this contribution is the current record of the widest set of protein aggregation data best fit by what is also the simplest model offered to date. Also provided is the mathematical connection between the 1997 F-W 2-step mechanism and the 2000 3-step mechanism proposed by Saitô and co-workers. In particular, the kinetic equation for Saitô's 3-step mechanism is shown to be mathematically identical to the earlier, 1997 2-step F-W mechanism under the 3 simplifying assumptions Saitô and co-workers used to derive their kinetic equation. A list of the 3 main caveats/limitations of the F-W kinetic model is provided, followed by the main conclusions from this study as well as some needed future experiments. link: http://identifiers.org/pubmed/18247636

The aggregation of proteins is believed to be intimately connected to many neurodegenerative disorders. We recently reported an "Ockham's razor"/minimalistic approach to analyze the kinetic data of protein aggregation using the Finke-Watzky (F-W) 2-step model of nucleation (A–>B, rate constant k(1)) and autocatalytic growth (A+B–>2B, rate constant k(2)). With that kinetic model we have analyzed 41 representative protein aggregation data sets in two recent publications, including amyloid beta, alpha-synuclein, polyglutamine, and prion proteins (Morris, A. M., et al. (2008) Biochemistry 47, 2413-2427; Watzky, M. A., et al. (2008) Biochemistry 47, 10790-10800). Herein we use the F-W model to reanalyze protein aggregation kinetic data obtained under the experimental conditions of variable temperature or pH 2.0 to 8.5. We provide the average nucleation (k(1)) and growth (k(2)) rate constants and correlations with variable temperature or varying pH for the protein alpha-synuclein. From the variable temperature data, activation parameters DeltaG(double dagger), DeltaH(double dagger), and DeltaS(double dagger) are provided for nucleation and growth, and those values are compared to the available parameters reported in the previous literature determined using an empirical method. Our activation parameters suggest that nucleation and growth are energetically similar for alpha-synuclein aggregation (DeltaG(double dagger)(nucleation)=23(3) kcal/mol; DeltaG(double dagger)(growth)=22(1) kcal/mol at 37 degrees C). From the variable pH data, the F-W analyses show a maximal k(1) value at pH approximately 3, as well as minimal k(1) near the isoelectric point (pI) of alpha-synuclein. Since solubility and net charge are minimized at the pI, either or both of these factors may be important in determining the kinetics of the nucleation step. On the other hand, the k(2) values increase with decreasing pH (i.e., do not appear to have a minimum or maximum near the pI) which, when combined with the k(1) vs. pH (and pI) data, suggest that solubility and charge are less important factors for growth, and that charge is important in the k(1), nucleation step of alpha-synuclein. The chemically well-defined nucleation (k(1)) rate constants obtained from the F-W analysis are, as expected, different than the 1/lag-time empirical constants previously obtained. However, k(2)xA (where k(2) is the rate constant for autocatalytic growth and A is the initial protein concentration) is related to the empirical constant, k(app) obtained previously. Overall, the average nucleation and average growth rate constants for alpha-synuclein aggregation as a function of pH and variable temperature have been quantitated. Those values support the previously suggested formation of a partially folded intermediate that promotes aggregation under high temperature or acidic conditions. link: http://identifiers.org/pubmed/19101068

A mathematical description of polyglutamated folate kinetics for human breast carcinoma cells (MCF-7) has been formulated based upon experimental folate, methotrexate (MTX), purine, and pyrimidine pool sizes as well as reaction rate parameters obtained from intact MCF-7 cells and their enzyme isolates. The schema accounts for the interconversion of highly polyglutamated tetrahydrofolate, 5-methyl-FH4, 5-10-CH2FH4, dihydrofolate (FH2), 10-formyl-FH4 (FFH4), and 10-formyl-FH2 (FFH2), as well as formation and transport of the MTX polyglutamates. Inhibition mechanisms have been chosen to reproduce all observed non-, un-, and pure competition inhibition patterns. Steady state folate concentrations and thymidylate and purine synthesis rates in drug-free intact cells were used to determine normal folate Vmax values. The resulting average-cell folate model, examined for its ability to predict folate pool behavior following exposure to 1 microM MTX over 21 h, agreed well with the experiment, including a relative preservation of the FFH4 and CH2FH4 pools. The results depend strongly on thymidylate synthase (TS) reaction mechanism, especially the assumption that MTX di- and triglutamates inhibit TS synthesis as greatly in the intact cell as they do with purified enzyme. The effects of cell cycle dependence of TS and dihydrofolate reductase activities were also examined by introducing G- to S-phase activity ratios of these enzymes into the model. For activity ratios down to at least 5%, cell population averaged folate pools were only slightly affected, while CH2FH4 pools in S-phase cells were reduced to as little as 10% of control values. Significantly, these folate pool dynamics were indicated to arise from both direct inhibition by MTX polyglutamates as well as inhibition by elevated levels of polyglutamated FH2 and FFH2. link: http://identifiers.org/pubmed/2732237

Signal transduction and gene regulation determine a major reorganization of metabolic activities in order to support cell proliferation. Protein Kinase B (PKB), also known as Akt, participates in the PI3K/Akt/mTOR pathway, a master regulator of aerobic glycolysis and cellular biosynthesis, two activities shown by both normal and cancer proliferating cells. Not surprisingly considering its relevance for cellular metabolism, Akt/PKB is often found hyperactive in cancer cells. In the last decade, many efforts have been made to improve the understanding of the control of glucose metabolism and the identification of a therapeutic window between proliferating cancer cells and proliferating normal cells. In this context, we have modeled the link between the PI3K/Akt/mTOR pathway, glycolysis, lactic acid production, and nucleotide biosynthesis. We used a computational model to compare two metabolic states generated by two different levels of signaling through the PI3K/Akt/mTOR pathway: one of the two states represents the metabolism of a growing cancer cell characterized by aerobic glycolysis and cellular biosynthesis, while the other state represents the same metabolic network with a reduced glycolytic rate and a higher mitochondrial pyruvate metabolism. Biochemical reactions that link glycolysis and pentose phosphate pathway revealed their importance for controlling the dynamics of cancer glucose metabolism. link: http://identifiers.org/pubmed/23181020

Iron is an essential element of most living organisms but is a dangerous substance when poorly liganded in solution. The hormone hepcidin regulates the export of iron from tissues to the plasma contributing to iron homeostasis and also restricting its availability to infectious agents. Disruption of iron regulation in mammals leads to disorders such as anemia and hemochromatosis, and contributes to the etiology of several other diseases such as cancer and neurodegenerative diseases. Here we test the hypothesis that hepcidin alone is able to regulate iron distribution in different dietary regimes in the mouse using a computational model of iron distribution calibrated with radioiron tracer data.A model was developed and calibrated to the data from adequate iron diet, which was able to simulate the iron distribution under a low iron diet. However simulation of high iron diet shows considerable deviations from the experimental data. Namely the model predicts more iron in red blood cells and less iron in the liver than what was observed in experiments.These results suggest that hepcidin alone is not sufficient to regulate iron homeostasis in high iron conditions and that other factors are important. The model was able to simulate anemia when hepcidin was increased but was unable to simulate hemochromatosis when hepcidin was suppressed, suggesting that in high iron conditions additional regulatory interactions are important. link: http://identifiers.org/pubmed/28521769

Iron is an essential element of most living organisms but is a dangerous substance when poorly liganded in solution. The hormone hepcidin regulates the export of iron from tissues to the plasma contributing to iron homeostasis and also restricting its availability to infectious agents. Disruption of iron regulation in mammals leads to disorders such as anemia and hemochromatosis, and contributes to the etiology of several other diseases such as cancer and neurodegenerative diseases. Here we test the hypothesis that hepcidin alone is able to regulate iron distribution in different dietary regimes in the mouse using a computational model of iron distribution calibrated with radioiron tracer data.A model was developed and calibrated to the data from adequate iron diet, which was able to simulate the iron distribution under a low iron diet. However simulation of high iron diet shows considerable deviations from the experimental data. Namely the model predicts more iron in red blood cells and less iron in the liver than what was observed in experiments.These results suggest that hepcidin alone is not sufficient to regulate iron homeostasis in high iron conditions and that other factors are important. The model was able to simulate anemia when hepcidin was increased but was unable to simulate hemochromatosis when hepcidin was suppressed, suggesting that in high iron conditions additional regulatory interactions are important. link: http://identifiers.org/pubmed/28521769

Iron is an essential element of most living organisms but is a dangerous substance when poorly liganded in solution. The hormone hepcidin regulates the export of iron from tissues to the plasma contributing to iron homeostasis and also restricting its availability to infectious agents. Disruption of iron regulation in mammals leads to disorders such as anemia and hemochromatosis, and contributes to the etiology of several other diseases such as cancer and neurodegenerative diseases. Here we test the hypothesis that hepcidin alone is able to regulate iron distribution in different dietary regimes in the mouse using a computational model of iron distribution calibrated with radioiron tracer data.A model was developed and calibrated to the data from adequate iron diet, which was able to simulate the iron distribution under a low iron diet. However simulation of high iron diet shows considerable deviations from the experimental data. Namely the model predicts more iron in red blood cells and less iron in the liver than what was observed in experiments.These results suggest that hepcidin alone is not sufficient to regulate iron homeostasis in high iron conditions and that other factors are important. The model was able to simulate anemia when hepcidin was increased but was unable to simulate hemochromatosis when hepcidin was suppressed, suggesting that in high iron conditions additional regulatory interactions are important. link: http://identifiers.org/pubmed/28521769

Iron is an essential element of most living organisms but is a dangerous substance when poorly liganded in solution. The hormone hepcidin regulates the export of iron from tissues to the plasma contributing to iron homeostasis and also restricting its availability to infectious agents. Disruption of iron regulation in mammals leads to disorders such as anemia and hemochromatosis, and contributes to the etiology of several other diseases such as cancer and neurodegenerative diseases. Here we test the hypothesis that hepcidin alone is able to regulate iron distribution in different dietary regimes in the mouse using a computational model of iron distribution calibrated with radioiron tracer data.A model was developed and calibrated to the data from adequate iron diet, which was able to simulate the iron distribution under a low iron diet. However simulation of high iron diet shows considerable deviations from the experimental data. Namely the model predicts more iron in red blood cells and less iron in the liver than what was observed in experiments.These results suggest that hepcidin alone is not sufficient to regulate iron homeostasis in high iron conditions and that other factors are important. The model was able to simulate anemia when hepcidin was increased but was unable to simulate hemochromatosis when hepcidin was suppressed, suggesting that in high iron conditions additional regulatory interactions are important. link: http://identifiers.org/pubmed/28521769

Iron is an essential element of most living organisms but is a dangerous substance when poorly liganded in solution. The hormone hepcidin regulates the export of iron from tissues to the plasma contributing to iron homeostasis and also restricting its availability to infectious agents. Disruption of iron regulation in mammals leads to disorders such as anemia and hemochromatosis, and contributes to the etiology of several other diseases such as cancer and neurodegenerative diseases. Here we test the hypothesis that hepcidin alone is able to regulate iron distribution in different dietary regimes in the mouse using a computational model of iron distribution calibrated with radioiron tracer data.A model was developed and calibrated to the data from adequate iron diet, which was able to simulate the iron distribution under a low iron diet. However simulation of high iron diet shows considerable deviations from the experimental data. Namely the model predicts more iron in red blood cells and less iron in the liver than what was observed in experiments.These results suggest that hepcidin alone is not sufficient to regulate iron homeostasis in high iron conditions and that other factors are important. The model was able to simulate anemia when hepcidin was increased but was unable to simulate hemochromatosis when hepcidin was suppressed, suggesting that in high iron conditions additional regulatory interactions are important. link: http://identifiers.org/pubmed/28521769

Metronomic dosing of chemotherapy-defined as frequent administration at lower doses-has been shown to be more efficacious than maximum tolerated dose treatment in preclinical studies, and is currently being tested in the clinic. Although multiple mechanisms of benefit from metronomic chemotherapy have been proposed, how these mechanisms are related to one another and which one is dominant for a given tumor-drug combination is not known. To this end, we have developed a mathematical model that incorporates various proposed mechanisms, and report here that improved function of tumor vessels is a key determinant of benefit from metronomic chemotherapy. In our analysis, we used multiple dosage schedules and incorporated interactions among cancer cells, stem-like cancer cells, immune cells, and the tumor vasculature. We found that metronomic chemotherapy induces functional normalization of tumor blood vessels, resulting in improved tumor perfusion. Improved perfusion alleviates hypoxia, which reprograms the immunosuppressive tumor microenvironment toward immunostimulation and improves drug delivery and therapeutic outcomes. Indeed, in our model, improved vessel function enhanced the delivery of oxygen and drugs, increased the number of effector immune cells, and decreased the number of regulatory T cells, which in turn killed a larger number of cancer cells, including cancer stem-like cells. Vessel function was further improved owing to decompression of intratumoral vessels as a result of increased killing of cancer cells, setting up a positive feedback loop. Our model enables evaluation of the relative importance of these mechanisms, and suggests guidelines for the optimal use of metronomic therapy. link: http://identifiers.org/pubmed/28174262

This paper focus on the quest for mechanisms that are able to create tolerance and an activation threshold in the extrinsic coagulation cascade. We propose that the interplay of coagulation inhibitor and blood flow creates threshold behavior. First we test this hypothesis in a minimal, four dimensional model. This model can be analysed by means of time scale analysis. We find indeed that only the interplay of blood flow and inhibition together are able to produce threshold behavior. The mechanism relays on a combination of raw substance supply and wash-out effect by the blood flow and a stabilization of the resting state by the inhibition. We use the insight into this minimal model to interpret the simulation results of a large model. Here, we find that the initiating steps (TF that produces together with fVII(a) factor Xa) does not exhibit threshold behavior, but the overall system does. Hence, the threshold behavior appears via the feedback loop (in that fIIa produces indirectly fXa that in turn produces fIIa again) inhibited by ATIII and blood flow. link: http://identifiers.org/pubmed/17936855

Liver regeneration is a tightly controlled process mainly achieved by proliferation of usually quiescent hepatocytes. The specific molecular mechanisms ensuring cell division only in response to proliferative signals such as hepatocyte growth factor (HGF) are not fully understood. Here, we combined quantitative time-resolved analysis of primary mouse hepatocyte proliferation at the single cell and at the population level with mathematical modeling. We showed that numerous G1/S transition components are activated upon hepatocyte isolation whereas DNA replication only occurs upon additional HGF stimulation. In response to HGF, Cyclin:CDK complex formation was increased, p21 rather than p27 was regulated, and Rb expression was enhanced. Quantification of protein levels at the restriction point showed an excess of CDK2 over CDK4 and limiting amounts of the transcription factor E2F-1. Analysis with our mathematical model revealed that T160 phosphorylation of CDK2 correlated best with growth factor-dependent proliferation, which we validated experimentally on both the population and the single cell level. In conclusion, we identified CDK2 phosphorylation as a gate-keeping mechanism to maintain hepatocyte quiescence in the absence of HGF. link: http://identifiers.org/pubmed/25771250

Understanding how cellular functions emerge from the underlying molecular mechanisms is a key challenge in biology. This will require computational models, whose predictive power is expected to increase with coverage and precision of formulation. Genome-scale models revolutionised the metabolic field and made the first whole-cell model possible. However, the lack of genome-scale models of signalling networks blocks the development of eukaryotic whole-cell models. Here, we present a comprehensive mechanistic model of the molecular network that controls the cell division cycle in Saccharomyces cerevisiae. We use rxncon, the reaction-contingency language, to neutralise the scalability issues preventing formulation, visualisation and simulation of signalling networks at the genome-scale. We use parameter-free modelling to validate the network and to predict genotype-to-phenotype relationships down to residue resolution. This mechanistic genome-scale model offers a new perspective on eukaryotic cell cycle control, and opens up for similar models—and eventually whole-cell models—of human cells. link: https://doi.org/10.1038/s41467-019-08903-w

Worldwide, breast cancer has become the second most common cancer in women. The disease has currently been named the most deadly cancer in women but little is known on what causes the disease. We present the effects of estrogen as a risk factor on the dynamics of breast cancer. We develop a deterministic mathematical model showing general dynamics of breast cancer with immune response. This is a four-population model that includes tumor cells, host cells, immune cells, and estrogen. The effects of estrogen are then incorporated in the model. The results show that the presence of extra estrogen increases the risk of developing breast cancer. link: http://identifiers.org/pubmed/23365616

A deterministic model for the co-interaction of HIV and malaria in a community is presented and rigorously analyzed. Two sub-models, namely the HIV-only and malaria-only sub-models, are considered first of all. Unlike the HIV-only sub-model, which has a globally-asymptotically stable disease-free equilibrium whenever the associated reproduction number is less than unity, the malaria-only sub-model undergoes the phenomenon of backward bifurcation, where a stable disease-free equilibrium co-exists with a stable endemic equilibrium, for a certain range of the associated reproduction number less than unity. Thus, for malaria, the classical requirement of having the associated reproduction number to be less than unity, although necessary, is not sufficient for its elimination. It is also shown, using centre manifold theory, that the full HIV-malaria co-infection model undergoes backward bifurcation. Simulations of the full HIV-malaria model show that the two diseases co-exist whenever their reproduction numbers exceed unity (with no competitive exclusion occurring). Further, the reduction in sexual activity of individuals with malaria symptoms decreases the number of new cases of HIV and the mixed HIV-malaria infection while increasing the number of malaria cases. Finally, these simulations show that the HIV-induced increase in susceptibility to malaria infection has marginal effect on the new cases of HIV and malaria but increases the number of new cases of the dual HIV-malaria infection. link: http://identifiers.org/pubmed/19364156

The emergence and fast global spread of COVID-19 has presented one of the greatest public health challenges in modern times with no proven cure or vaccine. Africa is still early in this epidemic, therefore the extent of disease severity is not yet clear. We used a mathematical model to fit to the observed cases of COVID-19 in South Africa to estimate the basic reproductive number and critical vaccination coverage to control the disease for different hypothetical vaccine efficacy scenarios. We also estimated the percentage reduction in effective contacts due to the social distancing measures implemented. Early model estimates show that COVID-19 outbreak in South Africa had a basic reproductive number of 2.95 (95% credible interval [CrI] 2.83-3.33). A vaccine with 70% efficacy had the capacity to contain COVID-19 outbreak but at very higher vaccination coverage 94.44% (95% Crl 92.44-99.92%) with a vaccine of 100% efficacy requiring 66.10% (95% Crl 64.72-69.95%) coverage. Social distancing measures put in place have so far reduced the number of social contacts by 80.31% (95% Crl 79.76-80.85%). These findings suggest that a highly efficacious vaccine would have been required to contain COVID-19 in South Africa. Therefore, the current social distancing measures to reduce contacts will remain key in controlling the infection in the absence of vaccines and other therapeutics. link: http://identifiers.org/pubmed/32706790

Receptor phosphorylation is thought to be tightly regulated because phosphorylated receptors initiate signaling cascades leading to cellular activation. The T cell antigen receptor (TCR) on the surface of T cells is phosphorylated by the kinase Lck and dephosphorylated by the phosphatase CD45 on multiple immunoreceptor tyrosine-based activation motifs (ITAMs). Intriguingly, Lck sequentially phosphorylates ITAMs and ZAP-70, a cytosolic kinase, binds to phosphorylated ITAMs with differential affinities. The purpose of multiple ITAMs, their sequential phosphorylation, and the differential ZAP-70 affinities are unknown. Here, we use a systems model to show that this signaling architecture produces emergent ultrasensitivity resulting in switch-like responses at the scale of individual TCRs. Importantly, this switch-like response is an emergent property, so that removal of multiple ITAMs, sequential phosphorylation, or differential affinities abolishes the switch. We propose that highly regulated TCR phosphorylation is achieved by an emergent switch-like response and use the systems model to design novel chimeric antigen receptors for therapy. link: http://identifiers.org/pubmed/23555234

A campaign for malaria control, using Long Lasting Insecticide Nets (LLINs) was launched in South Sudan in 2009. The success of such a campaign often depends upon adequate available resources and reliable surveillance data which help officials understand existing infections. An optimal allocation of resources for malaria control at a sub-national scale is therefore paramount to the success of efforts to reduce malaria prevalence. In this paper, we extend an existing SIR mathematical model to capture the effect of LLINs on malaria transmission. Available data on malaria is utilized to determine realistic parameter values of this model using a Bayesian approach via Markov Chain Monte Carlo (MCMC) methods. Then, we explore the parasite prevalence on a continued rollout of LLINs in three different settings in order to create a sub-national projection of malaria. Further, we calculate the model's basic reproductive number and study its sensitivity to LLINs' coverage and its efficacy. From the numerical simulation results, we notice a basic reproduction number, [Formula: see text], confirming a substantial increase of incidence cases if no form of intervention takes place in the community. This work indicates that an effective use of LLINs may reduce [Formula: see text] and hence malaria transmission. We hope that this study will provide a basis for recommending a scaling-up of the entry point of LLINs' distribution that targets households in areas at risk of malaria. link: http://identifiers.org/pubmed/29879166

Activation of the fibroblast growth factor (FGFR) and melanocyte stimulating hormone (MC1R) receptors stimulates B-Raf and C-Raf isoforms that regulate the dynamics of MAPK1,2 signaling. Network topology motifs in mammalian cells include feed-forward and feedback loops and bifans where signals from two upstream molecules integrate to modulate the activity of two downstream molecules. We computationally modeled and experimentally tested signal processing in the FGFR/MC1R/B-Raf/C-Raf/MAPK1,2 network in human melanoma cells; identifying 7 regulatory loops and a bifan motif. Signaling from FGFR leads to sustained activation of MAPK1,2, whereas signaling from MC1R results in transient activation of MAPK1,2. The dynamics of MAPK activation depends critically on the expression level and connectivity to C-Raf, which is critical for a sustained MAPK1,2 response. A partially incoherent bifan motif with a feedback loop acts as a logic gate to integrate signals and regulate duration of activation of the MAPK signaling cascade. Further reducing a 106-node ordinary differential equations network encompassing the complete network to a 6-node network encompassing rate-limiting processes sustains the feedback loops and the bifan, providing sufficient information to predict biological responses. link: http://identifiers.org/pubmed/18171696

This is the third of three papers [see also Mulquiney, Bubb and Kuchel (1999) Biochem. J. 342, 565-578; Mulquiney and Kuchel (1999) Biochem. J. 342, 579-594] for which the general goal was to explain the regulation and control of 2,3-bisphosphoglycerate (2,3-BPG) metabolism in human erythrocytes. 2,3-BPG is a major modulator of haemoglobin oxygen affinity and hence is vital in blood oxygen transport. A detailed mathematical model of erythrocyte metabolism was presented in the first two papers. The model was refined through an iterative loop of experiment and simulation and it was used to predict outcomes that are consistent with the metabolic behaviour of the erythrocyte under a wide variety of experimental and physiological conditions. For the present paper, the model was examined using computer simulation and Metabolic Control Analysis. The analysis yielded several new insights into the regulation and control of 2,3-BPG metabolism. Specifically it was found that: (1) the feedback inhibition of hexokinase and phosphofructokinase by 2, 3-BPG are equally as important as the product inhibition of 2,3-BPG synthase in controlling the normal in vivo steady-state concentration of 2,3-BPG; (2) H(+) and oxygen are effective regulators of 2,3-BPG concentration and that increases in 2,3-BPG concentrations are achieved with only small changes in glycolytic rate; (3) these two effectors exert most of their influence through hexokinase and phosphofructokinase; (4) flux through the 2,3-BPG shunt changes in absolute terms in response to different energy demands placed on the cell. This response of the 2,3-BPG shunt contributes an [ATP]-stabilizing effect. A 'cost' of this is that 2, 3-BPG concentrations are very sensitive to the energy demand of the cell and; (5) the flux through the 2,3-BPG shunt does not change in response to different non-glycolytic demands for NADH. link: http://identifiers.org/pubmed/10477270

Zombies are a popular figure in pop culture/entertainment and they are usually portrayed as being brought about through an outbreak or epidemic. Consequently, we model a zombie attack, using biological assumptions based on popular zombie movies. We introduce a basic model for zombie infection, determine equilibria and their stability, and illustrate the outcome with numerical solutions. We then refine the model to introduce a latent period of zombification, whereby humans are infected, but not infectious, before becoming undead. We then modify the model to include the effects of possible quarantine or a cure. Finally, we examine the impact of regular, impulsive reductions in the number of zombies and derive conditions under which eradication can occur. We show that only quick, aggressive attacks can stave off the doomsday scenario: the collapse of society as zombies overtake us all. link: http://www.mathworks.co.uk/matlabcentral/linkexchange/links/1749-when-zombies-attack-mathematical-modelling-of-an-outbreak-of-zombie-infection

Zombies are a popular figure in pop culture/entertainment and they are usually portrayed as being brought about through an outbreak or epidemic. Consequently, we model a zombie attack, using biological assumptions based on popular zombie movies. We introduce a basic model for zombie infection, determine equilibria and their stability, and illustrate the outcome with numerical solutions. We then refine the model to introduce a latent period of zombification, whereby humans are infected, but not infectious, before becoming undead. We then modify the model to include the effects of possible quarantine or a cure. Finally, we examine the impact of regular, impulsive reductions in the number of zombies and derive conditions under which eradication can occur. We show that only quick, aggressive attacks can stave off the doomsday scenario: the collapse of society as zombies overtake us all. link: http://www.mathworks.co.uk/matlabcentral/linkexchange/links/1749-when-zombies-attack-mathematical-modelling-of-an-outbreak-of-zombie-infection

Zombies are a popular figure in pop culture/entertainment and they are usually portrayed as being brought about through an outbreak or epidemic. Consequently, we model a zombie attack, using biological assumptions based on popular zombie movies. We introduce a basic model for zombie infection, determine equilibria and their stability, and illustrate the outcome with numerical solutions. We then refine the model to introduce a latent period of zombification, whereby humans are infected, but not infectious, before becoming undead. We then modify the model to include the effects of possible quarantine or a cure. Finally, we examine the impact of regular, impulsive reductions in the number of zombies and derive conditions under which eradication can occur. We show that only quick, aggressive attacks can stave off the doomsday scenario: the collapse of society as zombies overtake us all. link: http://www.mathworks.co.uk/matlabcentral/linkexchange/links/1749-when-zombies-attack-mathematical-modelling-of-an-outbreak-of-zombie-infection

Zombies are a popular figure in pop culture/entertainment and they are usually portrayed as being brought about through an outbreak or epidemic. Consequently, we model a zombie attack, using biological assumptions based on popular zombie movies. We introduce a basic model for zombie infection, determine equilibria and their stability, and illustrate the outcome with numerical solutions. We then refine the model to introduce a latent period of zombification, whereby humans are infected, but not infectious, before becoming undead. We then modify the model to include the effects of possible quarantine or a cure. Finally, we examine the impact of regular, impulsive reductions in the number of zombies and derive conditions under which eradication can occur. We show that only quick, aggressive attacks can stave off the doomsday scenario: the collapse of society as zombies overtake us all. link: http://www.mathworks.co.uk/matlabcentral/linkexchange/links/1749-when-zombies-attack-mathematical-modelling-of-an-outbreak-of-zombie-infection

Root growth and development in Arabidopsis thaliana are sustained by a specialised zone termed the meristem, which contains a population of dividing and differentiating cells that are functionally analogous to a stem cell niche in animals. The hormones auxin and cytokinin control meristem size antagonistically. Local accumulation of auxin promotes cell division and the initiation of a lateral root primordium. By contrast, high cytokinin concentrations disrupt the regular pattern of divisions that characterises lateral root development, and promote differentiation. The way in which the hormones interact is controlled by a genetic regulatory network. In this paper, we propose a deterministic mathematical model to describe this network and present model simulations that reproduce the experimentally observed effects of cytokinin on the expression of auxin regulated genes. We show how auxin response genes and auxin efflux transporters may be affected by the presence of cytokinin. We also analyse and compare the responses of the hormones auxin and cytokinin to changes in their supply with the responses obtained by genetic mutations of SHY2, which encodes a protein that plays a key role in balancing cytokinin and auxin regulation of meristem size. We show that although shy2 mutations can qualitatively reproduce the effect of varying auxin and cytokinin supply on their response genes, some elements of the network respond differently to changes in hormonal supply and to genetic mutations, implying a different, general response of the network. We conclude that an analysis based on the ratio between these two hormones may be misleading and that a mathematical model can serve as a useful tool for stimulate further experimental work by predicting the response of the network to changes in hormone levels and to other genetic mutations. link: http://identifiers.org/pubmed/21640126

As multicellular organisms grow, positional information is continually needed to regulate the pattern in which cells are arranged. In the Arabidopsis root, most cell types are organized in a radially symmetric pattern; however, a symmetry-breaking event generates bisymmetric auxin and cytokinin signaling domains in the stele. Bidirectional cross-talk between the stele and the surrounding tissues involving a mobile transcription factor, SHORT ROOT (SHR), and mobile microRNA species also determines vascular pattern, but it is currently unclear how these signals integrate. We use a multicellular model to determine a minimal set of components necessary for maintaining a stable vascular pattern. Simulations perturbing the signaling network show that, in addition to the mutually inhibitory interaction between auxin and cytokinin, signaling through SHR, microRNA165/6, and PHABULOSA is required to maintain a stable bisymmetric pattern. We have verified this prediction by observing loss of bisymmetry in shr mutants. The model reveals the importance of several features of the network, namely the mutual degradation of microRNA165/6 and PHABULOSA and the existence of an additional negative regulator of cytokinin signaling. These components form a plausible mechanism capable of patterning vascular tissues in the absence of positional inputs provided by the transport of hormones from the shoot. link: http://identifiers.org/pubmed/24381155

While mathematical models are often used to predict progression of cancer and treatment outcomes, there is still uncertainty over how to best model tumor growth. Seven ordinary differential equation (ODE) models of tumor growth (exponential, Mendelsohn, logistic, linear, surface, Gompertz, and Bertalanffy) have been proposed, but there is no clear guidance on how to choose the most appropriate model for a particular cancer.We examined all seven of the previously proposed ODE models in the presence and absence of chemotherapy. We derived equations for the maximum tumor size, doubling time, and the minimum amount of chemotherapy needed to suppress the tumor and used a sample data set to compare how these quantities differ based on choice of growth model.We find that there is a 12-fold difference in predicting doubling times and a 6-fold difference in the predicted amount of chemotherapy needed for suppression depending on which growth model was used.Our results highlight the need for careful consideration of model assumptions when developing mathematical models for use in cancer treatment planning. link: http://identifiers.org/pubmed/26921070

ARPP-16, ARPP-19, and ENSA are inhibitors of protein phosphatase PP2A. ARPP-19 and ENSA phosphorylated by Greatwall kinase inhibit PP2A during mitosis. ARPP-16 is expressed in striatal neurons where basal phosphorylation by MAST3 kinase inhibits PP2A and regulates key components of striatal signaling. The ARPP-16/19 proteins were discovered as substrates for PKA, but the function of PKA phosphorylation is unknown. We find that phosphorylation by PKA or MAST3 mutually suppresses the ability of the other kinase to act on ARPP-16. Phosphorylation by PKA also acts to prevent inhibition of PP2A by ARPP-16 phosphorylated by MAST3. Moreover, PKA phosphorylates MAST3 at multiple sites resulting in its inhibition. Mathematical modeling highlights the role of these three regulatory interactions to create a switch-like response to cAMP. Together the results suggest a complex antagonistic interplay between the control of ARPP-16 by MAST3 and PKA that creates a mechanism whereby cAMP mediates PP2A disinhibition. link: http://identifiers.org/doi/10.7554/eLife.24998

ARPP-16, ARPP-19, and ENSA are inhibitors of protein phosphatase PP2A. ARPP-19 and ENSA phosphorylated by Greatwall kinase inhibit PP2A during mitosis. ARPP-16 is expressed in striatal neurons where basal phosphorylation by MAST3 kinase inhibits PP2A and regulates key components of striatal signaling. The ARPP-16/19 proteins were discovered as substrates for PKA, but the function of PKA phosphorylation is unknown. We find that phosphorylation by PKA or MAST3 mutually suppresses the ability of the other kinase to act on ARPP-16. Phosphorylation by PKA also acts to prevent inhibition of PP2A by ARPP-16 phosphorylated by MAST3. Moreover, PKA phosphorylates MAST3 at multiple sites resulting in its inhibition. Mathematical modeling highlights the role of these three regulatory interactions to create a switch-like response to cAMP. Together the results suggest a complex antagonistic interplay between the control of ARPP-16 by MAST3 and PKA that creates a mechanism whereby cAMP mediates PP2A disinhibition. link: http://identifiers.org/doi/10.7554/eLife.24998

ARPP-16, ARPP-19, and ENSA are inhibitors of protein phosphatase PP2A. ARPP-19 and ENSA phosphorylated by Greatwall kinase inhibit PP2A during mitosis. ARPP-16 is expressed in striatal neurons where basal phosphorylation by MAST3 kinase inhibits PP2A and regulates key components of striatal signaling. The ARPP-16/19 proteins were discovered as substrates for PKA, but the function of PKA phosphorylation is unknown. We find that phosphorylation by PKA or MAST3 mutually suppresses the ability of the other kinase to act on ARPP-16. Phosphorylation by PKA also acts to prevent inhibition of PP2A by ARPP-16 phosphorylated by MAST3. Moreover, PKA phosphorylates MAST3 at multiple sites resulting in its inhibition. Mathematical modeling highlights the role of these three regulatory interactions to create a switch-like response to cAMP. Together the results suggest a complex antagonistic interplay between the control of ARPP-16 by MAST3 and PKA that creates a mechanism whereby cAMP mediates PP2A disinhibition. link: http://identifiers.org/doi/10.7554/eLife.24998

A mathematical model was designed to explore the co-interaction of gonorrhea and HIV in the presence of antiretroviral therapy and gonorrhea treatment. Qualitative and comprehensive mathematical techniques have been used to analyse the model. The gonorrhea-only and HIV-only sub-models are first considered. Analytic expressions for the threshold parameter in each sub-model and the co-interaction model are derived. Global dynamics of this co-interaction shows that whenever the threshold parameter for the respective sub-models and co-interaction model is less than unity, the epidemics dies out, while the reverse results in persistence of the epidemics in the community. The impact of gonorrhea and its treatment on HIV dynamics is also investigated. Numerical simulations using a set of reasonable parameter values show that the two epidemics co-exists whenever their reproduction numbers exceed unity (with no competitive exclusion). Further, simulations of the full HIV-gonorrhea model also suggests that an increase in the number of individuals infected with gonorrhea (either singly or dually with HIV) in the presence of treatment results in a decrease in gonorrhea-only cases, dual-infection cases but increases the number of HIV-only cases. link: http://identifiers.org/pubmed/20869424

OBJECTIVE:Coronavirus disease 2019 (COVID-19) is a pandemic respiratory illness spreading from person-to-person caused by a novel coronavirus and poses a serious public health risk. The goal of this study was to apply a modified susceptible-exposed-infectious-recovered (SEIR) compartmental mathematical model for prediction of COVID-19 epidemic dynamics incorporating pathogen in the environment and interventions. The next generation matrix approach was used to determine the basic reproduction number [Formula: see text]. The model equations are solved numerically using fourth and fifth order Runge-Kutta methods. RESULTS:We found an [Formula: see text] of 2.03, implying that the pandemic will persist in the human population in the absence of strong control measures. Results after simulating various scenarios indicate that disregarding social distancing and hygiene measures can have devastating effects on the human population. The model shows that quarantine of contacts and isolation of cases can help halt the spread on novel coronavirus. link: http://identifiers.org/pubmed/32703315

Cholera, an acute gastro-intestinal infection and a waterborne disease continues to emerge in developing countries and remains an important global health challenge. We formulate a mathematical model that captures some essential dynamics of cholera transmission to study the impact of public health educational campaigns, vaccination and treatment as control strategies in curtailing the disease. The education-induced, vaccination-induced and treatment-induced reproductive numbers R(E), R(V), R(T) respectively and the combined reproductive number R(C) are compared with the basic reproduction number R(0) to assess the possible community benefits of these control measures. A Lyapunov functional approach is also used to analyse the stability of the equilibrium points. We perform sensitivity analysis on the key parameters that drive the disease dynamics in order to determine their relative importance to disease transmission and prevalence. Graphical representations are provided to qualitatively support the analytical results. link: http://identifiers.org/pubmed/null

BACKGROUND: Higher plants and algae are able to fix atmospheric carbon dioxide through photosynthesis and store this fixed carbon in large quantities as starch, which can be hydrolyzed into sugars serving as feedstock for fermentation to biofuels and precursors. Rational engineering of carbon flow in plant cells requires a greater understanding of how starch breakdown fluxes respond to variations in enzyme concentrations, kinetic parameters, and metabolite concentrations. We have therefore developed and simulated a detailed kinetic ordinary differential equation model of the degradation pathways for starch synthesized in plants and green algae, which to our knowledge is the most complete such model reported to date. RESULTS: Simulation with 9 internal metabolites and 8 external metabolites, the concentrations of the latter fixed at reasonable biochemical values, leads to a single reference solution showing β-amylase activity to be the rate-limiting step in carbon flow from starch degradation. Additionally, the response coefficients for stromal glucose to the glucose transporter k(cat) and KM are substantial, whereas those for cytosolic glucose are not, consistent with a kinetic bottleneck due to transport. Response coefficient norms show stromal maltopentaose and cytosolic glucosylated arabinogalactan to be the most and least globally sensitive metabolites, respectively, and β-amylase k(cat) and KM for starch to be the kinetic parameters with the largest aggregate effect on metabolite concentrations as a whole. The latter kinetic parameters, together with those for glucose transport, have the greatest effect on stromal glucose, which is a precursor for biofuel synthetic pathways. Exploration of the steady-state solution space with respect to concentrations of 6 external metabolites and 8 dynamic metabolite concentrations show that stromal metabolism is strongly coupled to starch levels, and that transport between compartments serves to lower coupling between metabolic subsystems in different compartments. CONCLUSIONS: We find that in the reference steady state, starch cleavage is the most significant determinant of carbon flux, with turnover of oligosaccharides playing a secondary role. Independence of stationary point with respect to initial dynamic variable values confirms a unique stationary point in the phase space of dynamically varying concentrations of the model network. Stromal maltooligosaccharide metabolism was highly coupled to the available starch concentration. From the most highly converged trajectories, distances between unique fixed points of phase spaces show that cytosolic maltose levels depend on the total concentrations of arabinogalactan and glucose present in the cytosol. In addition, cellular compartmentalization serves to dampen much, but not all, of the effects of one subnetwork on another, such that kinetic modeling of single compartments would likely capture most dynamics that are fast on the timescale of the transport reactions. link: http://identifiers.org/pubmed/21682905

The present study began with mathematical modeling of how inhibitors of both factor Xa (fXa) and thrombin affect extrinsic pathway-triggered blood coagulation. Numerical simulation demonstrated a stronger inhibition of thrombin generation by a thrombin inhibitor than a fXa inhibitor, but both prolonged clot time to a similar extent when they were given an equal dissociation constant (30 nm) for interaction with their respective target enzymes. These differences were then tested by comparison with the real inhibitors DX-9065a and argatroban, specific competitive inhibitors of fXa and thrombin, respectively, with similar K(i) values. Comparisons were made in extrinsically triggered human citrated plasma, for which endogenous thrombin potential and clot formation were simultaneously measured with a Wallac multilabel counter equipped with both fluorometric and photometric detectors and a fluorogenic reporter substrate. The results demonstrated stronger inhibition of endogenous thrombin potential by argatroban than by DX-9065a, especially when coagulation was initiated at higher tissue factor concentrations, while argatroban appeared to be slightly less potent in its ability to prolong clot time. This study demonstrates differential inhibition of thrombin generation by fXa and thrombin inhibitors and has implications for the pharmacological regulation of blood coagulation by the anticoagulant protease inhibitors. link: http://identifiers.org/pubmed/12496240

Transient changes in striatal dopamine (DA) concentration are considered to encode a reward prediction error (RPE) in reinforcement learning tasks. Often, a phasic DA change occurs concomitantly with a dip in striatal acetylcholine (ACh), whereas other neuromodulators, such as adenosine (Adn), change slowly. There are abundant adenylyl cyclase (AC) coupled GPCRs for these neuromodulators in striatal medium spiny neurons (MSNs), which play important roles in plasticity. However, little is known about the interaction between these neuromodulators via GPCRs. The interaction between these transient neuromodulator changes and the effect on cAMP/PKA signaling via Golf- and Gi/o-coupled GPCR are studied here using quantitative kinetic modeling. The simulations suggest that, under basal conditions, cAMP/PKA signaling could be significantly inhibited in D1R+ MSNs via ACh/M4R/Gi/o and an ACh dip is required to gate a subset of D1R/Golf-dependent PKA activation. Furthermore, the interaction between ACh dip and DA peak, via D1R and M4R, is synergistic. In a similar fashion, PKA signaling in D2+ MSNs is under basal inhibition via D2R/Gi/o and a DA dip leads to a PKA increase by disinhibiting A2aR/Golf, but D2+ MSNs could also respond to the DA peak via other intracellular pathways. This study highlights the similarity between the two types of MSNs in terms of high basal AC inhibition by Gi/o and the importance of interactions between Gi/o and Golf signaling, but at the same time predicts differences between them with regard to the sign of RPE responsible for PKA activation.Dopamine transients are considered to carry reward-related signal in reinforcement learning. An increase in dopamine concentration is associated with an unexpected reward or salient stimuli, whereas a decrease is produced by omission of an expected reward. Often dopamine transients are accompanied by other neuromodulatory signals, such as acetylcholine and adenosine. We highlight the importance of interaction between acetylcholine, dopamine, and adenosine signals via adenylyl-cyclase coupled GPCRs in shaping the dopamine-dependent cAMP/PKA signaling in striatal neurons. Specifically, a dopamine peak and an acetylcholine dip must interact, via D1 and M4 receptor, and a dopamine dip must interact with adenosine tone, via D2 and A2a receptor, in direct and indirect pathway neurons, respectively, to have any significant downstream PKA activation. link: http://identifiers.org/pubmed/26468202

Transient changes in striatal dopamine (DA) concentration are considered to encode a reward prediction error (RPE) in reinforcement learning tasks. Often, a phasic DA change occurs concomitantly with a dip in striatal acetylcholine (ACh), whereas other neuromodulators, such as adenosine (Adn), change slowly. There are abundant adenylyl cyclase (AC) coupled GPCRs for these neuromodulators in striatal medium spiny neurons (MSNs), which play important roles in plasticity. However, little is known about the interaction between these neuromodulators via GPCRs. The interaction between these transient neuromodulator changes and the effect on cAMP/PKA signaling via Golf- and Gi/o-coupled GPCR are studied here using quantitative kinetic modeling. The simulations suggest that, under basal conditions, cAMP/PKA signaling could be significantly inhibited in D1R+ MSNs via ACh/M4R/Gi/o and an ACh dip is required to gate a subset of D1R/Golf-dependent PKA activation. Furthermore, the interaction between ACh dip and DA peak, via D1R and M4R, is synergistic. In a similar fashion, PKA signaling in D2+ MSNs is under basal inhibition via D2R/Gi/o and a DA dip leads to a PKA increase by disinhibiting A2aR/Golf, but D2+ MSNs could also respond to the DA peak via other intracellular pathways. This study highlights the similarity between the two types of MSNs in terms of high basal AC inhibition by Gi/o and the importance of interactions between Gi/o and Golf signaling, but at the same time predicts differences between them with regard to the sign of RPE responsible for PKA activation.Dopamine transients are considered to carry reward-related signal in reinforcement learning. An increase in dopamine concentration is associated with an unexpected reward or salient stimuli, whereas a decrease is produced by omission of an expected reward. Often dopamine transients are accompanied by other neuromodulatory signals, such as acetylcholine and adenosine. We highlight the importance of interaction between acetylcholine, dopamine, and adenosine signals via adenylyl-cyclase coupled GPCRs in shaping the dopamine-dependent cAMP/PKA signaling in striatal neurons. Specifically, a dopamine peak and an acetylcholine dip must interact, via D1 and M4 receptor, and a dopamine dip must interact with adenosine tone, via D2 and A2a receptor, in direct and indirect pathway neurons, respectively, to have any significant downstream PKA activation. link: http://identifiers.org/pubmed/26468202

Activation of ErbB receptors by epidermal growth factor (EGF) or heregulin (HRG) determines distinct cell-fate decisions, although signals propagate through shared pathways. Using mathematical modeling and experimental approaches, we unravel how HRG and EGF generate distinct, all-or-none responses of the phosphorylated transcription factor c-Fos. In the cytosol, EGF induces transient and HRG induces sustained ERK activation. In the nucleus, however, ERK activity and c-fos mRNA expression are transient for both ligands. Knockdown of dual-specificity phosphatases extends HRG-stimulated nuclear ERK activation, but not c-fos mRNA expression, implying the existence of a HRG-induced repressor of c-fos transcription. Further experiments confirmed that this repressor is mainly induced by HRG, but not EGF, and requires new protein synthesis. We show how a spatially distributed, signaling-transcription cascade robustly discriminates between transient and sustained ERK activities at the c-Fos system level. The proposed control mechanisms are general and operate in different cell types, stimulated by various ligands. link: http://identifiers.org/pubmed/20493519

Activation of ErbB receptors by epidermal growth factor (EGF) or heregulin (HRG) determines distinct cell-fate decisions, although signals propagate through shared pathways. Using mathematical modeling and experimental approaches, we unravel how HRG and EGF generate distinct, all-or-none responses of the phosphorylated transcription factor c-Fos. In the cytosol, EGF induces transient and HRG induces sustained ERK activation. In the nucleus, however, ERK activity and c-fos mRNA expression are transient for both ligands. Knockdown of dual-specificity phosphatases extends HRG-stimulated nuclear ERK activation, but not c-fos mRNA expression, implying the existence of a HRG-induced repressor of c-fos transcription. Further experiments confirmed that this repressor is mainly induced by HRG, but not EGF, and requires new protein synthesis. We show how a spatially distributed, signaling-transcription cascade robustly discriminates between transient and sustained ERK activities at the c-Fos system level. The proposed control mechanisms are general and operate in different cell types, stimulated by various ligands. link: http://identifiers.org/pubmed/20493519

Corticostriatal synapse plasticity of medium spiny neurons is regulated by glutamate input from the cortex and dopamine input from the substantia nigra. While cortical stimulation alone results in long-term depression (LTD), the combination with dopamine switches LTD to long-term potentiation (LTP), which is known as dopamine-dependent plasticity. LTP is also induced by cortical stimulation in magnesium-free solution, which leads to massive calcium influx through NMDA-type receptors and is regarded as calcium-dependent plasticity. Signaling cascades in the corticostriatal spines are currently under investigation. However, because of the existence of multiple excitatory and inhibitory pathways with loops, the mechanisms regulating the two types of plasticity remain poorly understood. A signaling pathway model of spines that express D1-type dopamine receptors was constructed to analyze the dynamic mechanisms of dopamine- and calcium-dependent plasticity. The model incorporated all major signaling molecules, including dopamine- and cyclic AMP-regulated phosphoprotein with a molecular weight of 32 kDa (DARPP32), as well as AMPA receptor trafficking in the post-synaptic membrane. Simulations with dopamine and calcium inputs reproduced dopamine- and calcium-dependent plasticity. Further in silico experiments revealed that the positive feedback loop consisted of protein kinase A (PKA), protein phosphatase 2A (PP2A), and the phosphorylation site at threonine 75 of DARPP-32 (Thr75) served as the major switch for inducing LTD and LTP. Calcium input modulated this loop through the PP2B (phosphatase 2B)-CK1 (casein kinase 1)-Cdk5 (cyclin-dependent kinase 5)-Thr75 pathway and PP2A, whereas calcium and dopamine input activated the loop via PKA activation by cyclic AMP (cAMP). The positive feedback loop displayed robust bi-stable responses following changes in the reaction parameters. Increased basal dopamine levels disrupted this dopamine-dependent plasticity. The present model elucidated the mechanisms involved in bidirectional regulation of corticostriatal synapses and will allow for further exploration into causes and therapies for dysfunctions such as drug addiction. link: http://identifiers.org/pubmed/20169176

HIV-infected individuals are increasingly becoming susceptible to liver disease and, hence, liver-related mortality is on a rise. The presence of CD4+ in the liver and the presence of C-X-C chemokine receptor type 4 (CXCR4) on human hepatocytes provide a conducive environment for HIV invasion. In this study, a mathematical model is used to analyse the dynamics of HIV in the liver with the aim of investigating the existence of liver enzyme elevation in HIV mono-infected individuals. In the presence of HIV-specific cytotoxic T-lymphocytes, the model depicts a unique endemic equilibrium with a transcritical bifurcation when the basic reproductive number is unity. Results of the study show that the level of liver enzyme alanine aminotransferase (ALT) increases with increase in the rate of hepatocytes production. Numerical simulations reveal significant elevation of alanine aminotransferase with increase in viral load. The findings presuppose that while liver damage in HIV infection has mostly been associated with HIV/HBV coinfection and use of antiretroviral therapy (ART), it is possible to have liver damage solely with HIV infection. link: http://identifiers.org/pubmed/23291466

B cell chronic lymphocytic leukemia (B-CLL) is known to havesubstantial clinical heterogeneity. There is no cure, but treatments allow fordisease management. However, the wide range of clinical courses experiencedby B-CLL patients makes prognosis and hence treatment a significant chal-lenge. In an attempt to study disease progression across different patients viaa unified yet flexible approach, we present a mathematical model of B-CLLwith immune response, that can capture both rapid and slow disease progres-sion. This model includes four different cell populations in the peripheral bloodof humans: B-CLL cells, NK cells, cytotoxic T cells and helper T cells. Weanalyze existing data in the medical literature, determine ranges of values forparameters of the model, and compare our model outcomes to clinical patientdata. The goal of this work is to provide a tool that may shed light on factorsaffecting the course of disease progression in patients. This modeling tool canserve as a foundation upon which future treatments can be based. link: http://identifiers.org/doi/10.3934/dcdsb.2013.18.1053

In this study we report a kinetic model for the alpha-thrombin-catalyzed production of fibrin I and fibrin II at pH 7.4, 37 degrees C, gamma/2 0.17. The fibrin is produced by the action of human alpha-thrombin on plasma levels of human fibrinogen in the presence of the major inhibitor of alpha-thrombin in plasma, antithrombin III (AT). This model quantitatively accounts for the time dependence of alpha-thrombin-catalyzed release of fibrinopeptides A and B concurrent with the inactivation of alpha-thrombin by AT and delineates the concerted interactions of alpha-thrombin, fibrin(ogen), and AT during the production of a fibrin clot. The model also provides a method for estimating the concentration of alpha-thrombin required to produce a clot of known composition and predicts a direct relationship between the plasma concentration of fibrinogen and the amount of fibrin produced by a bolus of alpha-thrombin. The predicted relationship between the concentration of fibrinogen and the amount of fibrin produced in plasma provides a plausible explanation for the observed linkage between plasma concentrations of fibrinogen and the risk for ischemic heart disease. link: http://identifiers.org/pubmed/2071587

We propose a new method to solve a system of complex ordinary differential equations (ODEs) with hidden hierarchy. Given a complex system of the ODE, the hierarchy of the system is generally hidden. Once we reveal the hierarchy of the system, the system can be reduced into subsystems called slow and fast subsystems. This division of slow and fast subsystems reduces the analysis and hence reduces the computation time, which can be expensive. In our new method, we first apply the singularly perturbed vector field method that is the global quasi-linearization method. This method exposes the hierarchy of a given complex system. Subsequently, we apply a version of the homotopy analysis method called the method of directly defining the inverse mapping. We applied our new method to the immunotherapy of advanced prostate cancer. link: http://identifiers.org/pubmed/30384811

A number of therapeutics have been developed or are under development aiming to modulate the coagulation network to treat various diseases. We used a systems model to better understand the effect of modulating various components on blood coagulation. A computational model of the coagulation network was built to match in-house in vitro thrombin generation and activated Partial Thromboplastin Time (aPTT) data with various concentrations of recombinant factor VIIa (FVIIa) or factor Xa added to normal human plasma or factor VIII-deficient plasma. Sensitivity analysis applied to the model revealed that lag time, peak thrombin concentration, area under the curve (AUC) of the thrombin generation profile, and aPTT show different sensitivity to changes in coagulation factors' concentrations and type of plasma used (normal or factor VIII-deficient). We also used the model to explore how variability in concentrations of the proteins in coagulation network can impact the response to FVIIa treatment. link: http://identifiers.org/pubmed/26312163

We revisit an old Russian paper by V.V. Dynnik, R. Heinrich and E.E. Sel'kov (1980a,b) describing: "A mathematical model of carbohydrate energy metabolism. Interaction between glycolysis, the Krebs cycle and the H-transporting shuttles at varying ATPases load". We analyse the model mathematically and calculate the control coefficients as a function of ATPase loads. We also evaluate the structure of the metabolic network in terms of elementary flux modes. We show how this model can respond to an ATPase load as well as to the glucose supply. We also show how this simple model can help in understanding the articulation between the major blocks of energetic metabolism, i.e. glycolysis, the Krebs cycle and the H-transporting shuttles. link: http://identifiers.org/pubmed/18304584

Mitochondria play a central role in cellular energetic metabolism. The essential parts of this metabolism are the tricarboxylic acid (TCA) cycle, the respiratory chain and the adenosine triphosphate (ATP) synthesis machinery. Here a simplified model of these three metabolic components with a limited set of differential equations is presented. The existence of a steady state is demonstrated and results of numerical simulations are presented. The relevance of a simple model to represent actual in vivo behavior is discussed. link: http://identifiers.org/pubmed/19007794

Targeting key regulators of the cancer stem cell phenotype to overcome their critical influence on tumor growth is a promising new strategy for cancer treatment. Here we present a modeling framework that operates at both the cellular and molecular levels, for investigating IL-6 mediated, cancer stem cell driven tumor growth and targeted treatment with anti-IL6 antibodies. Our immediate goal is to quantify the influence of IL-6 on cancer stem cell self-renewal and survival, and to characterize the subsequent impact on tumor growth dynamics. By including the molecular details of IL-6 binding, we are able to quantify the temporal changes in fractional occupancies of bound receptors and their influence on tumor volume. There is a strong correlation between the model output and experimental data for primary tumor xenografts. We also used the model to predict tumor response to administration of the humanized IL-6R monoclonal antibody, tocilizumab (TCZ), and we found that as little as 1mg/kg of TCZ administered weekly for 7 weeks is sufficient to result in tumor reduction and a sustained deceleration of tumor growth. link: http://identifiers.org/pubmed/29351275

We propose a compartmental mathematical model for the spread of the COVID-19 disease with special focus on the transmissibility of super-spreaders individuals. We compute the basic reproduction number threshold, we study the local stability of the disease free equilibrium in terms of the basic reproduction number, and we investigate the sensitivity of the model with respect to the variation of each one of its parameters. Numerical simulations show the suitability of the proposed COVID-19 model for the outbreak that occurred in Wuhan, China. link: http://identifiers.org/pubmed/32341628

Use of the bacterium Wolbachia is an innovative new strategy designed to break the cycle of dengue transmission. There are two main mechanisms by which Wolbachia could achieve this: by reducing the level of dengue virus in the mosquito and/or by shortening the host mosquito's lifespan. However, although Wolbachia shortens the lifespan, it also gives a breeding advantage which results in complex population dynamics. This study focuses on the development of a mathematical model to quantify the effect on human dengue cases of introducing Wolbachia into the mosquito population. The model consists of a compartment-based system of first-order differential equations; seasonal forcing in the mosquito population is introduced through the adult mosquito death rate. The analysis focuses on a single dengue outbreak typical of a region with a strong seasonally-varying mosquito population. We found that a significant reduction in human dengue cases can be obtained provided that Wolbachia-carrying mosquitoes persist when competing with mosquitoes without Wolbachia. Furthermore, using the Wolbachia strain WMel reduces the mosquito lifespan by at most 10% and allows them to persist in competition with non-Wolbachia-carrying mosquitoes. Mosquitoes carrying the WMelPop strain, however, are not likely to persist as it reduces the mosquito lifespan by up to 50%. When all other effects of Wolbachia on the mosquito physiology are ignored, cytoplasmic incompatibility alone results in a reduction in the number of human dengue cases. A sensitivity analysis of the parameters in the model shows that the transmission probability, the biting rate and the average adult mosquito death rate are the most important parameters for the outcome of the cumulative proportion of human individuals infected with dengue. link: http://identifiers.org/pubmed/25645184

The administration of a genetically engineered defective interfering virus (DIV) that interferes with HIV-1 replication has been proposed as a therapy for HIV-1 infection and AIDS. The proposed interfering virus, which is designed to superinfect HIV-1 infected cells, carries ribozymes that cleave conserved regions in HIV-1 RNA that code for the viral envelope protein. Thus DIV infection of HIV-1 infected cells should reduce or eliminate viral production by these cells. The success of this therapeutic strategy will depend both on the intercellular interaction of DIV and HIV-1, and on the overall dynamics of virus and T cells in the body. To study these dynamical issues, we have constructed a mathematical model of the interaction of HIV-1, DIV, and CD4+ cells in vivo. The results of both mathematical analysis and numerical simulation indicate that survival of the engineered DIV purely on a peripheral blood HIV-1 infection is unlikely. However, analytical results indicate that DIV might well survive on HIV-1 infected CD4+ cells in lymphoid organs such as lymph nodes and spleen, or on other HIV-1 infected cells in these organs. link: http://identifiers.org/pubmed/7881191

The administration of a genetically engineered defective interfering virus (DIV) that interferes with HIV-1 replication has been proposed as a therapy for HIV-1 infection and AIDS. The proposed interfering virus, which is designed to superinfect HIV-1 infected cells, carries ribozymes that cleave conserved regions in HIV-1 RNA that code for the viral envelope protein. Thus DIV infection of HIV-1 infected cells should reduce or eliminate viral production by these cells. The success of this therapeutic strategy will depend both on the intercellular interaction of DIV and HIV-1, and on the overall dynamics of virus and T cells in the body. To study these dynamical issues, we have constructed a mathematical model of the interaction of HIV-1, DIV, and CD4+ cells in vivo. The results of both mathematical analysis and numerical simulation indicate that survival of the engineered DIV purely on a peripheral blood HIV-1 infection is unlikely. However, analytical results indicate that DIV might well survive on HIV-1 infected CD4+ cells in lymphoid organs such as lymph nodes and spleen, or on other HIV-1 infected cells in these organs. link: http://identifiers.org/pubmed/7881191

Mathematical modeling combined with experimental measurements have yielded important insights into HIV-1 pathogenesis. For example, data from experiments in which HIV-infected patients are given potent antiretroviral drugs that perturb the infection process have been used to estimate kinetic parameters underlying HIV infection. Many of the models used to analyze data have assumed drug treatments to be completely efficacious and that upon infection a cell instantly begins producing virus. We consider a model that allows for less then perfect drug effects and which includes a delay in the initiation of virus production. We present detailed analysis of this delay differential equation model and compare the results to a model without delay. Our analysis shows that when drug efficacy is less than 100%, as may be the case in vivo, the predicted rate of decline in plasma virus concentration depends on three factors: the death rate of virus producing cells, the efficacy of therapy, and the length of the delay. Thus, previous estimates of infected cell loss rates can be improved upon by considering more realistic models of viral infection. link: http://identifiers.org/pubmed/10701304

Mathematical modeling combined with experimental measurements have yielded important insights into HIV-1 pathogenesis. For example, data from experiments in which HIV-infected patients are given potent antiretroviral drugs that perturb the infection process have been used to estimate kinetic parameters underlying HIV infection. Many of the models used to analyze data have assumed drug treatments to be completely efficacious and that upon infection a cell instantly begins producing virus. We consider a model that allows for less then perfect drug effects and which includes a delay in the initiation of virus production. We present detailed analysis of this delay differential equation model and compare the results to a model without delay. Our analysis shows that when drug efficacy is less than 100%, as may be the case in vivo, the predicted rate of decline in plasma virus concentration depends on three factors: the death rate of virus producing cells, the efficacy of therapy, and the length of the delay. Thus, previous estimates of infected cell loss rates can be improved upon by considering more realistic models of viral infection. link: http://identifiers.org/pubmed/10701304

This study explores the dilemma in cellular signaling that triggering of CD95 (Fas/APO-1) in some situations results in cell death and in others leads to the activation of NF-kappaB. We established an integrated kinetic mathematical model for CD95-mediated apoptotic and NF-kappaB signaling. Systematic model reduction resulted in a surprisingly simple model well approximating experimentally observed dynamics. The model postulates a new link between c-FLIP(L) cleavage in the death-inducing signaling complex (DISC) and the NF-kappaB pathway. We validated experimentally that CD95 stimulation resulted in an interaction of p43-FLIP with the IKK complex followed by its activation. Furthermore, we showed that the apoptotic and NF-kappaB pathways diverge already at the DISC. Model and experimental analysis of DISC formation showed that a subtle balance of c-FLIP(L) and procaspase-8 determines life/death decisions in a nonlinear manner. We present an integrated model describing the complex dynamics of CD95-mediated apoptosis and NF-kappaB signaling. link: http://identifiers.org/pubmed/20212524