This CellML model will not run in OpenCell as integration failed at t=0 and h=2.19671e-13, the corrector convergence test failed repeatedly or with |h| = hmin Need UNITS and INITIAL VALUES for concentrations

Model Structure

Mathematical models of the cell cycle can contribute to an understanding of its basic mechanisms. Modern simulation tools make the analysis of key components and their interactions very effective. This paper focuses on the role of small modules and feedbacks in the gene-protein network governing the G1/S transition in mammalian cells. Mutations in this network may lead to uncontrolled cell proliferation. Bifurcation analysis helps to identify the key components of this extremely complex interaction network. RESULTS: We identify various positive and negative feedback loops in the network controlling the G1/S transition. It is shown that the positive feedback regulation of E2F1 and a double activator-inhibitor module can lead to bistability. Extensions of the core module preserve the essential features such as bistability. The complete model exhibits a transcritical bifurcation in addition to bistability. We relate these bifurcations to the cell cycle checkpoint and the G1/S phase transition point. Thus, core modules can explain major features of the complex G1/S network and have a robust decision taking function.

The original paper reference is cited below:

'Bifurcation analysis of the regulatory modules of the mammalian G1/S transition', Maciej Swat, Alexander Kel,Hanspeter Herzel 2004 Bioinformatics, 10, 1506-1511. PubMed ID: 15231543

Image illustrating model 'Bifurcation analysis of the regulatory modules of the mammalian G1/S transition'

This CellML model will run in OpenCell but does not reproduce published results. This is the 20% Oxygen version, two more versions to follow.

Model Structure

Our small-scale bioreactor with a gas-permeable membrane has previously been shown to allow direct oxygenation of primary hepatocytes in collagenous sandwich cultures. In this work the applicability of this system for studying the response of hepatocytes to different ambient oxygen concentrations above the normoxic situation and the effect of the antioxidant vitamin C (ASC) on hepatocyte functionality in different oxygen cultures were evaluated. Determination of the parameters for functional levels (albumin and urea synthesis, biotransformation) combined with the model calculation of these parameters using a product inhibition model based on the concentration of hydrogen peroxide (H2 O2) indicated a relevance of oxygen levels for the maintenance of hepatic-specific functions. A model for the dynamics of oxidative stress was proposed to predict the time course of the qualitative concentrations of H2 O2 and the superoxide radical (O2 • − ) in different oxygen cultures. The 20% and 30% O2 cultures exhibited similar differentiated hepatic functions that were unequivocally lost in the 40% O2 cultures apparently due to oxidative damage. Metabolic functions in the 20% and 30% O2 cultures could be improved by ASC. These findings suggest that our bioreactor model not only allows a prediction of the liver response to variations in oxygen environments, but also serves as an in vitro tool to screen new compounds for antioxidant capacity.

The original paper reference is cited below:

'Improvement of metabolic performance of primary hepatocytes in hyperoxic cultures by vitamin C in a novel small-scale bioreactor, Stephanie Schmitmeier, Angelika Langsch, Wolfgang Schmidt-Heck, Inka Jasmund, Augustinus Bader 2007 Journal of Membrane Science, 298, 30-40.

Image illustrating model 'Improvement of metabolic performance of primary hepatocytes in hyperoxic cultures by vitamin C in a novel small-scale bioreactor '

This CellML model should work in OpenCell and COR to reproduce published results. The a model is based on equations 2 (wihout mitochondria) and the b model is based on equatios 2 and 3 (with mitochondria). Six other versions are as follows: 2a and 2b = equations 3 and 4, 3a and 3b = equations 5 and 6, 4a and 4b = equations 7 and 8. Does not reproduce published results but runs in OpenCell.

Model Structure

In a mathematical model for simple calcium oscillations [Biophys. Chem. 71 (1998) 125], it has been shown that mitochondria play an important role in the maintenance of constant amplitudes of cytosolic Ca[2+] oscillations. Simple plausible rate laws for [Ca+] fluxes across the inner mitochondrial membrane have been used in this model. Here we show that it is possible to use the same rate laws as a plug-in element in other existing mathematical models and obtain the same effect on amplitude regulation. This result appears to be universal, independent of the type of model and the type of Ca oscillations. We demonstrate this on two models for spiking Ca oscillations [J. Biol. Chem. 266 (1991) 11068; Cell Calcium 14 (1993) 311] and on two recent models for bursting Ca oscillations; one of them being a receptor-operated model [Biophys. J. 79 (2000) 1188] and the other one being a store-operated model [BioSystems 57 (2000) 75].

The original paper reference is cited below:

'Mitochondria regulate the amplitude of simple and complex calcium oscillations', Vladimir Grubelnik, Ann Zahle Larsen, Ursula Kummer, Lars Folke Olsen, Marko Marhl, 2001 Biophysical Chemistry, 94, 59-74. PubMed ID: 11744191

Schematic Diagram of Grubelnik model

This CellML model runs in OpenCell and COR to reproduce published results. Some traces need to be matched to the SVG diagram.

Model Structure

Inositol 1,4,5-trisphosphate (Ins-1,4,5-P3) is responsible for Ca2+ mobilization in response to external stimulation in many cell types. The latter phenomenon often occurs as repetitive Ca2+ spikes. In this study, the effect of the two Ins-1,4,5-P3 metabolizing enzymes (Ins-1,4,5-P3 3-kinase and 5-phosphatase) on the temporal pattern of Ca2+ oscillations has been investigated. On the basis of the well-documented Ins-1,4,5-P3 3-kinase stimulation by the Ca2+/calmodulin complex and of the experimentally-determined kinetic characteristics of these enzymes, we predict that 5-phosphatase primarily controls the levels of Ins-1,4,5-P3 and, thereby, the occurrence and frequency of Ca2+ oscillations. Consequently, the model reproduces the experimental observation performed in Chinese hamster ovary cells that 5-phosphatase overexpression has a much more pronounced effect on the pattern of Ca2+ oscillations than 3-kinase overexpression. We also investigated, in more detail, under which conditions a similar effect could be observed in other cell types expressing various Ins-1,4,5-P3 3-kinase activities.

The original paper reference is cited below:

'Simulations of the effects of inositol 1,4,5-trisphosphate 3-kinase and 5-phosphatase activities on Ca2+ oscillations.', G Dupont, C Erneux, 1997 Cell Calcium, 22(5), 321-331. PubMed ID: 9448939

Schemiatic diagram depicting theDupont Erneux model

This CellML model runs in OpenCell and COR but does not exactly reproduce published results of figure 6

Model Structure

Human liver cell bioreactors are used in extracorporeal liver support therapy. To optimize bioreactor operation with respect to clinical application an understanding of the central metabolism is desired. A two-compartment model consisting of a system of 48 differential equations was fitted to time series data of the concentrations of 18 amino acids, ammonia, urea, glucose, galactose, sorbitol and lactate, measured in the medium outflow of seven liver cell bioreactor runs. Using the presented model, the authors predict an amino acid secretion from proteolytic activities during the first day after inoculation of the bioreactor with primary liver cells. Furthermore, gluconeogenetic activites from amino acids and/or protein were predicted.

The original paper reference is cited below:

'Dynamic Model of Amino Acid and Carbohydrate Metabolism in Primary Human Liver Cells', Reinhard Guthke, Wolfgang Schmidt-Heck, Gesine Pless, Rolf Gebhardt, Michael Pfaff, Joerg C. Gerlach, and Katrin Zeilinger, 2006, N. Maglaveras et al. Eds. ISBMDA, 137-149.

Structure of the model Equations.

This CellML model will run in OpenCell and COR to reproduce published results. The a model is based on equations 1-3 and works to reproduce published results. The b model is based on equations 1 and 4-8 and oscillates but does not reproduce results.

Model Structure

Cytosolic calcium plays a crucial role as a second messenger in cellular signalling. Various cell types, including hepatocytes, display Ca2+ oscillations when stimulated by an extracellular signal. However, the biological relevance of this temporal organization remains unclear. In this paper, we investigate theoretically the effect of Ca2+ oscillations on a particular example of cell regulation: the phosphorylation/dephosphorylation cycle controlling the activation of glycogen phosphorylase in hepatocytes. By modelling periodic sinusoidal variations in the intracellular Ca2+ concentration, we show that Ca2+ oscillations reduce the threshold for the activation of the enzyme. Furthermore, as the activation of a given enzyme depends on the kinetics of its phosphorylation/dephosphorylation cycle, speciality can be encoded by the oscillation frequency. Finally, using a model for signal-induced Ca2+ oscillations based on Ca2+-induced Ca2+ release, we show that realistic Ca2+ oscillations can potentiate the response to a hormonal stimulation. These results indicate that Ca2+ oscillations in hepatocytes could contribute to increase the efficiency and speciality of cellular signalling, as shown experimentally for gene expression in lymphocytes (Dolmetsch et al., 1998).

The original paper reference is cited below:

Diagram depicting calcium movement in model.

This CellML model runs in OpenCell and COR to reproduce Figures 2, 3 and 4 from the published paper. The b model does not exactly recreate published results

Model Structure

Many different agonists use calcium as a second messenger. Despite intensive research in intracellular calcium signalling it is an unsolved riddle how the different types of information represented by the different agonists, is encoded using the universal carrier calcium. It is also still not clear how the information encoded is decoded again into the intracellular specific information at the site of enzymes and genes. After the discovery of calcium oscillations, one likely mechanism is that information is encoded in the frequency, amplitude and waveform of the oscillations. This hypothesis has received some experimental support. However, the mechanism of decoding of oscillatory signals is still not known. Here, we study a mechanistic model of calcium oscillations, which is able to reproduce both spiking and bursting calcium oscillations. We use the model to study the decoding of calcium signals on the basis of co-operativity of calcium binding to various proteins. We show that this co-operativity offers a simple way to decode different calcium dynamics into different enzyme activities.

The original paper reference is cited below:

On the encoding and decoding of calcium signals in hepatocytes, Ann Zahle Larsen, Lars Folke Olsen, Ursula Kummer, 2004 Biophysical Chemistry, 107, 83-89. PubMed ID: 14871603

Image depicting elements of the Larsen Olsen Kummer model

Encoded in CellML by Catherine Lloyd

Bioengineering Institute, University of Auckland

Model Status

This model has been curated by Penny Noble using Flavio Fenton's Java code as a reference (See http://thevirtualheart.org/ for Java applet rendering of model - Java code is available from Dr Fenton.) An artificial stimulus component has been added this model to allow it to reproduce the action potential simulation shown in Figure 4 of the publication. The model is known to run and integrate in the PCEnv and COR CellML environments. A PCEnv session file is also associated with this model.

ValidateCellML detects unit inconsistency within this model.

Model Structure

In contrast to the earlier Purkinje fibre ionic current models of D. Noble (1962) and R.E. McAllister, D. Noble and R.W. Tsien (1975), the G.W. Beeler and H. Reuter 1977 model was developed to describe the mammalian ventricular action potential. Not all the ionic currents of the Purkinje fibre model are present in ventricular tissue; therefore, this model is simpler than the MNT model. The total ionic flux is divided into only four discrete, individual ionic currents (see the figure below). The main additional feature of the Beeler-Reuter ionic current model is a representation of the intracellular calcium ion concentration.

The complete original paper reference is cited below:

Reconstruction of the action potential of ventricular myocardial fibres, Beeler, G.W. and Reuter, H. 1977, Journal of Physiology, 268, 177-210. PubMed ID: 874889

A schematic diagram describing the current flows across the cell membrane that are captured in the BR model.

The network defined in the CellML description of the Beeler-Reuter model. A key describing the significance of the shapes of the components and the colours of the connections between them is in the notation guide. For simplicity, not all the variables are shown.

The membrane physically contains the currents as indicated by the blue arrows in the figure above. The currents act independently and are not connected to each other. Several of the channels encapsulate and contain further components which represent activation and inactivation gates. The addition of an encapsulation relationship informs modellers and processing software that the gates are important parts of the current model. It also prevents any other components that aren't also encapsulated by the parent component from connecting to its gates, effectively hiding them from the rest of the model.

The breakdown of the model into components and the definition of encapsulation and containment relationships between them is somewhat arbitrary. When considering how a model should be broken into components, modellers are encouraged to consider which parts of a model might be re-used and how the physiological elements of the system being modelled are naturally bounded. Containment relationships should be used to provide simple rendering information for processing software (ideally, this will correspond to the layout of the physical system), and encapsulation should be used to group sets of components into sub-models.

Model Status

This CellML model is part of a CellML 1.1 model, this segment contains all the model equations describing cellular species. It is imported by smaller CellML models which describe different voltage protocols, and does not run as a standalone model. The units are consistent throughout.

Model Structure

ABSTRACT: We have developed a detailed mathematical model for Ca handling and ionic currents in the human ventricular myocyte. Our aims were to: (1) simulate basic excitation-contraction coupling phenomena; (2) use realistic repolarizing K current densities; (3) reach steady-state. The model relies on the framework of the rabbit myocyte model previously developed by our group, with subsarcolemmal and junctional compartments where ion channels sense higher [Ca] vs. bulk cytosol. Ion channels and transporters have been modeled on the basis of the most recent experimental data from human ventricular myocytes. Rapidly and slowly inactivating components of I(to) have been formulated to differentiate between endocardial and epicardial myocytes. Transmural gradients of Ca handling proteins and Na pump were also simulated. The model has been validated against a wide set of experimental data including action potential duration (APD) adaptation and restitution, frequency-dependent increase in Ca transient peak and [Na](i). Interestingly, Na accumulation at fast heart rate is a major determinant of APD shortening, via outward shifts in Na pump and Na-Ca exchange currents. We investigated the effects of blocking K currents on APD and repolarization reserve: I(Ks) block does not affect the former and slightly reduces the latter; I(K1) blockade modestly increases APD and more strongly reduces repolarization reserve; I(Kr) blockers significantly prolong APD, an effect exacerbated as pacing frequency is decreased, in good agreement with experimental results in human myocytes. We conclude that this model provides a useful framework to explore excitation-contraction coupling mechanisms and repolarization abnormalities at the single myocyte level.

The original paper reference is cited below:

A novel computational model of the human ventricular action potential and Ca transient, Eleonora Grandi, Francesco S. Pasqualini, Donald M. Bers, 2010, Journal of Molecular and Cellular Cardiology, volume 48, 112-121. PubMed ID: 19835882

Model Status

This CellML model is known to run in OpenCell and COR to recreate the published results. The units have been checked and are consistent.

Model Structure

ABSTRACT: Therapies for heart disease are based largely on our understanding of the adult myocardium. The dramatic differences in action potential (AP) shape between neonatal and adult cardiac myocytes, however, indicate that a different set of molecular interactions in neonatal myocytes necessitates different treatment for newborns. Computational modeling is useful for synthesizing data to determine how interactions between components lead to systems-level behavior, but this technique has not been used extensively to study neonatal heart cell function. We created a mathematical model of the neonatal (day 1) mouse myocyte by modifying, on the basis of experimental data, the densities and/or formulations of ion transport mechanisms in an adult cell model. The new model reproduces the characteristic AP shape of neonatal cells, with a brief plateau phase and longer duration than the adult (action potential duration at 80% repolarization = 60.1 vs. 12.6 ms). The simulation results are consistent with experimental data, including 1) decreased density and altered inactivation of transient outward K+ currents, 2) increased delayed rectifier K+ currents, 3) Ca2+ entry through T-type as well as L-type Ca2+ channels, 4) increased Ca2+ influx through Na+/Ca2+ exchange, and 5) Ca2+ transients resulting from transmembrane Ca2+ entry rather than release from the sarcoplasmic reticulum (SR). Simulations performed with the model generated novel predictions, including increased SR Ca2+ leak and elevated intracellular Na+ concentration in neonatal compared with adult myocytes. This new model can therefore be used for testing hypotheses and obtaining a better quantitative understanding of differences between neonatal and adult physiology.

The original paper reference is cited below:

Mathematical model of the neonatal mouse ventricular action potential, Linda J. Wang and Eric A. Sobie, 2008,American Journal of Physiology: Heart and Circulatory Physiology, 294, H2565-H2575. PubMed ID: 18408122

Schematic diagram of the neonatal mouse model.