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Document CellCycle-1991Gol (Goldbeter, 1991)
A minimal model for the mitotic oscillator is presented. The model, built on recent experimental advances, is based on the cascade of post-translational modification that modulates the activity of cdc2 kinase during the cell cycle. The model pertains to the situation encountered in early amphibian embryos, where the accumulation of cyclin suffices to trigger the onset of mitosis. In the first cycle of the bicyclic cascade model, cyclin promotes the activation of cdc2 kinase through reversible dephosphorylation, and in the second cycle, cdc2 kinase activates a cyclin protease by reversible phosphorylation. That cyclin activates cdc2 kinase while the kinase triggers the degradation of cyclin has suggested that oscillations may originate from such a negative feedback loop [Felix, M. A., Labbe, J. C., Doree, M., Hunt, T. & Karsenti, E. (1990) Nature (London) 346, 379-382]. This conjecture is corroborated by the model, which indicates that sustained oscillations of the limit cycle type can arise in the cascade, provided that a threshold exists in the activation of cdc2 kinase by cyclin and in the activation of cyclin proteolysis by cdc2 kinase. The analysis shows how mitotic oscillations may readily arise from time lags associated with these thresholds and from the delayed negative feedback provided by cdc2-induced cyclin degradation. A mechanism for the origin of the thresholds is proposed in terms of the phenomenon of zero-order ultrasensitivity previously described for biochemical systems regulated by covalent modification.
Document CellCycle-1991Tys (Tyson, 1991)
The proteins cdc2 and cyclin form a heterodimer (maturation promoting factor) that controls the major events of the cell cycle. A mathematical model for the interactions of cdc2 and cyclin is constructed. Simulation and analysis of the model show that the control system can operate in three modes: as a steady state with high maturation promoting factor activity, as a spontaneous oscillator, or as an excitable switch. We associate the steady state with metaphase arrest in unfertilized eggs, the spontaneous oscillations with rapid division cycles in early embryos, and the excitable switch with growth-controlled division cycles typical of nonembryonic cells.
Document CellCycle-1991Tys-2 (Tyson, 1991)
The proteins cdc2 and cyclin form a heterodimer (maturation promoting factor) that controls the major events of the cell cycle. A mathematical model for the interactions of cdc2 and cyclin is constructed. Simulation and analysis of the model show that the control system can operate in three modes: as a steady state with high maturation promoting factor activity, as a spontaneous oscillator, or as an excitable switch. We associate the steady state with metaphase arrest in unfertilized eggs, the spontaneous oscillations with rapid division cycles in early embryos, and the excitable switch with growth-controlled division cycles typical of nonembryonic cells.
Document CellCycle-1997Nov (Novak & Tyson, 1997)
A central event in the eukaryotic cell cycle is the decision to commence DNA replication (S phase). Strict controls normally operate to prevent repeated rounds of DNA replication without intervening mitoses ("endoreplication") or initiation of mitosis before DNA is fully replicated ("mitotic catastrophe"). Some of the genetic interactions involved in these controls have recently been identified in yeast. From this evidence we propose a molecular mechanism of "Start" control in Schizosaccharomyces pombe. Using established principles of biochemical kinetics, we compare the properties of this model in detail with the observed behavior of various mutant strains of fission yeast: wee1 (size control at Start), cdc13 and rum1OP (endoreplication), and wee1 rum1 (rapid division cycles of diminishing cell size). We discuss essential features of the mechanism that are responsible for characteristic properties of Start control in fission yeast, to expose our proposal to crucial experimental tests.
Document Genetic-2003Mar (Marwan, 2003)
Mutants of Physarum polycephalum can be complemented by fusion of plasmodial cells followed by cytoplasmic mixing. Complementation between strains carrying different mutational defects in the sporulation control network may depend on the signaling state of the network components. We have previously suggested that time-resolved somatic complementation (TRSC) analysis with such mutants may be used to probe network architecture and dynamics. By computer simulation it is now shown how and under which conditions the regulatory hierarchy of genes can be determined experimentally. A kinetic model of the sporulation control network is developed, which is then used to demonstrate how the mechanisms of TRSC can be understood and simulated at the kinetic level. On the basis of theoretical considerations, experimental parameters that determine whether functional complementation of two mutations will occur are identified. It is also shown how gene dosage-effect relationships can be employed for network analysis. The theoretical framework provided may be used to systematically analyze network structure and dynamics through time-resolved somatic complementation studies. The conclusions drawn are of general relevance in that they do not depend on the validity of the model from which they were derived.
Document CellCycle-1998Gar (Gardner et al., 1998)
We demonstrate, by using mathematical modeling of cell division cycle (CDC) dynamics, a potential mechanism for precisely controlling the frequency of cell division and regulating the size of a dividing cell. Control of the cell cycle is achieved by artificially expressing a protein that reversibly binds and inactivates any one of the CDC proteins. In the simplest case, such as the checkpoint-free situation encountered in early amphibian embryos, the frequency of CDC oscillations can be increased or decreased by regulating the rate of synthesis, the binding rate, or the equilibrium constant of the binding protein. In a more complex model of cell division, where size-control checkpoints are included, we show that the same reversible binding reaction can alter the mean cell mass in a continuously dividing cell. Because this control scheme is general and requires only the expression of a single protein, it provides a practical means for tuning the characteristics of the cell cycle in vivo.
Document CircClock-2001Ued (Ueda et al, 2001)
A mechanism for generating circadian rhythms has been of major interest in recent years. After the discovery of per and tim, a model with a simple feedback loop involving per and tim has been proposed. However, it is recognized that the simple feedback model cannot account for phenotypes generated by various mutants. A recent report by Glossop, Lyons & Hardin [Science286, 766 (1999)] on Drosophila suggests involvement of another feedback loop by dClk that is interlocked with per–tim feedback loop. In order to examine whether interlocked feedback loops can be a basic mechanism for circadian rhythms, a mathematical model was created and examined. Through extensive simulation and mathematical analysis, it was revealed that the interlocked feedback model accounts for the observations that are not explained by the simple feedback model. Moreover, the interlocked feedback model has robust properties in oscillations.
Document CircClock-2002Vil (Vilar et al, 2002)
A wide range of organisms use circadian clocks to keep internal sense of daily time and regulate their behavior accordingly. Most of these clocks use intracellular genetic networks based on positive and negative regulatory elements. The integration of these "circuits" at the cellular level imposes strong constraints on their functioning and design. Here, we study a recently proposed model [Barkai, N. & Leibler, S. (2000) Nature (London), 403, 267-268] that incorporates just the essential elements found experimentally. We show that this type of oscillator is driven mainly by two elements: the concentration of a repressor protein and the dynamics of an activator protein forming an inactive complex with the repressor. Thus, the clock does not need to rely on mRNA dynamics to oscillate, which makes it especially resistant to fluctuations. Oscillations can be present even when the time average of the number of mRNA molecules goes below one. Under some conditions, this oscillator is not only resistant to but, paradoxically, also enhanced by the intrinsic biochemical noise.
Document CircClock-1999Lel (Leloup & Goldbeter, 1999)
In Drosophila , circadian oscillations in the levels of two proteins, PER and TIM, result from the negative feedback exerted by a PER–TIM complex on the expression of the per and tim genes which code for these two proteins. On the basis of these experimental observations, we have recently proposed a theoretical model for circadian oscillations of the PER and TIM proteins in Drosophila . Here we show that for constant environmental conditions this model is capable of generating autonomous chaotic oscillations. For other parameter values, the model can also display birhythmicity, i.e. the coexistence between two stable regimes of limit cycle oscillations. We analyse the occurrence of chaos and birhythmicity by means of bifurcation diagrams and locate the different domains of complex oscillatory behavior in parameter space. The relative smallness of these domains raises doubts as to the possible physiological significance of chaos and birhythmicity in regard to circadian rhythm generation. Beyond the particular context of circadian rhythms we discuss the results in the light of other mechanisms underlying chaos and birhythmicity in regulated biological systems.
Document Metabolism-2002Hoe (Hoefnagel et al., 2002)
Everyone who has ever tried to radically change metabolic fluxes knows that it is often harder to determine which enzymes have to be modified than it is to actually implement these changes. In the more traditional genetic engineering approaches ’bottle-necks’ are pinpointed using qualitative, intuitive approaches, but the alleviation of suspected ’rate-limiting’ steps has not often been successful. Here the authors demonstrate that a model of pyruvate distribution in Lactococcus lactis based on enzyme kinetics in combination with metabolic control analysis clearly indicates the key control points in the flux to acetoin and diacetyl, important flavour compounds. The model presented here (available at http://jjj.biochem.sun.ac.za/wcfs.html) showed that the enzymes with the greatest effect on this flux resided outside the acetolactate synthase branch itself. Experiments confirmed the predictions of the model, i.e. knocking out lactate dehydrogenase and overexpressing NADH oxidase increased the flux through the acetolactate synthase branch from 0 to 75% of measured product formation rates.
Document Genetic-2000Elo (Elowitz & Leibler, 2000)
This file describes the repressilator system. The authors of this model (see reference) use three transcriptional repressor systems that are not part of any natural biological clock to build an oscillating network that they called the repressilator. The model system was induced in Escherichia coli. In this system, LacI (variable X is the mRNA, variable PX is the protein) inhibits the tetracycline-resistance transposon tetR (Y, PY describe mRNA and protein). Protein tetR inhibits the gene Cl from phage Lambda (Z, PZ: mRNA, protein), and protein Cl inhibits lacI expression. With appropriate parameter values this system oscillates. [referenced SBML]
Document MAPKcasc-2000Lev-2 (Levchenko et al, 2000)
In addition to preventing crosstalk among related signaling pathways, scaffold proteins might facilitate signal transduction by preforming multimolecular complexes that can be rapidly activated by incoming signal. In many cases, such as mitogen-activated protein kinase (MAPK) cascades, scaffold proteins are necessary for full activation of a signaling pathway. To date, however, no detailed biochemical model of scaffold action has been suggested. Here we describe a quantitative computer model of MAPK cascade with a generic scaffold protein. Analysis of this model reveals that formation of scaffold-kinase complexes can be used effectively to regulate the specificity, efficiency, and amplitude of signal propagation. In particular, for any generic scaffold there exists a concentration value optimal for signal amplitude. The location of the optimum is determined by the concentrations of the kinases rather than their binding constants and in this way is scaffold independent. This effect and the alteration of threshold properties of the signal propagation at high scaffold concentrations might alter local signaling properties at different subcellular compartments. Different scaffold levels and types might then confer specialized properties to tune evolutionarily conserved signaling modules to specific cellular contexts
Document MAPKcasc-2000Lev (Levchenko et al, 2000)
In addition to preventing crosstalk among related signaling pathways, scaffold proteins might facilitate signal transduction by preforming multimolecular complexes that can be rapidly activated by incoming signal. In many cases, such as mitogen-activated protein kinase (MAPK) cascades, scaffold proteins are necessary for full activation of a signaling pathway. To date, however, no detailed biochemical model of scaffold action has been suggested. Here we describe a quantitative computer model of MAPK cascade with a generic scaffold protein. Analysis of this model reveals that formation of scaffold-kinase complexes can be used effectively to regulate the specificity, efficiency, and amplitude of signal propagation. In particular, for any generic scaffold there exists a concentration value optimal for signal amplitude. The location of the optimum is determined by the concentrations of the kinases rather than their binding constants and in this way is scaffold independent. This effect and the alteration of threshold properties of the signal propagation at high scaffold concentrations might alter local signaling properties at different subcellular compartments. Different scaffold levels and types might then confer specialized properties to tune evolutionarily conserved signaling modules to specific cellular contexts.
Document Metabolism-2000Teu (Teusink et al, 2000)
This paper examines whether the in vivo behavior of yeast glycolysis can be understood in terms of the in vitro kinetic properties of the constituent enzymes. In nongrowing, anaerobic, compressed Saccharomyces cerevisiae the values of the kinetic parameters of most glycolytic enzymes were determined. For the other enzymes appropriate literature values were collected. By inserting these values into a kinetic model for glycolysis, fluxes and metabolites were calculated. Under the same conditions fluxes and metabolite levels were measured. In our first model, branch reactions were ignored. This model failed to reach the stable steady state that was observed in the experimental flux measurements. Introduction of branches towards trehalose, glycogen, glycerol and succinate did allow such a steady state. The predictions of this branched model were compared with the empirical behavior. Half of the enzymes matched their predicted flux in vivo within a factor of 2. For the other enzymes it was calculated what deviation between in vivo and in vitro kinetic characteristics could explain the discrepancy between in vitro rate and in vivo flux.
Document Metabolism-2001Kon (Kongas & van Beek, 2001)
The aim of this study was to explain the mode of functioning of the CK system in heart, and in particular the role of different CK isoenzymes in the dynamic response to workload steps. For this purpose we used a mathematical model of cardiac muscle cell energy metabolism containing the kinetics of the key processes of energy production, consumption and transfer pathways. The model underscores that CK plays indeed a dual role in the cardiac cells. The bu ering role of CK system is due to the activity of myo brillar CK (MMCK) while the energy transfer role depends on the activity of mitochondrial CK (MiCK). We propose that this may lead to the di erences in regulation mechanisms and energy transfer modes in species with relatively low MiCK activity such as rabbit in comparison with species with high MiCK activity such as rat.
Document CellCycle-1991Tys
 
Document Metabolism-2002Lam (Lambeth & Kushmeric, 2002)
A dynamic model of the glycogenolytic pathway to lactate in skeletal muscle was constructed with mammalian kinetic parameters obtained from the literature. Energetic buffers relevant to muscle were included. The model design features stoichiometric constraints, mass balance, and fully reversible thermodynamics as defined by the Haldane relation. We employed a novel method of validating the thermodynamics of the model by allowing the closed system to come to equilibrium; the combined mass action ratio of the pathway equaled the product of the individual enzymes’ equilibrium constants. Adding features physiologically relevant to muscle—a fixed glycogen concentration, efflux of lactate, and coupling to an ATPase—allowed for a steady-state flux far from equilibrium. The main result of our analysis is that coupling of the glycogenolytic network to the ATPase transformed the entire complex into an ATPase driven system. This steady-state system was most sensitive to the external ATPase activity and not to internal pathway mechanisms. The control distribution among the internal pathway enzymes—although small compared to control by ATPase—depended on the flux level and fraction of glycogen phosphorylase a. This model of muscle glycogenolysis thus has unique features compared to models developed for other cell types.
Document CellCycle-1998Gar
 
Document Miscellaneous-1963Lor (Lorenz, 1963)
Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow. Solutions of these equations can be identified with trajectories in phase space. For those systems with bounded solutions, it is found that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states. Systems with bounded solutions are shown to possess bounded numerical solutions. A simple system representing cellular convection is solved numerically. All of the solutions are found to be unstable, and almost all of them are nonperiodic. The feasibility of very-long-range weather prediction is examined in the light of these results.
Document CellCycle-1991Tys-2
 
Document MolMotors-2003Kol (Kolomeisky & Fisher, 2003)
Myosin-V is a motor protein responsible for organelle and vesicle transport in cells. Recent single-molecule experiments have shown that it is an efficient processive motor that walks along actin filaments taking steps of mean size close to 36 nm. A theoretical study of myosin-V motility is presented following an approach used successfully to analyze the dynamics of conventional kinesin but also taking some account of step-size variations. Much of the present experimental data for myosin-V can be well described by a two-state chemical kinetic model with three load-dependent rates. In addition, the analysis predicts the variation of the mean velocity and of the randomness—a quantitative measure of the stochastic deviations from uniform, constant-speed motion—with ATP concentration under both resisting and assisting loads, and indicates a substep of size d0 13–14 nm (from the ATP-binding state) that appears to accord with independent observations.
Document Receptor-1992DeY (DeYoung & Keizer, 2000)
Relying on quantitative measurements of Ca2+ activation and inhibition of the inositol 1,4,5-trisphosphate (IP3) receptor in the endoplasmic reticulum, we construct a simplified kinetic model to describe the properties of this channel. Selecting rate constants to fit key kinetic and equilibrium data, we find that the model reproduces a variety of in vivo and in vitro experiments. In combination with Ca2+-ATPase activity for Ca2+ uptake into the endoplasmic reticulum, the model leads to cytoplasmic oscillations in Ca2+ concentration at fixed IP3 concentration and only a single pool of releasable Ca2+, the endoplasmic reticulum. Incorporation of a positive-feedback mechanism of Ca2+ on IP3 production by phospholipase C enriches the properties of the oscillations and leads to oscillations in Ca2+ concentration accompanied by oscillations in IP3 concentration. We discuss the possible significance of these results for the interpretation of experiments.
Document CellCycle-1991Gol
 
Document CircClock-1999Lel
 
Document CellCycle-1997Nov
 
Document CircClock-2002Vil
 
Document Genetic-2000Elo
 
Document Metabolism-2002Hoe
 
Document CircClock-2001Ued
 
Document MAPKcasc-2000Lev
 
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