SBMLBioModels: F - G

We present a genome-scale metabolic model for the archaeal methanogen Methanosarcina barkeri. We characterize the metabolic network and compare it to reconstructions from the prokaryotic, eukaryotic and archaeal domains. Using the model in conjunction with constraint-based methods, we simulate the metabolic fluxes and resulting phenotypes induced by different environmental and genetic conditions. This represents the first large-scale simulation of either a methanogen or an archaeal species. Model predictions are validated by comparison to experimental growth measurements and phenotypes of M. barkeri on different substrates. The predicted growth phenotypes for wild type and mutants of the methanogenic pathway have a high level of agreement with experimental findings. We further examine the efficiency of the energy-conserving reactions in the methanogenic pathway, specifically the Ech hydrogenase reaction, and determine a stoichiometry for the nitrogenase reaction. This work demonstrates that a reconstructed metabolic network can serve as an analysis platform to predict cellular phenotypes, characterize methanogenic growth, improve the genome annotation and further uncover the metabolic characteristics of methanogenesis. link: http://identifiers.org/pubmed/16738551

We present a genome-scale metabolic model for the archaeal methanogen Methanosarcina barkeri. We characterize the metabolic network and compare it to reconstructions from the prokaryotic, eukaryotic and archaeal domains. Using the model in conjunction with constraint-based methods, we simulate the metabolic fluxes and resulting phenotypes induced by different environmental and genetic conditions. This represents the first large-scale simulation of either a methanogen or an archaeal species. Model predictions are validated by comparison to experimental growth measurements and phenotypes of M. barkeri on different substrates. The predicted growth phenotypes for wild type and mutants of the methanogenic pathway have a high level of agreement with experimental findings. We further examine the efficiency of the energy-conserving reactions in the methanogenic pathway, specifically the Ech hydrogenase reaction, and determine a stoichiometry for the nitrogenase reaction. This work demonstrates that a reconstructed metabolic network can serve as an analysis platform to predict cellular phenotypes, characterize methanogenic growth, improve the genome annotation and further uncover the metabolic characteristics of methanogenesis. link: http://identifiers.org/pubmed/16738551

We present a genome-scale metabolic model for the archaeal methanogen Methanosarcina barkeri. We characterize the metabolic network and compare it to reconstructions from the prokaryotic, eukaryotic and archaeal domains. Using the model in conjunction with constraint-based methods, we simulate the metabolic fluxes and resulting phenotypes induced by different environmental and genetic conditions. This represents the first large-scale simulation of either a methanogen or an archaeal species. Model predictions are validated by comparison to experimental growth measurements and phenotypes of M. barkeri on different substrates. The predicted growth phenotypes for wild type and mutants of the methanogenic pathway have a high level of agreement with experimental findings. We further examine the efficiency of the energy-conserving reactions in the methanogenic pathway, specifically the Ech hydrogenase reaction, and determine a stoichiometry for the nitrogenase reaction. This work demonstrates that a reconstructed metabolic network can serve as an analysis platform to predict cellular phenotypes, characterize methanogenic growth, improve the genome annotation and further uncover the metabolic characteristics of methanogenesis. link: http://identifiers.org/pubmed/16738551

An updated genome-scale reconstruction of the metabolic network in Escherichia coli K-12 MG1655 is presented. This updated metabolic reconstruction includes: (1) an alignment with the latest genome annotation and the metabolic content of EcoCyc leading to the inclusion of the activities of 1260 ORFs, (2) characterization and quantification of the biomass components and maintenance requirements associated with growth of E. coli and (3) thermodynamic information for the included chemical reactions. The conversion of this metabolic network reconstruction into an in silico model is detailed. A new step in the metabolic reconstruction process, termed thermodynamic consistency analysis, is introduced, in which reactions were checked for consistency with thermodynamic reversibility estimates. Applications demonstrating the capabilities of the genome-scale metabolic model to predict high-throughput experimental growth and gene deletion phenotypic screens are presented. The increased scope and computational capability using this new reconstruction is expected to broaden the spectrum of both basic biology and applied systems biology studies of E. coli metabolism. link: http://identifiers.org/pubmed/17593909

An updated genome-scale reconstruction of the metabolic network in Escherichia coli K-12 MG1655 is presented. This updated metabolic reconstruction includes: (1) an alignment with the latest genome annotation and the metabolic content of EcoCyc leading to the inclusion of the activities of 1260 ORFs, (2) characterization and quantification of the biomass components and maintenance requirements associated with growth of E. coli and (3) thermodynamic information for the included chemical reactions. The conversion of this metabolic network reconstruction into an in silico model is detailed. A new step in the metabolic reconstruction process, termed thermodynamic consistency analysis, is introduced, in which reactions were checked for consistency with thermodynamic reversibility estimates. Applications demonstrating the capabilities of the genome-scale metabolic model to predict high-throughput experimental growth and gene deletion phenotypic screens are presented. The increased scope and computational capability using this new reconstruction is expected to broaden the spectrum of both basic biology and applied systems biology studies of E. coli metabolism. link: http://identifiers.org/pubmed/17593909

In this paper, we develop a theoretical contribution towards the understanding of the complex behavior of conjoint tumor-normal cell growth under the influence of immuno-chemotherapeutic agents under simple immune system response. In particular, we consider a core model for the interaction of tumor cells with the surrounding normal cells. We then add the effects of a simple immune system, and both immune-suppression factors and immuno-chemotherapeutic agents as well. Through a series of numerical simulations, we illustrate that the interdependency of tumor-normal cells, together with choice of drug and the nature of the immunodeficiency, leads to a variety of interesting patterns in the evolution of both the tumor and the normal cell populations. link: http://identifiers.org/pubmed/21647303

Clinical investigations prove that blue light irradiation reduces the severity of psoriasis vulgaris. Nevertheless, the mechanisms involved in the management of this condition remain poorly defined. Despite the encouraging results of the clinical studies, no clear guidelines are specified in the literature for the irradiation scheme regime of blue light-based therapy for psoriasis. We investigated the underlying mechanism of blue light irradiation of psoriatic skin, and tested the hypothesis that regulation of proliferation is a key process. We implemented a mechanistic model of cellular epidermal dynamics to analyze whether a temporary decrease of keratinocytes hyper-proliferation can explain the outcome of phototherapy with blue light. Our results suggest that the main effect of blue light on keratinocytes impacts the proliferative cells. They show that the decrease in the keratinocytes proliferative capacity is sufficient to induce a transient decrease in the severity of psoriasis. To study the impact of the therapeutic regime on the efficacy of psoriasis treatment, we performed simulations for different combinations of the treatment parameters, i.e., length of treatment, fluence (also referred to as dose), and intensity. These simulations indicate that high efficacy is achieved by regimes with long duration and high fluence levels, regardless of the chosen intensity. Our modeling approach constitutes a framework for testing diverse hypotheses on the underlying mechanism of blue light-based phototherapy, and for designing effective strategies for the treatment of psoriasis. link: http://identifiers.org/pubmed/28184200

Wave propagation in ventricular muscle is rendered highly anisotropic by the intramural rotation of the fiber. This rotational anisotropy is especially important because it can produce a twist of electrical vortices, which measures the rate of rotation (in degree/mm) of activation wavefronts in successive planes perpendicular to a line of phase singularity, or filament. This twist can then significantly alter the dynamics of the filament. This paper explores this dynamics via numerical simulation. After a review of the literature, we present modeling tools that include: (i) a simplified ionic model with three membrane currents that approximates well the restitution properties and spiral wave behavior of more complex ionic models of cardiac action potential (Beeler-Reuter and others), and (ii) a semi-implicit algorithm for the fast solution of monodomain cable equations with rotational anisotropy. We then discuss selected results of a simulation study of vortex dynamics in a parallelepipedal slab of ventricular muscle of varying wall thickness (S) and fiber rotation rate (theta(z)). The main finding is that rotational anisotropy generates a sufficiently large twist to destabilize a single transmural filament and cause a transition to a wave turbulent state characterized by a high density of chaotically moving filaments. This instability is manifested by the propagation of localized disturbances along the filament and has no previously known analog in isotropic excitable media. These disturbances correspond to highly twisted and distorted regions of filament, or "twistons," that create vortex rings when colliding with the natural boundaries of the ventricle. Moreover, when sufficiently twisted, these rings expand and create additional filaments by further colliding with boundaries. This instability mechanism is distinct from the commonly invoked patchy failure or wave breakup that is not observed here during the initial instability. For modified Beeler-Reuter-like kinetics with stable reentry in two dimensions, decay into turbulence occurs in the left ventricle in about one second above a critical wall thickness in the range of 4-6 mm that matches experiment. However this decay is suppressed by uniformly decreasing excitability. Specific experiments to test these results, and a method to characterize the filament density during fibrillation are discussed. Results are contrasted with other mechanisms of fibrillation and future prospects are summarized. (c)1998 American Institute of Physics. link: http://identifiers.org/pubmed/12779708

Integration of neurotransmitter and neuromodulator signals in the striatum plays a central role in the functions and dysfunctions of the basal ganglia. DARPP-32 is a key actor of this integration in the GABAergic medium-size spiny neurons, in particular in response to dopamine and glutamate. When phosphorylated by cAMP-dependent protein kinase (PKA), DARPP-32 inhibits protein phosphatase-1 (PP1), whereas when phosphorylated by cyclin-dependent kinase 5 (CDK5) it inhibits PKA. DARPP-32 is also regulated by casein kinases and by several protein phosphatases. These complex and intricate regulations make simple predictions of DARPP-32 dynamic behaviour virtually impossible. We used detailed quantitative modelling of the regulation of DARPP-32 phosphorylation to improve our understanding of its function. The models included all the combinations of the three best-characterized phosphorylation sites of DARPP-32, their regulation by kinases and phosphatases, and the regulation of those enzymes by cAMP and Ca(2+) signals. Dynamic simulations allowed us to observe the temporal relationships between cAMP and Ca(2+) signals. We confirmed that the proposed regulation of protein phosphatase-2A (PP2A) by calcium can account for the observed decrease of Threonine 75 phosphorylation upon glutamate receptor activation. DARPP-32 is not simply a switch between PP1-inhibiting and PKA-inhibiting states. Sensitivity analysis showed that CDK5 activity is a major regulator of the response, as previously suggested. Conversely, the strength of the regulation of PP2A by PKA or by calcium had little effect on the PP1-inhibiting function of DARPP-32 in these conditions. The simulations showed that DARPP-32 is not only a robust signal integrator, but that its response also depends on the delay between cAMP and calcium signals affecting the response to the latter. This integration did not depend on the concentration of DARPP-32, while the absolute effect on PP1 varied linearly. In silico mutants showed that Ser137 phosphorylation affects the influence of the delay between dopamine and glutamate, and that constitutive phosphorylation in Ser137 transforms DARPP-32 in a quasi-irreversible switch. This work is a first attempt to better understand the complex interactions between cAMP and Ca(2+) regulation of DARPP-32. Progressive inclusion of additional components should lead to a realistic model of signalling networks underlying the function of striatal neurons. link: http://identifiers.org/pubmed/17194217

Integration of neurotransmitter and neuromodulator signals in the striatum plays a central role in the functions and dysfunctions of the basal ganglia. DARPP-32 is a key actor of this integration in the GABAergic medium-size spiny neurons, in particular in response to dopamine and glutamate. When phosphorylated by cAMP-dependent protein kinase (PKA), DARPP-32 inhibits protein phosphatase-1 (PP1), whereas when phosphorylated by cyclin-dependent kinase 5 (CDK5) it inhibits PKA. DARPP-32 is also regulated by casein kinases and by several protein phosphatases. These complex and intricate regulations make simple predictions of DARPP-32 dynamic behaviour virtually impossible. We used detailed quantitative modelling of the regulation of DARPP-32 phosphorylation to improve our understanding of its function. The models included all the combinations of the three best-characterized phosphorylation sites of DARPP-32, their regulation by kinases and phosphatases, and the regulation of those enzymes by cAMP and Ca(2+) signals. Dynamic simulations allowed us to observe the temporal relationships between cAMP and Ca(2+) signals. We confirmed that the proposed regulation of protein phosphatase-2A (PP2A) by calcium can account for the observed decrease of Threonine 75 phosphorylation upon glutamate receptor activation. DARPP-32 is not simply a switch between PP1-inhibiting and PKA-inhibiting states. Sensitivity analysis showed that CDK5 activity is a major regulator of the response, as previously suggested. Conversely, the strength of the regulation of PP2A by PKA or by calcium had little effect on the PP1-inhibiting function of DARPP-32 in these conditions. The simulations showed that DARPP-32 is not only a robust signal integrator, but that its response also depends on the delay between cAMP and calcium signals affecting the response to the latter. This integration did not depend on the concentration of DARPP-32, while the absolute effect on PP1 varied linearly. In silico mutants showed that Ser137 phosphorylation affects the influence of the delay between dopamine and glutamate, and that constitutive phosphorylation in Ser137 transforms DARPP-32 in a quasi-irreversible switch. This work is a first attempt to better understand the complex interactions between cAMP and Ca(2+) regulation of DARPP-32. Progressive inclusion of additional components should lead to a realistic model of signalling networks underlying the function of striatal neurons. link: http://identifiers.org/pubmed/17194217

The Maillard reaction between reducing sugars and amino groups of biomolecules generates complex structures known as AGEs (advanced glycation endproducts). These have been linked to protein modifications found during aging, diabetes and various amyloidoses. To investigate the contribution of alternative routes to the formation of AGEs, we developed a mathematical model that describes the generation of CML [ N(epsilon)-(carboxymethyl)lysine] in the Maillard reaction between glucose and collagen. Parameter values were obtained by fitting published data from kinetic experiments of Amadori compound decomposition and glycoxidation of collagen by glucose. These raw parameter values were subsequently fine-tuned with adjustment factors that were deduced from dynamic experiments taking into account the glucose and phosphate buffer concentrations. The fine-tuned model was used to assess the relative contributions of the reaction between glyoxal and lysine, the Namiki pathway, and Amadori compound degradation to the generation of CML. The model suggests that the glyoxal route dominates, except at low phosphate and high glucose concentrations. The contribution of Amadori oxidation is generally the least significant at low glucose concentrations. Simulations of the inhibition of CML generation by aminoguanidine show that this compound effectively blocks the glyoxal route at low glucose concentrations (5 mM). Model results are compared with literature estimates of the contributions to CML generation by the three pathways. The significance of the dominance of the glyoxal route is discussed in the context of possible natural defensive mechanisms and pharmacological interventions with the goal of inhibiting the Maillard reaction in vivo. link: http://identifiers.org/pubmed/12911334

Computational modeling and the theory of nonlinear dynamical systems allow one to not simply describe the events of the cell cycle, but also to understand why these events occur, just as the theory of gravitation allows one to understand why cannonballs fly in parabolic arcs. The simplest examples of the eukaryotic cell cycle operate like autonomous oscillators. Here, we present the basic theory of oscillatory biochemical circuits in the context of the Xenopus embryonic cell cycle. We examine Boolean models, delay differential equation models, and especially ordinary differential equation (ODE) models. For ODE models, we explore what it takes to get oscillations out of two simple types of circuits (negative feedback loops and coupled positive and negative feedback loops). Finally, we review the procedures of linear stability analysis, which allow one to determine whether a given ODE model and a particular set of kinetic parameters will produce oscillations. link: http://identifiers.org/pubmed/21414480

Computational modeling and the theory of nonlinear dynamical systems allow one to not simply describe the events of the cell cycle, but also to understand why these events occur, just as the theory of gravitation allows one to understand why cannonballs fly in parabolic arcs. The simplest examples of the eukaryotic cell cycle operate like autonomous oscillators. Here, we present the basic theory of oscillatory biochemical circuits in the context of the Xenopus embryonic cell cycle. We examine Boolean models, delay differential equation models, and especially ordinary differential equation (ODE) models. For ODE models, we explore what it takes to get oscillations out of two simple types of circuits (negative feedback loops and coupled positive and negative feedback loops). Finally, we review the procedures of linear stability analysis, which allow one to determine whether a given ODE model and a particular set of kinetic parameters will produce oscillations. link: http://identifiers.org/pubmed/21414480

Computational modeling and the theory of nonlinear dynamical systems allow one to not simply describe the events of the cell cycle, but also to understand why these events occur, just as the theory of gravitation allows one to understand why cannonballs fly in parabolic arcs. The simplest examples of the eukaryotic cell cycle operate like autonomous oscillators. Here, we present the basic theory of oscillatory biochemical circuits in the context of the Xenopus embryonic cell cycle. We examine Boolean models, delay differential equation models, and especially ordinary differential equation (ODE) models. For ODE models, we explore what it takes to get oscillations out of two simple types of circuits (negative feedback loops and coupled positive and negative feedback loops). Finally, we review the procedures of linear stability analysis, which allow one to determine whether a given ODE model and a particular set of kinetic parameters will produce oscillations. link: http://identifiers.org/pubmed/21414480

The chemical mechanism of Field, Körös, and Noyes for the oscillatory Belousov reaction has been generalized by a model composed of five steps involving three independent chemical intermediates. The behavior of the resulting differential equations has been examined numerically, and it has been shown that the system traces a stable closed trajectory in three dimensional phase space. The same trajectory is attained from other phase points and even from the point corresponding to steady state solution of the differential equations. The model appears to exhibit limit cycle behavior. By stiffly coupling the concentrations of two of the intermediates, the limit cycle model can be simplified to a system described by two independent variables; this coupled system is amenable to analysis by theoretical techniques already developed for such systems. ©1974 American Institute of Physics link: http://identifiers.org/doi/10.1063/1.1681288

Many advances in research regarding immuno-interactions with cancer were developed with the help of ordinary differential equation (ODE) models. These models, however, are not effectively capable of representing problems involving individual localisation, memory and emerging properties, which are common characteristics of cells and molecules of the immune system. Agent-based modelling and simulation is an alternative paradigm to ODE models that overcomes these limitations. In this paper we investigate the potential contribution of agent-based modelling and simulation when compared to ODE modelling and simulation. We seek answers to the following questions: Is it possible to obtain an equivalent agent-based model from the ODE formulation? Do the outcomes differ? Are there any benefits of using one method compared to the other? To answer these questions, we have considered three case studies using established mathematical models of immune interactions with early-stage cancer. These case studies were re-conceptualised under an agent-based perspective and the simulation results were then compared with those from the ODE models. Our results show that it is possible to obtain equivalent agent-based models (i.e. implementing the same mechanisms); the simulation output of both types of models however might differ depending on the attributes of the system to be modelled. In some cases, additional insight from using agent-based modelling was obtained. Overall, we can confirm that agent-based modelling is a useful addition to the tool set of immunologists, as it has extra features that allow for simulations with characteristics that are closer to the biological phenomena. link: http://identifiers.org/pubmed/23734575

Many advances in research regarding immuno-interactions with cancer were developed with the help of ordinary differential equation (ODE) models. These models, however, are not effectively capable of representing problems involving individual localisation, memory and emerging properties, which are common characteristics of cells and molecules of the immune system. Agent-based modelling and simulation is an alternative paradigm to ODE models that overcomes these limitations. In this paper we investigate the potential contribution of agent-based modelling and simulation when compared to ODE modelling and simulation. We seek answers to the following questions: Is it possible to obtain an equivalent agent-based model from the ODE formulation? Do the outcomes differ? Are there any benefits of using one method compared to the other? To answer these questions, we have considered three case studies using established mathematical models of immune interactions with early-stage cancer. These case studies were re-conceptualised under an agent-based perspective and the simulation results were then compared with those from the ODE models. Our results show that it is possible to obtain equivalent agent-based models (i.e. implementing the same mechanisms); the simulation output of both types of models however might differ depending on the attributes of the system to be modelled. In some cases, additional insight from using agent-based modelling was obtained. Overall, we can confirm that agent-based modelling is a useful addition to the tool set of immunologists, as it has extra features that allow for simulations with characteristics that are closer to the biological phenomena. link: http://identifiers.org/pubmed/23734575

Many advances in research regarding immuno-interactions with cancer were developed with the help of ordinary differential equation (ODE) models. These models, however, are not effectively capable of representing problems involving individual localisation, memory and emerging properties, which are common characteristics of cells and molecules of the immune system. Agent-based modelling and simulation is an alternative paradigm to ODE models that overcomes these limitations. In this paper we investigate the potential contribution of agent-based modelling and simulation when compared to ODE modelling and simulation. We seek answers to the following questions: Is it possible to obtain an equivalent agent-based model from the ODE formulation? Do the outcomes differ? Are there any benefits of using one method compared to the other? To answer these questions, we have considered three case studies using established mathematical models of immune interactions with early-stage cancer. These case studies were re-conceptualised under an agent-based perspective and the simulation results were then compared with those from the ODE models. Our results show that it is possible to obtain equivalent agent-based models (i.e. implementing the same mechanisms); the simulation output of both types of models however might differ depending on the attributes of the system to be modelled. In some cases, additional insight from using agent-based modelling was obtained. Overall, we can confirm that agent-based modelling is a useful addition to the tool set of immunologists, as it has extra features that allow for simulations with characteristics that are closer to the biological phenomena. link: http://identifiers.org/pubmed/23734575

Action potential repolarization in the mammalian heart is governed by interactions of a number of time- and voltage-dependent channel-mediated currents, as well as contributions from the Na+/Ca2+ exchanger and the Na+/K+ pump. Recent work has shown that one of the K+ currents (HERG) which contributes to repolarization in mammalian ventricle is a locus at which a number of point mutations can have significant functional consequences. In addition, the remarkable sensitivity of this K+ channel isoform to inhibition by a variety of pharmacological agents and clinical drugs has resulted in HERG being a major focus for Safety Pharmacology requirements. For these reasons we and others have attempted to define the functional role for HERG-mediated K+ currents in repolarization of the action potential in the human ventricle. Here, we describe and evaluate changes in the formulations for two K+ currents, IK1 and HERG (or IK,r), within the framework of ten Tusscher model of the human ventricular action potential. In this computational study, new mathematical formulations for the two nonlinear K+ conductances, IK1 and HERG, have been developed based upon experimental data obtained from electrophysiological studies of excised human ventricular tissue and/or myocytes. The resulting mathematical model provides much improved simulations of the relative sizes and time courses of the K+ currents which modulate repolarization. Our new formulation represents an important first step in defining the mechanism(s) of repolarization of the membrane action potential in the human ventricle. Our overall goal is to understand the genesis of the T-wave of the human electrocardiogram. link: http://identifiers.org/pubmed/17919688

Rate control analysis defines the in vivo control map governing yeast protein synthesis and generates an extensively parameterized digital model of the translation pathway. Among other non-intuitive outcomes, translation demonstrates a high degree of functional modularity and comprises a non-stoichiometric combination of proteins manifesting functional convergence on a shared maximal translation rate. In exponentially growing cells, polypeptide elongation (eEF1A, eEF2, and eEF3) exerts the strongest control. The two other strong control points are recruitment of mRNA and tRNA(i) to the 40S ribosomal subunit (eIF4F and eIF2) and termination (eRF1; Dbp5). In contrast, factors that are found to promote mRNA scanning efficiency on a longer than-average 5'untranslated region (eIF1, eIF1A, Ded1, eIF2B, eIF3, and eIF5) exceed the levels required for maximal control. This is expected to allow the cell to minimize scanning transition times, particularly for longer 5'UTRs. The analysis reveals these and other collective adaptations of control shared across the factors, as well as features that reflect functional modularity and system robustness. Remarkably, gene duplication is implicated in the fine control of cellular protein synthesis. link: http://identifiers.org/pubmed/23340841

Mathematical models for the regulation of the Ca(2+)-dependent transcription factors NFAT and NFkappaB that are involved in the activation of the immune and inflammatory responses in T lymphocytes have been developed. These pathways are important targets for drugs, which act as powerful immunosuppressants by suppressing activation of NFAT and NFkappaB in T cells. The models simulate activation and deactivation over physiological concentrations of Ca(2+), diacyl glycerol (DAG), and PKCtheta using single and periodic step increases. The model suggests the following: (1) the activation NFAT does not occur at low frequencies as NFAT requires calcineurin activated by Ca(2+) to remain dephosphorylated and in the nucleus; (2) NFkappaB is activated at lower Ca(2+) oscillation frequencies than NFAT as IkappaB is degraded in response to elevations in Ca(2+) allowing free NFkappaB to translocate into the nucleus; and (3) the degradation of IkappaB is essential for efficient translocation of NFkappaB to the nucleus. Through sensitivity analysis, the model also suggests that the largest controlling factor for NFAT activation is the dissociation/reassociation rate of the NFAT:calcineurin complex and the translocation rate of the complex into the nucleus and for NFkappaB is the degradation/resynthesis rate of IkappaB and the import rate of IkappaB into the nucleus. link: http://identifiers.org/pubmed/17031595

Mathematical models for the regulation of the Ca(2+)-dependent transcription factors NFAT and NFkappaB that are involved in the activation of the immune and inflammatory responses in T lymphocytes have been developed. These pathways are important targets for drugs, which act as powerful immunosuppressants by suppressing activation of NFAT and NFkappaB in T cells. The models simulate activation and deactivation over physiological concentrations of Ca(2+), diacyl glycerol (DAG), and PKCtheta using single and periodic step increases. The model suggests the following: (1) the activation NFAT does not occur at low frequencies as NFAT requires calcineurin activated by Ca(2+) to remain dephosphorylated and in the nucleus; (2) NFkappaB is activated at lower Ca(2+) oscillation frequencies than NFAT as IkappaB is degraded in response to elevations in Ca(2+) allowing free NFkappaB to translocate into the nucleus; and (3) the degradation of IkappaB is essential for efficient translocation of NFkappaB to the nucleus. Through sensitivity analysis, the model also suggests that the largest controlling factor for NFAT activation is the dissociation/reassociation rate of the NFAT:calcineurin complex and the translocation rate of the complex into the nucleus and for NFkappaB is the degradation/resynthesis rate of IkappaB and the import rate of IkappaB into the nucleus. link: http://identifiers.org/pubmed/17031595

Van der Pol's equation for a relaxation oscillator is generalized by the addition of terms to produce a pair of non-linear differential equations with either a stable singular point or a limit cycle. The resulting "BVP model" has two variables of state, representing excitability and refractoriness, and qualitatively resembles Bonhoeffer's theoretical model for the iron wire model of nerve. This BVP model serves as a simple representative of a class of excitable-oscillatory systems including the Hodgkin-Huxley (HH) model of the squid giant axon. The BVP phase plane can be divided into regions corresponding to the physiological states of nerve fiber (resting, active, refractory, enhanced, depressed, etc.) to form a "physiological state diagram," with the help of which many physiological phenomena can be summarized. A properly chosen projection from the 4-dimensional HH phase space onto a plane produces a similar diagram which shows the underlying relationship between the two models. Impulse trains occur in the BVP and HH models for a range of constant applied currents which make the singular point representing the resting state unstable. link: http://identifiers.org/pubmed/19431309

Lactococcus lactis subsp. cremoris MG1363 is a paradigm strain for lactococci used in industrial dairy fermentations. However, despite of its importance for process development, no genome-scale metabolic model has been reported thus far. Moreover, current models for other lactococci only focus on growth and sugar degradation. A metabolic model that includes nitrogen metabolism and flavor-forming pathways is instrumental for the understanding and designing new industrial applications of these lactic acid bacteria. A genome-scale, constraint-based model of the metabolism and transport in L. lactis MG1363, accounting for 518 genes, 754 reactions, and 650 metabolites, was developed and experimentally validated. Fifty-nine reactions are directly or indirectly involved in flavor formation. Flux Balance Analysis and Flux Variability Analysis were used to investigate flux distributions within the whole metabolic network. Anaerobic carbon-limited continuous cultures were used for estimating the energetic parameters. A thorough model-driven analysis showing a highly flexible nitrogen metabolism, e.g., branched-chain amino acid catabolism which coupled with the redox balance, is pivotal for the prediction of the formation of different flavor compounds. Furthermore, the model predicted the formation of volatile sulfur compounds as a result of the fermentation. These products were subsequently identified in the experimental fermentations carried out. Thus, the genome-scale metabolic model couples the carbon and nitrogen metabolism in L. lactis MG1363 with complete known catabolic pathways leading to flavor formation. The model provided valuable insights into the metabolic networks underlying flavor formation and has the potential to contribute to new developments in dairy industries and cheese-flavor research. link: http://identifiers.org/pubmed/23974365

Our understanding of the complex, transcriptional feedback loops in the circadian clock mechanism has depended upon quantitative, timeseries data from disparate sources. We measure clock gene RNA profiles in Arabidopsis thaliana seedlings, grown with or without exogenous sucrose, or in soil-grown plants and in wild-type and mutant backgrounds. The RNA profiles were strikingly robust across the experimental conditions, so current mathematical models are likely to be broadly applicable in leaf tissue. In addition to providing reference data, unexpected behaviours included co-expression of PRR9 and ELF4, and regulation of PRR5 by GI. Absolute RNA quantification revealed low levels of PRR9 transcripts (peak approx. 50 copies cell(-1)) compared with other clock genes, and threefold higher levels of LHY RNA (more than 1500 copies cell(-1)) than of its close relative CCA1. The data are disseminated from BioDare, an online repository for focused timeseries data, which is expected to benefit mechanistic modelling. One data subset successfully constrained clock gene expression in a complex model, using publicly available software on parallel computers, without expert tuning or programming. We outline the empirical and mathematical justification for data aggregation in understanding highly interconnected, dynamic networks such as the clock, and the observed design constraints on the resources required to make this approach widely accessible. link: http://identifiers.org/pubmed/26468131

Our understanding of the complex, transcriptional feedback loops in the circadian clock mechanism has depended upon quantitative, timeseries data from disparate sources. We measure clock gene RNA profiles in Arabidopsis thaliana seedlings, grown with or without exogenous sucrose, or in soil-grown plants and in wild-type and mutant backgrounds. The RNA profiles were strikingly robust across the experimental conditions, so current mathematical models are likely to be broadly applicable in leaf tissue. In addition to providing reference data, unexpected behaviours included co-expression of PRR9 and ELF4, and regulation of PRR5 by GI. Absolute RNA quantification revealed low levels of PRR9 transcripts (peak approx. 50 copies cell(-1)) compared with other clock genes, and threefold higher levels of LHY RNA (more than 1500 copies cell(-1)) than of its close relative CCA1. The data are disseminated from BioDare, an online repository for focused timeseries data, which is expected to benefit mechanistic modelling. One data subset successfully constrained clock gene expression in a complex model, using publicly available software on parallel computers, without expert tuning or programming. We outline the empirical and mathematical justification for data aggregation in understanding highly interconnected, dynamic networks such as the clock, and the observed design constraints on the resources required to make this approach widely accessible. link: http://identifiers.org/pubmed/26468131

Our understanding of the complex, transcriptional feedback loops in the circadian clock mechanism has depended upon quantitative, timeseries data from disparate sources. We measure clock gene RNA profiles in Arabidopsis thaliana seedlings, grown with or without exogenous sucrose, or in soil-grown plants and in wild-type and mutant backgrounds. The RNA profiles were strikingly robust across the experimental conditions, so current mathematical models are likely to be broadly applicable in leaf tissue. In addition to providing reference data, unexpected behaviours included co-expression of PRR9 and ELF4, and regulation of PRR5 by GI. Absolute RNA quantification revealed low levels of PRR9 transcripts (peak approx. 50 copies cell(-1)) compared with other clock genes, and threefold higher levels of LHY RNA (more than 1500 copies cell(-1)) than of its close relative CCA1. The data are disseminated from BioDare, an online repository for focused timeseries data, which is expected to benefit mechanistic modelling. One data subset successfully constrained clock gene expression in a complex model, using publicly available software on parallel computers, without expert tuning or programming. We outline the empirical and mathematical justification for data aggregation in understanding highly interconnected, dynamic networks such as the clock, and the observed design constraints on the resources required to make this approach widely accessible. link: http://identifiers.org/pubmed/26468131

Our understanding of the complex, transcriptional feedback loops in the circadian clock mechanism has depended upon quantitative, timeseries data from disparate sources. We measure clock gene RNA profiles in Arabidopsis thaliana seedlings, grown with or without exogenous sucrose, or in soil-grown plants and in wild-type and mutant backgrounds. The RNA profiles were strikingly robust across the experimental conditions, so current mathematical models are likely to be broadly applicable in leaf tissue. In addition to providing reference data, unexpected behaviours included co-expression of PRR9 and ELF4, and regulation of PRR5 by GI. Absolute RNA quantification revealed low levels of PRR9 transcripts (peak approx. 50 copies cell(-1)) compared with other clock genes, and threefold higher levels of LHY RNA (more than 1500 copies cell(-1)) than of its close relative CCA1. The data are disseminated from BioDare, an online repository for focused timeseries data, which is expected to benefit mechanistic modelling. One data subset successfully constrained clock gene expression in a complex model, using publicly available software on parallel computers, without expert tuning or programming. We outline the empirical and mathematical justification for data aggregation in understanding highly interconnected, dynamic networks such as the clock, and the observed design constraints on the resources required to make this approach widely accessible. link: http://identifiers.org/pubmed/26468131

Our understanding of the complex, transcriptional feedback loops in the circadian clock mechanism has depended upon quantitative, timeseries data from disparate sources. We measure clock gene RNA profiles in Arabidopsis thaliana seedlings, grown with or without exogenous sucrose, or in soil-grown plants and in wild-type and mutant backgrounds. The RNA profiles were strikingly robust across the experimental conditions, so current mathematical models are likely to be broadly applicable in leaf tissue. In addition to providing reference data, unexpected behaviours included co-expression of PRR9 and ELF4, and regulation of PRR5 by GI. Absolute RNA quantification revealed low levels of PRR9 transcripts (peak approx. 50 copies cell(-1)) compared with other clock genes, and threefold higher levels of LHY RNA (more than 1500 copies cell(-1)) than of its close relative CCA1. The data are disseminated from BioDare, an online repository for focused timeseries data, which is expected to benefit mechanistic modelling. One data subset successfully constrained clock gene expression in a complex model, using publicly available software on parallel computers, without expert tuning or programming. We outline the empirical and mathematical justification for data aggregation in understanding highly interconnected, dynamic networks such as the clock, and the observed design constraints on the resources required to make this approach widely accessible. link: http://identifiers.org/pubmed/26468131

Our understanding of the complex, transcriptional feedback loops in the circadian clock mechanism has depended upon quantitative, timeseries data from disparate sources. We measure clock gene RNA profiles in Arabidopsis thaliana seedlings, grown with or without exogenous sucrose, or in soil-grown plants and in wild-type and mutant backgrounds. The RNA profiles were strikingly robust across the experimental conditions, so current mathematical models are likely to be broadly applicable in leaf tissue. In addition to providing reference data, unexpected behaviours included co-expression of PRR9 and ELF4, and regulation of PRR5 by GI. Absolute RNA quantification revealed low levels of PRR9 transcripts (peak approx. 50 copies cell(-1)) compared with other clock genes, and threefold higher levels of LHY RNA (more than 1500 copies cell(-1)) than of its close relative CCA1. The data are disseminated from BioDare, an online repository for focused timeseries data, which is expected to benefit mechanistic modelling. One data subset successfully constrained clock gene expression in a complex model, using publicly available software on parallel computers, without expert tuning or programming. We outline the empirical and mathematical justification for data aggregation in understanding highly interconnected, dynamic networks such as the clock, and the observed design constraints on the resources required to make this approach widely accessible. link: http://identifiers.org/pubmed/26468131

During sea urchin development, secretion of Nodal and BMP2/4 ligands and their antagonists Lefty and Chordin from a ventral organizer region specifies the ventral and dorsal territories. This process relies on a complex interplay between the Nodal and BMP pathways through numerous regulatory circuits. To decipher the interplay between these pathways, we used a combination of treatments with recombinant Nodal and BMP2/4 proteins and a computational modelling approach. We assembled a logical model focusing on cell responses to signalling inputs along the dorsal-ventral axis, which was extended to cover ligand diffusion and enable multicellular simulations. Our model simulations accurately recapitulate gene expression in wild type embryos, accounting for the specification of ventral ectoderm, ciliary band and dorsal ectoderm. Our model simulations further recapitulate various morphant phenotypes, reveals a dominance of the BMP pathway over the Nodal pathway, and stresses the crucial impact of the rate of Smad activation in D/V patterning. These results emphasise the key role of the mutual antagonism between the Nodal and BMP2/4 pathways in driving early dorsal-ventral patterning of the sea urchin embryo. link: http://identifiers.org/pubmed/33298464

Although alternans of action potential duration (APD) is a robust feature of the rapidly paced canine ventricle, currently available ionic models of cardiac myocytes do not recreate this phenomenon. To address this problem, we developed a new ionic model using formulations of currents based on previous models and recent experimental data. Compared with existing models, the inward rectifier K(+) current (I(K1)) was decreased at depolarized potentials, the maximum conductance and rectification of the rapid component of the delayed rectifier K(+) current (I(Kr)) were increased, and I(Kr) activation kinetics were slowed. The slow component of the delayed rectifier K(+) current (I(Ks)) was increased in magnitude and activation shifted to less positive voltages, and the L-type Ca(2+) current (I(Ca)) was modified to produce a smaller, more rapidly inactivating current. Finally, a simplified form of intracellular calcium dynamics was adopted. In this model, APD alternans occurred at cycle lengths = 150-210 ms, with a maximum alternans amplitude of 39 ms. APD alternans was suppressed by decreasing I(Ca) magnitude or calcium-induced inactivation and by increasing the magnitude of I(K1), I(Kr), or I(Ks). These results establish an ionic basis for APD alternans, which should facilitate the development of pharmacological approaches to eliminating alternans. link: http://identifiers.org/pubmed/11788399

A coupled ordinary differential equation model of tumour-immune dynamics is presented and analysed. The model accounts for biological and clinical factors which regulate the interaction rates of cytotoxic T lymphocytes on the surface of the tumour mass. A phase plane analysis demonstrates that competition between tumour cells and lymphocytes can result in tumour eradication, perpetual oscillations, or unbounded solutions. To investigate the dependence of the dynamic behaviour on model parameters, the equations are solved analytically and conditions for unbounded versus bounded solutions are discussed. An analytic characterisation of the basin of attraction for oscillatory orbits is given. It is also shown that the tumour shape, characterised by a surface area to volume scaling factor, influences the size of the basin, with significant consequences for therapy design. The findings reveal that the tumour volume must surpass a threshold size that depends on lymphocyte parameters for the cancer to be completely eliminated. A semi-analytic procedure to calculate oscillation periods and determine their sensitivity to model parameters is also presented. Numerical results show that the period of oscillations exhibits notable nonlinear dependence on biologically relevant conditions. link: http://identifiers.org/pubmed/24759513

Viral antagonism of host responses is an essential component of virus pathogenicity. The study of the interplay between immune response and viral antagonism is challenging due to the involvement of many processes acting at multiple time scales. Here we develop an ordinary differential equation model to investigate the early, experimentally measured, responses of human monocyte-derived dendritic cells to infection by two H1N1 influenza A viruses of different clinical outcomes: pandemic A/California/4/2009 and seasonal A/New Caledonia/20/1999. Our results reveal how the strength of virus antagonism, and the time scale over which it acts to thwart the innate immune response, differs significantly between the two viruses, as is made clear by their impact on the temporal behavior of a number of measured genes. The model thus sheds light on the mechanisms that underlie the variability of innate immune responses to different H1N1 viruses. link: http://identifiers.org/pubmed/24594370

Viral antagonism of host responses is an essential component of virus pathogenicity. The study of the interplay between immune response and viral antagonism is challenging due to the involvement of many processes acting at multiple time scales. Here we develop an ordinary differential equation model to investigate the early, experimentally measured, responses of human monocyte-derived dendritic cells to infection by two H1N1 influenza A viruses of different clinical outcomes: pandemic A/California/4/2009 and seasonal A/New Caledonia/20/1999. Our results reveal how the strength of virus antagonism, and the time scale over which it acts to thwart the innate immune response, differs significantly between the two viruses, as is made clear by their impact on the temporal behavior of a number of measured genes. The model thus sheds light on the mechanisms that underlie the variability of innate immune responses to different H1N1 viruses. link: http://identifiers.org/pubmed/24594370

Viral antagonism of host responses is an essential component of virus pathogenicity. The study of the interplay between immune response and viral antagonism is challenging due to the involvement of many processes acting at multiple time scales. Here we develop an ordinary differential equation model to investigate the early, experimentally measured, responses of human monocyte-derived dendritic cells to infection by two H1N1 influenza A viruses of different clinical outcomes: pandemic A/California/4/2009 and seasonal A/New Caledonia/20/1999. Our results reveal how the strength of virus antagonism, and the time scale over which it acts to thwart the innate immune response, differs significantly between the two viruses, as is made clear by their impact on the temporal behavior of a number of measured genes. The model thus sheds light on the mechanisms that underlie the variability of innate immune responses to different H1N1 viruses. link: http://identifiers.org/pubmed/24594370

We have developed a detailed mathematical model of ionic flux in beta-cells that includes the most essential channels and pumps in the plasma membrane. This model is coupled to equations describing Ca2+, inositol 1,4,5-trisphosphate (IP3), ATP, and Na+ homeostasis, including the uptake and release of Ca2+ by the endoplasmic reticulum (ER). In our model, metabolically derived ATP activates inward Ca2+ flux by regulation of ATP-sensitive K+ channels and depolarization of the plasma membrane. Results from the simulations support the hypothesis that intracellular Na+ and Ca2+ in the ER can be the main variables driving both fast (2-7 osc/min) and slow intracellular Ca2+ concentration oscillations (0.3-0.9 osc/min) and that the effect of IP3 on Ca2+ leak from the ER contributes to the pattern of slow calcium oscillations. Simulations also show that filling the ER Ca2+ stores leads to faster electrical bursting and Ca2+ oscillations. Specific Ca2+ oscillations in isolated beta-cell lines can also be simulated. link: http://identifiers.org/pubmed/12644446

Pancreatic beta-cells respond to rising blood glucose by increasing oxidative metabolism, leading to an increased ATP/ADP ratio in the cytoplasm. This leads to a closure of KATP channels, depolarization of the plasma membrane, influx of calcium and the eventual secretion of insulin. Such mechanism suggests that beta-cell metabolism should have a functional regulation specific to secretion, as opposed to coupling to contraction. The goal of this work is to uncover contributions of the cytoplasmic and mitochondrial processes in this secretory coupling mechanism using mathematical modeling in a systems biology approach.We describe a mathematical model of beta-cell sensitivity to glucose. The cytoplasmic part of the model includes equations describing glucokinase, glycolysis, pyruvate reduction, NADH and ATP production and consumption. The mitochondrial part begins with production of NADH, which is regulated by pyruvate dehydrogenase. NADH is used in the electron transport chain to establish a proton motive force, driving the F1F0 ATPase. Redox shuttles and mitochondrial Ca2+ handling were also modeled.The model correctly predicts changes in the ATP/ADP ratio, Ca2+ and other metabolic parameters in response to changes in substrate delivery at steady-state and during cytoplasmic Ca2+ oscillations. Our analysis of the model simulations suggests that the mitochondrial membrane potential should be relatively lower in beta cells compared with other cell types to permit precise mitochondrial regulation of the cytoplasmic ATP/ADP ratio. This key difference may follow from a relative reduction in respiratory activity. The model demonstrates how activity of lactate dehydrogenase, uncoupling proteins and the redox shuttles can regulate beta-cell function in concert; that independent oscillations of cytoplasmic Ca2+ can lead to slow coupled metabolic oscillations; and that the relatively low production rate of reactive oxygen species in beta-cells under physiological conditions is a consequence of the relatively decreased mitochondrial membrane potential.This comprehensive model predicts a special role for mitochondrial control mechanisms in insulin secretion and ROS generation in the beta cell. The model can be used for testing and generating control hypotheses and will help to provide a more complete understanding of beta-cell glucose-sensing central to the physiology and pathology of pancreatic beta-cells. link: http://identifiers.org/pubmed/20497556

Pancreatic beta-cells respond to rising blood glucose by increasing oxidative metabolism, leading to an increased ATP/ADP ratio in the cytoplasm. This leads to a closure of KATP channels, depolarization of the plasma membrane, influx of calcium and the eventual secretion of insulin. Such mechanism suggests that beta-cell metabolism should have a functional regulation specific to secretion, as opposed to coupling to contraction. The goal of this work is to uncover contributions of the cytoplasmic and mitochondrial processes in this secretory coupling mechanism using mathematical modeling in a systems biology approach.We describe a mathematical model of beta-cell sensitivity to glucose. The cytoplasmic part of the model includes equations describing glucokinase, glycolysis, pyruvate reduction, NADH and ATP production and consumption. The mitochondrial part begins with production of NADH, which is regulated by pyruvate dehydrogenase. NADH is used in the electron transport chain to establish a proton motive force, driving the F1F0 ATPase. Redox shuttles and mitochondrial Ca2+ handling were also modeled.The model correctly predicts changes in the ATP/ADP ratio, Ca2+ and other metabolic parameters in response to changes in substrate delivery at steady-state and during cytoplasmic Ca2+ oscillations. Our analysis of the model simulations suggests that the mitochondrial membrane potential should be relatively lower in beta cells compared with other cell types to permit precise mitochondrial regulation of the cytoplasmic ATP/ADP ratio. This key difference may follow from a relative reduction in respiratory activity. The model demonstrates how activity of lactate dehydrogenase, uncoupling proteins and the redox shuttles can regulate beta-cell function in concert; that independent oscillations of cytoplasmic Ca2+ can lead to slow coupled metabolic oscillations; and that the relatively low production rate of reactive oxygen species in beta-cells under physiological conditions is a consequence of the relatively decreased mitochondrial membrane potential.This comprehensive model predicts a special role for mitochondrial control mechanisms in insulin secretion and ROS generation in the beta cell. The model can be used for testing and generating control hypotheses and will help to provide a more complete understanding of beta-cell glucose-sensing central to the physiology and pathology of pancreatic beta-cells. link: http://identifiers.org/pubmed/20497556

Synthetic gene networks can be constructed to emulate digital circuits and devices, giving one the ability to program and design cells with some of the principles of modern computing, such as counting. A cellular counter would enable complex synthetic programming and a variety of biotechnology applications. Here, we report two complementary synthetic genetic counters in Escherichia coli that can count up to three induction events: the first, a riboregulated transcriptional cascade, and the second, a recombinase-based cascade of memory units. These modular devices permit counting of varied user-defined inputs over a range of frequencies and can be expanded to count higher numbers. link: http://identifiers.org/pubmed/19478183

Piscirickettsia salmonis is a fish bacterium that causes the disease piscirickettsiosis in salmonids. This pathology is partially controlled by vaccines. The lack of knowledge has hindered its culture on laboratory and industrial scale. The study describes the metabolic phenotype of P. salmonis in culture. This study presents the first genome-scale model (iPF215) of the LF-89 strain of P. salmonis, describing the central metabolic pathway, biosynthesis and molecule degradation and transport mechanisms. The model was adjusted with experiment data, allowing the identification of the capacities that were not predicted by the automatic annotation of the genome sequences. The iPF215 model is comprised of 417 metabolites, 445 reactions and 215 genes, was used to reproduce the growth of P. salmonis (μmax 0.052±0.005h-1). The metabolic reconstruction of the P. salmonis LF-89 strain obtained in this research provides a baseline that describes the metabolic capacities of the bacterium and is the basis for developing improvements to its cultivation for vaccine formulation. link: http://identifiers.org/pubmed/27788423

A mathematical description was made of an autocatalytic zymogen activation mechanism involving both intra- and intermolecular routes. The reversible formation of an active intermediary enzyme-zymogen complex was included in the intermolecular activation route, thus allowing a Michaelis-Menten constant to be defined for the activation of the zymogen towards the active enzyme. Time-concentration equations describing the evolution of the species involved in the system were obtained. In addition, we have derived the corresponding kinetic equations for particular cases of the general model studied. Experimental design and kinetic data analysis procedures to evaluate the kinetic parameters, based on the derived kinetic equations, are suggested. The validity of the results obtained were checked by using simulated progress curves of the species involved. The model is generally good enough to be applied to the experimental kinetic study of the activation of different zymogens of physiological interest. The system is illustrated by following the transformation kinetics of pepsinogen into pepsin. link: http://identifiers.org/pubmed/15634334

In cellular signal transduction, the information in an external stimulus is encoded in temporal patterns in the activities of signaling molecules; for example, pulses of a stimulus may produce an increasing response or may produce pulsatile responses in the signaling molecules. Here, we show how the Akt pathway, which is involved in cell growth, specifically transmits temporal information contained in upstream signals to downstream effectors. We modeled the epidermal growth factor (EGF)-dependent Akt pathway in PC12 cells on the basis of experimental results. We obtained counterintuitive results indicating that the sizes of the peak amplitudes of receptor and downstream effector phosphorylation were decoupled; weak, sustained EGF receptor (EGFR) phosphorylation, rather than strong, transient phosphorylation, strongly induced phosphorylation of the ribosomal protein S6, a molecule downstream of Akt. Using frequency response analysis, we found that a three-component Akt pathway exhibited the property of a low-pass filter and that this property could explain decoupling of the peak amplitudes of receptor phosphorylation and that of downstream effectors. Furthermore, we found that lapatinib, an EGFR inhibitor used as an anticancer drug, converted strong, transient Akt phosphorylation into weak, sustained Akt phosphorylation, and, because of the low-pass filter characteristics of the Akt pathway, this led to stronger S6 phosphorylation than occurred in the absence of the inhibitor. Thus, an EGFR inhibitor can potentially act as a downstream activator of some effectors. link: http://identifiers.org/pubmed/20664065

In cellular signal transduction, the information in an external stimulus is encoded in temporal patterns in the activities of signaling molecules; for example, pulses of a stimulus may produce an increasing response or may produce pulsatile responses in the signaling molecules. Here, we show how the Akt pathway, which is involved in cell growth, specifically transmits temporal information contained in upstream signals to downstream effectors. We modeled the epidermal growth factor (EGF)-dependent Akt pathway in PC12 cells on the basis of experimental results. We obtained counterintuitive results indicating that the sizes of the peak amplitudes of receptor and downstream effector phosphorylation were decoupled; weak, sustained EGF receptor (EGFR) phosphorylation, rather than strong, transient phosphorylation, strongly induced phosphorylation of the ribosomal protein S6, a molecule downstream of Akt. Using frequency response analysis, we found that a three-component Akt pathway exhibited the property of a low-pass filter and that this property could explain decoupling of the peak amplitudes of receptor phosphorylation and that of downstream effectors. Furthermore, we found that lapatinib, an EGFR inhibitor used as an anticancer drug, converted strong, transient Akt phosphorylation into weak, sustained Akt phosphorylation, and, because of the low-pass filter characteristics of the Akt pathway, this led to stronger S6 phosphorylation than occurred in the absence of the inhibitor. Thus, an EGFR inhibitor can potentially act as a downstream activator of some effectors. link: http://identifiers.org/pubmed/20664065

In cellular signal transduction, the information in an external stimulus is encoded in temporal patterns in the activities of signaling molecules; for example, pulses of a stimulus may produce an increasing response or may produce pulsatile responses in the signaling molecules. Here, we show how the Akt pathway, which is involved in cell growth, specifically transmits temporal information contained in upstream signals to downstream effectors. We modeled the epidermal growth factor (EGF)-dependent Akt pathway in PC12 cells on the basis of experimental results. We obtained counterintuitive results indicating that the sizes of the peak amplitudes of receptor and downstream effector phosphorylation were decoupled; weak, sustained EGF receptor (EGFR) phosphorylation, rather than strong, transient phosphorylation, strongly induced phosphorylation of the ribosomal protein S6, a molecule downstream of Akt. Using frequency response analysis, we found that a three-component Akt pathway exhibited the property of a low-pass filter and that this property could explain decoupling of the peak amplitudes of receptor phosphorylation and that of downstream effectors. Furthermore, we found that lapatinib, an EGFR inhibitor used as an anticancer drug, converted strong, transient Akt phosphorylation into weak, sustained Akt phosphorylation, and, because of the low-pass filter characteristics of the Akt pathway, this led to stronger S6 phosphorylation than occurred in the absence of the inhibitor. Thus, an EGFR inhibitor can potentially act as a downstream activator of some effectors. link: http://identifiers.org/pubmed/20664065

Autonomous oscillations found in gene expression and metabolic, cardiac and neuronal systems have attracted significant attention both because of their obvious biological roles and their intriguing dynamics. In addition, de novo designed oscillators have been demonstrated, using components that are not part of the natural oscillators. Such oscillators are useful in testing the design principles and in exploring potential applications not limited by natural cellular behaviour. To achieve transcriptional and metabolic integration characteristic of natural oscillators, here we designed and constructed a synthetic circuit in Escherichia coli K12, using glycolytic flux to generate oscillation through the signalling metabolite acetyl phosphate. If two metabolite pools are interconverted by two enzymes that are placed under the transcriptional control of acetyl phosphate, the system oscillates when the glycolytic rate exceeds a critical value. We used bifurcation analysis to identify the boundaries of oscillation, and verified these experimentally. This work demonstrates the possibility of using metabolic flux as a control factor in system-wide oscillation, as well as the predictability of a de novo gene-metabolic circuit designed using nonlinear dynamic analysis. link: http://identifiers.org/pubmed/15875027

MOTIVATION: The protein tyrosine kinase Src is involved in a multitude of biochemical pathways and cellular functions. A complex network of interactions with other kinases and phosphatases obscures its precise mode of operation. RESULTS: We have constructed a semi-quantitative computational dynamic systems model of the activation of Src at mitosis based on protein interactions described in the literature. Through numerical simulation and bifurcation analysis we show that Src regulation involves a bistable switch, a pattern increasingly recognised as essential to biochemical signalling. The switch is operated by the tyrosine kinase CSK, which itself is involved in a negative feedback loop with Src. Negative feedback generates an excitable system, which produces transient activation of Src. One of the system parameters, which is linked to the cyclin dependent kinase cdc2, controls excitability via a second bistable switch. This topology allows for differentiated responses to a multitude of signals. The model offers explanations for the existence of the positive and negative feedback loops involving protein tyrosine phosphatase alpha (PTPalpha) and translocation of CSK and predicts a specific relationship between Src phosphorylation and activity. link: http://identifiers.org/pubmed/16873466

The metabolic network in the yeast Saccharomyces cerevisiae was reconstructed using currently available genomic, biochemical, and physiological information. The metabolic reactions were compartmentalized between the cytosol and the mitochondria, and transport steps between the compartments and the environment were included. A total of 708 structural open reading frames (ORFs) were accounted for in the reconstructed network, corresponding to 1035 metabolic reactions. Further, 140 reactions were included on the basis of biochemical evidence resulting in a genome-scale reconstructed metabolic network containing 1175 metabolic reactions and 584 metabolites. The number of gene functions included in the reconstructed network corresponds to approximately 16% of all characterized ORFs in S. cerevisiae. Using the reconstructed network, the metabolic capabilities of S. cerevisiae were calculated and compared with Escherichia coli. The reconstructed metabolic network is the first comprehensive network for a eukaryotic organism, and it may be used as the basis for in silico analysis of phenotypic functions. link: http://identifiers.org/pubmed/12566402

Few attempts have been made to model mathematically the progression of type 2 diabetes. A realistic representation of the long-term physiological adaptation to developing insulin resistance is necessary for effectively designing clinical trials and evaluating diabetes prevention or disease modification therapies. Writing a good model for diabetes progression is difficult because the long time span of the disease makes experimental verification of modeling hypotheses extremely awkward. In this context, it is of primary importance that the assumptions underlying the model equations properly reflect established physiology and that the mathematical formulation of the model give rise only to physically plausible behavior of the solutions. In the present work, a model of the pancreatic islet compensation is formulated, its physiological assumptions are presented, some fundamental qualitative characteristics of its solutions are established, the numerical values assigned to its parameters are extensively discussed (also with reference to available cross-sectional epidemiologic data), and its performance over the span of a lifetime is simulated under various conditions, including worsening insulin resistance and primary replication defects. The differences with respect to two previously proposed models of diabetes progression are highlighted, and therefore, the model is proposed as a realistic, robust description of the evolution of the compensation of the glucose-insulin system in healthy and diabetic individuals. Model simulations can be run from the authors' web page. link: http://identifiers.org/pubmed/18780774

The surface protein B7-H1, also called PD-L1 and CD274, is found on carcinomas of the lung, ovary, colon, and melanomas but not on most normal tissues. B7-H1 has been experimentally determined to be an antiapoptotic receptor on cancer cells, where B7-H1-positive cancer cells have been shown to be immune resistant, and in vitro experiments and mouse models have shown that B7-H1-negative tumor cells are significantly more susceptible to being repressed by the immune system. We derive a new mathematical model for studying the interaction between cytotoxic T cells and tumor cells as affected by B7-H1. By integrating experimental data into the model, we isolate the parameters that control the dynamics and obtain insights on the mechanisms that control apoptosis. link: http://identifiers.org/pubmed/21656310

Measurements of rates of glucose uptake and of glycerol and ethanol formation combined with knowledge of the metabolic pathways involved in S. cerevisiae were employed to obtain in vivo rates of reaction catalysed by pathway enzymes for suspended and alginate-entrapped cells at pH 4.5 and 5.5. Intracellular concentrations of substrates and effectors for most key pathway enzymes were estimated from in vivo phosphorus-31 nuclear magnetic resonance measurements. These data show the validity in vivo of kinetic models previously proposed for phosphofructokinase and pyruvate kinase based on in vitro studies. Kinetic representations of hexokinase, glycogen synthetase, and glyceraldehyde 3-phosphate dehydrogenase, which incorporate major regulatory properties of these enzymes, are all consistent with the in vivo data. This detailed model of pathway kinetics and these data on intracellular metabolite concentrations allow evaluation of flux-control coefficients for all key enzymes involved in glucose catabolism under the four different cell environments examined. This analysis indicates that alginate entrapment increases the glucose uptake rate and shifts the step most influencing ethanol production from glucose uptake to phosphofructokinase. The rate of ATP utilization in these nongrowing cells strongly limits ethanol production at pH 5.5 but is relatively insignificant at pH 4.5. link: http://identifiers.org/doi/10.1016/0141-0229(90)90033-M

In the presence of an insulinotropic glucose concentration, beta-cells, in intact pancreatic islets, exhibit periodic bursting electrical activity consisting of an alternation of active and silent phases. The fraction of time spent in the active phase over a period is called the plateau fraction and is correlated with the rate of insulin release. However, the mechanisms that regulate the plateau fraction remain unclear. In this paper we investigate the possible role of the plasma membrane Na+/Ca2+ exchange of the beta-cell in controlling the plateau fraction. We have extended different single-cell models to incorporate this Ca2+-activated electrogenic Ca2+ transporter. We find that the Na+/Ca2+ exchange can provide a physiological mechanism to increase the plateau fraction as the glucose concentration is raised. In addition, we show theoretically that the Na+/Ca2+ exchanger is a key regulator of the cytoplasmic calcium concentration in clusters of heterogeneous cells with gap-junctional electrical coupling. link: http://identifiers.org/pubmed/10388739

In the presence of an insulinotropic glucose concentration, beta-cells, in intact pancreatic islets, exhibit periodic bursting electrical activity consisting of an alternation of active and silent phases. The fraction of time spent in the active phase over a period is called the plateau fraction and is correlated with the rate of insulin release. However, the mechanisms that regulate the plateau fraction remain unclear. In this paper we investigate the possible role of the plasma membrane Na+/Ca2+ exchange of the beta-cell in controlling the plateau fraction. We have extended different single-cell models to incorporate this Ca2+-activated electrogenic Ca2+ transporter. We find that the Na+/Ca2+ exchange can provide a physiological mechanism to increase the plateau fraction as the glucose concentration is raised. In addition, we show theoretically that the Na+/Ca2+ exchanger is a key regulator of the cytoplasmic calcium concentration in clusters of heterogeneous cells with gap-junctional electrical coupling. link: http://identifiers.org/pubmed/10388739

In the presence of an insulinotropic glucose concentration, beta-cells, in intact pancreatic islets, exhibit periodic bursting electrical activity consisting of an alternation of active and silent phases. The fraction of time spent in the active phase over a period is called the plateau fraction and is correlated with the rate of insulin release. However, the mechanisms that regulate the plateau fraction remain unclear. In this paper we investigate the possible role of the plasma membrane Na+/Ca2+ exchange of the beta-cell in controlling the plateau fraction. We have extended different single-cell models to incorporate this Ca2+-activated electrogenic Ca2+ transporter. We find that the Na+/Ca2+ exchange can provide a physiological mechanism to increase the plateau fraction as the glucose concentration is raised. In addition, we show theoretically that the Na+/Ca2+ exchanger is a key regulator of the cytoplasmic calcium concentration in clusters of heterogeneous cells with gap-junctional electrical coupling. link: http://identifiers.org/pubmed/10388739

In this work, we analyze a mathematical model we introduced previously for the dynamics of multiple myeloma and the immune system. We focus on four main aspects: (1) obtaining and justifying ranges and values for all parameters in the model; (2) determining a subset of parameters to which the model is most sensitive; (3) determining which parameters in this subset can be uniquely estimated given cer- tain types of data; and (4) exploring the model numerically. Using global sensitivity analysis techniques, we found that the model is most sensitive to certain growth, loss, and efficacy parameters. This anal- ysis provides the foundation for a future application of the model: prediction of optimal combination regimens in patients with multiple myeloma. link: http://identifiers.org/doi/10.1016/j.jtbi.2018.08.037

The tumor microenvironment comprising of the immune cells and cytokines acts as the 'soil' that nourishes a developing tumor. Lack of a comprehensive study of the interactions of this tumor microenvironment with the heterogeneous sub-population of tumor cells that arise from the differentiation of Cancer Stem Cells (CSC), i.e. the 'seed', has limited our understanding of the development of drug resistance and treatment failures in Cancer. Based on this seed and soil hypothesis, for the very first time, we have captured the concept of CSC differentiation and tumor-immune interaction into a generic model that has been validated with known experimental data. Using this model we report that as the CSC differentiation shifts from symmetric to asymmetric pattern, resistant cancer cells start accumulating in the tumor that makes it refractory to therapeutic interventions. Model analyses unveiled the presence of feedback loops that establish the dual role of M2 macrophages in regulating tumor proliferation. The study further revealed oscillations in the tumor sub-populations in the presence of TH1 derived IFN-γ that eliminates CSC; and the role of IL10 feedback in the regulation of TH1/TH2 ratio. These analyses expose important observations that are indicative of Cancer prognosis. Further, the model has been used for testing known treatment protocols to explore the reasons of failure of conventional treatment strategies and propose an improvised protocol that shows promising results in suppressing the proliferation of all the cellular sub-populations of the tumor and restoring a healthy TH1/TH2 ratio that assures better Cancer remission. link: http://identifiers.org/pubmed/30183728

Cancer immunotherapies rely on how interactions between cancer and immune system cells are constituted. The more essential to the emergence of the dynamical behavior of cancer growth these are, the more effectively they may be used as mechanisms for interventions. Mathematical modeling can help unearth such connections, and help explain how they shape the dynamics of cancer growth. Here, we explored whether there exist simple, consistent properties of cancer-immune system interaction (CISI) models that might be harnessed to devise effective immunotherapy approaches. We did this for a family of three related models of increasing complexity. To this end, we developed a base model of CISI, which captures some essential features of the more complex models built on it. We find that the base model and its derivates can reproduce biologically plausible behavior. This behavior is consistent with situations in which the suppressive effects exerted by cancer cells on immune cells dominate their proliferative effects. Under these circumstances, the model family may display a pattern of bistability, where two distinct, stable states (a cancer-free, and a full-grown cancer state) are possible, consistent with the notion of an immunological barrier. Increasing the effectiveness of immune-caused cancer cell killing may remove the basis for bistability, and abruptly tip the dynamics of the system into cancer-free state. In combination with the administration of immune effector cells, modifications in cancer cell killing may also be harnessed for immunotherapy without resolving the bistability. We use these ideas to test immunotherapeutic interventions in silico in a stochastic version of the base model. This bistability-reliant approach to cancer interventions might offer advantages over those that comprise gradual declines in cancer cell numbers. link: http://identifiers.org/doi/10.1101/498741

Biofilms offer an excellent example of ecological interaction among bacteria. Temporal and spatial oscillations in biofilms are an emerging topic. In this paper, we describe the metabolic oscillations in Bacillus subtilis biofilms by applying the smallest theoretical chemical reaction system showing Hopf bifurcation proposed by Wilhelm and Heinrich in 1995. The system involves three differential equations and a single bilinear term. We specifically select parameters that are suitable for the biological scenario of biofilm oscillations. We perform computer simulations and a detailed analysis of the system including bifurcation analysis and quasi-steady-state approximation. We also discuss the feedback structure of the system and the correspondence of the simulations to biological observations. Our theoretical work suggests potential scenarios about the oscillatory behaviour of biofilms and also serves as an application of a previously described chemical oscillator to a biological system. link: http://identifiers.org/pubmed/32257302

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. link: http://identifiers.org/pubmed/9826676

It has been proposed' that gene-regulatory circuits with virtually any desired property can be constructed from networks of simple regulatory elements. These properties, which include multistability and oscillations, have been found in specialized gene circuits such as the bacteriophage lambda switch and the Cyanobacteria circadian oscillator. However, these behaviours have not been demonstrated in networks of non-specialized regulatory components. Here we present the construction of a genetic toggle switch-a synthetic, bistable gene-regulatory network-in Escherichia coli and provide a simple theory that predicts the conditions necessary for bistability. The toggle is constructed from any two repressible promoters arranged in a mutually inhibitory network. It is flipped between stable states using transient chemical or thermal induction and exhibits a nearly ideal switching threshold. As a practical device, the toggle switch forms a synthetic, addressable cellular memory unit and has implications for biotechnology, biocomputing and gene therapy. link: http://identifiers.org/pubmed/10659857

In this paper, we share with the biomathematics community a new coupled multiscale model which has the potential to inform policy and guide malaria control and elimination. The formulation of this multiscale model is based on integrating four submodels which are: (i) a sub-model for the mosquito-to-human transmission of malaria parasite, (ii) a sub-model for the human-to-mosquito transmission of malaria parasite, (iii) a within-mosquito malaria parasite population dynamics sub-model and (iv) a within-human malaria parasite population dynamics sub-model. The integration of the four submodels is achieved by assuming that the transmission parameters of the sub-model for the mosquito-to-human transmission of malaria at the epidemiological scale are functions of the dependent variables of the within-mosquito sporozoite population dynamics while the transmission parameters of the sub-model for the human-to-mosquito transmission of malaria are functions of the dependent variables of the within-human gametocyte population dynamics. This establishes a unidirectionally coupled multiscale model where the within-human and within-mosquito submodels are unidirectionally coupled to the human-to-mosquito and mosquito-to-human submodels. A fast and slow time scale analysis is performed on this system. The result is a simple multiscale model which describes the mechanics of malaria transmission in terms of the major components of the complete malaria parasite life-cycle. This multiscale modelling approach may be found useful in guiding malaria control and elimination. link: http://identifiers.org/pubmed/31128139

We present a genome-scale model of Caenorhabditis elegans metabolism along with the public database ElegCyc (http://elegcyc.bioinf.uni-jena.de:1100), which represents a reference for metabolic pathways in the worm and allows for the visualization as well as analysis of omics datasets. Our model reflects the metabolic peculiarities of C. elegans that make it distinct from other higher eukaryotes and mammals, including mice and humans. We experimentally verify one of these peculiarities by showing that the lifespan-extending effect of L-tryptophan supplementation is dose dependent (hormetic). Finally, we show the utility of our model for analyzing omics datasets through predicting changes in amino acid concentrations after genetic perturbations and analyzing metabolic changes during normal aging as well as during two distinct, reactive oxygen species (ROS)-related lifespan-extending treatments. Our analyses reveal a notable similarity in metabolic adaptation between distinct lifespan-extending interventions and point to key pathways affecting lifespan in nematodes. link: http://identifiers.org/pubmed/27211858

We present a genome-scale model of Caenorhabditis elegans metabolism along with the public database ElegCyc (http://elegcyc.bioinf.uni-jena.de:1100), which represents a reference for metabolic pathways in the worm and allows for the visualization as well as analysis of omics datasets. Our model reflects the metabolic peculiarities of C. elegans that make it distinct from other higher eukaryotes and mammals, including mice and humans. We experimentally verify one of these peculiarities by showing that the lifespan-extending effect of L-tryptophan supplementation is dose dependent (hormetic). Finally, we show the utility of our model for analyzing omics datasets through predicting changes in amino acid concentrations after genetic perturbations and analyzing metabolic changes during normal aging as well as during two distinct, reactive oxygen species (ROS)-related lifespan-extending treatments. Our analyses reveal a notable similarity in metabolic adaptation between distinct lifespan-extending interventions and point to key pathways affecting lifespan in nematodes. link: http://identifiers.org/pubmed/27211858

Integrin signaling regulates cell migration and plays a pivotal role in developmental processes and cancer metastasis. Integrin signaling has been studied extensively and much data is available on pathway components and interactions. Yet the data is fragmented and an integrated model is missing. We use a rule-based modeling approach to integrate available data and test biological hypotheses regarding the role of talin, Dok1 and PIPKI in integrin activation. The detailed biochemical characterization of integrin signaling provides us with measured values for most of the kinetics parameters. However, measurements are not fully accurate and the cellular concentrations of signaling proteins are largely unknown and expected to vary substantially across different cellular conditions. By sampling model behaviors over the physiologically realistic parameter range we find that the model exhibits only two different qualitative behaviors and these depend mainly on the relative protein concentrations, which offers a powerful point of control to the cell. Our study highlights the necessity to characterize model behavior not for a single parameter optimum, but to identify parameter sets that characterize different signaling modes. link: http://identifiers.org/pubmed/22110576

The complex interplay of a pathogen with the host immune response and the endogenous microbiome determines the course and outcome of gastrointestinal infection (GI). Expansion of a pathogen within the gastrointestinal tract implies an increased risk to develop systemic infection. Through computational modeling, we aimed to calculate bacterial population dynamics in GI in order to predict infection course and outcome. For the implementation and parameterization of the model, oral mouse infection experiments with Yersinia enterocolitica were used. Our model takes into account pathogen specific characteristics, such as virulence, as well as host properties, such as microbial colonization resistance or immune responses. We were able to confirm the model calculations in these scenarios by experimental mouse infections and show that it is possible to computationally predict the infection course. Far future clinical application of computational modeling of infections may pave the way for personalized treatment and prevention strategies of GI. link: http://identifiers.org/doi/10.1101/2020.08.11.244202

We propose an integrated computational model for the network of cyclin-dependent kinases (Cdks) that controls the dynamics of the mammalian cell cycle. The model contains four Cdk modules regulated by reversible phosphorylation, Cdk inhibitors, and protein synthesis or degradation. Growth factors (GFs) trigger the transition from a quiescent, stable steady state to self-sustained oscillations in the Cdk network. These oscillations correspond to the repetitive, transient activation of cyclin D/Cdk4-6 in G(1), cyclin E/Cdk2 at the G(1)/S transition, cyclin A/Cdk2 in S and at the S/G(2) transition, and cyclin B/Cdk1 at the G(2)/M transition. The model accounts for the following major properties of the mammalian cell cycle: (i) repetitive cell cycling in the presence of suprathreshold amounts of GF; (ii) control of cell-cycle progression by the balance between antagonistic effects of the tumor suppressor retinoblastoma protein (pRB) and the transcription factor E2F; and (iii) existence of a restriction point in G(1), beyond which completion of the cell cycle becomes independent of GF. The model also accounts for endoreplication. Incorporating the DNA replication checkpoint mediated by kinases ATR and Chk1 slows down the dynamics of the cell cycle without altering its oscillatory nature and leads to better separation of the S and M phases. The model for the mammalian cell cycle shows how the regulatory structure of the Cdk network results in its temporal self-organization, leading to the repetitive, sequential activation of the four Cdk modules that brings about the orderly progression along cell-cycle phases. link: http://identifiers.org/pubmed/20007375

We previously proposed a detailed, 39-variable model for the network of cyclin-dependent kinases (Cdks) that controls progression along the successive phases of the mammalian cell cycle. Here, we propose a skeleton, 5-variable model for the Cdk network that can be seen as the backbone of the more detailed model for the mammalian cell cycle. In the presence of sufficient amounts of growth factor, the skeleton model also passes from a stable steady state to sustained oscillations of the various cyclin/Cdk complexes. This transition corresponds to the switch from quiescence to cell proliferation. Sequential activation of the cyclin/Cdk complexes allows the ordered progression along the G1, S, G2 and M phases of the cell cycle. The 5-variable model can also account for the existence of a restriction point in G1, and for endoreplication. Like the detailed model, it contains multiple oscillatory circuits and can display complex oscillatory behaviour such as quasi-periodic oscillations and chaos. We compare the dynamical properties of the skeleton model with those of the more detailed model for the mammalian cell cycle. link: http://identifiers.org/pubmed/22419972

The eukaryotic cell cycle is characterized by alternating oscillations in the activities of cyclin-dependent kinase (Cdk) and the anaphase-promoting complex (APC). Successful completion of the cell cycle is dependent on the precise, temporally ordered appearance of these activities. A modest level of Cdk activity is sufficient to initiate DNA replication, but mitosis and APC activation require an elevated Cdk activity. In present-day eukaryotes, this temporal order is provided by a complex network of regulatory proteins that control both Cdk and APC activities via sharp thresholds, bistability, and time delays. Using simple computational models, we show here that these dynamical features of cell-cycle organization could emerge in a control system driven by a single Cdk/cyclin complex and APC wired in a negative-feedback loop. We show that ordered phosphorylation of cellular proteins could be explained by multisite phosphorylation/dephosphorylation and competition of substrates for interconverting kinase (Cdk) and phosphatase. In addition, the competition of APC substrates for ubiquitylation can create and maintain sustained oscillations in cyclin levels. We propose a sequence of models that gets closer and closer to a realistic model of cell-cycle control in yeast. Since these models lack the elaborate control mechanisms characteristic of modern eukaryotes, they suggest that bistability and time delay may have characterized eukaryotic cell divisions before the current cell-cycle control network evolved in all its complexity. link: http://identifiers.org/pubmed/23528096

High proliferation rate and robustness are vital characteristics of bacterial pathogens that successfully colonize their hosts. The observation of drastically slow growth in some pathogens is thus paradoxical and remains unexplained. In this study, we sought to understand the slow (fastidious) growth of the plant pathogen Xylella fastidiosa. Using genome-scale metabolic network reconstruction, modeling, and experimental validation, we explored its metabolic capabilities. Despite genome reduction and slow growth, the pathogen’s metabolic network is complete but strikingly minimalist and lacking in robustness. Most alternative reactions were missing, especially those favoring fast growth, and were replaced by less efficient paths. We also found that the production of some virulence factors imposes a heavy burden on growth. Interestingly, some specific determinants of fastidious growth were also found in other slow-growing pathogens, enriching the view that these metabolic peculiarities are a pathogenicity strategy to remain at a low population level. link: http://identifiers.org/doi/10.1128/mSystems.00698-19

Mathematical models of biological systems must strike a balance between being sufficiently complex to capture important biological features, while being simple enough that they remain tractable through analysis or simulation. In this work, we rigorously explore how to balance these competing interests when modeling murine melanoma treatment with oncolytic viruses and dendritic cell injections. Previously, we developed a system of six ordinary differential equations containing fourteen parameters that well describes experimental data on the efficacy of these treatments. Here, we explore whether this previously developed model is the minimal model needed to accurately describe the data. Using a variety of techniques, including sensitivity analyses and a parameter sloppiness analysis, we find that our model can be reduced by one variable and three parameters and still give excellent fits to the data. We also argue that our model is not too simple to capture the dynamics of the data, and that the original and minimal models make similar predictions about the efficacy and robustness of protocols not considered in experiments. Reducing the model to its minimal form allows us to increase the tractability of the system in the face of parametric uncertainty. link: http://identifiers.org/pubmed/30510594

Mathematical models of biological systems must strike a balance between being sufficiently complex to capture important biological features, while being simple enough that they remain tractable through analysis or simulation. In this work, we rigorously explore how to balance these competing interests when modeling murine melanoma treatment with oncolytic viruses and dendritic cell injections. Previously, we developed a system of six ordinary differential equations containing fourteen parameters that well describes experimental data on the efficacy of these treatments. Here, we explore whether this previously developed model is the minimal model needed to accurately describe the data. Using a variety of techniques, including sensitivity analyses and a parameter sloppiness analysis, we find that our model can be reduced by one variable and three parameters and still give excellent fits to the data. We also argue that our model is not too simple to capture the dynamics of the data, and that the original and minimal models make similar predictions about the efficacy and robustness of protocols not considered in experiments. Reducing the model to its minimal form allows us to increase the tractability of the system in the face of parametric uncertainty. link: http://identifiers.org/pubmed/30510594

We present a mathematical model for analyzing, simulating, and quantitating the dynamic and steady-state characteristics of receptor-mediated endocytosis. The basic processes considered by the model are ligand-receptor binding, diffusion of receptors and ligand-receptor complexes in the plane of the membrane toward and away from coated pits, binding of ligand-receptor complexes to coated pit proteins, endocytosis of coated pit contents, degradation of ligand, and recycling of undegraded receptors. The model accounts quantitatively for a wide variety of kinetic data and makes new predictions about steady-state characteristics. We show that for homogeneous receptors the slope of the Scatchard plot is not necessarily constant but can have a positive or negative derivative, depending on the concentration of coated pit proteins and their reactivity. This finding suggests that binding data, which show linear and concave curves, might be explainable be a simple coated pit-related mechanism. Similarly the relationship between the x-intercept and the number of receptors is also affected by kinetic parameters controlling endocytosis. We briefly discuss these results in terms of possible mechanisms for the action of tumor promoters, the large variations in receptor number and affinity in the literature, and methods for quantitative characterization of parameters. link: http://identifiers.org/pubmed/6149699

BACKGROUND:Clinical studies have shown that all-trans retinoic acid (RA), which is often used in treatment of cancer patients, improves hemostatic parameters and bleeding complications such as disseminated intravascular coagulation (DIC). However, the mechanisms underlying this improvement have yet to be elucidated. In vitro studies have reported that RA upregulates thrombomodulin (TM) expression on the endothelial cell surface. The objective of this study was to investigate how and to what extent the TM concentration changes after RA treatment in cancer patients, and how this variation influences the blood coagulation cascade. RESULTS:In this study, we introduced an ordinary differential equation (ODE) model of gene expression for the RA-induced upregulation of TM concentration. Coupling the gene expression model with a two-compartment pharmacokinetic model of RA, we obtained the time-dependent changes in TM and thrombomodulin-mRNA (TMR) concentrations following oral administration of RA. Our results indicated that the TM concentration reached its peak level almost 14 h after taking a single oral dose (110 [Formula: see text]) of RA. Continuous treatment with RA resulted in oscillatory expression of TM on the endothelial cell surface. We then coupled the gene expression model with a mechanistic model of the coagulation cascade, and showed that the elevated levels of TM over the course of RA therapy with a single daily oral dose (110 [Formula: see text]) of RA, reduced the peak thrombin levels and endogenous thrombin potential (ETP) up to 50 and 49%, respectively. We showed that progressive reductions in plasma levels of RA, observed in continuous RA therapy with a once-daily oral dose (110 [Formula: see text]) of RA, did not affect TM-mediated reduction of thrombin generation significantly. This finding prompts the hypothesis that continuous RA treatment has more consistent therapeutic effects on coagulation disorders than on cancer. CONCLUSIONS:Our results indicate that the oscillatory upregulation of TM expression on the endothelial cells over the course of RA therapy could potentially contribute to the treatment of coagulation abnormalities in cancer patients. Further studies on the impacts of RA therapy on the procoagulant activity of cancer cells are needed to better elucidate the mechanisms by which RA therapy improves hemostatic abnormalities in cancer. link: http://identifiers.org/pubmed/30764845

One of the common misconceptions about COVID-19 disease is to assume that we will not see a recurrence after the first wave of the disease has subsided. This completely wrong perception causes people to disregard the necessary protocols and engage in some misbehavior, such as routine socializing or holiday travel. These conditions will put double pressure on the medical staff and endanger the lives of many people around the world. In this research, we are interested in analyzing the existing data to predict the number of infected people in the second wave of out-breaking COVID-19 in Iran. For this purpose, a model is proposed. The mathematical analysis corresponded to the model is also included in this paper. Based on proposed numerical simulations, several scenarios of progress of COVID-19 corresponding to the second wave of the disease in the coming months, will be discussed. We predict that the second wave of will be most severe than the first one. From the results, improving the recovery rate of people with weak immune systems via appropriate medical incentives is resulted as one of the most effective prescriptions to prevent the widespread unbridled outbreak of the second wave of COVID-19. link: http://identifiers.org/pubmed/32834656

MOTIVATION: Val600Glu (V600E) mutation is the most common BRAF mutation detected in thyroid cancer. Hence, recent research efforts have been performed trying to explore several inhibitors of the V600E mutation-containing BRAF kinase as potential therapeutic options in thyroid cancer refractory to standard interventions. Among them, vemurafenib is a selective BRAF inhibitor approved by FDA for clinical practice. Unfortunately, vemurafenib often displays limited efficacy in poorly differentiated and anaplastic thyroid carcinomas probably because of intrinsic and/or acquired resistance mechanisms. In this view, cancer stem cells may represent a possible mechanism of resistance to vemurafenib, due to their self-renewal and chemo resistance properties.

RESULTS: We present a computational framework to suggest new potential targets to overcome drug resistance. It has been validated with an in vitro model based upon a spheroid-forming method able to isolate thyroid cancer stem cells that may mimic resistance to vemurafenib. Indeed, vemurafenib did not inhibit cell proliferation of BRAF V600E thyroid cancer stem cells, but rather stimulated cell proliferation along with a paradoxical overactivation of ERK and AKT pathways. The computational model identified a fundamental role of mitogen-activated protein kinase 8 (MAP3K8), a serine/threonine kinase expressed in thyroid cancer stem cells, in mediating this drug resistance. To confirm model prediction, we set a suitable in vitro experiment revealing that the treatment with MAP3K8 inhibitor restored the effect of vemurafenib in terms of both DNA fragmentation and PARP cleavage (apoptosis) in thyroid cancer stem cells. Moreover, MAP3K8 expression levels may be a useful marker to predict the response to vemurafenib. link: http://identifiers.org/pubmed/30481266