SBMLBioModels: L - M

Accurate prediction of first-pass metabolism is essential for improving the time and cost efficiency of drug development process. Here, we have developed a microfluidic gut-liver co-culture chip that aims to reproduce the first-pass metabolism of oral drugs. This chip consists of two separate layers for gut (Caco-2) and liver (HepG2) cell lines, where cells can be co-cultured in both 2D and 3D forms. Both cell lines were maintained well in the chip, verified by confocal microscopy and measurement of hepatic enzyme activity. We investigated the PK profile of paracetamol in the chip, and corresponding PK model was constructed, which was used to predict PK profiles for different chip design parameters. Simulation results implied that a larger absorption surface area and a higher metabolic capacity are required to reproduce the in vivo PK profile of paracetamol more accurately. Our study suggests the possibility of reproducing the human PK profile on a chip, contributing to accurate prediction of pharmacological effect of drugs. link: http://identifiers.org/pubmed/29116458

Wnt signalling is involved in a wide range of physiological and pathological processes. The presence of an extracellular Wnt stimulus induces cytoplasmic stabilisation and nuclear translocation of beta-catenin, a protein that also plays an essential role in cadherin-mediated adhesion. Two main hypotheses have been proposed concerning the balance between beta-catenin's adhesive and transcriptional functions: either beta-catenin's fate is determined by competition between its binding partners, or Wnt induces folding of beta-catenin into a conformation allocated preferentially to transcription. The experimental data supporting each hypotheses remain inconclusive. In this paper we present a new mathematical model of the Wnt pathway that incorporates beta-catenin's dual function. We use this model to carry out a series of in silico experiments and compare the behaviour of systems governed by each hypothesis. Our analytical results and model simulations provide further insight into the current understanding of Wnt signalling and, in particular, reveal differences in the response of the two modes of interaction between adhesion and signalling in certain in silico settings. We also exploit our model to investigate the impact of the mutations most commonly observed in human colorectal cancer. Simulations show that the amount of functional APC required to maintain a normal phenotype increases with increasing strength of the Wnt signal, a result which illustrates that the environment can substantially influence both tumour initiation and phenotype. link: http://identifiers.org/pubmed/17382967

The intrinsic, or mitochondrial, pathway of caspase activation is essential for apoptosis induction by various stimuli including cytotoxic stress. It depends on the cellular context, whether cytochrome c released from mitochondria induces caspase activation gradually or in an all-or-none fashion, and whether caspase activation irreversibly commits cells to apoptosis. By analyzing a quantitative kinetic model, we show that inhibition of caspase-3 (Casp3) and Casp9 by inhibitors of apoptosis (IAPs) results in an implicit positive feedback, since cleaved Casp3 augments its own activation by sequestering IAPs away from Casp9. We demonstrate that this positive feedback brings about bistability (i.e., all-or-none behaviour), and that it cooperates with Casp3-mediated feedback cleavage of Casp9 to generate irreversibility in caspase activation. Our calculations also unravel how cell-specific protein expression brings about the observed qualitative differences in caspase activation (gradual versus all-or-none and reversible versus irreversible). Finally, known regulators of the pathway are shown to efficiently shift the apoptotic threshold stimulus, suggesting that the bistable caspase cascade computes multiple inputs into an all-or-none caspase output. As cellular inhibitory proteins (e.g., IAPs) frequently inhibit consecutive intermediates in cellular signaling cascades (e.g., Casp3 and Casp9), the feedback mechanism described in this paper is likely to be a widespread principle on how cells achieve ultrasensitivity, bistability, and irreversibility. link: http://identifiers.org/pubmed/16978046

The intrinsic, or mitochondrial, pathway of caspase activation is essential for apoptosis induction by various stimuli including cytotoxic stress. It depends on the cellular context, whether cytochrome c released from mitochondria induces caspase activation gradually or in an all-or-none fashion, and whether caspase activation irreversibly commits cells to apoptosis. By analyzing a quantitative kinetic model, we show that inhibition of caspase-3 (Casp3) and Casp9 by inhibitors of apoptosis (IAPs) results in an implicit positive feedback, since cleaved Casp3 augments its own activation by sequestering IAPs away from Casp9. We demonstrate that this positive feedback brings about bistability (i.e., all-or-none behaviour), and that it cooperates with Casp3-mediated feedback cleavage of Casp9 to generate irreversibility in caspase activation. Our calculations also unravel how cell-specific protein expression brings about the observed qualitative differences in caspase activation (gradual versus all-or-none and reversible versus irreversible). Finally, known regulators of the pathway are shown to efficiently shift the apoptotic threshold stimulus, suggesting that the bistable caspase cascade computes multiple inputs into an all-or-none caspase output. As cellular inhibitory proteins (e.g., IAPs) frequently inhibit consecutive intermediates in cellular signaling cascades (e.g., Casp3 and Casp9), the feedback mechanism described in this paper is likely to be a widespread principle on how cells achieve ultrasensitivity, bistability, and irreversibility. link: http://identifiers.org/pubmed/16978046

A biochemically structured model for the aerobic growth of Saccharomyces cerevisiae on glucose and ethanol is presented. The model focuses on the pyruvate and acetaldehyde branch points where overflow metabolism occurs when the growth changes from oxidative to oxido-reductive. The model is designed to describe the onset of aerobic alcoholic fermentation during steady-state as well as under dynamical conditions, by triggering an increase in the glycolytic flux using a key signalling component which is assumed to be closely related to acetaldehyde. An investigation of the modelled process dynamics in a continuous cultivation revealed multiple steady states in a region of dilution rates around the transition between oxidative and oxido-reductive growth. A bifurcation analysis using the two external variables, the dilution rate, D, and the inlet concentration of glucose, S(f), as parameters, showed that a fold bifurcation occurs close to the critical dilution rate resulting in multiple steady-states. The region of dilution rates within which multiple steady states may occur depends strongly on the substrate feed concentration. Consequently a single steady state may prevail at low feed concentrations, whereas multiple steady states may occur over a relatively wide range of dilution rates at higher feed concentrations. link: http://identifiers.org/pubmed/11434967

A mathematical model has been developed to simulate the generation of thrombin by the tissue factor pathway. The model gives reasonable predictions of published experimental results without the adjustment of any parameter values. The model also accounts explicitly for the effects of serine protease inhibitors on thrombin generation. Simulations to define the optimum affinity profile of an inhibitor in this system indicate that for an inhibitor simultaneously potent against VIIa, IXa, and Xa, inhibition of thrombin generation decreases dramatically as the affinity for thrombin increases. Additional simulations show that the reason for this behavior is the sequestration of the inhibitor by small amounts of thrombin generated early in the reaction. This model is also useful for predicting the potency of compounds that inhibit thrombosis in rats. We believe that this is the first mathematical model of blood coagulation that considers the effects of exogenous inhibitors. Such a model, or extensions thereof, should be useful for evaluating targets for therapeutic intervention in the processes of blood coagulation. link: http://identifiers.org/pubmed/7592704

A mathematical model has been developed to simulate the generation of thrombin by the tissue factor pathway. The model gives reasonable predictions of published experimental results without the adjustment of any parameter values. The model also accounts explicitly for the effects of serine protease inhibitors on thrombin generation. Simulations to define the optimum affinity profile of an inhibitor in this system indicate that for an inhibitor simultaneously potent against VIIa, IXa, and Xa, inhibition of thrombin generation decreases dramatically as the affinity for thrombin increases. Additional simulations show that the reason for this behavior is the sequestration of the inhibitor by small amounts of thrombin generated early in the reaction. This model is also useful for predicting the potency of compounds that inhibit thrombosis in rats. We believe that this is the first mathematical model of blood coagulation that considers the effects of exogenous inhibitors. Such a model, or extensions thereof, should be useful for evaluating targets for therapeutic intervention in the processes of blood coagulation. link: http://identifiers.org/pubmed/7592704

The authors present a model for circadian oscillations of the Period (PER) and Timeless (TIM) proteins in Drosophila. The model for the circadian clock is based on multiple phosphorylation of PER and TIM and on the negative feedback exerted by a nuclear PER-TIM complex on the transcription of the per and tim genes. Periodic behavior occurs in a large domain of parameter space in the form of limit cycle oscillations. These sustained oscillations occur in conditions corresponding to continuous darkness or to entrainment by light-dark cycles and are in good agreement with experimental observations on the temporal variations of PER and TIM and of per and tim mRNAs. Birhythmicity (coexistence of two periodic regimes) and aperiodic oscillations (chaos) occur in a restricted range of parameter values. The results are compared to the predictions of a model based on the sole regulation by PER. Both the formation of a complex between PER and TIM and protein phosphorylation are found to favor oscillatory behavior. Determining how the period depends on several key parameters allows us to test possible molecular explanations proposed for the altered period in the per(l) and per(s) mutants. The extended model further allows the construction of phase-response curves based on the light-induced triggering of TIM degradation. These curves, established as a function of both the duration and magnitude of the effect of a light pulse, match the phase-response curves obtained experimentally in the wild type and per(s) mutant of Drosophila. link: http://identifiers.org/pubmed/9486845

We examine theoretical models for circadian oscillations based on transcriptional regulation in Drosophila and Neurospora. For Drosophila, the molecular model is based on the negative feedback exerted on the expression of the per and tim genes by the complex formed between the PER and TIM proteins. For Neurospora, similarly, the model relies on the feedback exerted on the expression of the frq gene by its protein product FRQ. In both models, sustained rhythmic variations in protein and mRNA levels occur in continuous darkness, in the form of limit cycle oscillations. The effect of light on circadian rhythms is taken into account in the models by considering that it triggers degradation of the TIM protein in Drosophila, and frq transcription in Neurospora. When incorporating the control exerted by light at the molecular level, we show that the models can account for the entrainment of circadian rhythms by light-dark cycles and for the damping of the oscillations in constant light, though such damping occurs more readily in the Drosophila model. The models account for the phase shifts induced by light pulses and allow the construction of phase response curves. These compare well with experimental results obtained in Drosophila. The model for Drosophila shows that when applied at the appropriate phase, light pulses of appropriate duration and magnitude can permanently or transiently suppress circadian rhythmicity. We investigate the effects of the magnitude of light-induced changes on oscillatory behavior. Finally, we discuss the common and distinctive features of circadian oscillations in the two organisms. link: http://identifiers.org/pubmed/10643740

We examine theoretical models for circadian oscillations based on transcriptional regulation in Drosophila and Neurospora. For Drosophila, the molecular model is based on the negative feedback exerted on the expression of the per and tim genes by the complex formed between the PER and TIM proteins. For Neurospora, similarly, the model relies on the feedback exerted on the expression of the frq gene by its protein product FRQ. In both models, sustained rhythmic variations in protein and mRNA levels occur in continuous darkness, in the form of limit cycle oscillations. The effect of light on circadian rhythms is taken into account in the models by considering that it triggers degradation of the TIM protein in Drosophila, and frq transcription in Neurospora. When incorporating the control exerted by light at the molecular level, we show that the models can account for the entrainment of circadian rhythms by light-dark cycles and for the damping of the oscillations in constant light, though such damping occurs more readily in the Drosophila model. The models account for the phase shifts induced by light pulses and allow the construction of phase response curves. These compare well with experimental results obtained in Drosophila. The model for Drosophila shows that when applied at the appropriate phase, light pulses of appropriate duration and magnitude can permanently or transiently suppress circadian rhythmicity. We investigate the effects of the magnitude of light-induced changes on oscillatory behavior. Finally, we discuss the common and distinctive features of circadian oscillations in the two organisms. link: http://identifiers.org/pubmed/10643740

In Drosophila, circadian oscillations in the levels of two proteins, PER and TIM, result from the negative feedback exerted by a PER-TIM complex on the expression of the per and tim genes which code for these two proteins. On the basis of these experimental observations, we have recently proposed a theoretical model for circadian oscillations of the PER and TIM proteins in Drosophila. Here we show that for constant environmental conditions this model is capable of generating autonomous chaotic oscillations. For other parameter values, the model can also display birhythmicity, i.e. the coexistence between two stable regimes of limit cycle oscillations. We analyse the occurrence of chaos and birhythmicity by means of bifurcation diagrams and locate the different domains of complex oscillatory behavior in parameter space. The relative smallness of these domains raises doubts as to the possible physiological significance of chaos and birhythmicity in regard to circadian rhythm generation. Beyond the particular context of circadian rhythms we discuss the results in the light of other mechanisms underlying chaos and birhythmicity in regulated biological systems. Copyright 1999 Academic Press. link: http://identifiers.org/pubmed/10366496

We present a computational model for the mammalian circadian clock based on the intertwined positive and negative regulatory loops involving the Per, Cry, Bmal1, Clock, and Rev-Erb alpha genes. In agreement with experimental observations, the model can give rise to sustained circadian oscillations in continuous darkness, characterized by an antiphase relationship between Per/Cry/Rev-Erbalpha and Bmal1 mRNAs. Sustained oscillations correspond to the rhythms autonomously generated by suprachiasmatic nuclei. For other parameter values, damped oscillations can also be obtained in the model. These oscillations, which transform into sustained oscillations when coupled to a periodic signal, correspond to rhythms produced by peripheral tissues. When incorporating the light-induced expression of the Per gene, the model accounts for entrainment of the oscillations by light-dark cycles. Simulations show that the phase of the oscillations can then vary by several hours with relatively minor changes in parameter values. Such a lability of the phase could account for physiological disorders related to circadian rhythms in humans, such as advanced or delayed sleep phase syndrome, whereas the lack of entrainment by light-dark cycles can be related to the non-24h sleep-wake syndrome. The model uncovers the possible existence of multiple sources of oscillatory behavior. Thus, in conditions where the indirect negative autoregulation of Per and Cry expression is inoperative, the model indicates the possibility that sustained oscillations might still arise from the negative autoregulation of Bmal1 expression. link: http://identifiers.org/pubmed/12775757

We present a computational model for the mammalian circadian clock based on the intertwined positive and negative regulatory loops involving the Per, Cry, Bmal1, Clock, and Rev-Erb alpha genes. In agreement with experimental observations, the model can give rise to sustained circadian oscillations in continuous darkness, characterized by an antiphase relationship between Per/Cry/Rev-Erbalpha and Bmal1 mRNAs. Sustained oscillations correspond to the rhythms autonomously generated by suprachiasmatic nuclei. For other parameter values, damped oscillations can also be obtained in the model. These oscillations, which transform into sustained oscillations when coupled to a periodic signal, correspond to rhythms produced by peripheral tissues. When incorporating the light-induced expression of the Per gene, the model accounts for entrainment of the oscillations by light-dark cycles. Simulations show that the phase of the oscillations can then vary by several hours with relatively minor changes in parameter values. Such a lability of the phase could account for physiological disorders related to circadian rhythms in humans, such as advanced or delayed sleep phase syndrome, whereas the lack of entrainment by light-dark cycles can be related to the non-24h sleep-wake syndrome. The model uncovers the possible existence of multiple sources of oscillatory behavior. Thus, in conditions where the indirect negative autoregulation of Per and Cry expression is inoperative, the model indicates the possibility that sustained oscillations might still arise from the negative autoregulation of Bmal1 expression. link: http://identifiers.org/pubmed/12775757

We present a computational model for the mammalian circadian clock based on the intertwined positive and negative regulatory loops involving the Per, Cry, Bmal1, Clock, and Rev-Erb alpha genes. In agreement with experimental observations, the model can give rise to sustained circadian oscillations in continuous darkness, characterized by an antiphase relationship between Per/Cry/Rev-Erbalpha and Bmal1 mRNAs. Sustained oscillations correspond to the rhythms autonomously generated by suprachiasmatic nuclei. For other parameter values, damped oscillations can also be obtained in the model. These oscillations, which transform into sustained oscillations when coupled to a periodic signal, correspond to rhythms produced by peripheral tissues. When incorporating the light-induced expression of the Per gene, the model accounts for entrainment of the oscillations by light-dark cycles. Simulations show that the phase of the oscillations can then vary by several hours with relatively minor changes in parameter values. Such a lability of the phase could account for physiological disorders related to circadian rhythms in humans, such as advanced or delayed sleep phase syndrome, whereas the lack of entrainment by light-dark cycles can be related to the non-24h sleep-wake syndrome. The model uncovers the possible existence of multiple sources of oscillatory behavior. Thus, in conditions where the indirect negative autoregulation of Per and Cry expression is inoperative, the model indicates the possibility that sustained oscillations might still arise from the negative autoregulation of Bmal1 expression. link: http://identifiers.org/pubmed/12775757

We present a computational model for the mammalian circadian clock based on the intertwined positive and negative regulatory loops involving the Per, Cry, Bmal1, Clock, and Rev-Erb alpha genes. In agreement with experimental observations, the model can give rise to sustained circadian oscillations in continuous darkness, characterized by an antiphase relationship between Per/Cry/Rev-Erbalpha and Bmal1 mRNAs. Sustained oscillations correspond to the rhythms autonomously generated by suprachiasmatic nuclei. For other parameter values, damped oscillations can also be obtained in the model. These oscillations, which transform into sustained oscillations when coupled to a periodic signal, correspond to rhythms produced by peripheral tissues. When incorporating the light-induced expression of the Per gene, the model accounts for entrainment of the oscillations by light-dark cycles. Simulations show that the phase of the oscillations can then vary by several hours with relatively minor changes in parameter values. Such a lability of the phase could account for physiological disorders related to circadian rhythms in humans, such as advanced or delayed sleep phase syndrome, whereas the lack of entrainment by light-dark cycles can be related to the non-24h sleep-wake syndrome. The model uncovers the possible existence of multiple sources of oscillatory behavior. Thus, in conditions where the indirect negative autoregulation of Per and Cry expression is inoperative, the model indicates the possibility that sustained oscillations might still arise from the negative autoregulation of Bmal1 expression. link: http://identifiers.org/pubmed/12775757

We extend the study of a computational model recently proposed for the mammalian circadian clock (Proc. Natl Acad. Sci. USA 100 (2003) 7051). The model, based on the intertwined positive and negative regulatory loops involving the Per, Cry, Bmal1, and Clock genes, can give rise to sustained circadian oscillations in conditions of continuous darkness. These limit cycle oscillations correspond to circadian rhythms autonomously generated by suprachiasmatic nuclei and by some peripheral tissues. By using different sets of parameter values producing circadian oscillations, we compare the effect of the various parameters and show that both the occurrence and the period of the oscillations are generally most sensitive to parameters related to synthesis or degradation of Bmal1 mRNA and BMAL1 protein. The mechanism of circadian oscillations relies on the formation of an inactive complex between PER and CRY and the activators CLOCK and BMAL1 that enhance Per and Cry expression. Bifurcation diagrams and computer simulations nevertheless indicate the possible existence of a second source of oscillatory behavior. Thus, sustained oscillations might arise from the sole negative autoregulation of Bmal1 expression. This second oscillatory mechanism may not be functional in physiological conditions, and its period need not necessarily be circadian. When incorporating the light-induced expression of the Per gene, the model accounts for entrainment of the oscillations by light-dark (LD) cycles. Long-term suppression of circadian oscillations by a single light pulse can occur in the model when a stable steady state coexists with a stable limit cycle. The phase of the oscillations upon entrainment in LD critically depends on the parameters that govern the level of CRY protein. Small changes in the parameters governing CRY levels can shift the peak in Per mRNA from the L to the D phase, or can prevent entrainment. The results are discussed in relation to physiological disorders of the sleep-wake cycle linked to perturbations of the human circadian clock, such as the familial advanced sleep phase syndrome or the non-24h sleep-wake syndrome. link: http://identifiers.org/pubmed/15363675

We propose a mathematical model explaining the interactions between osteoblasts and osteoclasts, two cell types specialized in the maintenance of the bone integrity. Bone is a dynamic, living tissue whose structure and shape continuously evolves during life. It has the ability to change architecture by removal of old bone and replacement with newly formed bone in a localized process called remodeling. The model described here is based on the idea that the relative proportions of immature and mature osteoblasts control the degree of osteoclastic activity. In addition, osteoclasts control osteoblasts differentially depending on their stage of differentiation. Despite the tremendous complexity of the bone regulatory system and its fragmentary understanding, we obtain surprisingly good correlations between the model simulations and the experimental observations extracted from the literature. The model results corroborate all behaviors of the bone remodeling system that we have simulated, including the tight coupling between osteoblasts and osteoclasts, the catabolic effect induced by continuous administration of PTH, the catabolic action of RANKL, as well as its reversal by soluble antagonist OPG. The model is also able to simulate metabolic bone diseases such as estrogen deficiency, vitamin D deficiency, senescence and glucocorticoid excess. Conversely, possible routes for therapeutic interventions are tested and evaluated. Our model confirms that anti-resorptive therapies are unable to partially restore bone loss, whereas bone formation therapies yield better results. The model enables us to determine and evaluate potential therapies based on their efficacy. In particular, the model predicts that combinations of anti-resorptive and anabolic therapies provide significant benefits compared with monotherapy, especially for certain type of skeletal disease. Finally, the model clearly indicates that increasing the size of the pool of preosteoblasts is an essential ingredient for the therapeutic manipulation of bone formation. This model was conceived as the first step in a bone turnover modeling platform. These initial modeling results are extremely encouraging and lead us to proceed with additional explorations into bone turnover and skeletal remodeling. link: http://identifiers.org/pubmed/15234198

A mathematical account is given of the processes governing the time courses of calcium ions (Ca2+), inositol 1,4,5-trisphosphate (IP(3)) and phosphatidylinositol 4,5-bisphosphate (PIP(2)) in single cells following the application of external agonist to metabotropic receptors. A model is constructed that incorporates the regulation of metabotropic receptor activity, the G-protein cascade and the Ca2+ dynamics in the cytosol. It is subsequently used to reproduce observations on the extent of desensitization and sequestration of the P(2)Y(2) receptor following its activation by uridine triphosphate (UTP). The theory predicts the dependence on agonist concentration of the change in the number of receptors in the membrane as well as the time course of disappearance of receptors from the plasmalemma, upon exposure to agonist. In addition, the extent of activation and desensitization of the receptor, using the calcium transients in cells initiated by exposure to agonist, is also predicted. Model predictions show the significance of membrane PIP(2) depletion and resupply on the time course of IP(3) and Ca2+ levels. Results of the modelling also reveal the importance of receptor recycling and PIP(2) resupply for maintaining Ca2+ and IP(3) levels during sustained application of agonist. link: http://identifiers.org/pubmed/12782119

A system of three non-linear differential equations with exponential feedback terms is proposed to model the self-regulating cortisol secretion system and explain the fluctuation patterns observed in clinical data. It is shown that the model exhibits bifurcation and chaos patterns for a certain range of parametric values. This helps us to explain clinical observations and characterize different dynamic behaviors of the self-regulative system. link: http://identifiers.org/pubmed/1668715

This paper presents a nonlinear mathematical model of the glucose-insulin feedback system, which has been extended to incorporate the beta-cells' function on maintaining and regulating plasma insulin level in man. Initially, a gastrointestinal absorption term for glucose is utilized to effect the glucose absorption by the intestine and the subsequent release of glucose into the bloodstream, taking place at a given initial rate and falling off exponentially with time. An analysis of the model is carried out by the singular perturbation technique in order to derive boundary conditions on the system parameters which identify, in particular, the existence of limit cycles in our model system consistent with the oscillatory patterns often observed in clinical data. We then utilize a sinusoidal term to incorporate the temporal absorption of glucose in order to study the responses in the patients under ambulatory-fed conditions. A numerical investigation is carried out in this case to construct a bifurcation diagram to identify the ranges of parametric values for which chaotic behavior can be expected, leading to interesting biological interpretations. link: http://identifiers.org/pubmed/11226623

This paper presents a nonlinear mathematical model of the glucose-insulin feedback system, which has been extended to incorporate the beta-cells' function on maintaining and regulating plasma insulin level in man. Initially, a gastrointestinal absorption term for glucose is utilized to effect the glucose absorption by the intestine and the subsequent release of glucose into the bloodstream, taking place at a given initial rate and falling off exponentially with time. An analysis of the model is carried out by the singular perturbation technique in order to derive boundary conditions on the system parameters which identify, in particular, the existence of limit cycles in our model system consistent with the oscillatory patterns often observed in clinical data. We then utilize a sinusoidal term to incorporate the temporal absorption of glucose in order to study the responses in the patients under ambulatory-fed conditions. A numerical investigation is carried out in this case to construct a bifurcation diagram to identify the ranges of parametric values for which chaotic behavior can be expected, leading to interesting biological interpretations. link: http://identifiers.org/pubmed/11226623

Immunotherapies use components of the patient immune system to selectively target can- cer cells. The use of chimeric antigenic receptor (CAR) T cells to treat B-cell malignancies –leukaemias and lymphomas–is one of the most successful examples, with many patients experiencing long-lasting full responses to this therapy. This treatment works by extract- ing the patient’s T cells and transducing them with the CAR, enabling them to recognize and target cells carrying the antigen CD19 + , which is expressed in these haematological cancers. Here we put forward a mathematical model describing the time response of leukaemias to the injection of CAR T cells. The model accounts for mature and progenitor B-cells, leukaemic cells, CAR T cells and side effects by including the main biological processes involved. The model explains the early post-injection dynamics of the different compart- ments and the fact that the number of CAR T cells injected does not critically affect the treatment outcome. An explicit formula is found that gives the maximum CAR T cell ex- pansion in vivo and the severity of side effects. Our mathematical model captures other known features of the response to this immunotherapy. It also predicts that CD19 + cancer relapses could be the result of competition between leukaemic and CAR T cells, analogous to predator-prey dynamics. We discuss this in the light of the available evidence and the possibility of controlling relapses by early re-challenging of the leukaemia cells with stored CAR T cells. link: http://identifiers.org/doi/10.1016/j.cnsns.2020.105570

Immunotherapies use components of the patient immune system to selectively target can- cer cells. The use of chimeric antigenic receptor (CAR) T cells to treat B-cell malignancies –leukaemias and lymphomas–is one of the most successful examples, with many patients experiencing long-lasting full responses to this therapy. This treatment works by extract- ing the patient’s T cells and transducing them with the CAR, enabling them to recognize and target cells carrying the antigen CD19 + , which is expressed in these haematological cancers. Here we put forward a mathematical model describing the time response of leukaemias to the injection of CAR T cells. The model accounts for mature and progenitor B-cells, leukaemic cells, CAR T cells and side effects by including the main biological processes involved. The model explains the early post-injection dynamics of the different compart- ments and the fact that the number of CAR T cells injected does not critically affect the treatment outcome. An explicit formula is found that gives the maximum CAR T cell ex- pansion in vivo and the severity of side effects. Our mathematical model captures other known features of the response to this immunotherapy. It also predicts that CD19 + cancer relapses could be the result of competition between leukaemic and CAR T cells, analogous to predator-prey dynamics. We discuss this in the light of the available evidence and the possibility of controlling relapses by early re-challenging of the leukaemia cells with stored CAR T cells. link: http://identifiers.org/doi/10.1016/j.cnsns.2020.105570

Chimeric antigen receptor (CAR)-T cell-based therapies have achieved substantial success against B-cell malignancies, which has led to a growing scientific and clinical interest in extending their use to solid cancers. However, results for solid tumours have been limited up to now, in part due to the immunosuppressive tumour microenvironment, which is able to inactivate CAR-T cell clones. In this paper we put forward a mathematical model describing the competition of CAR-T and tumour cells, taking into account their immunosuppressive capacity. Using the mathematical model, we show that the use of large numbers of CAR-T cells targetting the solid tumour antigens could overcome the immunosuppressive potential of cancer. To achieve such high levels of CAR-T cells we propose, and study computationally, the manufacture and injection of CAR-T cells targetting two antigens: CD19 and a tumour-associated antigen. We study in silico the resulting dynamics of the disease after the injection of this product and find that the expansion of the CAR-T cell population in the blood and lymphopoietic organs could lead to the massive production of an army of CAR-T cells targetting the solid tumour, and potentially overcoming its immune suppression capabilities. This strategy could benefit from the combination with PD-1 inhibitors and low tumour loads. Our computational results provide theoretical support for the treatment of different types of solid tumours using T cells engineered with combination treatments of dual CARs with on- and off-tumour activity and anti-PD-1 drugs after completion of classical cytoreductive treatments. link: http://identifiers.org/pubmed/33572301

Chimeric antigen receptor (CAR)-T cell-based therapies have achieved substantial success against B-cell malignancies, which has led to a growing scientific and clinical interest in extending their use to solid cancers. However, results for solid tumours have been limited up to now, in part due to the immunosuppressive tumour microenvironment, which is able to inactivate CAR-T cell clones. In this paper we put forward a mathematical model describing the competition of CAR-T and tumour cells, taking into account their immunosuppressive capacity. Using the mathematical model, we show that the use of large numbers of CAR-T cells targetting the solid tumour antigens could overcome the immunosuppressive potential of cancer. To achieve such high levels of CAR-T cells we propose, and study computationally, the manufacture and injection of CAR-T cells targetting two antigens: CD19 and a tumour-associated antigen. We study in silico the resulting dynamics of the disease after the injection of this product and find that the expansion of the CAR-T cell population in the blood and lymphopoietic organs could lead to the massive production of an army of CAR-T cells targetting the solid tumour, and potentially overcoming its immune suppression capabilities. This strategy could benefit from the combination with PD-1 inhibitors and low tumour loads. Our computational results provide theoretical support for the treatment of different types of solid tumours using T cells engineered with combination treatments of dual CARs with on- and off-tumour activity and anti-PD-1 drugs after completion of classical cytoreductive treatments. link: http://identifiers.org/pubmed/33572301

In addition to preventing crosstalk among related signaling pathways, scaffold proteins might facilitate signal transduction by preforming multimolecular complexes that can be rapidly activated by incoming signal. In many cases, such as mitogen-activated protein kinase (MAPK) cascades, scaffold proteins are necessary for full activation of a signaling pathway. To date, however, no detailed biochemical model of scaffold action has been suggested. Here we describe a quantitative computer model of MAPK cascade with a generic scaffold protein. Analysis of this model reveals that formation of scaffold-kinase complexes can be used effectively to regulate the specificity, efficiency, and amplitude of signal propagation. In particular, for any generic scaffold there exists a concentration value optimal for signal amplitude. The location of the optimum is determined by the concentrations of the kinases rather than their binding constants and in this way is scaffold independent. This effect and the alteration of threshold properties of the signal propagation at high scaffold concentrations might alter local signaling properties at different subcellular compartments. Different scaffold levels and types might then confer specialized properties to tune evolutionarily conserved signaling modules to specific cellular contexts. link: http://identifiers.org/pubmed/10823939

In addition to preventing crosstalk among related signaling pathways, scaffold proteins might facilitate signal transduction by preforming multimolecular complexes that can be rapidly activated by incoming signal. In many cases, such as mitogen-activated protein kinase (MAPK) cascades, scaffold proteins are necessary for full activation of a signaling pathway. To date, however, no detailed biochemical model of scaffold action has been suggested. Here we describe a quantitative computer model of MAPK cascade with a generic scaffold protein. Analysis of this model reveals that formation of scaffold-kinase complexes can be used effectively to regulate the specificity, efficiency, and amplitude of signal propagation. In particular, for any generic scaffold there exists a concentration value optimal for signal amplitude. The location of the optimum is determined by the concentrations of the kinases rather than their binding constants and in this way is scaffold independent. This effect and the alteration of threshold properties of the signal propagation at high scaffold concentrations might alter local signaling properties at different subcellular compartments. Different scaffold levels and types might then confer specialized properties to tune evolutionarily conserved signaling modules to specific cellular contexts. link: http://identifiers.org/pubmed/10823939

T cell activation is a crucial checkpoint in adaptive immunity, and this activation depends on the binding parameters that govern the interactions between T cell receptors (TCRs) and peptide-MHC complexes (pMHC complexes). Despite extensive experimental studies, the relationship between the TCR-pMHC binding parameters and T cell activation remains controversial. To make sense of conflicting experimental data, a variety of verbal and mathematical models have been proposed. However, it is currently unclear which model or models are consistent or inconsistent with experimental data. A key problem is that a direct comparison between the models has not been carried out, in part because they have been formulated in different frameworks. For this Analysis article, we reformulated published models of T cell activation into phenotypic models, which allowed us to directly compare them. We find that a kinetic proofreading model that is modified to include limited signalling is consistent with the majority of published data. This model makes the intriguing prediction that the stimulation hierarchy of two different pMHC complexes (or two different TCRs that are specific for the same pMHC complex) may reverse at different pMHC concentrations. link: http://identifiers.org/pubmed/25145757

The human adaptive immune response is known to weaken in advanced age, resulting in increased severity of pathogen-born illness, poor vaccine efficacy, and a higher prevalence of cancer in the elderly. Age-related erosion of the T cell compartment has been implicated as a likely cause, but the underlying mechanisms driving this immunosenescence have not been quantitatively modeled and systematically analyzed. T cell receptor diversity, or the extent of pathogen-derived antigen responsiveness of the T cell pool, is known to diminish with age, but inherent experimental difficulties preclude accurate analysis on the full organismal level. In this paper, we formulate a mechanistic mathematical model of T cell population dynamics on the immunoclonal subpopulation level, which provides quantitative estimates of diversity. We define different estimates for diversity that depend on the individual number of cells in a specific immunoclone. We show that diversity decreases with age primarily due to diminished thymic output of new T cells and the resulting overall loss of small immunoclones. link: http://identifiers.org/pubmed/31201663

Progression of a cell through the division cycle is tightly controlled at different steps to ensure the integrity of genome replication and partitioning to daughter cells. From published experimental evidence, we propose a molecular mechanism for control of the cell division cycle in Caulobacter crescentus. The mechanism, which is based on the synthesis and degradation of three "master regulator" proteins (CtrA, GcrA, and DnaA), is converted into a quantitative model, in order to study the temporal dynamics of these and other cell cycle proteins. The model accounts for important details of the physiology, biochemistry, and genetics of cell cycle control in stalked C. crescentus cell. It reproduces protein time courses in wild-type cells, mimics correctly the phenotypes of many mutant strains, and predicts the phenotypes of currently uncharacterized mutants. Since many of the proteins involved in regulating the cell cycle of C. crescentus are conserved among many genera of alpha-proteobacteria, the proposed mechanism may be applicable to other species of importance in agriculture and medicine. link: http://identifiers.org/pubmed/18225942

The asymmetric cell division cycle of Caulobacter crescentus is orchestrated by an elaborate gene-protein regulatory network, centered on three major control proteins, DnaA, GcrA and CtrA. The regulatory network is cast into a quantitative computational model to investigate in a systematic fashion how these three proteins control the relevant genetic, biochemical and physiological properties of proliferating bacteria. Different controls for both swarmer and stalked cell cycles are represented in the mathematical scheme. The model is validated against observed phenotypes of wild-type cells and relevant mutants, and it predicts the phenotypes of novel mutants and of known mutants under novel experimental conditions. Because the cell cycle control proteins of Caulobacter are conserved across many species of alpha-proteobacteria, the model we are proposing here may be applicable to other genera of importance to agriculture and medicine (e.g., Rhizobium, Brucella). link: http://identifiers.org/pubmed/19680425

The behaviour of biological systems can be deduced from their mathematical models. However, multiple sources of data in diverse forms are required in the construction of a model in order to define its components and their biochemical reactions, and corresponding parameters. Automating the assembly and use of systems biology models is dependent upon data integration processes involving the interoperation of data and analytical resources.Taverna workflows have been developed for the automated assembly of quantitative parameterised metabolic networks in the Systems Biology Markup Language (SBML). A SBML model is built in a systematic fashion by the workflows which starts with the construction of a qualitative network using data from a MIRIAM-compliant genome-scale model of yeast metabolism. This is followed by parameterisation of the SBML model with experimental data from two repositories, the SABIO-RK enzyme kinetics database and a database of quantitative experimental results. The models are then calibrated and simulated in workflows that call out to COPASIWS, the web service interface to the COPASI software application for analysing biochemical networks. These systems biology workflows were evaluated for their ability to construct a parameterised model of yeast glycolysis.Distributed information about metabolic reactions that have been described to MIRIAM standards enables the automated assembly of quantitative systems biology models of metabolic networks based on user-defined criteria. Such data integration processes can be implemented as Taverna workflows to provide a rapid overview of the components and their relationships within a biochemical system. link: http://identifiers.org/pubmed/21114840

NMDA receptor dependent long-term potentiation (LTP) and long-term depression (LTD) are two prominent forms of synaptic plasticity, both of which are triggered by post-synaptic calcium elevation. To understand how calcium selectively stimulates two opposing processes, we developed a detailed computational model and performed simulations with different calcium input frequencies, amplitudes, and durations. We show that with a total amount of calcium ions kept constant, high frequencies of calcium pulses stimulate calmodulin more efficiently. Calcium input activates both calcineurin and Ca(2+)/calmodulin-dependent protein kinase II (CaMKII) at all frequencies, but increased frequencies shift the relative activation from calcineurin to CaMKII. Irrespective of amplitude and duration of the inputs, the total amount of calcium ions injected adjusts the sensitivity of the system to calcium input frequencies. At a given frequency, the quantity of CaMKII activated is proportional to the total amount of calcium. Thus, an input of a small amount of calcium at high frequencies can induce the same activation of CaMKII as a larger amount, at lower frequencies. Finally, the extent of activation of CaMKII signals with high calcium frequency is further controlled by other factors, including the availability of calmodulin, and by the potency of phosphatase inhibitors. link: http://identifiers.org/pubmed/22962589

Pancreatic cancer is one of the most deadly types of cancer since it typically spreads rapidly and can seldom be detected in its early stage. Pancreatic cancer therapy is thus a challenging task, and appropriate prognosis or assessment for pancreatic cancer therapy is of critical importance. In this work, based on available clinical data in Niu et al. (2013) we develop a mathematical prognosis model that can predict the overall survival of pancreatic cancer patients who receive immunotherapy. The mathematical model incorporates pancreatic cancer cells, pancreatic stellate cells, three major classes of immune effector cells CD8+ T cells, natural killer cells, helper T cells, and two major classes of cytokines interleukin-2 (IL-2) and interferon-γ (IFN-γ). The proposed model describes the dynamic interaction between tumor and immune cells. In order for the model to be able to generate appropriate prognostic results for disease progression, the distribution and stability properties of equilibria in the mathematical model are computed and analysed in absence of treatments. In addition, numerical simulations for disease progression with or without treatments are performed. It turns out that the median overall survival associated with CIK immunotherapy is prolonged from 7 to 13months compared with the survival without treatment, this is consistent with the clinical data observed in Niu et al. (2013). The validity of the proposed mathematical prognosis model is thus verified. Our study confirms that immunotherapy offers a better prognosis for pancreatic cancer patients. As a direct extension of this work, various new therapy methods that are under exploration and clinical trials could be assessed or evaluated using the newly developed mathematical prognosis model. link: http://identifiers.org/pubmed/27338302

Calmodulin sits at the centre of molecular mechanisms underlying learning and memory. Its complex, and sometimes opposite influences, via the binding to various proteins, are yet to be fully understood. Calcium/calmodulin-dependent protein kinase II (CaMKII) and calcineurin (CaN) both bind open calmodulin, favouring Long-term potentiation (LTP) or depression (LTD) respectively. Neurogranin binds to the closed conformation of calmodulin and its impact on synaptic plasticity is less clear. We set up a mechanistic computational model based on allosteric principles to simulate calmodulin state transitions and its interaction with calcium ions and the three binding partners mentioned above. We simulated calcium spikes at various frequencies and show that neurogranin regulates synaptic plasticity along three modalities. At low spike frequencies, neurogranin inhibits the onset of LTD by limiting CaN activation. At intermediate frequencies, neurogranin limits LTP by precluding binding of CaMKII with calmodulin. Finally, at high spike frequencies, neurogranin promotes LTP by enhancing CaMKII autophosphorylation. While neurogranin might act as a calmodulin buffer, it does not significantly preclude the calmodulin opening by calcium. On the contrary, neurogranin synchronizes the opening of calmodulin’s two lobes and promotes their activation at specific frequencies, increasing the chance of CaMKII trans-autophosphorylation. Taken together, our study reveals dynamic regulatory roles played by neurogranin on synaptic plasticity, which provide mechanistic explanations to opposing experimental findings. link: http://identifiers.org/doi/10.1101/597278

Klebsiella pneumoniae is a Gram-negative bacterium of the family Enterobacteriaceae that possesses diverse metabolic capabilities: many strains are leading causes of hospital-acquired infections that are often refractory to multiple antibiotics, yet other strains are metabolically engineered and used for production of commercially valuable chemicals. To study its metabolism, we constructed a genome-scale metabolic model (iYL1228) for strain MGH 78578, experimentally determined its biomass composition, experimentally determined its ability to grow on a broad range of carbon, nitrogen, phosphorus and sulfur sources, and assessed the ability of the model to accurately simulate growth versus no growth on these substrates. The model contains 1,228 genes encoding 1,188 enzymes that catalyze 1,970 reactions and accurately simulates growth on 84% of the substrates tested. Furthermore, quantitative comparison of growth rates between the model and experimental data for nine of the substrates also showed good agreement. The genome-scale metabolic reconstruction for K. pneumoniae presented here thus provides an experimentally validated in silico platform for further studies of this important industrial and biomedical organism. link: http://identifiers.org/pubmed/21296962

In Bacillus subtilis the σ(B) mediated general stress response provides protection against various environmental and energy related stress conditions. To better understand the general stress response, we need to explore the mechanism by which the components interact. Here, we performed experiments in B. subtilis wild type and mutant strains to test and validate a mathematical model of the dynamics of σ(B) activity. In the mutant strain BSA115, σ(B) transcription is inducible by the addition of IPTG and negative control of σ(B) activity by the anti-sigma factor RsbW is absent. In contrast to our expectations of a continuous β-galactosidase activity from a ctc::lacZ fusion, we observed a transient activity in the mutant. To explain this experimental finding, we constructed mathematical models reflecting different hypotheses regarding the regulation of σ(B) and β-galactosidase dynamics. Only the model assuming instability of either ctc::lacZ mRNA or β-galactosidase protein is able to reproduce the experiments in silico. Subsequent Northern blot experiments revealed stable high-level ctc::lacZ mRNA concentrations after the induction of the σ(B) response. Therefore, we conclude that protein instability following σ(B) activation is the most likely explanation for the experimental observations. Our results thus support the idea that B. subtilis increases the cytoplasmic proteolytic degradation to adapt the proteome in face of environmental challenges following activation of the general stress response. The findings also have practical implications for the analysis of stress response dynamics using lacZ reporter gene fusions, a frequently used strategy for the σ(B) response. link: http://identifiers.org/pubmed/22511268

In Bacillus subtilis the σ(B) mediated general stress response provides protection against various environmental and energy related stress conditions. To better understand the general stress response, we need to explore the mechanism by which the components interact. Here, we performed experiments in B. subtilis wild type and mutant strains to test and validate a mathematical model of the dynamics of σ(B) activity. In the mutant strain BSA115, σ(B) transcription is inducible by the addition of IPTG and negative control of σ(B) activity by the anti-sigma factor RsbW is absent. In contrast to our expectations of a continuous β-galactosidase activity from a ctc::lacZ fusion, we observed a transient activity in the mutant. To explain this experimental finding, we constructed mathematical models reflecting different hypotheses regarding the regulation of σ(B) and β-galactosidase dynamics. Only the model assuming instability of either ctc::lacZ mRNA or β-galactosidase protein is able to reproduce the experiments in silico. Subsequent Northern blot experiments revealed stable high-level ctc::lacZ mRNA concentrations after the induction of the σ(B) response. Therefore, we conclude that protein instability following σ(B) activation is the most likely explanation for the experimental observations. Our results thus support the idea that B. subtilis increases the cytoplasmic proteolytic degradation to adapt the proteome in face of environmental challenges following activation of the general stress response. The findings also have practical implications for the analysis of stress response dynamics using lacZ reporter gene fusions, a frequently used strategy for the σ(B) response. link: http://identifiers.org/pubmed/22511268

In Bacillus subtilis the σ(B) mediated general stress response provides protection against various environmental and energy related stress conditions. To better understand the general stress response, we need to explore the mechanism by which the components interact. Here, we performed experiments in B. subtilis wild type and mutant strains to test and validate a mathematical model of the dynamics of σ(B) activity. In the mutant strain BSA115, σ(B) transcription is inducible by the addition of IPTG and negative control of σ(B) activity by the anti-sigma factor RsbW is absent. In contrast to our expectations of a continuous β-galactosidase activity from a ctc::lacZ fusion, we observed a transient activity in the mutant. To explain this experimental finding, we constructed mathematical models reflecting different hypotheses regarding the regulation of σ(B) and β-galactosidase dynamics. Only the model assuming instability of either ctc::lacZ mRNA or β-galactosidase protein is able to reproduce the experiments in silico. Subsequent Northern blot experiments revealed stable high-level ctc::lacZ mRNA concentrations after the induction of the σ(B) response. Therefore, we conclude that protein instability following σ(B) activation is the most likely explanation for the experimental observations. Our results thus support the idea that B. subtilis increases the cytoplasmic proteolytic degradation to adapt the proteome in face of environmental challenges following activation of the general stress response. The findings also have practical implications for the analysis of stress response dynamics using lacZ reporter gene fusions, a frequently used strategy for the σ(B) response. link: http://identifiers.org/pubmed/22511268

Human T-lymphotropic virus type I (HTLV-I) causes chronic infection for which there is no cure or neutralising vaccine. HTLV-I has been clinically linked to the development of adult T-cell leukaemia/lymphoma (ATL), an aggressive blood cancer, and HAM/TSP, a progressive neurological and inflammatory disease. Infected individuals typically mount a large, persistently activated CD8(+) cytotoxic T-lymphocyte (CTL) response against HTLV-I-infected cells, but ultimately fail to effectively eliminate the virus. Moreover, the identification of determinants to disease manifestation has thus far been elusive. A key issue in current HTLV-I research is to better understand the dynamic interaction between persistent infection by HTLV-I and virus-specific host immunity. Recent experimental hypotheses for the persistence of HTLV-I in vivo have led to the development of mathematical models illuminating the balance between proviral latency and activation in the target cell population. We investigate the role of a constantly changing anti-viral immune environment acting in response to the effects of infected T-cell activation and subsequent viral expression. The resulting model is a four-dimensional, non-linear system of ordinary differential equations that describes the dynamic interactions among viral expression, infected target cell activation, and the HTLV-I-specific CTL response. The global dynamics of the model is established through the construction of appropriate Lyapunov functions. Examining the particular roles of viral expression and host immunity during the chronic phase of HTLV-I infection offers important insights regarding the evolution of viral persistence and proposes a hypothesis for pathogenesis. link: http://identifiers.org/pubmed/24583256

We have developed a mathematical model of the rabbit atrial myocyte and have used it in an examination of the ionic basis of the atrial action potential. Available biophysical data have been incorporated into the model to quantify the specific ultrastructural morphology, intracellular ion buffering, and time- and voltage-dependent currents and transport mechanisms of the rabbit atrial cell. When possible, mathematical expressions describing ionic currents identified in rabbit atrium are based on whole cell voltage-clamp data from enzymatically isolated rabbit atrial myocytes. This membrane model is coupled to equations describing Na+, K+, and Ca2+ homeostasis, including the uptake and release of Ca2+ by the sarcoplasmic reticulum and Ca2+ buffering. The resulting formulation can accurately simulate the whole cell voltage-clamp data on which it is based and provides fits to a family of rabbit atrial cell action potentials obtained at 35 degrees C over a range of stimulus rates (0.2-3.0 Hz). The model is utilized to provide a qualitative prediction of the intracellular Ca2+ concentration transient during the action potential and to illustrate the interactions between membrane currents that underlie repolarization in the rabbit atrial myocyte. link: http://identifiers.org/pubmed/8897964

Precise timing of cell division is achieved by coupling waves of cyclin-dependent kinase (Cdk) activity with a transcriptional oscillator throughout cell cycle progression. Although details of transcription of cyclin genes are known, it is unclear which is the transcriptional cascade that modulates their expression in a timely fashion. Here, we demonstrate that a Clb/Cdk1-mediated regulation of the Fkh2 transcription factor synchronizes the temporal mitotic CLB expression in budding yeast. A simplified kinetic model of the cyclin/Cdk network predicts a linear cascade where a Clb/Cdk1-mediated regulation of an activator molecule drives CLB3 and CLB2 expression. Experimental validation highlights Fkh2 as modulator of CLB3 transcript levels, besides its role in regulating CLB2 expression. A Boolean model based on the minimal number of interactions needed to capture the information flow of the Clb/Cdk1 network supports the role of an activator molecule in the sequential activation, and oscillatory behavior, of mitotic Clb cyclins. This work illustrates how transcription and phosphorylation networks can be coupled by a Clb/Cdk1-mediated regulation that synchronizes them. link: http://identifiers.org/pubmed/28649434

The two-feedback-loop regulatory module of nuclear factor kappaB (NF-kappaB) signaling pathway is modeled by means of ordinary differential equations. The constructed model involves two-compartment kinetics of the activators IkappaB (IKK) and NF-kappaB, the inhibitors A20 and IkappaBalpha, and their complexes. In resting cells, the unphosphorylated IkappaBalpha binds to NF-kappaB and sequesters it in an inactive form in the cytoplasm. In response to extracellular signals such as tumor necrosis factor or interleukin-1, IKK is transformed from its neutral form (IKKn) into its active form (IKKa), a form capable of phosphorylating IkappaBalpha, leading to IkappaBalpha degradation. Degradation of IkappaBalpha releases the main activator NF-kappaB, which then enters the nucleus and triggers transcription of the inhibitors and numerous other genes. The newly synthesized IkappaBalpha leads NF-kappaB out of the nucleus and sequesters it in the cytoplasm, while A20 inhibits IKK converting IKKa into the inactive form (IKKi), a form different from IKKn, no longer capable of phosphorylating IkappaBalpha. After parameter fitting, the proposed model is able to properly reproduce time behavior of all variables for which the data are available: NF-kappaB, cytoplasmic IkappaBalpha, A20 and IkappaBalpha mRNA transcripts, IKK and IKK catalytic activity in both wild-type and A20-deficient cells. The model allows detailed analysis of kinetics of the involved proteins and their complexes and gives the predictions of the possible responses of whole kinetics to the change in the level of a given activator or inhibitor. link: http://identifiers.org/pubmed/15094015

We propose a dynamical model for the hypothalamo-pituitary-thyroid axis. This model takes into account both the interactions of hormones in this axis and the binding of thyroid hormones with proteins in plasma and tissues. It can account for the pulsatile character of hormone secretion in this axis as well as many experimental results. link: http://identifiers.org/pubmed/7772725

A new molecular mathematical model is developed by considering the kinetics of GLUT2, GLUT3, and GLUT4, the process of glucose mobilization by glycogen phosphorylase and glycogen synthase in liver, and the dynamics of the insulin signaling pathway. The new model can qualitatively reproduce the experimental glucose and insulin data. It also enables us to use the Bendixson criterion about the existence of periodic orbits of a two-dimensional dynamical system to mathematically predict that the oscillations of glucose and insulin are not caused by liver, instead they would be caused by the mechanism of insulin secretion from pancreatic beta cells. Furthermore it enables us to conduct a parametric sensitivity analysis. The analysis shows that both glucose and insulin are most sensitive to the rate constant for conversion of PI(3,4,5)P(3) to PI(4,5)P(2), the multiplicative factor modulating the rate constant for conversion of PI(3,4,5)P(3) to PI(4,5)P(2), the multiplicative factor that modulates insulin receptor dephosphorylation rate, and the maximum velocity of GLUT4. Moreover, the sensitivity analysis predicts that an increase of the apparent velocity of GLUT4, a combination of elevated mobilization rate of GLUT4 to the plasma membrane and an extended duration of GLUT4 on the plasma membrane, will result in a decrease in the needs of plasma insulin. On the other hand, an increase of the GLUT4 internalization rate results in an elevated demand of insulin to stimulate the mobilization of GLUT4 from the intracellular store to the plasma membrane. link: http://identifiers.org/pubmed/19651146

An important question in plant biology is how genes influence the crosstalk between hormones to regulate growth. In this study, we model POLARIS (PLS) gene function and crosstalk between auxin, ethylene and cytokinin in Arabidopsis. Experimental evidence suggests that PLS acts on or close to the ethylene receptor ETR1, and a mathematical model describing possible PLS-ethylene pathway interactions is developed, and used to make quantitative predictions about PLS-hormone interactions. Modelling correctly predicts experimental results for the effect of the pls gene mutation on endogenous cytokinin concentration. Modelling also reveals a role for PLS in auxin biosynthesis in addition to a role in auxin transport. The model reproduces available mutants, and with new experimental data provides new insights into how PLS regulates auxin concentration, by controlling the relative contribution of auxin transport and biosynthesis and by integrating auxin, ethylene and cytokinin signalling. Modelling further reveals that a bell-shaped dose-response relationship between endogenous auxin and root length is established via PLS. This combined modelling and experimental analysis provides new insights into the integration of hormonal signals in plants. link: http://identifiers.org/pubmed/20531403

The complement system is key to innate immunity and its activation is necessary for the clearance of bacteria and apoptotic cells. However, insufficient or excessive complement activation will lead to immune-related diseases. It is so far unknown how the complement activity is up- or down- regulated and what the associated pathophysiological mechanisms are. To quantitatively understand the modulatory mechanisms of the complement system, we built a computational model involving the enhancement and suppression mechanisms that regulate complement activity. Our model consists of a large system of Ordinary Differential Equations (ODEs) accompanied by a dynamic Bayesian network as a probabilistic approximation of the ODE dynamics. Applying Bayesian inference techniques, this approximation was used to perform parameter estimation and sensitivity analysis. Our combined computational and experimental study showed that the antimicrobial response is sensitive to changes in pH and calcium levels, which determines the strength of the crosstalk between CRP and L-ficolin. Our study also revealed differential regulatory effects of C4BP. While C4BP delays but does not decrease the classical complement activation, it attenuates but does not significantly delay the lectin pathway activation. We also found that the major inhibitory role of C4BP is to facilitate the decay of C3 convertase. In summary, the present work elucidates the regulatory mechanisms of the complement system and demonstrates how the bio-pathway machinery maintains the balance between activation and inhibition. The insights we have gained could contribute to the development of therapies targeting the complement system. link: http://identifiers.org/pubmed/21283780

As one of the best xylose utilization microorganisms, Scheffersomyces stipitis exhibits great potential for the efficient lignocellulosic biomass fermentation. Therefore, a comprehensive understanding of its unique physiological and metabolic characteristics is required to further improve its performance on cellulosic ethanol production.A constraint-based genome-scale metabolic model for S. stipitis CBS 6054 was developed on the basis of its genomic, transcriptomic and literature information. The model iTL885 consists of 885 genes, 870 metabolites, and 1240 reactions. During the reconstruction process, 36 putative sugar transporters were reannotated and the metabolisms of 7 sugars were illuminated. Essentiality study was conducted to predict essential genes on different growth media. Key factors affecting cell growth and ethanol formation were investigated by the use of constraint-based analysis. Furthermore, the uptake systems and metabolic routes of xylose were elucidated, and the optimization strategies for the overproduction of ethanol were proposed from both genetic and environmental perspectives.Systems biology modelling has proven to be a powerful tool for targeting metabolic changes. Thus, this systematic investigation of the metabolism of S. stipitis could be used as a starting point for future experiment designs aimed at identifying the metabolic bottlenecks of this important yeast. link: http://identifiers.org/pubmed/22998943

The eukaryotic cell cycle is regulated by a complicated chemical reaction network. Although many deterministic models have been proposed, stochastic models are desired to capture noise in the cell resulting from low numbers of critical species. However, converting a deterministic model into one that accurately captures stochastic effects can result in a complex model that is hard to build and expensive to simulate. In this paper, we first apply a hybrid (mixed deterministic and stochastic) simulation method to such a stochastic model. With proper partitioning of reactions between deterministic and stochastic simulation methods, the hybrid method generates the same primary characteristics and the same level of noise as Gillespie's stochastic simulation algorithm, but with better efficiency. By studying the results generated by various partitionings of reactions, we developed a new strategy for hybrid stochastic modeling of the cell cycle. The new approach is not limited to using mass-action rate laws. Numerical experiments demonstrate that our approach is consistent with characteristics of noisy cell cycle progression, and yields cell cycle statistics in accord with experimental observations. link: http://identifiers.org/pubmed/22280742

Considering the targeted chemotherapy, a mathematical model of tumor-immune system was constructed on the basis of de Pillis’s model. In this paper, we conducted qualitative analysis on the mathematical model, including the positivity and boundedness of solutions, local stability and global stability of equi- librium solutions. Some numerical simulations were given to illustrate the analytic results. Comparing the targeted chemotherapy model with regular chemotherapy model, we found that the targeted chemother- apy was benefit to kill tumor cells. link: http://identifiers.org/doi/10.1016/j.chaos.2017.03.002

Alternans of cardiac repolarization is associated with arrhythmias and sudden death. At the cellular level, alternans involves beat-to-beat oscillation of the action potential (AP) and possibly Ca(2+) transient (CaT). Because of experimental difficulty in independently controlling the Ca(2+) and electrical subsystems, mathematical modeling provides additional insights into mechanisms and causality. Pacing protocols were conducted in a canine ventricular myocyte model with the following results: 1) CaT alternans results from refractoriness of the sarcoplasmic reticulum Ca(2+) release system; alternation of the L-type calcium current has a negligible effect; 2) CaT-AP coupling during late AP occurs through the sodium-calcium exchanger and underlies AP duration (APD) alternans; 3) increased Ca(2+)/calmodulin-dependent protein kinase II (CaMKII) activity extends the range of CaT and APD alternans to slower frequencies and increases alternans magnitude; its decrease suppresses CaT and APD alternans, exerting an antiarrhythmic effect; and 4) increase of the rapid delayed rectifier current (I(Kr)) also suppresses APD alternans but without suppressing CaT alternans. Thus CaMKII inhibition eliminates APD alternans by eliminating its cause (CaT alternans) while I(Kr) enhancement does so by weakening CaT-APD coupling. The simulations identify combined CaMKII inhibition and I(Kr) enhancement as a possible antiarrhythmic intervention. link: http://identifiers.org/pubmed/17277017

Tumor microenvironments contain multiple cell types interacting among one another via different signaling pathways. Furthermore, both cancer cells and different immune cells can display phenotypic plasticity in response to these communicating signals, thereby leading to complex spatiotemporal patterns that can impact therapeutic response. Here, we investigate the crosstalk between cancer cells and macrophages in a tumor microenvironment through in silico (computational) co-culture models. In particular, we investigate how macrophages of different polarization (M1 vs. M2) can interact with epithelial-mesenchymal plasticity of cancer cells, and conversely, how cancer cells exhibiting different phenotypes (epithelial vs. mesenchymal) can influence the polarization of macrophages. Based on interactions documented in the literature, an interaction network of cancer cells and macrophages is constructed. The steady states of the network are then analyzed. Various interactions were removed or added into the constructed-network to test the functions of those interactions. Also, parameters in the mathematical models were varied to explore their effects on the steady states of the network. In general, the interactions between cancer cells and macrophages can give rise to multiple stable steady-states for a given set of parameters and each steady state is stable against perturbations. Importantly, we show that the system can often reach one type of stable steady states where cancer cells go extinct. Our results may help inform efficient therapeutic strategies. link: http://identifiers.org/pubmed/30729096

BACKGROUND: This work focuses on the computational modelling of osteomyelitis, a bone pathology caused by bacteria infection (mostly Staphylococcus aureus). The infection alters the RANK/RANKL/OPG signalling dynamics that regulates osteoblasts and osteoclasts behaviour in bone remodelling, i.e. the resorption and mineralization activity. The infection rapidly leads to severe bone loss, necrosis of the affected portion, and it may even spread to other parts of the body. On the other hand, osteoporosis is not a bacterial infection but similarly is a defective bone pathology arising due to imbalances in the RANK/RANKL/OPG molecular pathway, and due to the progressive weakening of bone structure. RESULTS: Since both osteoporosis and osteomyelitis cause loss of bone mass, we focused on comparing the dynamics of these diseases by means of computational models. Firstly, we performed meta-analysis on a gene expression data of normal, osteoporotic and osteomyelitis bone conditions. We mainly focused on RANKL/OPG signalling, the TNF and TNF receptor superfamilies and the NF-kB pathway. Using information from the gene expression data we estimated parameters for a novel model of osteoporosis and of osteomyelitis. Our models could be seen as a hybrid ODE and probabilistic verification modelling framework which aims at investigating the dynamics of the effects of the infection in bone remodelling. Finally we discuss different diagnostic estimators defined by formal verification techniques, in order to assess different bone pathologies (osteopenia, osteoporosis and osteomyelitis) in an effective way. CONCLUSIONS: We present a modeling framework able to reproduce aspects of the different bone remodeling defective dynamics of osteomyelitis and osteoporosis. We report that the verification-based estimators are meaningful in the light of a feed forward between computational medicine and clinical bioinformatics. link: http://identifiers.org/pubmed/23095605

cis-Encoded antisense RNAs (asRNAs) are widespread along bacterial transcriptomes. However, the role of most of these RNAs remains unknown, and there is an ongoing discussion as to what extent these transcripts are the result of transcriptional noise. We show, by comparative transcriptomics of 20 bacterial species and one chloroplast, that the number of asRNAs is exponentially dependent on the genomic AT content and that expression of asRNA at low levels exerts little impact in terms of energy consumption. A transcription model simulating mRNA and asRNA production indicates that the asRNA regulatory effect is only observed above certain expression thresholds, substantially higher than physiological transcript levels. These predictions were verified experimentally by overexpressing nine different asRNAs in Mycoplasma pneumoniae. Our results suggest that most of the antisense transcripts found in bacteria are the consequence of transcriptional noise, arising at spurious promoters throughout the genome. link: http://identifiers.org/pubmed/26973873

cis-Encoded antisense RNAs (asRNAs) are widespread along bacterial transcriptomes. However, the role of most of these RNAs remains unknown, and there is an ongoing discussion as to what extent these transcripts are the result of transcriptional noise. We show, by comparative transcriptomics of 20 bacterial species and one chloroplast, that the number of asRNAs is exponentially dependent on the genomic AT content and that expression of asRNA at low levels exerts little impact in terms of energy consumption. A transcription model simulating mRNA and asRNA production indicates that the asRNA regulatory effect is only observed above certain expression thresholds, substantially higher than physiological transcript levels. These predictions were verified experimentally by overexpressing nine different asRNAs in Mycoplasma pneumoniae. Our results suggest that most of the antisense transcripts found in bacteria are the consequence of transcriptional noise, arising at spurious promoters throughout the genome. link: http://identifiers.org/pubmed/26973873

cis-Encoded antisense RNAs (asRNAs) are widespread along bacterial transcriptomes. However, the role of most of these RNAs remains unknown, and there is an ongoing discussion as to what extent these transcripts are the result of transcriptional noise. We show, by comparative transcriptomics of 20 bacterial species and one chloroplast, that the number of asRNAs is exponentially dependent on the genomic AT content and that expression of asRNA at low levels exerts little impact in terms of energy consumption. A transcription model simulating mRNA and asRNA production indicates that the asRNA regulatory effect is only observed above certain expression thresholds, substantially higher than physiological transcript levels. These predictions were verified experimentally by overexpressing nine different asRNAs in Mycoplasma pneumoniae. Our results suggest that most of the antisense transcripts found in bacteria are the consequence of transcriptional noise, arising at spurious promoters throughout the genome. link: http://identifiers.org/pubmed/26973873

A kinetic Monte Carlo simulation was developed using the deterministic reaction network developed by the Mann laboratory for tissue-factor (TF)-initiated blood coagulation. The model predicted thrombin dynamics in recalcified whole blood (3-fold diluted) pretreated with convulxin (platelet GPVI activator) and picomolar levels of TF (0-14 pM). The model did not accurately predict coagulation times at low TF (0-0.7 pM). The simulation revealed that approximately 0.2 pM TF was the critical concentration to cause 50% of reactions containing 3-fold diluted whole blood to reach a clotting threshold of 0.05 U/ml thrombin by 1 h. Simulations of 1 nl of blood (5 pM TF) revealed small stochastic variations in thrombin initiation time, while 16.6 pl simulations were highly stochastic at this level of TF (50 molecules/16.6 pl). Further experiment and simulation will require evaluation of mechanisms of coagulation kinetics at subpicomolar levels of TF. link: http://identifiers.org/pubmed/16432310

Perfluoroalkyl acid carboxylates and sulfonates (PFAAs) have many consumer and industrial applications. The persistence and widespread distribution of these compounds in humans have brought them under intense scrutiny. Limited pharmacokinetic data is available in humans; however, human data exists for two communities with drinking water contaminated by PFAAs. Also, there is toxicological and pharmacokinetic data for monkeys, which can be quite useful for cross-species extrapolation to humans. The goal of this research was to develop a physiologically-based pharmacokinetic (PBPK) model for PFOA and PFOS for monkeys and then scale this model to humans in order to describe available human drinking water data. The monkey model simulations were consistent with available PK data for monkeys. The monkey model was then extrapolated to the human and then used to successfully simulate the data collected from residents of two communities exposed to PFOA in drinking water. Human PFOS data is minimal; however, using the half-life estimated from occupational exposure, our model exhibits reasonable agreement with the available human serum PFOS data. It is envisioned that our PBPK model will be useful in supporting human health risk assessments for PFOA and PFOS by aiding in understanding of human pharmacokinetics. link: http://identifiers.org/pubmed/21168463

Circadian clocks involve feedback loops that generate rhythmic expression of key genes. Molecular genetic studies in the higher plant Arabidopsis thaliana have revealed a complex clock network. The first part of the network to be identified, a transcriptional feedback loop comprising TIMING OF CAB EXPRESSION 1 (TOC1), LATE ELONGATED HYPOCOTYL (LHY) and CIRCADIAN CLOCK ASSOCIATED 1 (CCA1), fails to account for significant experimental data. We develop an extended model that is based upon a wider range of data and accurately predicts additional experimental results. The model comprises interlocking feedback loops comparable to those identified experimentally in other circadian systems. We propose that each loop receives input signals from light, and that each loop includes a hypothetical component that had not been explicitly identified. Analysis of the model predicted the properties of these components, including an acute light induction at dawn that is rapidly repressed by LHY and CCA1. We found this unexpected regulation in RNA levels of the evening-expressed gene GIGANTEA (GI), supporting our proposed network and making GI a strong candidate for this component. link: http://identifiers.org/pubmed/16729048

Our computational model of the circadian clock comprised the feedback loop between LATE ELONGATED HYPOCOTYL (LHY), CIRCADIAN CLOCK ASSOCIATED 1 (CCA1) and TIMING OF CAB EXPRESSION 1 (TOC1), and a predicted, interlocking feedback loop involving TOC1 and a hypothetical component Y. Experiments based on model predictions suggested GIGANTEA (GI) as a candidate for Y. We now extend the model to include a recently demonstrated feedback loop between the TOC1 homologues PSEUDO-RESPONSE REGULATOR 7 (PRR7), PRR9 and LHY and CCA1. This three-loop network explains the rhythmic phenotype of toc1 mutant alleles. Model predictions fit closely to new data on the gi;lhy;cca1 mutant, which confirm that GI is a major contributor to Y function. Analysis of the three-loop network suggests that the plant clock consists of morning and evening oscillators, coupled intracellularly, which may be analogous to coupled, morning and evening clock cells in Drosophila and the mouse. link: http://identifiers.org/pubmed/17102804

BACKGROUND: Virtually all living organisms have evolved a circadian (~24 hour) clock that controls physiological and behavioural processes with exquisite precision throughout the day/night cycle. The suprachiasmatic nucleus (SCN), which generates these ~24 h rhythms in mammals, consists of several thousand neurons. Each neuron contains a gene-regulatory network generating molecular oscillations, and the individual neuron oscillations are synchronised by intercellular coupling, presumably via neurotransmitters. Although this basic mechanism is currently accepted and has been recapitulated in mathematical models, several fundamental questions about the design principles of the SCN remain little understood. For example, a remarkable property of the SCN is that the phase of the SCN rhythm resets rapidly after a 'jet lag' type experiment, i.e. when the light/dark (LD) cycle is abruptly advanced or delayed by several hours. RESULTS: Here, we describe an extensive parameter optimization of a previously constructed simplified model of the SCN in order to further understand its design principles. By examining the top 50 solutions from the parameter optimization, we show that the neurotransmitters' role in generating the molecular circadian rhythms is extremely important. In addition, we show that when a neurotransmitter drives the rhythm of a system of coupled damped oscillators, it exhibits very robust synchronization and is much more easily entrained to light/dark cycles. We were also able to recreate in our simulations the fast rhythm resetting seen after a 'jet lag' type experiment. CONCLUSION: Our work shows that a careful exploration of parameter space for even an extremely simplified model of the mammalian clock can reveal unexpected behaviours and non-trivial predictions. Our results suggest that the neurotransmitter feedback loop plays a crucial role in the robustness and phase resetting properties of the mammalian clock, even at the single neuron level. link: http://identifiers.org/pubmed/18312618

Clinical trial simulation (CTS) was used to select a robust design to test the hypothesis that a new treatment was effective for Alzheimer's disease (AD). Typically, a parallel group, placebo controlled, 12-week trial in 200-400 AD patients would be used to establish drug effect relative to placebo (i.e., Ho: Drug Effect = 0). We evaluated if a crossover design would allow smaller and shorter duration trials.A family of plausible drug and disease models describing the time course of the AD assessment scale (ADAS-Cog) was developed based on Phase I data and literature reports of other treatments for AD. The models included pharmacokinetic, pharmacodynamic, disease progression, and placebo components. Eight alternative trial designs were explored via simulation. One hundred replicates of each combination of drug and disease model and trial design were simulated. A 'positive trial' reflecting drug activity was declared considering both a dose trend test (p < 0.05) and pair-wise comparisons to placebo (p < 0.025).A 4 x 4 Latin Square design was predicted to have at least 80% power to detect activity across a range of drug and disease models. The trial design was subsequently implemented and the trial was completed. Based on the results of the actual trial, a conclusive decision about further development was taken. The crossover design provided enhanced power over a parallel group design due to the lower residual variability.CTS aided the decision to use a more efficient proof of concept trial design, leading to savings of up to US 4 M dollars in direct costs and a firm decision 8-12 months earlier than a 12-week parallel group trial. link: http://identifiers.org/pubmed/16906456

BACKGROUND: Yarrowia lipolytica is an oleaginous yeast which has emerged as an important microorganism for several biotechnological processes, such as the production of organic acids, lipases and proteases. It is also considered a good candidate for single-cell oil production. Although some of its metabolic pathways are well studied, its metabolic engineering is hindered by the lack of a genome-scale model that integrates the current knowledge about its metabolism. RESULTS: Combining in silico tools and expert manual curation, we have produced an accurate genome-scale metabolic model for Y. lipolytica. Using a scaffold derived from a functional metabolic model of the well-studied but phylogenetically distant yeast S. cerevisiae, we mapped conserved reactions, rewrote gene associations, added species-specific reactions and inserted specialized copies of scaffold reactions to account for species-specific expansion of protein families. We used physiological measures obtained under lab conditions to validate our predictions. CONCLUSIONS: Y. lipolytica iNL895 represents the first well-annotated metabolic model of an oleaginous yeast, providing a base for future metabolic improvement, and a starting point for the metabolic reconstruction of other species in the Yarrowia clade and other oleaginous yeasts. link: http://identifiers.org/pubmed/22558935

It is well-known that tumours induce the formation of a lymphatic and a blood vasculature around themselves. A similar but far less studied process occurs in relation to the nervous system and is referred to as neoneurogenesis. The relationship between tumour progression and the nervous system is still poorly understood and is likely to involve a multitude of factors. It is therefore relevant to study tumour-nerve interactions through mathematical modelling: this may reveal the most significant factors of the plethora of interacting elements regulating neoneurogenesis. The present work is a first attempt to model the neurobiological aspect of cancer development through a system of differential equations. The model confirms the experimental observations that a tumour is able to promote nerve formation/elongation around itself, and that high levels of nerve growth factor and axon guidance molecules are recorded in the presence of a tumour. Our results also reflect the observation that high stress levels (represented by higher norepinephrine release by sympathetic nerves) contribute to tumour development and spread, indicating a mutually beneficial relationship between tumour cells and neurons. The model predictions suggest novel therapeutic strategies, aimed at blocking the stress effects on tumour growth and dissemination. link: http://identifiers.org/pubmed/26861829

Immunotherapy is a promising new therapeutic approach for neuroblastoma (NBM): an anti‐GD2 vaccine combined with orally administered soluble beta‐glucan is undergoing a phase II clinical trial and nivolumab and ipilimumab are being tested in recurrent and refractory tumors. Unfortunately, predictive biomarkers of response to immunotherapy are currently not available for NBM patients. The aim of this study was to create a computational network model simulating the different intracellular pathways involved in NBM, in order to predict how the tumor phenotype may be influenced to increase the sensitivity to anti‐programmed cell death‐ligand‐1 (PD‐L1)/programmed cell death‐1 (PD‐1) immunotherapy. The model runs on COPASI software. In order to determine the influence of intracellular signaling pathways on the expression of PD‐L1 in NBM, we first developed an integrated network of protein kinase cascades. Michaelis–Menten kinetics were associated to each reaction in order to tailor the different enzymes kinetics, creating a system of ordinary differential equations (ODEs). The data of this study offers a first tool to be considered in the therapeutic management of the NBM patient undergoing immunotherapeutic treatment. link: http://identifiers.org/doi/10.3390/brainsci9090221

We consider a dynamical model of cancer growth including three interacting cell populations of tumor cells, healthy host cells and immune effector cells. The tumor-immune and the tumor-host interactions are characterized to reproduce experimental results. A thorough dynamical analysis of the model is carried out, showing its capability to explain theoretical and empirical knowledge about tumor development. A chemotherapy treatment reproducing different experiments is also introduced. We believe that this simple model can serve as a foundation for the development of more complicated and specific cancer models. link: http://identifiers.org/pubmed/25348062

Pancreatic cancer is one of the most deadly types of cancer and has extremely poor prognosis. This malignancy typically induces only limited cellular immune responses, the magnitude of which can increase with the number of encountered cancer cells. On the other hand, pancreatic cancer is highly effective at evading immune responses by inducing polarization of pro-inflammatory M1 macrophages into anti-inflammatory M2 macrophages, and promoting expansion of myeloid derived suppressor cells, which block the killing of cancer cells by cytotoxic T cells. These factors allow immune evasion to predominate, promoting metastasis and poor responsiveness to chemotherapies and immunotherapies. In this paper we develop a mathematical model of pancreatic cancer, and use it to qualitatively explain a variety of biomedical and clinical data. The model shows that drugs aimed at suppressing cancer growth are effective only if the immune induced cancer cell death lies within a specific range, that is, the immune system has a specific window of opportunity to effectively suppress cancer under treatment. The model results suggest that tumor growth rate is affected by complex feedback loops between the tumor cells, endothelial cells and the immune response. The relative strength of the different loops determines the cancer growth rate and its response to immunotherapy. The model could serve as a starting point to identify optimal nodes for intervention against pancreatic cancer. link: http://identifiers.org/pubmed/24594371

The role that mechanistic mathematical modeling and systems biology will play in molecular medicine and clinical development remains uncertain. In this study, mathematical modeling and sensitivity analysis were used to explore the working hypothesis that mechanistic models of human cascades, despite model uncertainty, can be computationally screened for points of fragility, and that these sensitive mechanisms could serve as therapeutic targets. We tested our working hypothesis by screening a model of the well-studied coagulation cascade, developed and validated from literature. The predicted sensitive mechanisms were then compared with the treatment literature. The model, composed of 92 proteins and 148 protein-protein interactions, was validated using 21 published datasets generated from two different quiescent in vitro coagulation models. Simulated platelet activation and thrombin generation profiles in the presence and absence of natural anticoagulants were consistent with measured values, with a mean correlation of 0.87 across all trials. Overall state sensitivity coefficients, which measure the robustness or fragility of a given mechanism, were calculated using a Monte Carlo strategy. In the absence of anticoagulants, fluid and surface phase factor X/activated factor X (fX/FXa) activity and thrombin-mediated platelet activation were found to be fragile, while fIX/FIXa and fVIII/FVIIIa activation and activity were robust. Both anti-fX/FXa and direct thrombin inhibitors are important classes of anticoagulants; for example, anti-fX/FXa inhibitors have FDA approval for the prevention of venous thromboembolism following surgical intervention and as an initial treatment for deep venous thrombosis and pulmonary embolism. Both in vitro and in vivo experimental evidence is reviewed supporting the prediction that fIX/FIXa activity is robust. When taken together, these results support our working hypothesis that computationally derived points of fragility of human relevant cascades could be used as a rational basis for target selection despite model uncertainty. link: http://identifiers.org/pubmed/17658944

The role of mechanistic modeling and systems biology in molecular medicine remains unclear. In this study, we explored whether uncertain models could be used to understand how a network responds to a therapeutic intervention. As a proof of concept, we modeled and analyzed the response of the human coagulation cascade to recombinant factor VIIa (rFVIIa) and prothrombin (fII) addition in normal and hemophilic plasma. An ensemble of parametrically uncertain human coagulation models was developed (N = 437). Each model described the time evolution of 193 proteins and protein complexes interconnected by 301 interactions under quiescent flow. The 467 unknown model parameters were estimated, using multiobjective optimization, from published in vitro coagulation studies. The model ensemble was validated using published in vitro thrombin measurements and thrombin measurements taken from coronary artery disease patients. Sensitivity analysis was then used to rank-order the importance of model parameters as a function of experimental or physiological conditions. A novel strategy for the systematic comparison of ranks identified a family of fX/FXa and fII/FIIa interactions that became more sensitive with decreasing fVIII/fIX. The fragility of these interactions was preserved following the addition of exogenous rFVIIa and fII. This suggested that exogenous rFVIIa did not alter the qualitative operation of the cascade. Rather, exogenous rFVIIa and fII took advantage of existing fluid and interfacial fX/FXa and fII/FIIa sensitivity to restore normal coagulation in low fVIII/fIX conditions. The proposed rFVIIa mechanism of action was consistent with experimental literature not used in model training. Thus, we demonstrated that an ensemble of uncertain models could unravel key facets of the mechanism of action of a focused intervention. Whereas the current study was limited to coagulation, perhaps the general strategy used could be extended to other molecular networks relevant to human health. link: http://identifiers.org/pubmed/20844798

A mathematical model of the membrane action potential of the mammalian ventricular cell is introduced. The model is based, whenever possible, on recent single-cell and single-channel data and incorporates the possibility of changing extracellular potassium concentration [K]o. The fast sodium current, INa, is characterized by fast upstroke velocity (Vmax = 400 V/sec) and slow recovery from inactivation. The time-independent potassium current, IK1, includes a negative-slope phase and displays significant crossover phenomenon as [K]o is varied. The time-dependent potassium current, IK, shows only a minimal degree of crossover. A novel potassium current that activates at plateau potentials is included in the model. The simulated action potential duplicates the experimentally observed effects of changes in [K]o on action potential duration and rest potential. Physiological simulations focus on the interaction between depolarization and repolarization (i.e., premature stimulation). Results demonstrate the importance of the slow recovery of INa in determining the response of the cell. Simulated responses to periodic stimulation include monotonic Wenckebach patterns and alternans at normal [K]o, whereas at low [K]o nonmonotonic Wenckebach periodicities, aperiodic patterns, and enhanced supernormal excitability that results in unstable responses ("chaotic activity") are observed. The results are consistent with recent experimental observations, and the model simulations relate these phenomena to the underlying ionic channel kinetics. link: http://identifiers.org/pubmed/1709839

A mathematical model of the cardiac ventricular action potential is presented. In our previous work, the membrane Na+ current and K+ currents were formulated. The present article focuses on processes that regulate intracellular Ca2+ and depend on its concentration. The model presented here for the mammalian ventricular action potential is based mostly on the guinea pig ventricular cell. However, it provides the framework for modeling other types of ventricular cells with appropriate modifications made to account for species differences. The following processes are formulated: Ca2+ current through the L-type channel (ICa), the Na(+)-Ca2+ exchanger, Ca2+ release and uptake by the sarcoplasmic reticulum (SR), buffering of Ca2+ in the SR and in the myoplasm, a Ca2+ pump in the sarcolemma, the Na(+)-K+ pump, and a nonspecific Ca(2+)-activated membrane current. Activation of ICa is an order of magnitude faster than in previous models. Inactivation of ICa depends on both the membrane voltage and [Ca2+]i. SR is divided into two subcompartments, a network SR (NSR) and a junctional SR (JSR). Functionally, Ca2+ enters the NSR and translocates to the JSR following a monoexponential function. Release of Ca2+ occurs at JSR and can be triggered by two different mechanisms, Ca(2+)-induced Ca2+ release and spontaneous release. The model provides the basis for the study of arrhythmogenic activity of the single myocyte including afterdepolarizations and triggered activity. It can simulate cellular responses under different degrees of Ca2+ overload. Such simulations are presented in our accompanying article in this issue of Circulation Research. link: http://identifiers.org/pubmed/7514509

BACKGROUND: Robustness of mathematical models of biochemical networks is important for validation purposes and can be used as a means of selecting between different competing models. Tools for quantifying parametric robustness are needed. RESULTS: Two techniques for describing quantitatively the robustness of an oscillatory model were presented and contrasted. Single-parameter bifurcation analysis was used to evaluate the stability robustness of the limit cycle oscillation as well as the frequency and amplitude of oscillations. A tool from control engineering–the structural singular value (SSV)–was used to quantify robust stability of the limit cycle. Using SSV analysis, we find very poor robustness when the model's parameters are allowed to vary. CONCLUSION: The results show the usefulness of incorporating SSV analysis to single parameter sensitivity analysis to quantify robustness. link: http://identifiers.org/pubmed/12482327

Recent observations show that the single-cell response of p53 to ionizing radiation (IR) is "digital" in that it is the number of oscillations rather than the amplitude of p53 that shows dependence on the radiation dose. We present a model of this phenomenon. In our model, double-strand break (DSB) sites induced by IR interact with a limiting pool of DNA repair proteins, forming DSB-protein complexes at DNA damage foci. The persisting complexes are sensed by ataxia telangiectasia mutated (ATM), a protein kinase that activates p53 once it is phosphorylated by DNA damage. The ATM-sensing module switches on or off the downstream p53 oscillator, consisting of a feedback loop formed by p53 and its negative regulator, Mdm2. In agreement with experiments, our simulations show that by assuming stochasticity in the initial number of DSBs and the DNA repair process, p53 and Mdm2 exhibit a coordinated oscillatory dynamics upon IR stimulation in single cells, with a stochastic number of oscillations whose mean increases with IR dose. The damped oscillations previously observed in cell populations can be explained as the aggregate behavior of single cells. link: http://identifiers.org/pubmed/16186499

The pervasive influence of resident microorganisms on the phenotype of their hosts is exemplified by the intracellular bacterium Buchnera aphidicola, which provides its aphid partner with essential amino acids (EAAs). We investigated variation in the dietary requirement for EAAs among four pea aphid (Acyrthosiphon pisum) clones. Buchnera-derived nitrogen contributed to the synthesis of all EAAs for which aphid clones required a dietary supply, and to none of the EAAs for which all four clones had no dietary requirement, suggesting that low total dietary nitrogen may select for reduced synthesis of certain EAAs in some aphid clones. The sequenced Buchnera genomes showed that the EAA nutritional phenotype (i.e. the profile of dietary EAAs required by the aphid) cannot be attributed to sequence variation of Buchnera genes coding EAA biosynthetic enzymes. Metabolic modelling by flux balance analysis demonstrated that EAA output from Buchnera can be determined precisely by the flux of host metabolic precursors to Buchnera. Specifically, the four EAA nutritional phenotypes could be reproduced by metabolic models with unique profiles of host inputs, dominated by variation in supply of aspartate, homocysteine and glutamate. This suggests that the nutritional phenotype of the symbiosis is determined principally by host metabolism and transporter genes that regulate nutrient supply to Buchnera. Intraspecific variation in the nutritional phenotype of symbioses is expected to mediate partitioning of plant resources among aphid genotypes, potentially promoting the genetic subdivision of aphid populations. In this way, microbial symbioses may play an important role in the evolutionary diversification of phytophagous insects. link: http://identifiers.org/pubmed/21392141

Here, we construct a mathematical model of the hypothalamic systems that control the secretion of growth hormone (GH). The work extends a recent model of the pituitary GH system, adding representations of the hypothalamic GH-releasing hormone (GHRH) and somatostatin neurones, each modelled as a single synchronised unit. An unpatterned stochastic input drives the GHRH neurones generating pulses of GHRH release that trigger GH pulses. Delayed feedback from GH results in increased somatostatin release, which inhibits both GH secretion and GHRH release, producing an overall pattern of 3-h pulses of GH secretion that is very similar to the secretory profile observed in male rats. Rather than directly stimulating somatostatin release, GH feedback triggers a priming effect, increasing releasable stores of somatostatin. Varying this priming effect to reduce the effect of GH can reproduce the less pulsatile form of GH release observed in the female rat. The model behaviour is tested by comparison with experimental observations with a range of different experimental protocols involving GHRH injections and somatostatin and GH infusion. link: http://identifiers.org/pubmed/16280026

Curcumin is a natural compound obtained from turmeric, and is well known for its pharmacological effects. In this work, we design a heterologous pathway for industrial production of curcumin in Escherichia coli. A kinetic model of the pathway is then developed and connected to a kinetic model of the central carbon metabolism of E. coli. This model is used for optimization of the mutant strain through a rational design approach, and two manipulation targets are identified for overexpression. Dynamic simulations are then performed to compare the curcumin production profiles of the different mutant strains. Our results show that it is possible to obtain a significant improvement in the curcumin production rates with the proposed mutants. The kinetic model here developed can be an important framework to optimize curcumin production at an industrial scale and add value to its biomedical potential. link: http://identifiers.org/pubmed/25218090

The Na+-dependent, low affinity glucose transporter SGLT2 cloned from pig kidney is 76% identical (at the amino acid level) to its high affinity homologue SGLT1. Using two-microelectrode voltage clamp, we have characterized the presteady-state and steady-state kinetics of SGLT2 expressed in Xenopus oocytes. The kinetic properties of the steady-state sugar-evoked currents as a function of external Na+ and alpha-methyl-D-glucopyranoside (alphaMG) concentrations were consistent with an ordered, simultaneous transport model in which Na+ binds first. Na+ binding was voltage-dependent and saturated with hyperpolarizing voltages. Phlorizin was a potent inhibitor of the sugar-evoked currents (KiPz approximately 10 microM) and blocked an inward Na+ current in the absence of sugar. SGLT2 exhibited Na+-dependent presteady-state currents with time constants 3-7 ms. Charge movements were described by Boltzmann relations with apparent valence approximately 1 and maximal charge transfer approximately 11 nC, and were reduced by the addition of sugar or phlorizin. The differences between SGLT1 and SGLT2 were that (i) the apparent affinity constant (K0.5) for alphaMG (approximately 3 mM) was an order of magnitude higher for SGLT2; (ii) SGLT2 excluded galactose, suggesting discrete sugar binding; (iii) K0.5 for Na+ was lower in SGLT2; and (iv) the Hill coefficient for Na+ was 1 for SGLT2 but 2 for SGLT1. Simulations of the six-state kinetic model previously proposed for SGLT1 indicated that many of the kinetic properties observed in SGLT2 are expected by simply reducing the Na+/glucose coupling from 2 to 1. link: http://identifiers.org/pubmed/8955098

Despite the current wealth of high-throughput data, our understanding of signal transduction is still incomplete. Mathematical modeling can be a tool to gain an insight into such processes. Detailed biochemical modeling provides deep understanding, but does not scale well above relatively a few proteins. In contrast, logic modeling can be used where the biochemical knowledge of the system is sparse and, because it is parameter free (or, at most, uses relatively a few parameters), it scales well to large networks that can be derived by manual curation or retrieved from public databases. Here, we present an overview of logic modeling formalisms in the context of training logic models to data, and specifically the different approaches to modeling qualitative to quantitative data (state) and dynamics (time) of signal transduction. We use a toy model of signal transduction to illustrate how different logic formalisms (Boolean, fuzzy logic and differential equations) treat state and time. Different formalisms allow for different features of the data to be captured, at the cost of extra requirements in terms of computational power and data quality and quantity. Through this demonstration, the assumptions behind each formalism are discussed, as well as their advantages and disadvantages and possible future developments. link: http://identifiers.org/pubmed/22871648

The main priority when designing cancer immuno-therapies has been to seek viable biological mechanisms that lead to permanent cancer eradication or cancer control. Understanding the delicate balance between the role of effector and memory cells on eliminating cancer cells remains an elusive problem in immunology. Here we make an initial investigation into this problem with the help of a mathematical model for oncolytic virotherapy; although the model can in fact be made general enough to be applied also to other immunological problems. According to this model, we find that long-term cancer control is associated with a large number of persistent effector cells (irrespective of the initial peak in effector cell numbers). However, this large number of persistent effector cells is sustained by a relatively large number of memory cells. Moreover, the results of the mathematical model suggest that cancer control from a dormant state cannot be predicted by the size of the memory population. link: http://identifiers.org/pubmed/25882747