SBMLBioModels: D - F

Postsynaptic Ca2+ signals of different amplitudes and durations are able to induce either long-lasting potentiation (LPT) or depression (LTD). The bidirectional character of synaptic plasticity may result at least in part from an increased or decreased responsiveness of the glutamatergic alpha-amino-3-hydroxy-5-methylisoxazole-4-propionic acid receptor (AMPA-R) due to the modification of conductance and/or channel number, and controlled by the balance between the activities of phosphorylation and dephosphorylation pathways. AMPA-R depression can be induced by a long-lived Ca2+ signal of moderate amplitude favouring the activation of the dephosphorylation pathway, whereas a shorter but higher Ca2+ signal would induce AMPA-R potentiation resulting from the preferential activation of the phosphorylation pathway. Within the framework of a model involving calcium/calmodulin-dependent protein kinase II (CaMKII), calcineurin (PP2B) and type 1 protein phosphatase (PP1), we aimed at delineating the conditions allowing a biphasic U-shaped relationship between AMPA-R and Ca2+ signal amplitude, and thus bidirectional plasticity. Our theoretical analysis shows that such a property may be observed if the phosphorylation pathway: (i) displays higher cooperativity in its Ca2+-dependence than the dephosphorylation pathway; (ii) displays a basal Ca2+-independent activity; or (iii) is directly inhibited by the dephosphorylation pathway. Because the experimentally observed inactivation of CaMKII by PP1 accounts for this latter characteristic, we aimed at verifying whether a realistic model using reported parameters values can simulate the induction of either LTP or LTD, depending on the time and amplitude characteristics of the Ca2+ signal. Our simulations demonstrate that the experimentally observed bidirectional nature of Ca2+-dependent synaptic plasticity could be the consequence of the PP1-mediated inactivation of CaMKII. link: http://identifiers.org/pubmed/12823459

A simulation model of the glucose-insulin system in the postprandial state can be useful in several circumstances, including testing of glucose sensors, insulin infusion algorithms and decision support systems for diabetes. Here, we present a new simulation model in normal humans that describes the physiological events that occur after a meal, by employing the quantitative knowledge that has become available in recent years. Model parameters were set to fit the mean data of a large normal subject database that underwent a triple tracer meal protocol which provided quasi-model-independent estimates of major glucose and insulin fluxes, e.g., meal rate of appearance, endogenous glucose production, utilization of glucose, insulin secretion. By decomposing the system into subsystems, we have developed parametric models of each subsystem by using a forcing function strategy. Model results are shown in describing both a single meal and normal daily life (breakfast, lunch, dinner) in normal. The same strategy is also applied on a smaller database for extending the model to type 2 diabetes. link: http://identifiers.org/pubmed/17926672

The kinase mammalian target of rapamycin (mTOR) exists in two multiprotein complexes (mTORC1 and mTORC2) and is a central regulator of growth and metabolism. Insulin activation of mTORC1, mediated by phosphoinositide 3-kinase (PI3K), Akt, and the inhibitory tuberous sclerosis complex 1/2 (TSC1-TSC2), initiates a negative feedback loop that ultimately inhibits PI3K. We present a data-driven dynamic insulin-mTOR network model that integrates the entire core network and used this model to investigate the less well understood mechanisms by which insulin regulates mTORC2. By analyzing the effects of perturbations targeting several levels within the network in silico and experimentally, we found that, in contrast to current hypotheses, the TSC1-TSC2 complex was not a direct or indirect (acting through the negative feedback loop) regulator of mTORC2. Although mTORC2 activation required active PI3K, this was not affected by the negative feedback loop. Therefore, we propose an mTORC2 activation pathway through a PI3K variant that is insensitive to the negative feedback loop that regulates mTORC1. This putative pathway predicts that mTORC2 would be refractory to Akt, which inhibits TSC1-TSC2, and, indeed, we found that mTORC2 was insensitive to constitutive Akt activation in several cell types. Our results suggest that a previously unknown network structure connects mTORC2 to its upstream cues and clarifies which molecular connectors contribute to mTORC2 activation. link: http://identifiers.org/pubmed/22457331

Cellular senescence, a state of irreversible cell cycle arrest, is thought to help protect an organism from cancer, yet also contributes to ageing. The changes which occur in senescence are controlled by networks of multiple signalling and feedback pathways at the cellular level, and the interplay between these is difficult to predict and understand. To unravel the intrinsic challenges of understanding such a highly networked system, we have taken a systems biology approach to cellular senescence. We report a detailed analysis of senescence signalling via DNA damage, insulin-TOR, FoxO3a transcription factors, oxidative stress response, mitochondrial regulation and mitophagy. We show in silico and in vitro that inhibition of reactive oxygen species can prevent loss of mitochondrial membrane potential, whilst inhibition of mTOR shows a partial rescue of mitochondrial mass changes during establishment of senescence. Dual inhibition of ROS and mTOR in vitro confirmed computational model predictions that it was possible to further reduce senescence-induced mitochondrial dysfunction and DNA double-strand breaks. However, these interventions were unable to abrogate the senescence-induced mitochondrial dysfunction completely, and we identified decreased mitochondrial fission as the potential driving force for increased mitochondrial mass via prevention of mitophagy. Dynamic sensitivity analysis of the model showed the network stabilised at a new late state of cellular senescence. This was characterised by poor network sensitivity, high signalling noise, low cellular energy, high inflammation and permanent cell cycle arrest suggesting an unsatisfactory outcome for treatments aiming to delay or reverse cellular senescence at late time points. Combinatorial targeted interventions are therefore possible for intervening in the cellular pathway to senescence, but in the cases identified here, are only capable of delaying senescence onset. link: http://identifiers.org/pubmed/25166345

Amino acids (aa) are not only building blocks for proteins, but also signalling molecules, with the mammalian target of rapamycin complex 1 (mTORC1) acting as a key mediator. However, little is known about whether aa, independently of mTORC1, activate other kinases of the mTOR signalling network. To delineate aa-stimulated mTOR network dynamics, we here combine a computational-experimental approach with text mining-enhanced quantitative proteomics. We report that AMP-activated protein kinase (AMPK), phosphatidylinositide 3-kinase (PI3K) and mTOR complex 2 (mTORC2) are acutely activated by aa-readdition in an mTORC1-independent manner. AMPK activation by aa is mediated by Ca2+/calmodulin-dependent protein kinase kinase β (CaMKKβ). In response, AMPK impinges on the autophagy regulators Unc-51-like kinase-1 (ULK1) and c-Jun. AMPK is widely recognized as an mTORC1 antagonist that is activated by starvation. We find that aa acutely activate AMPK concurrently with mTOR. We show that AMPK under aa sufficiency acts to sustain autophagy. This may be required to maintain protein homoeostasis and deliver metabolite intermediates for biosynthetic processes. link: http://identifiers.org/pubmed/27869123

Amino acids (aa) are not only building blocks for proteins, but also signalling molecules, with the mammalian target of rapamycin complex 1 (mTORC1) acting as a key mediator. However, little is known about whether aa, independently of mTORC1, activate other kinases of the mTOR signalling network. To delineate aa-stimulated mTOR network dynamics, we here combine a computational-experimental approach with text mining-enhanced quantitative proteomics. We report that AMP-activated protein kinase (AMPK), phosphatidylinositide 3-kinase (PI3K) and mTOR complex 2 (mTORC2) are acutely activated by aa-readdition in an mTORC1-independent manner. AMPK activation by aa is mediated by Ca2+/calmodulin-dependent protein kinase kinase β (CaMKKβ). In response, AMPK impinges on the autophagy regulators Unc-51-like kinase-1 (ULK1) and c-Jun. AMPK is widely recognized as an mTORC1 antagonist that is activated by starvation. We find that aa acutely activate AMPK concurrently with mTOR. We show that AMPK under aa sufficiency acts to sustain autophagy. This may be required to maintain protein homoeostasis and deliver metabolite intermediates for biosynthetic processes. link: http://identifiers.org/pubmed/27869123

Amino acids (aa) are not only building blocks for proteins, but also signalling molecules, with the mammalian target of rapamycin complex 1 (mTORC1) acting as a key mediator. However, little is known about whether aa, independently of mTORC1, activate other kinases of the mTOR signalling network. To delineate aa-stimulated mTOR network dynamics, we here combine a computational-experimental approach with text mining-enhanced quantitative proteomics. We report that AMP-activated protein kinase (AMPK), phosphatidylinositide 3-kinase (PI3K) and mTOR complex 2 (mTORC2) are acutely activated by aa-readdition in an mTORC1-independent manner. AMPK activation by aa is mediated by Ca2+/calmodulin-dependent protein kinase kinase β (CaMKKβ). In response, AMPK impinges on the autophagy regulators Unc-51-like kinase-1 (ULK1) and c-Jun. AMPK is widely recognized as an mTORC1 antagonist that is activated by starvation. We find that aa acutely activate AMPK concurrently with mTOR. We show that AMPK under aa sufficiency acts to sustain autophagy. This may be required to maintain protein homoeostasis and deliver metabolite intermediates for biosynthetic processes. link: http://identifiers.org/pubmed/27869123

The complexity of full-scale metabolic models is a major obstacle for their effective use in computational systems biology. The aim of model reduction is to circumvent this problem by eliminating parts of a model that are unimportant for the properties of interest. The choice of reduction method is influenced both by the type of model complexity and by the objective of the reduction; therefore, no single method is superior in all cases. In this study we present a comparative study of two different methods applied to a 20D model of yeast glycolytic oscillations. Our objective is to obtain biochemically meaningful reduced models, which reproduce the dynamic properties of the 20D model. The first method uses lumping and subsequent constrained parameter optimization. The second method is a novel approach that eliminates variables not essential for the dynamics. The applications of the two methods result in models of eight (lumping), six (elimination) and three (lumping followed by elimination) dimensions. All models have similar dynamic properties and pin-point the same interactions as being crucial for generation of the oscillations. The advantage of the novel method is that it is algorithmic, and does not require input in the form of biochemical knowledge. The lumping approach, however, is better at preserving biochemical properties, as we show through extensive analyses of the models. link: http://identifiers.org/pubmed/17010168

Aggregation of the small peptide amyloid beta (Aβ) into oligomers and fibrils in the brain is believed to be a precursor to Alzheimer's disease. Aβ is produced via multiple proteolytic cleavages of amyloid precursor protein (APP), mediated by the enzymes β- and γ-secretase. In this study, we examine the temporal dynamics of soluble (unaggregated) Aβ in the plasma and cerebral-spinal fluid (CSF) of rhesus monkeys treated with different oral doses of a γ-secretase inhibitor. A dose-dependent reduction of Aβ concentration was observed within hours of drug ingestion, for all doses tested. Aβ concentration in the CSF returned to its predrug level over the monitoring period. In contrast, Aβ concentration in the plasma exhibited an unexpected overshoot to as high as 200% of the predrug concentration, and this overshoot persisted as late as 72 hours post-drug ingestion. To account for these observations, we proposed and analyzed a minimal physiological model for Aβ dynamics that could fit the data. Our analysis suggests that the overshoot arises from the attenuation of an Aβ clearance mechanism, possibly due to the inhibitor. Our model predicts that the efficacy of Aβ clearance recovers to its basal (pretreatment) value with a characteristic time of >48 hours, matching the time-scale of the overshoot. These results point to the need for a more detailed investigation of soluble Aβ clearance mechanisms and their interaction with Aβ-reducing drugs. link: http://identifiers.org/pubmed/20411345

The process of clustering of plasma membrane receptors in response to their agonist is the first step in signal transduction. The rate of the clustering process and the size of the clusters determine further cell responses. Here we aim to demonstrate that a simple 2-differential equation mathematical model is capable of quantitative description of the kinetics of 2D or 3D cluster formation in various processes. Three mathematical models based on mass action kinetics were considered and compared with each other by their ability to describe experimental data on GPVI or CR3 receptor clustering (2D) and albumin or platelet aggregation (3D) in response to activation. The models were able to successfully describe experimental data without losing accuracy after switching between complex and simple models. However, additional restrictions on parameter values are required to match a single set of parameters for the given experimental data. The extended clustering model captured several properties of the kinetics of cluster formation, such as the existence of only three typical steady states for this system: unclustered receptors, receptor dimers, and clusters. Therefore, a simple kinetic mass-action-law-based model could be utilized to adequately describe clustering in response to activation both in 2D and in 3D. link: http://identifiers.org/pubmed/32604803

BACKGROUND: Aspergillus nidulans is a member of a diverse group of filamentous fungi, sharing many of the properties of its close relatives with significance in the fields of medicine, agriculture and industry. Furthermore, A. nidulans has been a classical model organism for studies of development biology and gene regulation, and thus it has become one of the best-characterized filamentous fungi. It was the first Aspergillus species to have its genome sequenced, and automated gene prediction tools predicted 9,451 open reading frames (ORFs) in the genome, of which less than 10% were assigned a function. RESULTS: In this work, we have manually assigned functions to 472 orphan genes in the metabolism of A. nidulans, by using a pathway-driven approach and by employing comparative genomics tools based on sequence similarity. The central metabolism of A. nidulans, as well as biosynthetic pathways of relevant secondary metabolites, was reconstructed based on detailed metabolic reconstructions available for A. niger and Saccharomyces cerevisiae, and information on the genetics, biochemistry and physiology of A. nidulans. Thereby, it was possible to identify metabolic functions without a gene associated, and to look for candidate ORFs in the genome of A. nidulans by comparing its sequence to sequences of well-characterized genes in other species encoding the function of interest. A classification system, based on defined criteria, was developed for evaluating and selecting the ORFs among the candidates, in an objective and systematic manner. The functional assignments served as a basis to develop a mathematical model, linking 666 genes (both previously and newly annotated) to metabolic roles. The model was used to simulate metabolic behavior and additionally to integrate, analyze and interpret large-scale gene expression data concerning a study on glucose repression, thereby providing a means of upgrading the information content of experimental data and getting further insight into this phenomenon in A. nidulans. CONCLUSION: We demonstrate how pathway modeling of A. nidulans can be used as an approach to improve the functional annotation of the genome of this organism. Furthermore we show how the metabolic model establishes functional links between genes, enabling the upgrade of the information content of transcriptome data. link: http://identifiers.org/pubmed/18405346

A mathematical model of the early inflammatory response in transplantation is formulated with ordinary differential equations. We first consider the inflammatory events associated only with the initial surgical procedure and the subsequent ischemia/reperfusion (I/R) events that cause tissue damage to the host as well as the donor graft. These events release damage-associated molecular pattern molecules (DAMPs), thereby initiating an acute inflammatory response. In simulations of this model, resolution of inflammation depends on the severity of the tissue damage caused by these events and the patient's (co)-morbidities. We augment a portion of a previously published mathematical model of acute inflammation with the inflammatory effects of T cells in the absence of antigenic allograft mismatch (but with DAMP release proportional to the degree of graft damage prior to transplant). Finally, we include the antigenic mismatch of the graft, which leads to the stimulation of potent memory T cell responses, leading to further DAMP release from the graft and concomitant increase in allograft damage. Regulatory mechanisms are also included at the final stage. Our simulations suggest that surgical injury and I/R-induced graft damage can be well-tolerated by the recipient when each is present alone, but that their combination (along with antigenic mismatch) may lead to acute rejection, as seen clinically in a subset of patients. An emergent phenomenon from our simulations is that low-level DAMP release can tolerize the recipient to a mismatched allograft, whereas different restimulation regimens resulted in an exaggerated rejection response, in agreement with published studies. We suggest that mechanistic mathematical models might serve as an adjunct for patient- or sub-group-specific predictions, simulated clinical studies, and rational design of immunosuppression. link: http://identifiers.org/doi/10.3389/fimmu.2015.00484

The cell fate decision of multi-potent pancreatic progenitor cells between the exocrine and endocrine lineages is regulated by Notch signalling, mediated by cell-cell interactions. However, canonical models of Notch-mediated lateral inhibition cannot explain the scattered spatial distribution of endocrine cells and the cell-type ratio in the developing pancreas. Based on evidence from acinar-to-islet cell transdifferentiation in vitro, we propose that lateral stabilization, i.e. positive feedback between adjacent progenitor cells, acts in parallel with lateral inhibition to regulate pattern formation in the pancreas. A simple mathematical model of transcriptional regulation and cell-cell interaction reveals the existence of multi-stability of spatial patterns whose simultaneous occurrence causes scattering of endocrine cells in the presence of noise. The scattering pattern allows for control of the endocrine-to-exocrine cell-type ratio by modulation of lateral stabilization strength. These theoretical results suggest a previously unrecognized role for lateral stabilization in lineage specification, spatial patterning and cell-type ratio control in organ development. link: http://identifiers.org/pubmed/23193107

The circadian clock is an endogenous timekeeper that allows organisms to anticipate and adapt to the daily variations of their environment. The plant clock is an intricate network of interlocked feedback loops, in which transcription factors regulate each other to generate oscillations with expression peaks at specific times of the day. Over the last decade, mathematical modeling approaches have been used to understand the inner workings of the clock in the model plant Arabidopsis thaliana. Those efforts have produced a number of models of ever increasing complexity. Here, we present an alternative model that combines a low number of equations and parameters, similar to the very earliest models, with the complex network structure found in more recent ones. This simple model describes the temporal evolution of the abundance of eight clock gene mRNA/protein and captures key features of the clock on a qualitative level, namely the entrained and free-running behaviors of the wild type clock, as well as the defects found in knockout mutants (such as altered free-running periods, lack of entrainment, or changes in the expression of other clock genes). Additionally, our model produces complex responses to various light cues, such as extreme photoperiods and non-24 h environmental cycles, and can describe the control of hypocotyl growth by the clock. Our model constitutes a useful tool to probe dynamical properties of the core clock as well as clock-dependent processes. link: http://identifiers.org/pubmed/26904049

We analyze on a model biochemical system the effect of a coupling between two instability-generating mechanisms. The system considered is that of two allosteric enzymes coupled in series and activated by their respective products. In addition to simple periodic oscillations, the system can exhibit a variety of new modes of dynamic behavior; coexistence between two stable periodic regimes (birhythmicity), random oscillations (chaos), and coexistence of a stable periodic regime with a stable steady state (hard excitation) or with chaos. The relationship between these patterns of temporal self-organization is analyzed as a function of the control parameters of the model. Chaos and birhythmicity appear to be rare events in comparison with simple periodic behavior. We discuss the relevance of these results with respect to the regularity of most biological rhythms. link: http://identifiers.org/pubmed/6960354

The study of the molecular mechanisms determining cellular programs of proliferation, differentiation, and apoptosis is currently attracting much attention. Recent studies have demonstrated that the system of cell-cycle control based on the transcriptional regulation of the expression of specific genes is responsible for the transition between programs. These groups of functionally connected genes from so-called gene networks characterized by numerous feedbacks and a complex behavioral dynamics. Computer simulation methods have been applied to studying the dynamics of gene networks regulating the cell cycle of vertebrates. The data on the regulation of the key genes obtained from the CYCLE-TRRD database have been used as a basis to construct gene networks of different degrees of complexity controlling the G1/S transition, one of the most important stages of the cell cycle. The behavior dynamics of the model constructed has been analyzed. Two qualitatively different functional modes of the system has been obtained. It has also been shown that the transition between these modes depends on the duration of the proliferation signal. It has also been demonstrated that the additional feedback from factor E2F to genes c-fos and c-jun, which was predicted earlier based on the computer analysis of promoters, plays an important role in the transition of the cell to the S phase. link: http://identifiers.org/pubmed/14582399

Cut-out switch model

Membrane identity and GTPase cascades regulated by toggle and cut-out switches

Perla Del Conte-Zerial, Lutz Brusch, Jochen C Rink, Claudio Collinet, Yannis Kalaidzidis, Marino Zerial, and Andreas Deutsch: Molecular Systems Biology, 4:206, 15 July 2008, doi:10.1038/msb.2008.45

This is the cut-out switch model for the Rab5 - Rab7 transition, also referred to as model 2 in the original publication.

This model is not completely described in all details in the publication. Thanks go to Barbara Szomolay and Lutz Brusch for finding and clarifying this. According to Dr. Brusch this model represents the mechanism identified by the qualitative analysis in the article in the scenario deemed most useful by the authors. For the time-course simulations it was necessary to add a time dependency to one of the parameters, which is only verbally described in the article.

As argued in the publication the switch between early and late endosomes can be triggered by a parameter change. While with fixed parameter values each switch just converges to one steady state from its initial conditions and stays there, endosomes should switch between two different states. These changes would in reality of course depend on many different factors, such as cargo composition and amount in the specific endosome, its location and some additional cellular control mechanisms and encompass many different parameters. To keep the model simple the authors chose to add a time dependency to only one reaction - ke in the activation of RAB5 is multiplied with a term monotonously increasing over time from 0 to 1. They also hard coded a time dependence in this term, 100 minutes, to make the switch occur after several hundred minutes. As long as this modulating term remains monotonic all resulting time courses should look similar, with the switching behavior depending on the initial conditions and whether the term is increasing or decreasing. Monotonic increase is a reasonable assumption for the described mechanism of cargo accumulation.

Not explicitly described in the article:

activation of Rab5 (time): $r*ke*time/(100+time)/(1+e_{(kg-R)*kf})$ instead of $r*ke/(1+e_{(kg-R)*kf})$

This model originates from BioModels Database: A Database of Annotated Published Models. It is copyright (c) 2005-2009 The BioModels Team.

For more information see the terms of use.

To cite BioModels Database, please use Le Novère N., Bornstein B., Broicher A., Courtot M., Donizelli M., Dharuri H., Li L., Sauro H., Schilstra M., Shapiro B., Snoep J.L., Hucka M. (2006) BioModels Database: A Free, Centralized Database of Curated, Published, Quantitative Kinetic Models of Biochemical and Cellular Systems Nucleic Acids Res., 34: D689-D691.

Viruses rely on their host for reproduction. Here, we made use of genomic and structural information to create a biomass function capturing the amino and nucleic acid requirements of SARSCoV- 2. Incorporating this biomass function into a stoichiometric metabolic model of the human lung cell and applying metabolic flux balance analysis, we identified host-based metabolic perturbations inhibiting SARS-CoV-2 reproduction. Our results highlight reactions in the central metabolism, as well as amino acid and nucleotide biosynthesis pathways. By incorporating host cellular maintenance into the model based on available protein expression data from human lung cells, we find thaViruses rely on their host for reproduction. Here, we made use of genomic and structural information to create a biomass function capturing the amino and nucleic acid requirements of SARSCoV- 2. Incorporating this biomass function into a stoichiometric metabolic model of the human lung cell and applying metabolic flux balance analysis, we identified host-based metabolic perturbations inhibiting SARS-CoV-2 reproduction. Our results highlight reactions in the central metabolism, as well as amino acid and nucleotide biosynthesis pathways. By incorporating host cellular maintenance into the model based on available protein expression data from human lung cells, we find that only few of these metabolic perturbations are able to selectively inhibit virus reproduction. Some of the catalysing enzymes of such reactions have demonstrated interactions with existing drugs, which can be used for experimental testing of the presented predictions using gene knockouts and RNA interference techniques. In summary, the developed computational approach offers a platform for rapid, experimentally testable generation of drug predictions against existing and emerging viruses based on their biomass requirements.t only few of these metabolic perturbations are able to selectively inhibit virus reproduction. Some of the catalysing enzymes of such reactions have demonstrated interactions with existing drugs, which can be used for experimental testing of the presented predictions using gene knockouts and RNA interference techniques. In summary, the developed computational approach offers a platform for rapid, experimentally testable generation of drug predictions against existing and emerging viruses based on their biomass requirements. link: http://identifiers.org/doi/10.26508/LSA.202000869

Photoreceptor cells finely adjust their sensitivity and electrical response according to changes in light stimuli as a direct consequence of the feedback and regulation mechanisms in the phototransduction cascade. In this study, we employed a systems biology approach to develop a dynamic model of vertebrate rod phototransduction that accounts for the details of the underlying biochemistry. Following a bottom-up strategy, we first reproduced the results of a robust model developed by Hamer et al. (Vis. Neurosci., 2005, 22(4), 417), and then added a number of additional cascade reactions including: (a) explicit reactions to simulate the interaction between the activated effector and the regulator of G-protein signalling (RGS); (b) a reaction for the reformation of the G-protein from separate subunits; (c) a reaction for rhodopsin (R) reconstitution from the association of the opsin apoprotein with the 11-cis-retinal chromophore; (d) reactions for the slow activation of the cascade by opsin. The extended network structure successfully reproduced a number of experimental conditions that were inaccessible to prior models. With a single set of parameters the model was able to predict qualitative and quantitative features of rod photoresponses to light stimuli ranging over five orders of magnitude, in normal and altered conditions, including genetic manipulations of the cascade components. In particular, the model reproduced the salient dynamic features of the rod from Rpe65(-/-) animals, a well established model for Leber congenital amaurosis and vitamin A deficiency. The results of this study suggest that a systems-level approach can help to unravel the adaptation mechanisms in normal and in disease-associated conditions on a molecular basis. link: http://identifiers.org/pubmed/19756313

Zileuton, a 5-lipoxygenase (5LO) inhibitor, displays complex pharmaokinetic (PK)-pharmacodynamic (PD) behavior. Available clinical data indicate a lack of dose-bronchodilatory response during initial treatment, with a dose response developing after ~1-2 weeks. We developed a quantitative systems pharmacology (QSP) model to understand the mechanism behind this phenomenon. The model described the release, maturation, and trafficking of eosinophils into the airways, leukotriene synthesis by the 5LO enzyme, leukotriene signaling and bronchodilation, and the PK of zileuton. The model provided a plausible explanation for the two-phase bronchodilatory effect of zileuton-the short-term bronchodilation was due to leukotriene inhibition and the long-term bronchodilation was due to inflammatory cell infiltration blockade. The model also indicated that the theoretical maximum bronchodilation of both 5LO inhibition and leukotriene receptor blockade is likely similar. QSP modeling provided interesting insights into the effects of leukotriene modulation.CPT: Pharmacometrics & Systems Pharmacology (2013) 2, e74; doi:10.1038/psp.2013.49; advance online publication 11 September 2013. link: http://identifiers.org/pubmed/24026253

A mathematical model for the electrophysiological responses of a rabbit sinoatrial node cell that is based on whole cell recordings from enzymatically isolated single pacemaker cells at 37 degrees C has been developed. The ion channels, Na(+)-K+ and Ca2+ pumps, and Na(+)-Ca2+ exchanger in the surface membrane (sarcolemma) are described using equations for these known currents in mammalian pacemaker cells. The extracellular environment is treated as a diffusion-limited space, and the myoplasm contains Ca(2+)-binding proteins (calmodulin and troponin). Original features of this model include 1) new equations for the hyperpolarization-activated inward current, 2) assessment of the role of the transient-type Ca2+ current during pacemaker depolarization, 3) inclusion of an Na+ current based on recent experimental data, and 4) demonstration of the possible influence of pump and exchanger currents and background currents on the pacemaker rate. This model provides acceptable fits to voltage-clamp and action potential data and can be used to seek biophysically based explanations of the electrophysiological activity in the rabbit sinoatrial node cell. link: http://identifiers.org/pubmed/8166247

We have extended our compartmental model [Am. J. Physiol. 266 (Cell Physiol. 35): C832-C852, 1994] of the single rabbit sinoatrial node (SAN) cell so that it can simulate cellular responses to bath applications of ACh and isoprenaline as well as the effects of neuronally released ACh. The model employs three different types of muscarinic receptors to explain the variety of responses observed in mammalian cardiac pacemaking cells subjected to vagal stimulation. The response of greatest interest is the ACh-sensitive change in cycle length that is not accompanied by a change in action potential duration or repolarization or hyperpolarization of the maximum diastolic potential. In this case, an ACh-sensitive K+ current is not involved. Membrane hyperpolarization occurs in response to much higher levels of vagal stimulation, and this response is also mimicked by the model. Here, an ACh-sensitive K+ current is involved. The well-known phase-resetting response of the SAN cell to single and periodically applied vagal bursts of impulses is also simulated in the presence and absence of the beta-agonist isoprenaline. Finally, the responses of the SAN cell to longer continuous trains of periodic vagal stimulation are simulated, and this can result in the complete cessation of pacemaking. Therefore, this model is 1) applicable over the full range of intensity and pattern of vagal input and 2) can offer biophysically based explanations for many of the phenomena associated with the autonomic control of cardiac pacemaking. link: http://identifiers.org/pubmed/10362707

Adrenal secretory rates of cortisol and arterial concentrations of adrenocorticotropin (ACTH) were measured in conscious trained dogs subjected to intravenous infusion of ACTH. To investigate the causal relation of ACTH to the secretion of cortisol, a mechanistic mathematical model based on current hypotheses of adrenocortical function was constructed and tested. It is widely believed that ACTH stimulates cortisol secretion through adenosine 3',5'-cyclic monophosphate (cAMP), which provides substrate cholesterol by activating cholesterol ester hydrolase and facilitating transport of cholesterol to the side-chain cleavage enzyme. In addition, cholesterol modulates its own synthesis by inhibiting beta-hydroxy-beta-methylglutaryl (HMG)-CoA reductase in the adrenocortical cell. These and other steps in the biosynthetic reaction sequence were described using differential equations subject to the additional constraints imposed by available measurements of intracellular quantities. The resulting model is consistent with many of the known characteristics of the canine adrenal response to ACTH. In this model, steady-state nonlinearities arise from cooperative binding of cAMP to its receptor protein and saturation of mitochondrial pregnenolone transport. The transient response is dominated by a depletable pool of intracellular free cholesterol. Other inferences based on the model are presented, and a quantifiable cellular basis for increased adrenal sensitivity to ACTH is proposed. link: http://identifiers.org/pubmed/6326602

The anti-tumour and pro-tumour roles of Th1/Th2 immune cells and M1/M2 macrophages have been documented by numerous experimental studies. However, it is still unknown how these immune cells interact with each other to control tumour dynamics. Here, we use a mathematical model for the interactions between mouse melanoma cells, Th2/Th1 cells and M2/M1 macrophages, to investigate the unknown role of the re-polarisation between M1 and M2 macrophages on tumour growth. The results show that tumour growth is associated with a type-II immune response described by large numbers of Th2 and M2 cells. Moreover, we show that (i) the ratio k of the transition rates k12 (for the re-polarisation M1→M2) and k21 (for the re-polarisation M2→M1) is important in reducing tumour population, and (ii) the particular values of these transition rates control the delay in tumour growth and the final tumour size. We also perform a sensitivity analysis to investigate the effect of various model parameters on changes in the tumour cell population, and confirm that the ratio k alone and the ratio of M2 and M1 macrophage populations at earlier times (e.g., day 7) cannot always predict the final tumour size. link: http://identifiers.org/pubmed/26551154

Genome-scale metabolic network models have been successfully used to describe metabolism in a variety of microbial organisms as well as specific mammalian cell types and organelles. This systems-based framework enables the exploration of global phenotypic effects of gene knockouts, gene insertion, and up-regulation of gene expression. We have developed a genome-scale metabolic network model (AraGEM) covering primary metabolism for a compartmentalized plant cell based on the Arabidopsis (Arabidopsis thaliana) genome. AraGEM is a comprehensive literature-based, genome-scale metabolic reconstruction that accounts for the functions of 1,419 unique open reading frames, 1,748 metabolites, 5,253 gene-enzyme reaction-association entries, and 1,567 unique reactions compartmentalized into the cytoplasm, mitochondrion, plastid, peroxisome, and vacuole. The curation process identified 75 essential reactions with respective enzyme associations not assigned to any particular gene in the Kyoto Encyclopedia of Genes and Genomes or AraCyc. With the addition of these reactions, AraGEM describes a functional primary metabolism of Arabidopsis. The reconstructed network was transformed into an in silico metabolic flux model of plant metabolism and validated through the simulation of plant metabolic functions inferred from the literature. Using efficient resource utilization as the optimality criterion, AraGEM predicted the classical photorespiratory cycle as well as known key differences between redox metabolism in photosynthetic and nonphotosynthetic plant cells. AraGEM is a viable framework for in silico functional analysis and can be used to derive new, nontrivial hypotheses for exploring plant metabolism. link: http://identifiers.org/pubmed/20044452

Circulatory autregulation is the phenomenon whereby an isolated organ can maintain a constant or almost-constant blood flow rate over a range of perfusion pressures. A mathematical model is developed, based on work reported in the physiological literature, and tuned to show that autoregulation can be accomplished by pressure-induced oscillations in arteriolar radius. Various features known lo be exhibited by skeletal muscle and by stretch receptors are incorporated in the model ofsmooth muscle surrounding the arterioles. link: http://identifiers.org/doi/10.1080/00207178608933494

Abstract

We present a phase-space analysis of a mathematical model of tumor growth with an immune response and chemotherapy. We prove that all orbits are bounded and must converge to one of several possible equilibrium points. Therefore, the long-term behavior of an orbit is classified according to the basin of attraction in which it starts. The addition of a drug term to the system can move the solution trajectory into a desirable basin of attraction. We show that the solutions of the model with a time-varying drug term approach the solutions of the system without the drug once traatment has stopped. We present numerical experiments in which optimal control therapy is able to drive the system into a desirable basin of attraction, whereas traditional pulsed chemotherapy is not.

Volume 37, Issue 11, June 2003, Pages 1221-1244 link: http://identifiers.org/doi/10.1016/S0895-7177(03)00133-X

Mathematical models of tumor-immune interactions provide an analytic framework in which to address specific questions about tumor-immune dynamics. We present a new mathematical model that describes tumor-immune interactions, focusing on the role of natural killer (NK) and CD8+ T cells in tumor surveillance, with the goal of understanding the dynamics of immune-mediated tumor rejection. The model describes tumor-immune cell interactions using a system of differential equations. The functions describing tumor-immune growth, response, and interaction rates, as well as associated variables, are developed using a least-squares method combined with a numerical differential equations solver. Parameter estimates and model validations use data from published mouse and human studies. Specifically, CD8+ T-tumor and NK-tumor lysis data from chromium release assays as well as in vivo tumor growth data are used. A variable sensitivity analysis is done on the model. The new functional forms developed show that there is a clear distinction between the dynamics of NK and CD8+ T cells. Simulations of tumor growth using different levels of immune stimulating ligands, effector cells, and tumor challenge are able to reproduce data from the published studies. A sensitivity analysis reveals that the variable to which the model is most sensitive is patient specific, and can be measured with a chromium release assay. The variable sensitivity analysis suggests that the model can predict which patients may positively respond to treatment. Computer simulations highlight the importance of CD8+ T-cell activation in cancer therapy. link: http://identifiers.org/pubmed/16140967

We investigate a mathematical model of tumor-immune interactions with chemotherapy, and strategies for optimally administering treatment. In this paper we analyze the dynamics of this model, characterize the optimal controls related to drug therapy, and discuss numerical results of the optimal strategies. The form of the model allows us to test and compare various optimal control strategies, including a quadratic control, a linear control, and a state-constraint. We establish the existence of the optimal control, and solve for the control in both the quadratic and linear case. In the linear control case, we show that we cannot rule out the possibility of a singular control. An interesting aspect of this paper is that we provide a graphical representation of regions on which the singular control is optimal. link: http://identifiers.org/pubmed/17306310

It is known that a beneficial cancer treatment approach for a single patient often involves the administration of more than one type of therapy. The question of how best to combine multiple cancer therapies, however, is still open. In this study, we investigate the theoretical interaction of three treatment types (two biological therapies and one chemotherapy) with a growing cancer, and present an analysis of an optimal control strategy for administering all three therapies in combination. In the situations with controls introduced linearly, we find that there are conditions on which the controls exist singularly. Although bang-bang controls (on-off) reflect the drug treatment approach that is often implemented clinically, we have demonstrated, in the context of our mathematical model, that there can exist regions on which this may not be the best strategy for minimizing a tumor burden. We characterize the controls in singular regions by taking time derivatives of the switching functions. We will examine these representations and the conditions necessary for the controls to be minimizing in the singular region. We begin by assuming only one of the controls is singular on a given interval. Then we analyze the conditions on which a pair and then all three controls are singular. link: https://scholarship.claremont.edu/hmcfacpub/439/

We investigate a mathematical population model of tumor-immune interactions. Thepopulations involved are tumor cells, specific and non-specific immune cells, and con-centrations of therapeutic treatments. We establish the existence of an optimal con-trol for this model and provide necessary conditions for the optimal control triple forsimultaneous application of chemotherapy, tumor infiltrating lymphocyte (TIL) ther-apy, and interleukin-2 (IL-2) treatment. We discuss numerical results for the combina-tion of the chemo-immunotherapy regimens. We find that the qualitative nature of ourresults indicates that chemotherapy is the dominant intervention with TIL interactingin a complementary fashion with the chemotherapy. However, within the optimal con-trol context, the interleukin-2 treatment does not become activated for the estimatedparameter ranges. link: http://identifiers.org/doi/10.1142/S0218339008002435

One of the most challenging tasks in constructing a mathematical model of cancer treatment is the calculation of biological parameters from empirical data. This task becomes increasingly difficult if a model involves several cell populations and treatment modalities. A sophisticated model constructed by de Pillis et al., Mixed immunotherapy and chemotherapy of tumours: Modelling, applications and biological interpretations, J. Theor. Biol. 238 (2006), pp. 841-862; involves tumour cells, specific and non-specific immune cells (natural killer (NK) cells, CD8+T cells and other lymphocytes) and employs chemotherapy and two types of immunotherapy (IL-2 supplementation and CD8+T-cell infusion) as treatment modalities. Despite the overall success of the aforementioned model, the problem of illustrating the effects of IL-2 on a growing tumour remains open. In this paper, we update the model of de Pillis et al. and then carefully identify appropriate values for the parameters of the new model according to recent empirical data. We determine new NK and tumour antigen-activated CD8+T-cell count equilibrium values; we complete IL-2 dynamics; and we modify the model in de Pillis et al. to allow for endogenous IL-2 production, IL-2-stimulated NK cell proliferation and IL-2-dependent CD8+T-cell self-regulations. Finally, we show that the potential patient-specific efficacy of immunotherapy may be dependent on experimentally determinable parameters. link: http://identifiers.org/doi/10.1080/17486700802216301

Abstract. We present a mathematical model to study the effects of the regu-latory T cells (T reg ) on Renal Cell Carcinoma (RCC) treatment with sunitinib.The drug sunitinib inhibits the natural self-regulation of the immune system,allowing the effector components of the immune system to function for longerperiods of time. This mathematical model builds upon our non-linear ODEmodel by de Pillis et al. (2009) [13] to incorporate sunitinib treatment, regula-tory T cell dynamics, and RCC-specific parameters. The model also elucidatesthe roles of certain RCC-specific parameters in determining key differences be-tween in silico patients whose immune profiles allowed them to respond wellto sunitinib treatment, and those whose profiles did not.Simulations from our model are able to produce results that reflect clinicaloutcomes to sunitinib treatment such as: (1) sunitinib treatments followingstandard protocols led to improved tumor control (over no treatment) in about40% of patients; (2) sunitinib treatments at double the standard dose led to agreater response rate in about 15% the patient population; (3) simulations ofpatient response indicated improved responses to sunitinib treatment when thepatient’s immune strength scaling and the immune system strength coefficientsparameters were low, allowing for a slightly stronger natural immune response link: http://identifiers.org/doi/10.3934/dcdsb.2013.18.915

Secretion of insulin by electrically coupled populations of pancreatic beta -cells is governed by bursting electrical activity. Isolated beta -cells, however, exhibit atypical bursting or continuous spike activity. We study bursting as an emergent property of the population, focussing on interactions among the subclass of spiking cells. These are modelled by equipping the fast subsystem with a saddle-node-loop bifurcation, which makes it monostable. Such cells can only spike tonically or remain silent when isolated, but can be induced to burst with weak diffusive coupling. With stronger coupling, the cells revert to tonic spiking. We demonstrate that the addition of noise dramatically increases, via a phenomenon like stochastic resonance, the coupling range over which bursting is seen. link: http://identifiers.org/pubmed/11093836

Oscillations are crucial to the normal function of living organisms, across a wide variety of biological processes. In eukaryotes, oscillatory dynamics are thought to arise from interactions at the protein and RNA levels; however, the role of non-coding RNA in regulating these dynamics remains understudied. In this work, we show how non-coding RNA acting as microRNA (miRNA) sponges in a conserved miRNA - transcription factor feedback motif, can give rise to oscillatory behaviour, and how to test for this experimentally. Control of these non-coding RNA can dynamically create oscillations or stability, and we show how this behaviour predisposes to oscillations in the stochastic limit. These results, supported by emerging evidence for the role of miRNA sponges in development, point towards key roles of different species of miRNA sponges, such as circular RNA, potentially in the maintenance of yet unexplained oscillatory behaviour. These results help to provide a paradigm for understanding functional differences between the many redundant, but distinct RNA species thought to act as miRNA sponges in nature, such as long non-coding RNA, pseudogenes, competing mRNA, circular RNA, and3' UTRs. link: http://identifiers.org/pubmed/30385313

The mutualistic association between leguminous plants and endosymbiotic rhizobial bacteria is a paradigmatic example of a symbiosis driven by metabolic exchanges. Here, we report the reconstruction and modelling of a genome-scale metabolic network of Medicago truncatula (plant) nodulated by Sinorhizobium meliloti (bacterium). The reconstructed nodule tissue contains five spatially distinct developmental zones and encompasses the metabolism of both the plant and the bacterium. Flux balance analysis (FBA) suggests that the metabolic costs associated with symbiotic nitrogen fixation are primarily related to supporting nitrogenase activity, and increasing N2-fixation efficiency is associated with diminishing returns in terms of plant growth. Our analyses support that differentiating bacteroids have access to sugars as major carbon sources, ammonium is the main nitrogen export product of N2-fixing bacteria, and N2 fixation depends on proton transfer from the plant cytoplasm to the bacteria through acidification of the peribacteroid space. We expect that our model, called 'Virtual Nodule Environment' (ViNE), will contribute to a better understanding of the functioning of legume nodules, and may guide experimental studies and engineering of symbiotic nitrogen fixation. link: http://identifiers.org/pubmed/32444627

The vertebrate unfolded protein response (UPR) is characterized by multiple interacting nodes among its three pathways, yet the logic underlying this regulatory complexity is unclear. To begin to address this issue, we created a computational model of the vertebrate UPR that was entrained upon and then validated against experimental data. As part of this validation, the model successfully predicted the phenotypes of cells with lesions in UPR signaling, including a surprising and previously unreported differential role for the eIF2α phosphatase GADD34 in exacerbating severe stress but ameliorating mild stress. We then used the model to test the functional importance of a feedforward circuit within the PERK/CHOP axis and of cross-regulatory control of BiP and CHOP expression. We found that the wiring structure of the UPR appears to balance the ability of the response to remain sensitive to endoplasmic reticulum stress and to be deactivated rapidly by improved protein-folding conditions. This model should serve as a valuable resource for further exploring the regulatory logic of the UPR. link: http://identifiers.org/pubmed/29668363

link: http://identifiers.org/pubmed/2578676

Metabolic networks adapt to changes in their environment by modulating the activity of their enzymes and transporters; often by changing their abundance. Understanding such quantitative changes can shed light onto how metabolic adaptation works, or how it can fail and lead to a metabolically dysfunctional state. We propose a strategy to quantify metabolic protein requirements for cofactor-utilising enzymes and transporters through constraint-based modelling. The first eukaryotic genome-scale metabolic model to comprehensively represent iron metabolism was constructed, extending the most recent community model of the Saccharomyces cerevisiae metabolic network. Partial functional impairment of the genes involved in the maturation of iron-sulphur (Fe-S) proteins was investigated employing the model and the in silico analysis revealed extensive rewiring of the fluxes in response to this functional impairment, despite its marginal phenotypic effect. The optimal turnover rate of enzymes bearing ion cofactors can be determined via this novel approach; yeast metabolism, at steady state, was determined to employ a constant turnover of its iron-recruiting enzyme at a rate of 3.02 × 10 -11  mmol·(g biomass) -1 ·h  -1 . link: http://identifiers.org/pubmed/30578666

How cells manage to get equal distribution of their structures and molecules at cell division is a crucial issue in biology. In principle, a feedback mechanism could always ensure equality by measuring and correcting the distribution in the progeny. However, an elegant alternative could be a mechanism relying on self-organization, with the interplay between system properties and cell geometry leading to the emergence of equal partitioning. The problem is exemplified by the bacterial Min system that defines the division site by oscillating from pole to pole. Unequal partitioning of Min proteins at division could negatively impact system performance and cell growth because of loss of Min oscillations and imprecise mid-cell determination. In this study, we combine live cell and computational analyses to show that known properties of the Min system together with the gradual reduction of protein exchange through the constricting septum are sufficient to explain the observed highly precise spontaneous protein partitioning. Our findings reveal a novel and effective mechanism of protein partitioning in dividing cells and emphasize the importance of self-organization in basic cellular processes. link: http://identifiers.org/pubmed/21206490

The ionic currents underlying autorhythmicity of the mammalian sinoatrial node and their wider contribution to each phase of the action potential have been investigated in this study using a new single cell mathematical model. The new model provides a review and update of existing formulations of sinoatrial node membrane currents, derived from a wide range of electrophysiological data available in the literature. Simulations of spontaneous activity suggest that the dominant mechanism underlying pacemaker depolarisation is the inward background Na+ current, ib,Na. In contrast to previous models, the decay of the delayed rectifying K+ current, iK, was insignificant during this phase. Despite the presence of a pseudo-outward background current throughout the pacemaker range of potentials (Na-K pump+leak currents), the hyperpolarisation-activated current i(f) was not essential to pacemaker activity. A closer inspection of the current-voltage characteristics of the model revealed that the "instantaneous" time-independent current was inward for holding potentials in the pacemaker range, which rapidly became outward within 2 ms due to the inactivation of the L-type Ca2+ current, iCa,L. This suggests that reports in the literature in which the net background current is outward throughout the pacemaker range of potentials may be exaggerated. The magnitudes of the action potential overshoot and the maximum diastolic potential were determined largely by the reversal potentials of iCa,L and iK respectively. The action potential was sustained by the incomplete deactivation of iCa,L and the Na-Ca exchanger, iNaCa. Despite the incorporation of "square-root" activation by [K]o of all K+ currents, the model was unable to correctly simulate the response to elevated [K]o. link: http://identifiers.org/pubmed/8869126

Chimeric drugs with selective potential toward specific cell types constitute one of the most promising forefronts of modern Pharmacology. We present a mathematical model to test and optimize these synthetic constructs, as an alternative to conventional empirical design. We take as a case study a chimeric construct composed of epidermal growth factor (EGF) linked to different mutants of interferon (IFN). Our model quantitatively reproduces all the experimental results, illustrating how chimeras using mutants of IFN with reduced affinity exhibit enhanced selectivity against cell overexpressing EGF receptor. We also investigate how chimeric selectivity can be improved based on the balance between affinity rates, receptor abundance, activity of ligand subunits, and linker length between subunits. The simplicity and generality of the model facilitate a straightforward application to other chimeric constructs, providing a quantitative systematic design and optimization of these selective drugs against certain cell-based diseases, such as Alzheimer's and cancer.CPT: Pharmacometrics & Systems Pharmacology (2013) 2, e26; doi:10.1038/psp.2013.2; advance online publication 13 February 2013. link: http://identifiers.org/pubmed/23887616

Activation of CD8+ cytotoxic T lymphocytes (CTLs) is naturally regarded as a major antitumor mechanism of the immune system. In contrast, CD4+ T cells are commonly classified as helper T cells (HTCs) on the basis of their roles in providing help to the generation and maintenance of effective CD8+ cytotoxic and memory T cells. In order to get a better insight on the role of HTCs in a tumor immune system, we incorporate the third population of HTCs into a previous two dimensional ordinary differential equations (ODEs) model. Further we introduce the adoptive cellular immunotherapy (ACI) as the treatment to boost the immune system to fight against tumors. Compared tumor cells (TCs) and effector cells (ECs), the recruitment of HTCs changes the dynamics of the system substantially, by the effects through particular parameters, i.e., the activation rate of ECs by HTCs, π (scaled as π), and the HTCs stimulation rate by the presence of identified tumor antigens, k2 (scaled as υ2). We describe the stability regions of the interior equilibria É (no treatment case) and E+ (treatment case) in the scaled (π,υ2) parameter space respectively. Both π and υ2 can destabilize É and E+ and cause Hopf bifurcations. Our results show that HTCs might play a crucial role in the long term periodic oscillation behaviors of tumor immune system interactions. They also show that TCs may be eradicated from the patient's body under the ACI treatment. link: http://identifiers.org/doi/10.3934/dcdsb.2014.19.55

The length of the G1 phase in the cell cycle shows significant variability in different cell types and tissue types. To gain insights into the control of G1 length, we generated an E2F activity reporter that captures free E2F activity after dissociation from Rb sequestration and followed its kinetics of activation at the single-cell level, in real time. Our results demonstrate that its activity is precisely coordinated with S phase progression. Quantitative analysis indicates that there is a pre-S phase delay between E2F transcriptional dynamic and activity dynamics. This delay is variable among different cell types and is strongly modulated by the cyclin D/CDK4/6 complex activity through Rb phosphorylation. Our findings suggest that the main function of this complex is to regulate the appropriate timing of G1 length. link: http://identifiers.org/pubmed/29309421

Signal integration has a crucial role in the cell fate decision and dysregulation of the cellular signaling pathways is a primary characteristic of cancer. As a signal integrator, mTOR shows a complex dynamical behavior which determines the cell fate at different cellular processes levels, including cell cycle progression, cell survival, cell death, metabolic reprogramming, and aging. The dynamics of the complex responses to rapamycin in cancer cells have been attributed to its differential time-dependent inhibitory effects on mTORC1 and mTORC2, the two main complexes of mTOR. Two explanations were previously provided for this phenomenon: 1-Rapamycin does not inhibit mTORC2 directly, whereas it prevents mTORC2 formation by sequestering free mTOR protein (Le Chatelier's principle). 2-Components like Phosphatidic Acid (PA) further stabilize mTORC2 compared with mTORC1. To understand the mechanism by which rapamycin differentially inhibits the mTOR complexes in the cancer cells, we present a mathematical model of rapamycin mode of action based on the first explanation, i.e., Le Chatelier's principle. Translating the interactions among components of mTORC1 and mTORC2 into a mathematical model revealed the dynamics of rapamycin action in different doses and time-intervals of rapamycin treatment. This model shows that rapamycin has stronger effects on mTORC1 compared with mTORC2, simply due to its direct interaction with free mTOR and mTORC1, but not mTORC2, without the need to consider other components that might further stabilize mTORC2. Based on our results, even when mTORC2 is less stable compared with mTORC1, it can be less inhibited by rapamycin. link: http://identifiers.org/pubmed/31493485

Adenocarcinoma is the most frequent cancer affecting the prostate walnut-size gland in the male reproductive system. Such cancer may have a very slow progression or may be associated with a "dark prognosis" when tumor cells are spreading very quickly. Prostate cancers have the particular properties to be marked by the level of prostate specific antigen (PSA) in blood which allows to follow its evolution. At least in its first phase, prostate adenocarcinoma is most often hormone-dependent and, consequently, hormone therapy is a possible treatment. Since few years, hormone therapy started to be provided intermittently for improving patient's quality of life. Today, durations of on- and off-treatment periods are still chosen empirically, most likely explaining why there is no clear benefit from the survival point of view. We therefore developed a model for describing the interaction between the tumor environment, the PSA produced by hormone-dependent and hormone-independent tumor cells, respectively, and the level of androgens. Model parameters were identified using a genetic algorithm applied to the PSA time series measured in a few patients who initially received prostatectomy and were then treated by intermittent hormone therapy (LHRH analogs and anti-androgen). The measured PSA time series is quite correctly reproduced by free runs over the whole follow-up. Model parameter values allow for distinguishing different types of patient (age and Gleason score) meaning that the model can be individualized. We thus showed that the long-term evolution of the cancer can be affected by durations of on- and off-treatment periods. link: http://identifiers.org/pubmed/30292801

The filamentous fungus Neurospora crassa played a central role in the development of twentieth-century genetics, biochemistry and molecular biology, and continues to serve as a model organism for eukaryotic biology. Here, we have reconstructed a genome-scale model of its metabolism. This model consists of 836 metabolic genes, 257 pathways, 6 cellular compartments, and is supported by extensive manual curation of 491 literature citations. To aid our reconstruction, we developed three optimization-based algorithms, which together comprise Fast Automated Reconstruction of Metabolism (FARM). These algorithms are: LInear MEtabolite Dilution Flux Balance Analysis (limed-FBA), which predicts flux while linearly accounting for metabolite dilution; One-step functional Pruning (OnePrune), which removes blocked reactions with a single compact linear program; and Consistent Reproduction Of growth/no-growth Phenotype (CROP), which reconciles differences between in silico and experimental gene essentiality faster than previous approaches. Against an independent test set of more than 300 essential/non-essential genes that were not used to train the model, the model displays 93% sensitivity and specificity. We also used the model to simulate the biochemical genetics experiments originally performed on Neurospora by comprehensively predicting nutrient rescue of essential genes and synthetic lethal interactions, and we provide detailed pathway-based mechanistic explanations of our predictions. Our model provides a reliable computational framework for the integration and interpretation of ongoing experimental efforts in Neurospora, and we anticipate that our methods will substantially reduce the manual effort required to develop high-quality genome-scale metabolic models for other organisms. link: http://identifiers.org/pubmed/23935467

We develop a mathematical model to examine the role of helper and cytotoxic T cells in an anti-tumour immune response. The model comprises three ordinary differential equations describing the dynamics of the tumour cells, the helper and the cytotoxic T cells, and implicitly accounts for immunosuppressive effects. The aim is to investigate how the anti-tumour immune response varies with the level of infiltrating helper and cytotoxic T cells. Through a combination of analytical studies and numerical simulations, our model exemplifies the three Es of immunoediting: elimination, equilibrium and escape. Specifically, it reveals that the three Es of immunoediting depend highly on the infiltration rates of the helper and cytotoxic T cells. The model’s results indicate that both the helper and cytotoxic T cells play a key role in tumour elimination. They also show that combination therapies that boost the immune system and block tumour-induced immunosuppression may have a synergistic effect in reducing tumour growth. link: http://identifiers.org/doi/10.1080/23737867.2018.1465863

A fully compartmentalized genome-scale metabolic model of Saccharomyces cerevisiae that accounts for 750 genes and their associated transcripts, proteins, and reactions has been reconstructed and validated. All of the 1149 reactions included in this in silico model are both elementally and charge balanced and have been assigned to one of eight cellular locations (extracellular space, cytosol, mitochondrion, peroxisome, nucleus, endoplasmic reticulum, Golgi apparatus, or vacuole). When in silico predictions of 4154 growth phenotypes were compared to two published large-scale gene deletion studies, an 83% agreement was found between iND750's predictions and the experimental studies. Analysis of the failure modes showed that false predictions were primarily caused by iND750's limited inclusion of cellular processes outside of metabolism. This study systematically identified inconsistencies in our knowledge of yeast metabolism that require specific further experimental investigation. link: http://identifiers.org/pubmed/15197165

Metabolism is a vital cellular process, and its malfunction is a major contributor to human disease. Metabolic networks are complex and highly interconnected, and thus systems-level computational approaches are required to elucidate and understand metabolic genotype-phenotype relationships. We have manually reconstructed the global human metabolic network based on Build 35 of the genome annotation and a comprehensive evaluation of >50 years of legacy data (i.e., bibliomic data). Herein we describe the reconstruction process and demonstrate how the resulting genome-scale (or global) network can be used (i) for the discovery of missing information, (ii) for the formulation of an in silico model, and (iii) as a structured context for analyzing high-throughput biological data sets. Our comprehensive evaluation of the literature revealed many gaps in the current understanding of human metabolism that require future experimental investigation. Mathematical analysis of network structure elucidated the implications of intracellular compartmentalization and the potential use of correlated reaction sets for alternative drug target identification. Integrated analysis of high-throughput data sets within the context of the reconstruction enabled a global assessment of functional metabolic states. These results highlight some of the applications enabled by the reconstructed human metabolic network. The establishment of this network represents an important step toward genome-scale human systems biology. link: http://identifiers.org/pubmed/17267599

In this paper, a nonlinear mathematical model is proposed and analyzed to study the effect of environmental toxicant on the immune response of the body. Criteria for local stability, instability and global stability are obtained. It is shown that the immune response of the body decreases as the concentration of environmental toxicant increases, and certain criteria are obtained under which it settles down at its equilibrium level. In the absence of toxicant, an oscillatory behavior of immune system and pathogenic growth is observed. However, in the presence of toxicant, oscillatory behavior is not observed. These studies show that the toxicant may have a grave effect on our body's defense mechanism. link: http://identifiers.org/doi/10.1142/S0218339007002301

In this paper, a nonlinear mathematical model is proposed and analyzed to study the effect of environmental toxicant on the immune response of the body. Criteria for local stability, instability and global stability are obtained. It is shown that the immune response of the body decreases as the concentration of environmental toxicant increases, and certain criteria are obtained under which it settles down at its equilibrium level. In the absence of toxicant, an oscillatory behavior of immune system and pathogenic growth is observed. However, in the presence of toxicant, oscillatory behavior is not observed. These studies show that the toxicant may have a grave effect on our body's defense mechanism. link: http://identifiers.org/doi/10.1142/S0218339007002301

This paper deals with the interaction between dispersed cancer cells and the major populations of the immune system, namely, the T helper cells, T Cytotoxic cells, B cells, and antibodies produced. The system is described by a set of five ordinary differential equations. Both local and global stability of the system has been investigated. It has been observed that under appropriate conditions this interaction is capable of controlling the growth of these cancer cells. The analytical findings are supported by numerical and computational analytical methods. link: http://identifiers.org/doi/10.1142/S0218339008002605

The main purpose of this article is to formulate a deterministic mathematical model for the transmission of malaria that considers two host types in the human population. The first type is called "non-immune" comprising all humans who have never acquired immunity against malaria and the second type is called "semi-immune". Non-immune are divided into susceptible, exposed and infectious and semi-immune are divided into susceptible, exposed, infectious and immune. We obtain an explicit formula for the reproductive number, R(0) which is a function of the weight of the transmission semi-immune-mosquito-semi-immune, R(0a), and the weight of the transmission non-immune-mosquito-non-immune, R(0e). Then, we study the existence of endemic equilibria by using bifurcation analysis. We give a simple criterion when R(0) crosses one for forward and backward bifurcation. We explore the possibility of a control for malaria through a specific sub-group such as non-immune or semi-immune or mosquitoes. link: http://identifiers.org/pubmed/22880962

A proper response to rapid environmental changes is essential for cell survival and requires efficient modifications in the pattern of gene expression. In this respect, a prominent example is Hsp70, a chaperone protein whose synthesis is dynamically regulated in stress conditions. In this paper, we expand a formal model of Hsp70 heat induction originally proposed in previous articles. To accurately capture various modes of heat shock effects, we not only introduce temperature dependencies in transcription to Hsp70 mRNA and in dissociation of transcriptional complexes, but we also derive a new formal expression for the temperature dependence in protein denaturation. We calibrate our model using comprehensive sets of both previously published experimental data and also biologically justified constraints. Interestingly, we obtain a biologically plausible temperature dependence of the transcriptional complex dissociation, despite the lack of biological constraints imposed in the calibration process. Finally, based on a sensitivity analysis of the model carried out in both deterministic and stochastic settings, we suggest that the regulation of the binding of transcriptional complexes plays a key role in Hsp70 induction upon heat shock. In conclusion, we provide a model that is able to capture the essential dynamics of the Hsp70 heat induction whilst being biologically sound in terms of temperature dependencies, description of protein denaturation and imposed calibration constraints. link: http://identifiers.org/pubmed/31181241

There is growing interest in inflammation due to its involvement in many diverse medical conditions, including Alzheimer's disease, cancer, arthritis and asthma. The traditional view that resolution of inflammation is a passive process is now being superceded by an alternative hypothesis whereby its resolution is an active, anti-inflammatory process that can be manipulated therapeutically. This shift in mindset has stimulated a resurgence of interest in the biological mechanisms by which inflammation resolves. The anti-inflammatory processes central to the resolution of inflammation revolve around macrophages and are closely related to pro-inflammatory processes mediated by neutrophils and their ability to damage healthy tissue. We develop a spatially averaged model of inflammation centring on its resolution, accounting for populations of neutrophils and macrophages and incorporating both pro- and anti-inflammatory processes. Our ordinary differential equation model exhibits two outcomes that we relate to healthy and unhealthy states. We use bifurcation analysis to investigate how variation in the system parameters affects its outcome. We find that therapeutic manipulation of the rate of macrophage phagocytosis can aid in resolving inflammation but success is critically dependent on the rate of neutrophil apoptosis. Indeed our model predicts that an effective treatment protocol would take a dual approach, targeting macrophage phagocytosis alongside neutrophil apoptosis. link: http://identifiers.org/pubmed/25053556

We undertake a mathematical investigation of a model for the generation of thrombin, an enzyme central to haemostatic blood coagulation, as well as to thrombotic disorders, that is the end product of a complicated protein cascade with multiple feedbacks that ensures its production in the right place at the right time. In a laboratory setting, its central role is reflected in thrombin evolution over time being used as a measure of the ability of a patient's blood to clot. Here, we present a model for the generation of thrombin (based on earlier work) and analyse it using the method of matched asymptotic expansions to derive a sequence of simplified models that characterize the roles of distinct interactions over various timescales. In particular, we are able through the asymptotic analysis to provide simplified models that are an excellent substitute for the full model (capturing the explosive growth and decay of thrombin) and approximations for the key experimental measurements used to describe thrombin's characteristic evolution over time. The asymptotic results are validated against numerical simulations. link: http://identifiers.org/doi/10.1093/imamat/hxw007

Abscisic acid (ABA) is a key hormone regulating plant growth, development and the response to biotic and abiotic stress. ABA binding to pyrabactin resistance (PYR)/PYR1-like (PYL)/Regulatory Component of Abscisic acid Receptor (RCAR) intracellular receptors promotes the formation of stable complexes with certain protein phosphatases type 2C (PP2Cs), leading to the activation of ABA signalling. The PYR/PYL/RCAR family contains 14 genes in Arabidopsis and is currently the largest plant hormone receptor family known; however, it is unclear what functional differentiation exists among receptors. Here, we identify two distinct classes of receptors, dimeric and monomeric, with different intrinsic affinities for ABA and whose differential properties are determined by the oligomeric state of their apo forms. Moreover, we find a residue in PYR1, H60, that is variable between family members and plays a key role in determining oligomeric state. In silico modelling of the ABA activation pathway reveals that monomeric receptors have a competitive advantage for binding to ABA and PP2Cs. This work illustrates how receptor oligomerization can modulate hormonal responses and more generally, the sensitivity of a ligand-dependent signalling system. link: http://identifiers.org/pubmed/21847091

Abscisic acid (ABA) is a key hormone regulating plant growth, development and the response to biotic and abiotic stress. ABA binding to pyrabactin resistance (PYR)/PYR1-like (PYL)/Regulatory Component of Abscisic acid Receptor (RCAR) intracellular receptors promotes the formation of stable complexes with certain protein phosphatases type 2C (PP2Cs), leading to the activation of ABA signalling. The PYR/PYL/RCAR family contains 14 genes in Arabidopsis and is currently the largest plant hormone receptor family known; however, it is unclear what functional differentiation exists among receptors. Here, we identify two distinct classes of receptors, dimeric and monomeric, with different intrinsic affinities for ABA and whose differential properties are determined by the oligomeric state of their apo forms. Moreover, we find a residue in PYR1, H60, that is variable between family members and plays a key role in determining oligomeric state. In silico modelling of the ABA activation pathway reveals that monomeric receptors have a competitive advantage for binding to ABA and PP2Cs. This work illustrates how receptor oligomerization can modulate hormonal responses and more generally, the sensitivity of a ligand-dependent signalling system. link: http://identifiers.org/pubmed/21847091

We consider a simple, minimal model for signal-induced Ca2+ oscillations based on Ca(2+)-induced Ca2+ release. The model takes into account the existence of two pools of intracellular Ca2+, namely, one sensitive to inositol 1,4,5 trisphosphate (InsP3) whose synthesis is elicited by the stimulus, and one insensitive to InsP3. The discharge of the latter pool into the cytosol is activated by cytosolic Ca2+. Oscillations in cytosolic Ca2+ arise in this model either spontaneously or in an appropriate range of external stimulation; these oscillations do not require the concomitant, periodic variation of InsP3. The following properties of the model are reviewed and compared with experimental observations: (a) Control of the frequency of Ca2+ oscillations by the external stimulus or extracellular Ca2+; (b) correlation of latency with period of Ca2+ oscillations obtained at different levels of stimulation; (c) effect of a transient increase in InsP3; (d) phase shift and transient suppression of Ca2+ oscillations by Ca2+ pulses, and (e) propagation of Ca2+ waves. It is shown that on all these counts the model provides a simple, unified explanation for a number of experimental observations in a variety of cell types. The model based on Ca(2+)-induced Ca2+ release can be extended to incorporate variations in the level of InsP3 as well as desensitization of the InsP3 receptor; besides accounting for the phenomena described by the minimal model, the extended model might also account for the occurrence of complex Ca2+ oscillations. link: http://identifiers.org/pubmed/1647878

Given the ubiquitous nature of signal-induced Ca2+ oscillations, the question arises as to how cellular responses are affected by repetitive Ca2+ spikes. Among these responses, we focus on those involving protein phosphorylation. We examine, by numerical simulations of a theoretical model, the situation where a protein is phosphorylated by a Ca(2+)-activated kinase and dephosphorylated by a phosphatase. This reversible phosphorylation system is coupled to a mechanism generating cytosolic Ca2+ oscillations; for definiteness, this oscillatory mechanism is based on the process of Ca(2+)-induced Ca2+ release. The analysis shows that the average fraction of phosphorylated protein increases with the frequency of repetitive Ca2+ spikes; the latter frequency generally rises with the extent of external stimulation. Protein phosphorylation therefore provides a mechanism for the encoding of the external stimulation in terms of the frequency of signal-induced Ca2+ oscillations. Such a frequency encoding requires precise kinetic conditions on the Michaelis-Menten constants of the kinase and phosphatase, their maximal rates, and the degree of cooperativity in kinase activation by Ca2+. In particular, the most efficient encoding of Ca2+ oscillations based on protein phosphorylation occurs in conditions of zero-order ultrasensitivity, when the kinase and phosphatase are saturated by their protein substrate. The kinetic analysis uncovers a wide variety of temporal patterns of phosphorylation that could be driven by signal-induced Ca2+ oscillations. link: http://identifiers.org/pubmed/1316185

BACKGROUND: Genome-scale metabolic models are powerful tools to study global properties of metabolic networks. They provide a way to integrate various types of biological information in a single framework, providing a structured representation of available knowledge on the metabolism of the respective species. RESULTS: We reconstructed a constraint-based metabolic model of Acinetobacter baylyi ADP1, a soil bacterium of interest for environmental and biotechnological applications with large-spectrum biodegradation capabilities. Following initial reconstruction from genome annotation and the literature, we iteratively refined the model by comparing its predictions with the results of large-scale experiments: (1) high-throughput growth phenotypes of the wild-type strain on 190 distinct environments, (2) genome-wide gene essentialities from a knockout mutant library, and (3) large-scale growth phenotypes of all mutant strains on 8 minimal media. Out of 1412 predictions, 1262 were initially consistent with our experimental observations. Inconsistencies were systematically examined, leading in 65 cases to model corrections. The predictions of the final version of the model, which included three rounds of refinements, are consistent with the experimental results for (1) 91% of the wild-type growth phenotypes, (2) 94% of the gene essentiality results, and (3) 94% of the mutant growth phenotypes. To facilitate the exploitation of the metabolic model, we provide a web interface allowing online predictions and visualization of results on metabolic maps. CONCLUSION: The iterative reconstruction procedure led to significant model improvements, showing that genome-wide mutant phenotypes on several media can significantly facilitate the transition from genome annotation to a high-quality model. link: http://identifiers.org/pubmed/18840283

Modulation of the properties of AMPA receptors at the post-synaptic membrane is one of the main suggested mechanisms underlying fast synaptic transmission in the central nervous system of vertebrates. Electrophysiological recordings of single channels stimulated with agonists showed that both recombinant and native AMPA receptors visit multiple conductance states in an agonist concentration dependent manner. We propose an allosteric model of the multiple conductance states based on concerted conformational transitions of the four subunits, as an iris diaphragm. Our model predicts that the thermodynamic behaviour of the conductance states upon full and partial agonist stimulations can be described with increased affinity of receptors as they progress to higher conductance states. The model also predicts the existence of AMPA receptors in non-liganded conductive substates. However, the probability of spontaneous openings decreases with increasing conductances. Finally, we predict that the large conductance states are stabilized within the rise phase of a whole-cell EPSC in glutamatergic hippocampal neurons. Our model provides a mechanistic link between ligand concentration and conductance states that can explain thermodynamic and kinetic features of AMPA receptor gating. link: http://identifiers.org/pubmed/25629405

In this study, we have developed a multiscale systems model of interleukin (IL)-6-mediated immune regulation in Crohn's disease, by integrating intracellular signaling with organ-level dynamics of pharmacological markers underlying the disease. This model was linked to a general pharmacokinetic model for therapeutic monoclonal antibodies and used to comparatively study various biotherapeutic strategies targeting IL-6-mediated signaling in Crohn's disease. Our work illustrates techniques to develop mechanistic models of disease biology to study drug-system interaction. Despite a sparse training data set, predictions of the model were qualitatively validated by clinical biomarker data from a pilot trial with tocilizumab. Model-based analysis suggests that strategies targeting IL-6, IL-6Rα, or the IL-6/sIL-6Rα complex are less effective at suppressing pharmacological markers of Crohn's than dual targeting the IL-6/sIL-6Rα complex in addition to IL-6 or IL-6Rα. The potential value of multiscale system pharmacology modeling in drug discovery and development is also discussed.CPT: Pharmacometrics & Systems Pharmacology (2014) 3, e89; doi:10.1038/psp.2013.64; advance online publication 8 January 2014. link: http://identifiers.org/pubmed/24402116

In this study, we have developed a multiscale systems model of interleukin (IL)-6-mediated immune regulation in Crohn's disease, by integrating intracellular signaling with organ-level dynamics of pharmacological markers underlying the disease. This model was linked to a general pharmacokinetic model for therapeutic monoclonal antibodies and used to comparatively study various biotherapeutic strategies targeting IL-6-mediated signaling in Crohn's disease. Our work illustrates techniques to develop mechanistic models of disease biology to study drug-system interaction. Despite a sparse training data set, predictions of the model were qualitatively validated by clinical biomarker data from a pilot trial with tocilizumab. Model-based analysis suggests that strategies targeting IL-6, IL-6Rα, or the IL-6/sIL-6Rα complex are less effective at suppressing pharmacological markers of Crohn's than dual targeting the IL-6/sIL-6Rα complex in addition to IL-6 or IL-6Rα. The potential value of multiscale system pharmacology modeling in drug discovery and development is also discussed.CPT: Pharmacometrics & Systems Pharmacology (2014) 3, e89; doi:10.1038/psp.2013.64; advance online publication 8 January 2014. link: http://identifiers.org/pubmed/24402116

In this study, we have developed a multiscale systems model of interleukin (IL)-6-mediated immune regulation in Crohn's disease, by integrating intracellular signaling with organ-level dynamics of pharmacological markers underlying the disease. This model was linked to a general pharmacokinetic model for therapeutic monoclonal antibodies and used to comparatively study various biotherapeutic strategies targeting IL-6-mediated signaling in Crohn's disease. Our work illustrates techniques to develop mechanistic models of disease biology to study drug-system interaction. Despite a sparse training data set, predictions of the model were qualitatively validated by clinical biomarker data from a pilot trial with tocilizumab. Model-based analysis suggests that strategies targeting IL-6, IL-6Rα, or the IL-6/sIL-6Rα complex are less effective at suppressing pharmacological markers of Crohn's than dual targeting the IL-6/sIL-6Rα complex in addition to IL-6 or IL-6Rα. The potential value of multiscale system pharmacology modeling in drug discovery and development is also discussed.CPT: Pharmacometrics & Systems Pharmacology (2014) 3, e89; doi:10.1038/psp.2013.64; advance online publication 8 January 2014. link: http://identifiers.org/pubmed/24402116

In this study, we have developed a multiscale systems model of interleukin (IL)-6-mediated immune regulation in Crohn's disease, by integrating intracellular signaling with organ-level dynamics of pharmacological markers underlying the disease. This model was linked to a general pharmacokinetic model for therapeutic monoclonal antibodies and used to comparatively study various biotherapeutic strategies targeting IL-6-mediated signaling in Crohn's disease. Our work illustrates techniques to develop mechanistic models of disease biology to study drug-system interaction. Despite a sparse training data set, predictions of the model were qualitatively validated by clinical biomarker data from a pilot trial with tocilizumab. Model-based analysis suggests that strategies targeting IL-6, IL-6Rα, or the IL-6/sIL-6Rα complex are less effective at suppressing pharmacological markers of Crohn's than dual targeting the IL-6/sIL-6Rα complex in addition to IL-6 or IL-6Rα. The potential value of multiscale system pharmacology modeling in drug discovery and development is also discussed.CPT: Pharmacometrics & Systems Pharmacology (2014) 3, e89; doi:10.1038/psp.2013.64; advance online publication 8 January 2014. link: http://identifiers.org/pubmed/24402116

Estrogen is a vital hormone that regulates many biological functions within the body. These include roles in the development of the secondary sexual organs in both sexes, plus uterine angiogenesis and proliferation during the menstrual cycle and pregnancy in women. The varied biological roles of estrogens in human health also make them a therapeutic target for contraception, mitigation of the adverse effects of the menopause, and treatment of estrogen-responsive tumours. In addition, endogenous (e.g. genetic variation) and external (e.g. exposure to estrogen-like chemicals) factors are known to impact estrogen biology. To understand how these multiple factors interact to determine an individual's response to therapy is complex, and may be best approached through a systems approach.We present a physiologically-based pharmacokinetic model (PBPK) of estradiol, and validate it against plasma kinetics in humans following intravenous and oral exposure. We extend this model by replacing the intrinsic clearance term with: a detailed kinetic model of estrogen metabolism in the liver; or, a genome-scale model of liver metabolism. Both models were validated by their ability to reproduce clinical data on estradiol exposure. We hypothesise that the enhanced mechanistic information contained within these models will lead to more robust predictions of the biological phenotype that emerges from the complex interactions between estrogens and the body.To demonstrate the utility of these models we examine the known drug-drug interactions between phenytoin and oral estradiol. We are able to reproduce the approximate 50% reduction in area under the concentration-time curve for estradiol associated with this interaction. Importantly, the inclusion of a genome-scale metabolic model allows the prediction of this interaction without directly specifying it within the model. In addition, we predict that PXR activation by drugs results in an enhanced ability of the liver to excrete glucose. This has important implications for the relationship between drug treatment and metabolic syndrome.We demonstrate how the novel coupling of PBPK models with genome-scale metabolic networks has the potential to aid prediction of drug action, including both drug-drug interactions and changes to the metabolic landscape that may predispose an individual to disease development. link: http://identifiers.org/pubmed/29246152

The hypothesis that calcium release from the sarcoplasmic reticulum in cardiac muscle is induced by rises in free cytosolic calcium (Fabiato 1983, Am. J. Physiol 245) allows the possibility that the release could be at least partly regenerative. There would then be a non-linear relation between calcium current and calcium release. We have investigated this possibility in a single-cell version of the rabbit-atrial model developed by Hilgemann & Noble (1987, Proc. R. Soc. Lond. B 230). The model predicts different voltage ranges of activation for calcium-dependent processes (like the sodium-calcium exchange current, contraction or Fura-2 signals) and the calcium current, in agreement with the experimental results obtained by Earm et al. (1990, Proc. R. Soc. Lond. B 240) on exchange current tails, Cannell et al. (1987, Science, Wash. 238) by using Fura-2 signals, and Fedida et al. (1987, J. Physiol., Lond. 385) and Talo et al. (1988, Biology of isolated adult cardiac myocytes) by using contraction. However, when the Fura-2 concentration is sufficiently high (greater than 200 microM) the activation ranges become very similar as the buffering properties of Fura-2 are sufficient to remove the regenerative effect. It is therefore important to allow for the buffering properties of calcium indicators when investigating the correlation between calcium current and calcium release. link: http://identifiers.org/pubmed/1972993

Nicotinic acetylcholine receptors are transmembrane oligomeric proteins that mediate interconversions between open and closed channel states under the control of neurotransmitters. Fast in vitro chemical kinetics and in vivo electrophysiological recordings are consistent with the following multi-step scheme. Upon binding of agonists, receptor molecules in the closed but activatable resting state (the Basal state, B) undergo rapid transitions to states of higher affinities with either open channels (the Active state, A) or closed channels (the initial Inactivatable and fully Desensitized states, I and D). In order to represent the functional properties of such receptors, we have developed a kinetic model that links conformational interconversion rates to agonist binding and extends the general principles of the Monod-Wyman-Changeux model of allosteric transitions. The crucial assumption is that the linkage is controlled by the position of the interconversion transition states on a hypothetical linear reaction coordinate. Application of the model to the peripheral nicotine acetylcholine receptor (nAChR) accounts for the main properties of ligand-gating, including single-channel events, and several new relationships are predicted. Kinetic simulations reveal errors inherent in using the dose-response analysis, but justify its application under defined conditions. The model predicts that (in order to overcome the intrinsic stability of the B state and to produce the appropriate cooperativity) channel activation is driven by an A state with a Kd in the 50 nM range, hence some 140-fold stronger than the apparent affinity of the open state deduced previously. According to the model, recovery from the desensitized states may occur via rapid transit through the A state with minimal channel opening, thus without necessarily undergoing a distinct recovery pathway, as assumed in the standard 'cycle' model. Transitions to the desensitized states by low concentration 'pre-pulses' are predicted to occur without significant channel opening, but equilibrium values of IC50 can be obtained only with long pre-pulse times. Predictions are also made concerning allosteric effectors and their possible role in coincidence detection. In terms of future developments, the analysis presented here provides a physical basis for constructing more biologically realistic models of synaptic modulation that may be applied to artificial neural networks. link: http://identifiers.org/pubmed/8983160

Nicotinic acetylcholine receptors are transmembrane oligomeric proteins that mediate interconversions between open and closed channel states under the control of neurotransmitters. Fast in vitro chemical kinetics and in vivo electrophysiological recordings are consistent with the following multi-step scheme. Upon binding of agonists, receptor molecules in the closed but activatable resting state (the Basal state, B) undergo rapid transitions to states of higher affinities with either open channels (the Active state, A) or closed channels (the initial Inactivatable and fully Desensitized states, I and D). In order to represent the functional properties of such receptors, we have developed a kinetic model that links conformational interconversion rates to agonist binding and extends the general principles of the Monod-Wyman-Changeux model of allosteric transitions. The crucial assumption is that the linkage is controlled by the position of the interconversion transition states on a hypothetical linear reaction coordinate. Application of the model to the peripheral nicotine acetylcholine receptor (nAChR) accounts for the main properties of ligand-gating, including single-channel events, and several new relationships are predicted. Kinetic simulations reveal errors inherent in using the dose-response analysis, but justify its application under defined conditions. The model predicts that (in order to overcome the intrinsic stability of the B state and to produce the appropriate cooperativity) channel activation is driven by an A state with a Kd in the 50 nM range, hence some 140-fold stronger than the apparent affinity of the open state deduced previously. According to the model, recovery from the desensitized states may occur via rapid transit through the A state with minimal channel opening, thus without necessarily undergoing a distinct recovery pathway, as assumed in the standard 'cycle' model. Transitions to the desensitized states by low concentration 'pre-pulses' are predicted to occur without significant channel opening, but equilibrium values of IC50 can be obtained only with long pre-pulse times. Predictions are also made concerning allosteric effectors and their possible role in coincidence detection. In terms of future developments, the analysis presented here provides a physical basis for constructing more biologically realistic models of synaptic modulation that may be applied to artificial neural networks. link: http://identifiers.org/pubmed/8983160

Recent experiments indicate that CD4(+) Th2 cells can reject skin tumors in mice, while CD4(+) Th1 cells cannot (Mattes et al., 2003; Zhang et al., 2009). These results are surprising because CD4(+) Th1 cells are typically considered to be capable of tumor rejection. We used mathematical models to investigate this unexpected outcome. We found that neither CD4(+) Th1 nor CD4(+) Th2 cells could eliminate the cancer cells when acting alone, but that tumor elimination could be induced by recruitment of eosinophils by the Th2 cells. These recruited eosinophils had unexpected indirect effects on the decay rate of type 2 cytokines and the rate at which Th2 cells are inactivated through interactions with cancer cells. Strikingly, the presence of eosinophils impacted tumor growth more significantly than the release of tumor-suppressing cytokines such as IFN-gamma and TNF-alpha. Our simulations suggest that novel strategies to enhance eosinophil recruitment into skin tumors may improve cancer immunotherapies. link: http://identifiers.org/pubmed/20450922

It is generally accepted that tumour cells can be eliminated by M1 anti-tumour macrophages and CD8+ T cells. However, experimental results over the past 10-15 years have shown that B16 mouse melanoma cells can be eliminated by the CD4+ T cells alone (either Th1 or Th2 sub-types), in the absence of CD8+ T cells. In some studies, elimination of B16 melanoma was associated with a Th1 immune response (i.e., elimination occurred in the presence of cytokines produced by Th1 cells), while in other studies melanoma elimination was associated with a Th2 immune response (i.e., elimination occurred in the presence of cytokines produced by Th2 cells). Moreover, macrophages have been shown to be present inside the tumours, during both Th1 and Th2 immune responses. To investigate the possible biological mechanisms behind these apparently contradictory results, we develop a class of mathematical models for the dynamics of Th1 and Th2 cells, and M1 and M2 macrophages in the presence/absence of tumour cells. Using this mathematical model, we show that depending on the re-polarisation rates between M1 and M2 macrophages, we obtain tumour elimination in the presence of a type-I immune response (i.e., more Th1 and M1 cells, compared to the Th2 and M2 cells), or in the presence of a type-II immune response (i.e., more Th2 and M2 cells). Moreover, tumour elimination is also possible in the presence of a mixed type-I/type-II immune response. Tumour growth always occurs in the presence of a type-II immune response, as observed experimentally. Finally, tumour dormancy is the result of a delicate balance between the pro-tumour effects of M2 cells and the anti-tumour effects of M1 and Th1 cells. link: http://identifiers.org/pubmed/28219660

It is generally accepted that tumour cells can be eliminated by M1 anti-tumour macrophages and CD8+ T cells. However, experimental results over the past 10-15 years have shown that B16 mouse melanoma cells can be eliminated by the CD4+ T cells alone (either Th1 or Th2 sub-types), in the absence of CD8+ T cells. In some studies, elimination of B16 melanoma was associated with a Th1 immune response (i.e., elimination occurred in the presence of cytokines produced by Th1 cells), while in other studies melanoma elimination was associated with a Th2 immune response (i.e., elimination occurred in the presence of cytokines produced by Th2 cells). Moreover, macrophages have been shown to be present inside the tumours, during both Th1 and Th2 immune responses. To investigate the possible biological mechanisms behind these apparently contradictory results, we develop a class of mathematical models for the dynamics of Th1 and Th2 cells, and M1 and M2 macrophages in the presence/absence of tumour cells. Using this mathematical model, we show that depending on the re-polarisation rates between M1 and M2 macrophages, we obtain tumour elimination in the presence of a type-I immune response (i.e., more Th1 and M1 cells, compared to the Th2 and M2 cells), or in the presence of a type-II immune response (i.e., more Th2 and M2 cells). Moreover, tumour elimination is also possible in the presence of a mixed type-I/type-II immune response. Tumour growth always occurs in the presence of a type-II immune response, as observed experimentally. Finally, tumour dormancy is the result of a delicate balance between the pro-tumour effects of M2 cells and the anti-tumour effects of M1 and Th1 cells. link: http://identifiers.org/pubmed/28219660