Metabotropic receptor activation, desensitization and sequestration-I: modelling calcium and inositol 1,4,5-trisphosphate dynamics following receptor activation

Ca2+ waves in astrocytes: computational modeling and experimental data

This paper examines different computational models for Calcium wave propagation in astrocytes. Through a comparative analysis of models by Goldbeter, De Young-Keizer, Atri, Li-Rinzel, and De Pittà and of experimental data, the study highlights the model contributions for the understanding of Calcium dynamics. Tracing the evolution from simple to complex models, this work emphasizes the importance of integrating experimental data in order to further refine these models. The results allow to improve our understanding of the physiological functions of astrocytes, suggesting the importance of more accurate astrocyte models.

Unveiling the Negative Synergistic Effect of Wall Shear Stress and Insulin on Endothelial NO Dynamics by Mathematical Modeling

Diabetic vascular complications (DVCs) are diabetes-induced vascular dysfunction and pathologies, leading to the major causes of morbidity and mortality in millions of diabetic patients worldwide. DVCs are provoked by endothelial dysfunction which is closely coordinated with two important hallmarks: one is the insufficient insulin secretion or insulin resistance, and another is the decrease in intracellular nitric oxide (NO) influenced by dynamic wall shear stress (WSS). Although the intracellular NO dynamics in endothelial cells (ECs) is crucial for endothelial function, the regulation of NO production by dynamic WSS and insulin is still poorly understood. In this study, we have proposed a mathematical model of intracellular NO production in ECs under the stimulation of dynamic WSS combined with insulin. The model integrates simultaneously the biochemical signaling pathways of insulin and the mechanotransduction pathways induced by dynamic WSS. The accuracy and reliability of the model to quantitatively describe NO production in ECs were compared and validated with reported experimental data. According to the validated model, inhibition of protein kinase B (AKT) phosphorylation and Ca2+ influx by dynamic oscillatory WSS disrupts the dual nature of endothelial nitric oxide synthase (eNOS) enzyme activation. This disruption leads to the decrease in NO production and the bimodal disappearance of NO waveforms. Moreover, the results reveal that dynamic WSS combined with insulin promote endothelial NO production through negative synergistic effects, which is resulted from the temporal differences in mechanical and biochemical signaling. In brief, the proposed model elucidates the mechanism of NO generation activated by dynamic WSS combined with insulin, providing a potential target and theoretical framework for future treatment of DVCs.

Basal State Calibration of a Chemical Reaction Network Model for Autophagy

The modulation of autophagy plays a dual role in tumor cells, with the potential to both promote and suppress tumor proliferation. In order to gain a deeper understanding of the nature of autophagy, we have developed a chemical reaction kinetic model of autophagy and apoptosis based on the mass action kinetic models that have been previously described in the literature. It is regrettable that the authors did not provide all of the information necessary to reconstruct their model, which made their simulation results irreproducible. In this study, based on an extensive literature review, we have identified concentrations for each species in the stress-free, homeostatic state. These ranges were randomly sampled to generate sets of initial concentrations, from which the simulations were run. In every case, abnormal behavior was observed, with apoptosis and autophagy being activated, even in the absence of stress. Consequently, the model failed to reproduce even the basal conditions. Detailed examination of the model revealed erroneous reactions, which were corrected. The influential kinetic parameters of the corrected model were identified and optimized using the Optima++ code. The model is now capable of simulating homeostatic states, and provides a suitable basis for further model development to describe cell response to various stresses.

Mathematical Modeling of PI3K/Akt Pathway in Microglia

The motility of microglia involves intracellular signaling pathways that are predominantly controlled by changes in cytosolic Ca2+ and activation of PI3K/Akt (phosphoinositide-3-kinase/protein kinase B). In this letter, we develop a novel biophysical model for cytosolic Ca2+ activation of the PI3K/Akt pathway in microglia where Ca2+ influx is mediated by both P2Y purinergic receptors (P2YR) and P2X purinergic receptors (P2XR). The model parameters are estimated by employing optimization techniques to fit the model to phosphorylated Akt (pAkt) experimental modeling/in vitro data. The integrated model supports the hypothesis that Ca2+ influx via P2YR and P2XR can explain the experimentally reported biphasic transient responses in measuring pAkt levels. Our predictions reveal new quantitative insights into P2Rs on how they regulate Ca2+ and Akt in terms of physiological interactions and transient responses. It is shown that the upregulation of P2X receptors through a repetitive application of agonist results in a continual increase in the baseline [Ca2+], which causes the biphasic response to become a monophasic response which prolongs elevated levels of pAkt.

A mathematical model for intracellular NO and ROS dynamics in vascular endothelial cells activated by exercise-induced wall shear stress

Vascular endothelial cells (ECs) residing in the innermost layer of blood vessels are exposed to dynamic wall shear stress (WSS) induced by blood flow. The intracellular nitric oxide (NO) and reactive oxygen species (ROS) in ECs modulated by the dynamic WSS play important roles in endothelial functions. Mathematical modeling is a popular methodology for biophysical studies. It can not only explain existing cell experiments, but also reveal the underlying mechanism. However, the previous mathematical models of NO dynamics in ECs are limited to the static WSS induced by constant flow, while arterial blood flow is a periodic pulsatile flow with varying amplitude and frequency at different exercise intensities. In this study, a mathematical model of intracellular NO and ROS dynamics activated by dynamic WSS based on the in vitro cell experiments is developed. With the hypothesis of the viscoelastic body, the Kelvin model is adopted to simulate the mechanosensors on EC. Thus, the NO dynamics activated by dynamic shear stresses induced by constant flow, pulsatile flow, and oscillatory flow are analyzed and compared. Moreover, the roles of ROS have been considered for the first time in the modeling of NO dynamics in ECs based on the analysis of cell experiments. The predictions of the proposed model coincide fairly well with the experimental data when ECs are subjected to exercise-induced WSS. The mechanism is elucidated that WSS induced by moderate-intensity exercise is most favorable to NO production in ECs. This study can provide valuable insights for further study of NO and ROS dynamics in ECs and help develop appropriate exercise regimens for improving endothelial functions.

Analysis of Network Models with Neuron-Astrocyte Interactions

Neural networks, composed of many neurons and governed by complex interactions between them, are a widely accepted formalism for modeling and exploring global dynamics and emergent properties in brain systems. In the past decades, experimental evidence of computationally relevant neuron-astrocyte interactions, as well as the astrocytic modulation of global neural dynamics, have accumulated. These findings motivated advances in computational glioscience and inspired several models integrating mechanisms of neuron-astrocyte interactions into the standard neural network formalism. These models were developed to study, for example, synchronization, information transfer, synaptic plasticity, and hyperexcitability, as well as classification tasks and hardware implementations. We here focus on network models of at least two neurons interacting bidirectionally with at least two astrocytes that include explicitly modeled astrocytic calcium dynamics. In this study, we analyze the evolution of these models and the biophysical, biochemical, cellular, and network mechanisms used to construct them. Based on our analysis, we propose how to systematically describe and categorize interaction schemes between cells in neuron-astrocyte networks. We additionally study the models in view of the existing experimental data and present future perspectives. Our analysis is an important first step towards understanding astrocytic contribution to brain functions. However, more advances are needed to collect comprehensive data about astrocyte morphology and physiology in vivo and to better integrate them in data-driven computational models. Broadening the discussion about theoretical approaches and expanding the computational tools is necessary to better understand astrocytes' roles in brain functions.

Mathematical modeling of intracellular calcium in presence of receptor: a homeostatic model for endothelial cell

Calcium is a ubiquitous molecule and second messenger that regulates many cellular functions ranging from exocytosis to cell proliferation at different time scales. In the vasculature, a constant adenosine triphosphate (ATP) concentration is maintained because of ATP released by red blood cells (RBCs). These ATP molecules continuously react with purinergic receptors on the surface of endothelial cells (ECs). Consequently, a cascade of chemical reactions are triggered that result in a transient cytoplasmic calcium (Ca[Formula: see text]), followed by return to its basal concentration. The mathematical models proposed in the literature are able to reproduce the transient peak. However, the trailing concentration is always higher than the basal cytoplasmic Ca[Formula: see text] concentrations, and the Ca[Formula: see text] concentration in endoplasmic reticulum (ER) remains lower than its initial concentration. This means that the intracellular homeostasis is not recovered. We propose, herein, a minimal model of calcium kinetics. We find that the desensitization of EC surface receptors due to phosphorylation and recycling plays a vital role in maintaining calcium homeostasis in the presence of a constant stimulus (ATP). The model is able to capture several experimental observations such as refilling of Ca[Formula: see text] in the ER, variation of cytoplasmic Ca[Formula: see text] transient peak in ECs, the resting cytoplasmic Ca[Formula: see text] concentration, the effect of removing ATP from the plasma on Ca[Formula: see text] homeostasis, and the saturation of cytoplasmic Ca[Formula: see text] transient peak with increase in ATP concentration. Direct confrontation with several experimental results is conducted. This work paves the way for systematic studies on coupling between blood flow and chemical signaling, and should contribute to a better understanding of the relation between (patho)physiological conditions and Ca[Formula: see text] kinetics.

Proteolytic activation of Growth-blocking peptides triggers calcium responses through the GPCR Mthl10 during epithelial wound detection

The presence of a wound triggers surrounding cells to initiate repair mechanisms, but it is not clear how cells initially detect wounds. In epithelial cells, the earliest known wound response, occurring within seconds, is a dramatic increase in cytosolic calcium. Here, we show that wounds in the Drosophila notum trigger cytoplasmic calcium increase by activating extracellular cytokines, Growth-blocking peptides (Gbps), which initiate signaling in surrounding epithelial cells through the G-protein-coupled receptor Methuselah-like 10 (Mthl10). Latent Gbps are present in unwounded tissue and are activated by proteolytic cleavage. Using wing discs, we show that multiple protease families can activate Gbps, suggesting that they act as a generalized protease-detector system. We present experimental and computational evidence that proteases released during wound-induced cell damage and lysis serve as the instructive signal: these proteases liberate Gbp ligands, which bind to Mthl10 receptors on surrounding epithelial cells, and activate downstream release of calcium.

Modeling of Ca2+ transients initiated by GPCR agonists in mesenchymal stromal cells

The integrative study that included experimentation and mathematical modeling was carried out to analyze dynamic aspects of transient Ca²⁺ signaling induced by brief pulses of GPCR agonists in mesenchymal stromal cells from the human adipose tissue (AD-MSCs). The experimental findings argued for IP₃/Ca²⁺-regulated Ca²⁺ release via IP₃ receptors (IP₃Rs) as a key mechanism mediating agonist-dependent Ca²⁺ transients. The consistent signaling circuit was proposed to formalize coupling of agonist binding to Ca²⁺ mobilization for mathematical modeling. The model properly simulated the basic phenomenology of agonist transduction in AD-MSCs, which mostly produced single Ca²⁺ spikes upon brief stimulation. The spike-like responses were almost invariantly shaped at different agonist doses above a threshold, while response lag markedly decreased with stimulus strength. In AD-MSCs, agonists and IP₃ uncaging elicited similar Ca²⁺ transients but IP₃ pulses released Ca²⁺ without pronounced delay. This suggested that IP₃ production was rate-limiting in agonist transduction. In a subpopulation of AD-MSCs, brief agonist pulses elicited Ca²⁺ bursts crowned by damped oscillations. With properly adjusted parameters of IP₃R inhibition by cytosolic Ca²⁺, the model reproduced such oscillatory Ca²⁺ responses as well. GEM-GECO1 and R-CEPIA1er, the genetically encoded sensors of cytosolic and reticular Ca²⁺, respectively, were co-expressed in HEK-293 cells that also responded to agonists in an "all-or-nothing" manner. The experimentally observed Ca²⁺ signals triggered by ACh in both compartments were properly simulated with the suggested signaling circuit. Thus, the performed modeling of the transduction process provides sufficient theoretical basis for deeper interpretation of experimental findings on agonist-induced Ca²⁺ signaling in AD-MSCs.

A mathematical model for persistent post-CSD vasoconstriction

Cortical spreading depression (CSD) is the propagation of a relatively slow wave in cortical brain tissue that is linked to a number of pathological conditions such as stroke and migraine. Most of the existing literature investigates the dynamics of short term phenomena such as the depolarization and repolarization of membrane potentials or large ion shifts. Here, we focus on the clinically-relevant hour-long state of neurovascular malfunction in the wake of CSDs. This dysfunctional state involves widespread vasoconstriction and a general disruption of neurovascular coupling. We demonstrate, using a mathematical model, that dissolution of calcium that has aggregated within the mitochondria of vascular smooth muscle cells can drive an hour-long disruption. We model the rate of calcium clearance as well as the dynamical implications on overall blood flow. Based on reaction stoichiometry, we quantify a possible impact of calcium phosphate dissolution on the maintenance of F0F1-ATP synthase activity.

Intercellular Bridge Mediates Ca2+ Signals between Micropatterned Cells via IP3 and Ca2+ Diffusion

Intercellular bridges are plasma continuities formed at the end of the cytokinesis process that facilitate intercellular mass transport between the two daughter cells. However, it remains largely unknown how the intercellular bridge mediates Ca²⁺ communication between postmitotic cells. In this work, we utilize BV-2 microglial cells planted on dumbbell-shaped micropatterned assemblies to resolve spatiotemporal characteristics of Ca²⁺ signal transfer over the intercellular bridges. With the use of such micropatterns, considerably longer and more regular intercellular bridges can be obtained than in conventional cell cultures. The initial Ca²⁺ signal is evoked by mechanical stimulation of one of the daughter cells. A considerable time delay is observed between the arrivals of passive Ca²⁺ diffusion and endogenous Ca²⁺ response in the intercellular-bridge-connected cell, indicating two different pathways of the Ca²⁺ communication. Extracellular Ca²⁺ and the paracrine pathway have practically no effect on the endogenous Ca²⁺ response, demonstrated by application of Ca²⁺-free medium, exogenous ATP, and P2Y₁₃ receptor antagonist. In contrast, the endoplasmic reticulum Ca²⁺-ATPase inhibitor thapsigargin and inositol trisphosphate (IP₃) receptor blocker 2-aminoethyl diphenylborate significantly inhibit the endogenous Ca²⁺ increase, which signifies involvement of IP₃-sensitive calcium store release. Notably, passive Ca²⁺ diffusion into the connected cell can clearly be detected when IP₃-sensitive calcium store release is abolished by 2-aminoethyl diphenylborate. Those observations prove that both passive Ca²⁺ diffusion and IP₃-mediated endogenous Ca²⁺ response contribute to the Ca²⁺ increase in intercellular-bridge-connected cells. Moreover, a simulation model agreed well with the experimental observations.

Coronary Smooth Muscle Cell Calcium Dynamics: Effects of Bifurcation Angle on Atheroprone Conditions

This work investigates the effect of arterial bifurcation angulation on atherosclerosis development through in-silico simulations of coupled cell dynamics. The computational model presented here combines cellular pathways, fluid dynamics, and physiologically-realistic vessel geometries as observed in the human vasculature. The coupled cells model includes endothelial cells (ECs) and smooth muscle cells (SMCs) with ion dynamics, hetero and homotypic coupling, as well as electro-diffusive coupling. Three arterial bifurcation surface models were used in the coupled cells simulations. All three simulations showed propagating waves of Ca²⁺ in both the SMC and EC layers, following the introduction of a luminal agonist, in this case ATP. Immediately following the introduction of ATP concentration Ca²⁺ waves propagate from the area of high ATP toward the areas of low ATP concentration, forming complex patterns where waves interact with eachother, collide and fade. These dynamic phenomena are repeated with a series of waves of slower velocity. The underlying motivation of this research was to examine the macro-scale phenomena, given that the characteristic length scales of atherosclerotic plaques are much larger than a single cell. The micro-scale dynamics were modeled on macro-scale arterial bifurcation surfaces containing over one million cells. The results of the simulations presented here suggest that susceptibility to atherosclerosis development depends on the bifurcation angulation. In conjunction with findings reported in the literature, the simulation results demonstrate that arterial bifurcations containing wider angles have a more prominent influence on the coupled cells pathways associated with the development of atherosclerosis, by means of disturbed flow and lower SMC Ca²⁺ concentrations. The discussion of the results considers the findings of this research within the context of the potential link between information transport through frequency encoding of Ca²⁺ wave dynamics and development of atheroprone conditions.

Importance of Altered Levels of SERCA, IP3R, and RyR in Vascular Smooth Muscle Cell

Calcium cycling between the sarcoplasmic reticulum (SR) and the cytosol via the sarco-/endoplasmic reticulum Ca-ATPase (SERCA) pump, inositol-1,4,5-triphosphate receptor (IP₃R), and Ryanodine receptor (RyR), plays a major role in agonist-induced intracellular calcium ([Ca²⁺]_cyt) dynamics in vascular smooth muscle cells (VSMC). Levels of these calcium handling proteins in SR get altered under disease conditions. We have developed a mathematical model to understand the significance of altered levels of SERCA, IP₃R, and RyR on the intracellular calcium dynamics of VSMC and to understand how variation in protein levels that arise due to diabetes contribute to different VSMC behavior and thus vascular disease. SR is modeled as a single continuous entity with homogeneous intra-SR calcium. Model results show that agonist-induced intracellular calcium dynamics can be modified by changing the levels of SERCA, IP₃R, and/or RyR. Lowering SERCA level will enable intracellular calcium oscillations at low agonist concentrations whereas lowered levels of IP₃R and RyR need higher agonist concentration for intracellular calcium oscillations. This research suggests that reduced SERCA level is the main factor responsible for the reduced intracellular calcium transients and contractility in VSMCs.

Shear-Induced Nitric Oxide Production by Endothelial Cells

We present a biochemical model of the wall shear stress-induced activation of endothelial nitric oxide synthase (eNOS) in an endothelial cell. The model includes three key mechanotransducers: mechanosensing ion channels, integrins, and G protein-coupled receptors. The reaction cascade consists of two interconnected parts. The first is rapid activation of calcium, which results in formation of calcium-calmodulin complexes, followed by recruitment of eNOS from caveolae. The second is phosphorylation of eNOS by protein kinases PKC and AKT. The model also includes a negative feedback loop due to inhibition of calcium influx into the cell by cyclic guanosine monophosphate (cGMP). In this feedback, increased nitric oxide (NO) levels cause an increase in cGMP levels, so that cGMP inhibition of calcium influx can limit NO production. The model was used to predict the dynamics of NO production by an endothelial cell subjected to a step increase of wall shear stress from zero to a finite physiologically relevant value. Among several experimentally observed features, the model predicts a highly nonlinear, biphasic transient behavior of eNOS activation and NO production: a rapid initial activation due to the very rapid influx of calcium into the cytosol (occurring within 1-5 min) is followed by a sustained period of activation due to protein kinases.

3D time-varying simulations of Ca2+ dynamics in arterial coupled cells: A massively parallel implementation

Preferential locations of atherosclerotic plaque are strongly associated with the areas of low wall shear stress and disturbed haemodynamic characteristics such as flow detachment, flow recirculation and oscillatory flow. The areas of low wall shear stress are also associated with the reduced production of adenosine triphosphate in the endothelial layer, as well as the resulting reduced production of inositol trisphosphate (IP³ ). The subsequent variation in Ca²⁺ signalling and nitric oxide synthesis could lead to the impairment of the atheroprotective function played by nitric oxide. In previous studies, it has been suggested that the reduced IP³ and Ca²⁺ signalling can explain the correlation of atherosclerosis with induced low WSS and disturbed flow characteristics. The massively parallel implementation described in this article provides insight into the dynamics of coupled smooth muscle cells and endothelial cells mapped onto the surface of an idealised arterial bifurcation. We show that variations in coupling parameters, which model normal and pathological conditions, provide vastly different smooth muscle cell Ca²⁺ dynamics and wave propagation profiles. The extensibility of the coupled cells model and scalability of the implementation provide a solid framework for in silico investigations of the interaction between complex cellular chemistry and the macro-scale processes determined by fluid dynamics. © 2016 The Authors. International Journal for Numerical Methods in Biomedical Engineering published by John Wiley & Sons Ltd.

Distinct cellular states determine calcium signaling response

The heterogeneity in mammalian cells signaling response is largely a result of pre‐existing cell‐to‐cell variability. It is unknown whether cell‐to‐cell variability rises from biochemical stochastic fluctuations or distinct cellular states. Here, we utilize calcium response to adenosine trisphosphate as a model for investigating the structure of heterogeneity within a population of cells and analyze whether distinct cellular response states coexist. We use a functional definition of cellular state that is based on a mechanistic dynamical systems model of calcium signaling. Using Bayesian parameter inference, we obtain high confidence parameter value distributions for several hundred cells, each fitted individually. Clustering the inferred parameter distributions revealed three major distinct cellular states within the population. The existence of distinct cellular states raises the possibility that the observed variability in response is a result of structured heterogeneity between cells. The inferred parameter distribution predicts, and experiments confirm that variability in IP3R response explains the majority of calcium heterogeneity. Our work shows how mechanistic models and single‐cell parameter fitting can uncover hidden population structure and demonstrate the need for parameter inference at the single‐cell level.

Critical role of ATP-induced ATP release for Ca2+ signaling in nonsensory cell networks of the developing cochlea

Spatially and temporally coordinated variations of the cytosolic free calcium concentration ([Ca²⁺]_c) play a crucial role in a variety of tissues. In the developing sensory epithelium of the mammalian cochlea, elevation of extracellular adenosine trisphosphate concentration ([ATP]_e) triggers [Ca²⁺]_c oscillations and propagation of intercellular inositol 1,4,5-trisphosphate (IP₃)-dependent Ca²⁺ waves. What remains uncertain is the relative contribution of gap junction channels and connexin hemichannels to these fundamental mechanisms, defects in which impair hearing acquisition. Another related open question is whether [Ca²⁺]_c oscillations require oscillations of the cytosolic IP₃ concentration ([IP₃]_c) in this system. To address these issues, we performed Ca²⁺ imaging experiments in the lesser epithelial ridge of the mouse cochlea around postnatal day 5 and constructed a computational model in quantitative adherence to experimental data. Our results indicate that [Ca²⁺]_c oscillations are governed by Hopf-type bifurcations within the experimental range of [ATP]_e and do not require [IP₃]_c oscillations. The model replicates accurately the spatial extent and propagation speed of intercellular Ca²⁺ waves and predicts that ATP-induced ATP release is the primary mechanism underlying intercellular propagation of Ca²⁺ signals. The model also uncovers a discontinuous transition from propagating regimes (intercellular Ca²⁺ wave speed > 11 μm⋅s^-1) to propagation failure (speed = 0), which occurs upon lowering the maximal ATP release rate below a minimal threshold value. The approach presented here overcomes major limitations due to lack of specific connexin channel inhibitors and can be extended to other coupled cellular systems.

Signal Transduction at the Single-Cell Level: Approaches to Study the Dynamic Nature of Signaling Networks

Signal transduction, or how cells interpret and react to external events, is a fundamental aspect of cellular function. Traditional study of signal transduction pathways involves mapping cellular signaling pathways at the population level. However, population-averaged readouts do not adequately illuminate the complex dynamics and heterogeneous responses found at the single-cell level. Recent technological advances that observe cellular response, computationally model signaling pathways, and experimentally manipulate cells now enable studying signal transduction at the single-cell level. These studies will enable deeper insights into the dynamic nature of signaling networks.

A mechanistic model of a PDGFRα(+) cell

A novel platelet-derived growth factor receptor alpha-positive cell (PDGFRα(+)) has recently been identified as part of the purinergic inhibitory neural control mechanism in the gastrointestinal (GI) tract. The mechanism through which PDGFRα(+) cells mediate GI muscle relaxation has been found to be associated with the purine receptors P2Y1 and apamin-sensitive SK3 channels that are highly expressed in these cells. This study aims to develop a mechanistic model elucidating a proposed mechanism through which PDGFRα(+) cells contribute to purinergic inhibitory neuromuscular transmission. In accordance with recent experimental findings, the model describes how the binding of neurotransmitters, released from enteric neurons, triggers the release of Ca(2+) from the endoplasmic reticulum in the PDGFRα(+) cells, and how this subsequently leads to large amplitude transient outward currents, which in turn hyperpolarize the cell. The model has been validated against experimental recordings and good agreement was found under normal and pharmacologically-altered conditions. This model demonstrates the feasibility of the proposed mechanism and provides a basis for understanding the mechanism underlying purinergic control of colonic motility.

Pancreatic Beta Cell G-Protein Coupled Receptors and Second Messenger Interactions: A Systems Biology Computational Analysis

Insulin secretory in pancreatic beta-cells responses to nutrient stimuli and hormonal modulators include multiple messengers and signaling pathways with complex interdependencies. Here we present a computational model that incorporates recent data on glucose metabolism, plasma membrane potential, G-protein-coupled-receptors (GPCR), cytoplasmic and endoplasmic reticulum calcium dynamics, cAMP and phospholipase C pathways that regulate interactions between second messengers in pancreatic beta-cells. The values of key model parameters were inferred from published experimental data. The model gives a reasonable fit to important aspects of experimentally measured metabolic and second messenger concentrations and provides a framework for analyzing the role of metabolic, hormones and neurotransmitters changes on insulin secretion. Our analysis of the dynamic data provides support for the hypothesis that activation of Ca²⁺-dependent adenylyl cyclases play a critical role in modulating the effects of glucagon-like peptide 1 (GLP-1), glucose-dependent insulinotropic polypeptide (GIP) and catecholamines. The regulatory properties of adenylyl cyclase isoforms determine fluctuations in cytoplasmic cAMP concentration and reveal a synergistic action of glucose, GLP-1 and GIP on insulin secretion. On the other hand, the regulatory properties of phospholipase C isoforms determine the interaction of glucose, acetylcholine and free fatty acids (FFA) (that act through the FFA receptors) on insulin secretion. We found that a combination of GPCR agonists activating different messenger pathways can stimulate insulin secretion more effectively than a combination of GPCR agonists for a single pathway. This analysis also suggests that the activators of GLP-1, GIP and FFA receptors may have a relatively low risk of hypoglycemia in fasting conditions whereas an activator of muscarinic receptors can increase this risk. This computational analysis demonstrates that study of second messenger pathway interactions will improve understanding of critical regulatory sites, how different GPCRs interact and pharmacological targets for modulating insulin secretion in type 2 diabetes.

Respiratory modulated sympathetic activity: a putative mechanism for developing vascular resistance?

KEY POINTS

Sympathetic activity exhibits respiratory modulation that is amplified in hypertensive rats. Respiratory modulated sympathetic activity produces greater changes in vascular resistance than tonic stimulation of the same stimulus magnitude in normotensive but not hypertensive rats. Mathematical modelling demonstrates that respiratory modulated sympathetic activity may fail to produce greater vascular resistance changes in hypertensive rats because the system is saturated as a consequence of a dysfunctional noradrenaline reuptake mechanism. Respiratory modulated sympathetic activity is an efficient mechanism to raise vascular resistance promptly, corroborating its involvement in the ontogenesis of hypertension.

ABSTRACT

Sympathetic nerve activity (SNA) exhibits respiratory modulation. This component of SNA is important - being recruited under cardiorespiratory reflex conditions and elevated in the spontaneously hypertensive (SH) rat - and yet the exact influence of this modulation on vascular tone is not understood, even in normotensive conditions. We constructed a mathematical model of the sympathetic innervation of an arteriole, and used it to test the hypothesis that respiratory modulation of SNA preferentially increases vasoconstriction compared to a frequency-matched tonic pattern. Simulations supported the hypothesis, where respiratory modulated increases in vasoconstriction were mediated by a noradrenergic mechanism. These predictions were tested in vivo in adult Wistar rats. Stimulation of the sympathetic chain (L3) with respiratory modulated bursting patterns, revealed that bursting increases vascular resistance (VR) more than tonic stimulation (57.8 ± 3.3% vs. 44.8 ± 4.2%; P < 0.001; n = 8). The onset of the VR response was also quicker for bursting stimulation (rise time constant = 1.98 ± 0.09 s vs. 2.35 ± 0.20 s; P < 0.01). In adult SH rats (n = 8), the VR response to bursting (44.6 ± 3.9%) was not different to tonic (37.4 ± 3.5%; P = 0.57). Using both mathematical modelling and in vivo techniques, we have shown that VR depends critically on respiratory modulation and revealed that this pattern dependency in Wistar rats is due to a noradrenergic mechanism. This respiratory component may therefore contribute to the ontogenesis of hypertension in the pre-hypertensive SH rat - raising VR and driving vascular remodelling. Why adult SH rats do not exhibit a pattern-dependent response is not known, but further modelling revealed that this may be due to dysfunctional noradrenaline reuptake.

Computational Model of Ca2+ Wave Propagation in Human Retinal Pigment Epithelial ARPE-19 Cells

Objective

Computational models of calcium (Ca²⁺) signaling have been constructed for several cell types. There are, however, no such models for retinal pigment epithelium (RPE). Our aim was to construct a Ca²⁺ signaling model for RPE based on our experimental data of mechanically induced Ca²⁺ wave in the in vitro model of RPE, the ARPE-19 monolayer.

Methods

We combined six essential Ca²⁺ signaling components into a model: stretch-sensitive Ca²⁺ channels (SSCCs), P₂Y₂ receptors, IP₃ receptors, ryanodine receptors, Ca²⁺ pumps, and gap junctions. The cells in our epithelial model are connected to each other to enable transport of signaling molecules. Parameterization was done by tuning the above model components so that the simulated Ca²⁺ waves reproduced our control experimental data and data where gap junctions were blocked.

Results

Our model was able to explain Ca²⁺ signaling in ARPE-19 cells, and the basic mechanism was found to be as follows: 1) Cells near the stimulus site are likely to conduct Ca²⁺ through plasma membrane SSCCs and gap junctions conduct the Ca²⁺ and IP³ between cells further away. 2) Most likely the stimulated cell secretes ligand to the extracellular space where the ligand diffusion mediates the Ca²⁺ signal so that the ligand concentration decreases with distance. 3) The phosphorylation of the IP₃ receptor defines the cell’s sensitivity to the extracellular ligand attenuating the Ca²⁺ signal in the distance.

Conclusions

The developed model was able to simulate an array of experimental data including drug effects. Furthermore, our simulations predict that suramin may interfere ligand binding on P₂Y₂ receptors or accelerate P₂Y₂ receptor phosphorylation, which may partially be the reason for Ca²⁺ wave attenuation by suramin. Being the first RPE Ca²⁺ signaling model created based on experimental data on ARPE-19 cell line, the model offers a platform for further modeling of native RPE functions.

Modelling the vascular response to sympathetic postganglionic nerve activity

This paper explores the influence of burst properties of the sympathetic nervous system on arterial contractility. Specifically, a mathematical model is constructed of the pathway from action potential generation in a sympathetic postganglionic neurone to contraction of an arterial smooth muscle cell. The differential equation model is a synthesis of models of the individual physiological processes, and is shown to be consistent with physiological data.

The model is found to be unresponsive to tonic (regular) stimulation at typical frequencies recorded in sympathetic efferents. However, when stimulated at the same average frequency, but with repetitive respiratory-modulated burst patterns, it produces marked contractions. Moreover, the contractile force produced is found to be highly dependent on the number of spikes in each burst. In particular, when the model is driven by preganglionic spike trains recorded from wild-type and spontaneously hypertensive rats (which have increased spiking during each burst) the contractile force was found to be 10-fold greater in the hypertensive case. An explanation is provided in terms of the summative increased release of noradrenaline. Furthermore, the results suggest the marked effect that hypertensive spike trains had on smooth muscle cell tone can provide a significant contribution to the pathology of hypertension.

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We model the sympathetic-driven contraction of a vascular smooth muscle cell.

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The cell is unresponsive to tonic stimulation at typical sympathetic frequencies.

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We quantify the force produced by the cell in response to sympathetic bursting.

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The response of the cell is strongly dependent on burst amplitude and duration.

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Recordings from hypertensive animals produce significant contractile forces.

Mast cell-nerve cell interaction at acupoint: modeling mechanotransduction pathway induced by acupuncture

Mast cells are found abundant at sites of acupoints. Nerve cells share perivascular localization with mast cells. Acupuncture (mechanical stimuli) can activate mast cells to release adenosine triphosphate (ATP) which can activate nerve cells and modulates pain-processing pathways in response to acupuncture. In this paper, a mathematical model was constructed for describing intracellular Ca²⁺ signal and ATP release in a coupled mast cell and nerve cell system induced by mechanical stimuli. The results showed mechanical stimuli lead to a intracellular Ca²⁺ rise in the mast cell and ATP release, ATP diffuses in the extracellular space (ECS) and activates the nearby nerve cells, then induces electrical current in the nerve cell which spreads in the neural network. This study may facilitate our understanding of the mechanotransduction process induced by acupuncture and provide a methodology for quantitatively analyzing acupuncture treatment.

Quantitative properties and receptor reserve of the DAG and PKC branch of G(q)-coupled receptor signaling

G_q protein–coupled receptors (G_qPCRs) of the plasma membrane activate the phospholipase C (PLC) signaling cascade. PLC cleaves the membrane lipid phosphatidylinositol 4,5-bisphosphate (PIP₂) into the second messengers diacylgycerol (DAG) and inositol 1,4,5-trisphosphate (IP₃), leading to calcium release, protein kinase C (PKC) activation, and in some cases, PIP₂ depletion. We determine the kinetics of each of these downstream endpoints and also ask which is responsible for the inhibition of KCNQ2/3 (K_V7.2/7.3) potassium channels in single living tsA-201 cells. We measure DAG production and PKC activity by Förster resonance energy transfer–based sensors, and PIP₂ by KCNQ2/3 channels. Fully activating endogenous purinergic receptors by uridine 5′triphosphate (UTP) leads to calcium release, DAG production, and PKC activation, but no net PIP₂ depletion. Fully activating high-density transfected muscarinic receptors (M₁Rs) by oxotremorine-M (Oxo-M) leads to similar calcium, DAG, and PKC signals, but PIP₂ is depleted. KCNQ2/3 channels are inhibited by the Oxo-M treatment (85%) and not by UTP (<1%), indicating that depletion of PIP₂ is required to inhibit KCNQ2/3 in response to receptor activation. Overexpression of A kinase–anchoring protein (AKAP)79 or calmodulin (CaM) does not increase KCNQ2/3 inhibition by UTP. From these results and measurements of IP₃ and calcium presented in our companion paper (Dickson et al. 2013. J. Gen. Physiol.http://dx.doi.org/10.1085/jgp.201210886), we extend our kinetic model for signaling from M₁Rs to DAG/PKC and IP₃/calcium signaling. We conclude that calcium/CaM and PKC-mediated phosphorylation do not underlie dynamic KCNQ2/3 channel inhibition during G_qPCR activation in tsA-201 cells. Finally, our experimental data provide indirect evidence for cleavage of PI(4)P by PLC in living cells, and our modeling revisits/explains the concept of receptor reserve with measurements from all steps of G_qPCR signaling.

Cell-type-specific modelling of intracellular calcium signalling: a urothelial cell model

Calcium signalling plays a central role in regulating a wide variety of cell processes. A number of calcium signalling models exist in the literature that are capable of reproducing a variety of experimentally observed calcium transients. These models have been used to examine in more detail the mechanisms underlying calcium transients, but very rarely has a model been directly linked to a particular cell type and experimentally verified. It is important to show that this can be achieved within the general theoretical framework adopted by these models. Here, we develop a framework designed specifically for modelling cytosolic calcium transients in urothelial cells. Where possible, we draw upon existing calcium signalling models, integrating descriptions of components known to be important in this cell type from a number of studies in the literature. We then add descriptions of several additional pathways that play a specific role in urothelial cell signalling, including an explicit ionic influx term and an active pumping mechanism that drives the cytosolic calcium concentration to a target equilibrium. The resulting one-pool model of endoplasmic reticulum (ER)-dependent calcium signalling relates the cytosolic, extracellular and ER calcium concentrations and can generate a wide range of calcium transients, including spikes, bursts, oscillations and sustained elevations in the cytosolic calcium concentration. Using single-variate robustness and multivariate sensitivity analyses, we quantify how varying each of the parameters of the model leads to changes in key features of the calcium transient, such as initial peak amplitude and the frequency of bursting or spiking, and in the transitions between bursting- and plateau-dominated modes. We also show that, novel to our urothelial cell model, the ionic and purinergic P2Y pathways make distinct contributions to the calcium transient. We then validate the model using human bladder epithelial cells grown in monolayer cell culture and show that the model robustly captures the key features of the experimental data in a way that is not possible using more generic calcium models from the literature.

A positive feedback cell signaling nucleation model of astrocyte dynamics

We constructed a model of calcium signaling in astrocyte neural glial cells that incorporates a positive feedback nucleation mechanism, whereby small microdomain increases in local calcium can stochastically produce global cellular and intercellular network scale dynamics. The model is able to simultaneously capture dynamic spatial and temporal heterogeneities associated with intracellular calcium transients in individual cells and intercellular calcium waves (ICW) in spatially realistic networks of astrocytes, i.e., networks where the positions of cells were taken from real in vitro experimental data of spontaneously forming sparse networks, as opposed to artificially constructed grid networks or other non-realistic geometries. This is the first work we are aware of where an intracellular model of calcium signaling that reproduces intracellular dynamics inherently accounts for intercellular network dynamics. These results suggest that a nucleation type mechanism should be further investigated experimentally in order to test its contribution to calcium signaling in astrocytes and in other cells more broadly. It may also be of interest in engineered neuromimetic network systems that attempt to emulate biological signaling and information processing properties in synthetic hardwired neuromorphometric circuits or coded algorithms.

The discovery of a new class of synaptic transmitters in smooth muscle 50 years ago and amelioration of coronary artery thrombosis

Clopidogrel and ticagrelor, antagonists to P2Y(12) receptor molecules on platelet membranes, significantly ameliorate acute myocardial infarction due to coronary artery thrombosis, the most common cause of death in the developed world. A personal account is given here of the foundational research that lead to the identification of P2Y receptors, carried out 50 years ago in the Melbourne University Zoology Department headed by Geoffrey Burnstock. In Christmas 1962, I made the serendipitous observation of large hyperpolarizing changes across the membranes of smooth muscle cells in the taenia coli of the intestine on stimulating its nerve supply. I then showed that these potentials relaxed the muscle and were not due to noradrenaline or acetylcholine, which were then the only substances known to be released from nerves. I called these non-adrenergic, non-cholinergic (NANC) terminals in the laboratory and showed that this NANC transmitter acted at receptor molecules on the muscle cells, promoting efflux of potassium ions, and so the observed potential changes. In 1968, Graeme Campbell showed that ATP relaxed the taenia coli muscle, and in 1969, David Satchell, using purine chromatography, showed that ATP was likely to be released from NANC terminals. The receptor molecules involved were shown to be exceptionally sensitive to 2-methylthio-ATP (Satchell and Macguire, 1975, J Pharmacol Exp Ther, 195, 540), and so belonged to the class P2Y receptors as designated by Abbracchio and Burnstock, with subclasses P2Y(1)-P2Y(12). The discovery of the role of P2Y(12) receptors in increasing thrombosis lead to the focused research that resulted in clopidogrel and ticagrelor.

A computational model of neuro-glio-vascular loop interactions

We present a computational, biophysical model of neuron-astrocyte-vessel interaction. Unlike other cells, neurons convey “hunger” signals to the vascular network via an intervening layer of glial cells (astrocytes); vessels dilate and release glucose which fuels neuronal firing. Existing computational models focus on only parts of this loop (neuron→astrocyte→vessel→neuron), whereas the proposed model describes the entire loop. Neuronal firing causes release of a neurotransmitter like glutamate which triggers release of vasodilator by astrocytes via a cascade of biochemical events. Vasodilators released from astrocytic endfeet cause blood vessels to dilate and release glucose into the interstitium, part of which is taken up by the astrocyticendfeet. Glucose is converted into lactate in the astrocyte and transported into the neuron. Glucose from the interstitium and lactate (produced from glucose) influx from astrocyte are converted into ATP in the neuron. Neuronal ATP is used to drive the Na⁺/K⁺ATPase pumps, which maintain ionic gradients necessary for neuronal firing. When placed in the metabolic loop, the neuron exhibits sustained firing only when the stimulation current is more than a minimum threshold. For various combinations of initial neuronal [ATP] and external current, the neuron exhibits a variety of firing patterns including sustained firing, firing after an initial pause, burst firing etc. Neurovascular interactions under conditions of constricted vessels are also studied. Most models of cerebral circulation describe neurovascular interactions exclusively in the “forward” neuron→vessel direction. The proposed model indicates possibility of “reverse” influence also, with vasomotion rhythms influencing neural firing patterns. Another idea that emerges out of the proposed work is that brain's computations may be more comprehensively understood in terms of neuro-glial-vascular dynamics and not in terms of neural firing alone.

Models of neurovascular coupling via potassium and EET signalling

Functional hyperemia is an important metabolic autoregulation mechanism by which increased neuronal activity is matched by a rapid and regional increase in blood supply. This mechanism is facilitated by a process known as "neurovascular coupling"--the orchestrated communication system involving neurons, astrocytes and arterioles. Important steps in this process are the production of EETs in the astrocyte and the release of potassium, via two potassium channels (BK and KIR), into the perivascular space. We provide a model which successfully accounts for several observations seen in experiment. The model is capable of simulating the approximate 15% arteriolar dilation caused by a 60-s neuronal activation (modelled as a release of potassium and glutamate into the synaptic cleft). This model also successfully emulates the paradoxical experimental finding that vasoconstriction follows vasodilation when the astrocytic calcium concentration (or perivascular potassium concentration) is increased further. We suggest that the interaction of the changing smooth muscle cell membrane potential and the changing potassium-dependent resting potential of the KIR channel are responsible for this effect. Finally, we demonstrate that a well-controlled mechanism of potassium buffering is potentially important for successful neurovascular coupling.

Stochastic hybrid modeling of intracellular calcium dynamics

Deterministic models of biochemical processes at the subcellular level might become inadequate when a cascade of chemical reactions is induced by a few molecules. Inherent randomness of such phenomena calls for the use of stochastic simulations. However, being computationally intensive, such simulations become infeasible for large and complex reaction networks. To improve their computational efficiency in handling these networks, we present a hybrid approach, in which slow reactions and fluxes are handled through exact stochastic simulation and their fast counterparts are treated partially deterministically through chemical Langevin equation. The classification of reactions as fast or slow is accompanied by the assumption that in the time-scale of fast reactions, slow reactions do not occur and hence do not affect the probability of the state. Our new approach also handles reactions with complex rate expressions such as Michaelis-Menten kinetics. Fluxes which cannot be modeled explicitly through reactions, such as flux of Ca(2+) from endoplasmic reticulum to the cytosol through inositol 1,4,5-trisphosphate receptor channels, are handled deterministically. The proposed hybrid algorithm is used to model the regulation of the dynamics of cytosolic calcium ions in mouse macrophage RAW 264.7 cells. At relatively large number of molecules, the response characteristics obtained with the stochastic and deterministic simulations coincide, which validates our approach in the limit of large numbers. At low doses, the response characteristics of some key chemical species, such as levels of cytosolic calcium, predicted with stochastic simulations, differ quantitatively from their deterministic counterparts. These observations are ubiquitous throughout dose response, sensitivity, and gene-knockdown response analyses. While the relative differences between the peak-heights of the cytosolic [Ca(2+)] time-courses obtained from stochastic (mean of 16 realizations) and deterministic simulations are merely 1%-4% for most perturbations, it is specially sensitive to levels of G(βγ) (relative difference as large as 90% at very low G(βγ)).

Lipid rafts in mast cell biology

Mast cells have long been recognized to have a direct and critical role in allergic and inflammatory reactions. In allergic diseases, these cells exert both local and systemic responses, including allergic rhinitis and anaphylaxis. Mast cell mediators are also related to many chronic inflammatory conditions. Besides the roles in pathological conditions, the biological functions of mast cells include roles in innate immunity, involvement in host defense mechanisms against parasites, immunomodulation of the immune system, tissue repair, and angiogenesis. Despite their growing significance in physiological and pathological conditions, much still remains to be learned about mast cell biology. This paper presents evidence that lipid rafts or raft components modulate many of the biological processes in mast cells, such as degranulation and endocytosis, play a role in mast cell development and recruitment, and contribute to the overall preservation of mast cell structure and organization.

Mathematical modelling and analysis of cellular signalling in macrophages

Cell signalling pathways play a crucial role in proper cell development and behaviour, with implications to survival, chemotaxis, proliferation, and even programmed cell death known as apoptosis. In this article, we outline a mathematical model of the G-protein signalling pathway in a particular cell line of macrophages, focusing on activation of a particular G-protein-coupled receptor, P2Y(6). The model is based on the kinetics of P2Y(6) surface receptors, inositol trisphosphate, cytosolic calcium, and differential dynamics of multiple species of diacylglycerol. Insight into the dynamics of the system is given through recently available experimental results and incorporated into the model. Mathematical analysis of the model, including establishment of global existence, uniqueness, positivity, and boundedness of solutions, and global stability of a unique steady-state solution is discussed.

A model for Ca2+ waves in networks of glial cells incorporating both intercellular and extracellular communication pathways

Networks of glial cells, and in particular astrocytes, are capable of sustaining calcium (Ca(2+)) waves both in vivo and in vitro. Experimentally, it has been shown that there are two separate modes of communication: the first by the passage of an agent (inositol 1,4,5-triphosphate, IP(3)) through gap junctions (GJs) joining cells; the second by the diffusion of an extracellular agent (adenosine triphosphate, ATP) that binds to receptors on the cells. In both cases, the outcome is the release of Ca(2+) from internal stores in the glial cells. These two modes of communication are not mutually exclusive, but probably work in conjunction in many cases. We present a model of a two-dimensional network of glial cells that incorporates regenerative intercellular (GJ) and extracellular (ATP) pathways. In the extreme cases of only one type of pathway, the results are in agreement with previous models. Adding an extracellular pathway to the GJ model increased the extent and duration of the Ca(2+) wave, but did not significantly change the speed of propagation. Conversely, adding GJs to the extracellular model did increase the wave speed. The model was modified to apply to the retina by extending it to include both astrocytes and Müller cells, with GJs the dominant coupling between astrocytes and ATP responsible for most of the remaining communication. It was found that both pathways are necessary to account for experimental results.

Modeling species-specific diacylglycerol dynamics in the RAW 264.7 macrophage

A mathematical model of the G protein signaling pathway in RAW 264.7 macrophages downstream of P2Y(6) receptors activated by the ubiquitous signaling nucleotide uridine 5'-diphosphate is developed. The model, which is based on time-course measurements of inositol trisphosphate, cytosolic calcium, and diacylglycerol, focuses particularly on differential dynamics of multiple chemical species of diacylglycerol. When using the canonical pathway representation, the model predicted that key interactions were missing from the current network structure. Indeed, the model suggested that accurate depiction of experimental observations required an additional branch to the signaling pathway. An intracellular pool of diacylglycerol is immediately phosphorylated upon stimulation of an extracellular receptor for uridine 5'-diphosphate and subsequently used to aid replenishment of phosphatidylinositol. As a result of sensitivity analysis of the model parameters, key predictions can be made regarding which of these parameters are the most sensitive to perturbations and are therefore most responsible for output uncertainty.

Modeling and analysis of the molecular basis of pain in sensory neurons

Intracellular calcium dynamics are critical to cellular functions like pain transmission. Extracellular ATP plays an important role in modulating intracellular calcium levels by interacting with the P2 family of surface receptors. In this study, we developed a mechanistic mathematical model of ATP-induced P2 mediated calcium signaling in archetype sensory neurons. The model architecture, which described 90 species connected by 162 interactions, was formulated by aggregating disparate molecular modules from literature. Unlike previous models, only mass action kinetics were used to describe the rate of molecular interactions. Thus, the majority of the 252 unknown model parameters were either association, dissociation or catalytic rate constants. Model parameters were estimated from nine independent data sets taken from multiple laboratories. The training data consisted of both dynamic and steady-state measurements. However, because of the complexity of the calcium network, we were unable to estimate unique model parameters. Instead, we estimated a family or ensemble of probable parameter sets using a multi-objective thermal ensemble method. Each member of the ensemble met an error criterion and was located along or near the optimal trade-off surface between the individual training data sets. The model quantitatively reproduced experimental measurements from dorsal root ganglion neurons as a function of extracellular ATP forcing. Hypothesized architecture linking phosphoinositide regulation with P2X receptor activity explained the inhibition of P2X-mediated current flow by activated metabotropic P2Y receptors. Sensitivity analysis using individual and the whole system outputs suggested which molecular subsystems were most important following P2 activation. Taken together, modeling and analysis of ATP-induced P2 mediated calcium signaling generated qualitative insight into the critical interactions controlling ATP induced calcium dynamics. Understanding these critical interactions may prove useful for the design of the next generation of molecular pain management strategies.

Mathematical modelling of calcium wave propagation in mammalian airway epithelium: evidence for regenerative ATP release

Airway epithelium has been shown to exhibit intracellular calcium waves after mechanical stimulation. Two classes of mechanism have been proposed to explain calcium wave propagation: diffusion through gap junctions of the intracellular messenger inositol 1,4,5-trisphosphate (IP3), and diffusion of paracrine extracellular messengers such as ATP. We have used single cell recordings of airway epithelium to parameterize a model of an airway epithelial cell. This was then incorporated into a spatial model of a cell culture where both mechanisms for calcium wave propagation are possible. It is shown that a decreasing return on the radius of Ca2+ wave propagation is achieved as the amount of ATP released from the stimulated cell increases. It is therefore shown that for a Ca2+ wave to propagate large distances, a significant fraction of the intracellular ATP pool would be required to be released. Further to this, the radial distribution of maximal calcium response from the stimulated cell does not produce the same flat profile of maximal calcium response seen in experiential studies. This suggests that an additional mechanism is important in Ca2+ wave propagation, such as regenerative release of ATP from cells downstream of the stimulated cell.

P2X7 regenerative-loop potentiation of glutamate synaptic transmission by microglia and astrocytes

P2X7 purinergic receptors have been implicated in chronic neuropathic and neuroinflammatory pain as well as in depression. These receptors are predominantly found in the central nervous system on microglial cells and on glutamatergic nerve terminals. Here, we develop hypotheses concerning mechanisms by which transient high-frequency impulse firing in glutamatergic terminals, such as occurs in nociceptor terminals accompanying neuropathic/neuroinflammatory pain, can lead to long-lasting changes in neural network function that is mediated by surrounding glial cells. The hypothesis consists of two parts. In the first, glutamate released by low-frequency (2Hz) terminal action potentials is insufficient to generate postsynaptic action potentials, but these are generated by brief high-frequency input bursts. Glutamate released by these bursts is partly removed by transporters on the enveloping astrocyte processes and also excites AMPA receptors on these processes, which then release ATP. This ATP is partly metabolised to adenosine, which acts on presynaptic A1 receptors to inhibit glutamate release. The remaining ATP acts on the presynaptic P2X7 receptors to facilitate glutamate release by both the high-frequency burst of action potentials as well as by a continuous low-frequency (2Hz) action potential firing that occurs in the absence of a neuropathic/neuroinflammatory insult. The positive feedback of terminal glutamate release, triggering astrocyte ATP release and leading to further glutamate release through activation of P2X7 receptors, is then sufficient to allow the normal low-frequency (2Hz) action potentials to now elicit postsynaptic action potentials after the insult is removed. In the second part of this model, the high concentration of ATP derived from astrocytes at the terminal attracts microglia by chemotaxis. The P2X7 receptors on these microglia are then engaged, resulting in microglia secreting the cytokine TNFalpha. This acts on postsynaptic TNF-R1 receptors to increase the number of AMPA receptors there, thus enhancing the efficacy of synaptic transmission. The TNFalpha also acts on presynaptic TNF-R1 to increase the amount of glutamate released by each nerve terminal impulse. Experimental tests can be made of this hypothesis that P2X7 receptors on the presynaptic terminal and those on the microglia synergistically act to ensure feedback pathways that reset to a high level the efficacy of synaptic transmission, thus ensuring chronic neuropathic/neuroinflammatory pain even when the initial insult has subsided.

Modelling of the activation of G-protein coupled receptors: drug free constitutive receptor activity

G-protein coupled receptors (GPCRs) form a crucial component of approximately 80% of hormone pathways. In this paper, the most popular mechanism for activation of GPCRs-the shuttling mechanism-is modelled mathematically. An asymptotic analysis of this model clarifies the dynamics of the system in the absence of drug, in particular which reactions dominate during the different timescales. Equilibrium analysis of the model demonstrates the model's ability to predict constitutive receptor activity.

A dual receptor crosstalk model of G-protein-coupled signal transduction

Macrophage cells that are stimulated by two different ligands that bind to G-protein-coupled receptors (GPCRs) usually respond as if the stimulus effects are additive, but for a minority of ligand combinations the response is synergistic. The G-protein-coupled receptor system integrates signaling cues from the environment to actuate cell morphology, gene expression, ion homeostasis, and other physiological states. We analyze the effects of the two signaling molecules complement factors 5a (C5a) and uridine diphosphate (UDP) on the intracellular second messenger calcium to elucidate the principles that govern the processing of multiple signals by GPCRs. We have developed a formal hypothesis, in the form of a kinetic model, for the mechanism of action of this GPCR signal transduction system using data obtained from RAW264.7 macrophage cells. Bayesian statistical methods are employed to represent uncertainty in both data and model parameters and formally tie the model to experimental data. When the model is also used as a tool in the design of experiments, it predicts a synergistic region in the calcium peak height dose response that results when cells are simultaneously stimulated by C5a and UDP. An analysis of the model reveals a potential mechanism for crosstalk between the Galphai-coupled C5a receptor and the Galphaq-coupled UDP receptor signaling systems that results in synergistic calcium release.

beta2-adrenergic receptor signaling and desensitization elucidated by quantitative modeling of real time cAMP dynamics

G protein-coupled receptor signaling is dynamically regulated by multiple feedback mechanisms, which rapidly attenuate signals elicited by ligand stimulation, causing desensitization. The individual contributions of these mechanisms, however, are poorly understood. Here, we use an improved fluorescent biosensor for cAMP to measure second messenger dynamics stimulated by endogenous beta(2)-adrenergic receptor (beta(2)AR) in living cells. beta(2)AR stimulation with isoproterenol results in a transient pulse of cAMP, reaching a maximal concentration of approximately 10 microm and persisting for less than 5 min. We investigated the contributions of cAMP-dependent kinase, G protein-coupled receptor kinases, and beta-arrestin to the regulation of beta(2)AR signal kinetics by using small molecule inhibitors, small interfering RNAs, and mouse embryonic fibroblasts. We found that the cAMP response is restricted in duration by two distinct mechanisms in HEK-293 cells: G protein-coupled receptor kinase (GRK6)-mediated receptor phosphorylation leading to beta-arrestin mediated receptor inactivation and cAMP-dependent kinase-mediated induction of cAMP metabolism by phosphodiesterases. A mathematical model of beta(2)AR signal kinetics, fit to these data, revealed that direct receptor inactivation by cAMP-dependent kinase is insignificant but that GRK6/beta-arrestin-mediated inactivation is rapid and profound, occurring with a half-time of 70 s. This quantitative system analysis represents an important advance toward quantifying mechanisms contributing to the physiological regulation of receptor signaling.

Systems biology of macrophages

Cells and tissues function in context. Under a given growth or survival medium they perform tasks, replicate and die. Given a stimulus they respond by invoking myriad biomolecular networks that result in a specified cellular outcome. At any given instant it can be argued that the cell is in a "state" defined by its components--their concentrations and locations, the interactions between components--that are modulated in space and time, and the complex circuitry--that involves a large number of interacting networks and a snapshot of the dynamical processes--such as gene expression, cell cycle, transport of components, etc. At present, we can measure, using high and low throughput methods, several cellular components in a context-dependent manner and obtain a partial picture of cellular networks and dynamical processes. Are these measurements sufficient to answer important biological questions and help reconstruct a systems-level understanding of a mammalian cell? This chapter will address systems biology strategies developed to address this question and demonstrate the power of integration of diverse cellular data for answering interesting biological questions in macrophages. We will use this systems biology approach to address the following questions: (1) How good are macrophage cell lines in addressing phenotypic biology of primary macrophages? (2) How do signals associated with inflammatory molecules regulate gene transcription in macrophages? (3) How can we combine proteomic and other cellular measurements to characterize the repertoire of upstream signaling networks invoked by macrophages? (4) How do designed knockdowns of proteins influence cellular phenotypes?

Origins of blood volume change due to glutamatergic synaptic activity at astrocytes abutting on arteriolar smooth muscle cells

The cellular mechanisms that couple activity of glutamatergic synapses with changes in blood flow, measured by a variety of techniques including the BOLD signal, have not previously been modelled. Here we provide such a model, that successfully accounts for the main observed changes in blood flow in both visual cortex and somatosensory cortex following their stimulation by high-contrast drifting grating or by single whisker stimulation, respectively. Coupling from glutamatergic synapses to smooth muscle cells of arterioles is effected by astrocytes releasing epoxyeicosatrienoic acids (EETs) onto them, following glutamate stimulation of the astrocyte. Coupling of EETs to the smooth muscle of arterioles is by means of potassium channels in their membranes, leading to hyperpolarization, relaxation and hence an increase in blood flow. This model predicts a linear increase in blood flow with increasing numbers of activated astrocytes, but a non-linear increase with increasing glutamate release.

A kinetic model for calcium dynamics in RAW 264.7 cells: 1. Mechanisms, parameters, and subpopulational variability

Calcium (Ca(2+)) is an important second messenger and has been the subject of numerous experimental measurements and mechanistic studies in intracellular signaling. Calcium profile can also serve as a useful cellular phenotype. Kinetic models of calcium dynamics provide quantitative insights into the calcium signaling networks. We report here the development of a complex kinetic model for calcium dynamics in RAW 264.7 cells stimulated by the C5a ligand. The model is developed using the vast number of measurements of in vivo calcium dynamics carried out in the Alliance for Cellular Signaling (AfCS) Laboratories. Ligand binding, phospholipase C-beta (PLC-beta) activation, inositol 1,4,5-trisphosphate (IP(3)) receptor (IP(3)R) dynamics, and calcium exchange with mitochondria and extracellular matrix have all been incorporated into the model. The experimental data include data from both native and knockdown cell lines. Subpopulational variability in measurements is addressed by allowing nonkinetic parameters to vary across datasets. The model predicts temporal response of Ca(2+) concentration for various doses of C5a under different initial conditions. The optimized parameters for IP(3)R dynamics are in agreement with the legacy data. Further, the half-maximal effect concentration of C5a and the predicted dose response are comparable to those seen in AfCS measurements. Sensitivity analysis shows that the model is robust to parametric perturbations.

A kinetic model for calcium dynamics in RAW 264.7 cells: 2. Knockdown response and long-term response

This article addresses how quantitative models such as the one proposed in the companion article can be used to study cellular network perturbations such as knockdowns and pharmacological perturbations in a predictive manner. Using the kinetic model for cytosolic calcium dynamics in RAW 264.7 cells developed in the companion article, the calcium response to complement 5a (C5a) for the knockdown of seven proteins (C5a receptor; G-beta-2; G-alpha,i-2,3; regulator of G-protein signaling-10; G-protein coupled receptor kinase-2; phospholipase C beta-3; arrestin) is predicted and validated against the data from the Alliance for Cellular Signaling. The knockdown responses provide insights into how altered expressions of important proteins in disease states result in intermediate measurable phenotypes. Long-term response and long-term dose response have also been predicted, providing insights into how the receptor desensitization, internalization, and recycle result in tolerance. Sensitivity analysis of long-term response shows that the mechanisms and parameters in the receptor recycle path are important for long-term calcium dynamics.