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

Modeling transcriptional regulation of the cell cycle using a novel cybernetic-inspired approach

Quantitative understanding of cellular processes, such as cell cycle and differentiation, is impeded by various forms of complexity ranging from myriad molecular players and their multilevel regulatory interactions, cellular evolution with multiple intermediate stages, lack of elucidation of cause-effect relationships among the many system players, and the computational complexity associated with the profusion of variables and parameters. In this paper, we present a modeling framework based on the cybernetic concept that biological regulation is inspired by objectives embedding rational strategies for dimension reduction, process stage specification through the system dynamics, and innovative causal association of regulatory events with the ability to predict the evolution of the dynamical system. The elementary step of the modeling strategy involves stage-specific objective functions that are computationally determined from experiments, augmented with dynamical network computations involving endpoint objective functions, mutual information, change-point detection, and maximal clique centrality. We demonstrate the power of the method through application to the mammalian cell cycle, which involves thousands of biomolecules engaged in signaling, transcription, and regulation. Starting with a fine-grained transcriptional description obtained from RNA sequencing measurements, we develop an initial model, which is then dynamically modeled using the cybernetic-inspired method, based on the strategies described above. The cybernetic-inspired method is able to distill the most significant interactions from a multitude of possibilities. In addition to capturing the complexity of regulatory processes in a mechanistically causal and stage-specific manner, we identify the functional network modules, including novel cell cycle stages. Our model is able to predict future cell cycles consistent with experimental measurements. We posit that this innovative framework has the promise to extend to the dynamics of other biological processes, with a potential to provide novel mechanistic insights.

Modeling transcriptional regulation of the cell cycle using a novel cybernetic-inspired approach

Quantitative understanding of cellular processes, such as cell cycle and differentiation, is impeded by various forms of complexity ranging from myriad molecular players and their multilevel regulatory interactions, cellular evolution with multiple intermediate stages, lack of elucidation of cause-effect relationships among the many system players, and the computational complexity associated with the profusion of variables and parameters. In this paper, we present an elegant modeling framework based on the cybernetic concept that biological regulation is inspired by objectives embedding entirely novel strategies for dimension reduction, process stage specification through the system dynamics, and innovative causal association of regulatory events with the ability to predict the evolution of the dynamical system. The elementary step of the modeling strategy involves stage-specific objective functions that are computationally-determined from experiments, augmented with dynamical network computations involving end point objective functions, mutual information, change point detection, and maximal clique centrality. We demonstrate the power of the method through application to the mammalian cell cycle, which involves thousands of biomolecules engaged in signaling, transcription, and regulation. Starting with a fine-grained transcriptional description obtained from RNA sequencing measurements, we develop an initial model, which is then dynamically modeled using the cybernetic-inspired method (CIM), utilizing the strategies described above. The CIM is able to distill the most significant interactions from a multitude of possibilities. In addition to capturing the complexity of regulatory processes in a mechanistically causal and stage-specific manner, we identify the functional network modules, including novel cell cycle stages. Our model is able to predict future cell cycles consistent with experimental measurements. We posit that this state-of-the-art framework has the promise to extend to the dynamics of other biological processes, with a potential to provide novel mechanistic insights.

STATEMENT OF SIGNIFICANCE

Cellular processes like cell cycle are overly complex, involving multiple players interacting at multiple levels, and explicit modeling of such systems is challenging. The availability of longitudinal RNA measurements provides an opportunity to "reverse-engineer" for novel regulatory models. We develop a novel framework, inspired using goal-oriented cybernetic model, to implicitly model transcriptional regulation by constraining the system using inferred temporal goals. A preliminary causal network based on information-theory is used as a starting point, and our framework is used to distill the network to temporally-based networks containing essential molecular players. The strength of this approach is its ability to dynamically model the RNA temporal measurements. The approach developed paves the way for inferring regulatory processes in many complex cellular processes.

Mathematical Modeling of Eicosanoid Metabolism in Macrophage Cells: Cybernetic Framework Combined with Novel Information-Theoretic Approaches

Cellular response to inflammatory stimuli leads to the production of eicosanoids—prostanoids (PRs) and leukotrienes (LTs)—and signaling molecules—cytokines and chemokines—by macrophages. Quantitative modeling of the inflammatory response is challenging owing to a lack of knowledge of the complex regulatory processes involved. Cybernetic models address these challenges by utilizing a well-defined cybernetic goal and optimizing a coarse-grained model toward this goal. We developed a cybernetic model to study arachidonic acid (AA) metabolism, which included two branches, PRs and LTs. We utilized a priori biological knowledge to define the branch-specific cybernetic goals for PR and LT branches as the maximization of TNFα and CCL2, respectively. We estimated the model parameters by fitting data from three experimental conditions. With these parameters, we were able to capture a novel fourth independent experimental condition as part of the model validation. The cybernetic model enhanced our understanding of enzyme dynamics by predicting their profiles. The success of the model implies that the cell regulates the synthesis and activity of the associated enzymes, through cybernetic control variables, to accomplish the chosen biological goal. The results indicated that the dominant metabolites are PGD2 (a PR) and LTB4 (an LT), aligning with their corresponding known prominent biological roles during inflammation. Using heuristic arguments, we also infer that eicosanoid overproduction can lead to increased secretion of cytokines/chemokines. This novel model integrates mechanistic knowledge, known biological understanding of signaling pathways, and data-driven methods to study the dynamics of eicosanoid metabolism.

Mechanisms underlying divergent relationships between Ca2+ and YAP/TAZ signalling

Yes-associated protein (YAP) and its homologue TAZ are transducers of several biochemical and biomechanical signals, integrating multiplexed inputs from the microenvironment into higher level cellular functions such as proliferation, differentiation and migration. Emerging evidence suggests that Ca2+ is a key second messenger that connects microenvironmental input signals and YAP/TAZ regulation. However, studies that directly modulate Ca2+ have reported contradictory YAP/TAZ responses: in some studies, a reduction in Ca2+ influx increases the activity of YAP/TAZ, while in others, an increase in Ca2+ influx activates YAP/TAZ. Importantly, Ca2+ and YAP/TAZ exhibit distinct spatiotemporal dynamics, making it difficult to unravel their connections from a purely experimental approach. In this study, we developed a network model of Ca2+ -mediated YAP/TAZ signalling to investigate how temporal dynamics and crosstalk of signalling pathways interacting with Ca2+ can alter the YAP/TAZ response, as observed in experiments. By including six signalling modules (e.g. GPCR, IP3-Ca2+ , kinases, RhoA, F-actin and Hippo-YAP/TAZ) that interact with Ca2+ , we investigated both transient and steady-state cell response to angiotensin II and thapsigargin stimuli. The model predicts that stimuli, Ca2+ transients and frequency-dependent relationships between Ca2+ and YAP/TAZ are primarily mediated by cPKC, DAG, CaMKII and F-actin. Simulation results illustrate the role of Ca2+ dynamics and CaMKII bistable response in switching the direction of changes in Ca2+ -induced YAP/TAZ activity. A frequency-dependent YAP/TAZ response revealed the competition between upstream regulators of LATS1/2, leading to the YAP/TAZ non-monotonic response to periodic GPCR stimulation. This study provides new insights into underlying mechanisms responsible for the controversial Ca2+ -YAP/TAZ relationship observed in experiments. KEY POINTS: YAP/TAZ integrates biochemical and biomechanical inputs to regulate cellular functions, and Ca2+ acts as a key second messenger linking cellular inputs to YAP/TAZ. Studies have reported contradictory Ca2+ -YAP/TAZ relationships for different cell types and stimuli. A network model of Ca2+ -mediated YAP/TAZ signalling was developed to investigate the underlying mechanisms of divergent Ca2+ -YAP/TAZ relationships. The model predicts context-dependent Ca2+ transient, CaMKII bistable response and frequency-dependent activation of LATS1/2 upstream regulators as mechanisms governing the Ca2+ -YAP/TAZ relationship. This study provides new insights into the underlying mechanisms of the controversial Ca2+ -YAP/TAZ relationship to better understand the dynamics of cellular functions controlled by YAP/TAZ activity.

Modeling of Endothelial Calcium Responses within a Microfluidic Generator of Spatio-Temporal ATP and Shear Stress Signals

Intracellular calcium dynamics play essential roles in the proper functioning of cellular activities. It is a well known important chemosensing and mechanosensing process regulated by the spatio-temporal microenvironment. Nevertheless, how spatio-temporal biochemical and biomechanical stimuli affect calcium dynamics is not fully understood and the underlying regulation mechanism remains missing. Herein, based on a developed microfluidic generator of biochemical and biomechanical signals, we theoretically analyzed the generation of spatio-temporal ATP and shear stress signals within the microfluidic platform and investigated the effect of spatial combination of ATP and shear stress stimuli on the intracellular calcium dynamics. The simulation results demonstrate the capacity and flexibility of the microfluidic system in generating spatio-temporal ATP and shear stress. Along the transverse direction of the microchannel, dynamic ATP signals of distinct amplitudes coupled with identical shear stress are created, which induce the spatio-temporal diversity in calcium responses. Interestingly, to the multiple combinations of stimuli, the intracellular calcium dynamics reveal two main modes: unimodal and oscillatory modes, showing significant dependence on the features of the spatio-temporal ATP and shear stress stimuli. The present study provides essential information for controlling calcium dynamics by regulating spatio-temporal biochemical and biomechanical stimuli, which shows the potential in directing cellular activities and understanding the occurrence and development of disease.

Dendritic spine geometry and spine apparatus organization govern the spatiotemporal dynamics of calcium

Dendritic spines are small subcompartments that protrude from the dendrites of neurons and are important for signaling activity and synaptic communication. These subcompartments have been characterized to have different shapes. While it is known that these shapes are associated with spine function, the specific nature of these shape-function relationships is not well understood. In this work, we systematically investigated the relationship between the shape and size of both the spine head and spine apparatus, a specialized endoplasmic reticulum compartment within the spine head, in modulating rapid calcium dynamics using mathematical modeling. We developed a spatial multicompartment reaction-diffusion model of calcium dynamics in three dimensions with various flux sources, including N-methyl-D-aspartate receptors (NMDARs), voltage-sensitive calcium channels (VSCCs), and different ion pumps on the plasma membrane. Using this model, we make several important predictions. First, the volume to surface area ratio of the spine regulates calcium dynamics. Second, membrane fluxes impact calcium dynamics temporally and spatially in a nonlinear fashion. Finally, the spine apparatus can act as a physical buffer for calcium by acting as a sink and rescaling the calcium concentration. These predictions set the stage for future experimental investigations of calcium dynamics in dendritic spines.

Human T cells in silico: Modelling dynamic intracellular calcium and its influence on cellular electrophysiology

A network of ion currents influences basic cellular T cell functions. After T cell receptor activation, changes in highly regulated calcium levels play a central role in triggering effector functions and cell differentiation. A dysregulation of these processes might be involved in the pathogenesis of several diseases. We present a mathematical model based on the NEURON simulation environment that computes dynamic calcium levels in combination with the current output of diverse ion channels (K_V1.3, K_Ca3.1, K_2P channels (TASK1-3, TRESK), VRAC, TRPM7, CRAC). In line with experimental data, the simulation shows a strong increase in intracellular calcium after T cell receptor stimulation before reaching a new, elevated calcium plateau in the T cell's activated state. Deactivation of single ion channel modules, mimicking the application of channel blockers, reveals that two types of potassium channels are the main regulators of intracellular calcium level: calcium-dependent potassium (K_Ca3.1) and two-pore-domain potassium (K_2P) channels.

Two independent but synchronized Gβγ subunit-controlled pathways are essential for trailing-edge retraction during macrophage migration

Chemokine-induced directional cell migration is a universal cellular mechanism and plays crucial roles in numerous biological processes, including embryonic development, immune system function, and tissue remodeling and regeneration. During the migration of a stationary cell, the cell polarizes, forms lamellipodia at the leading edge (LE), and triggers the concurrent retraction of the trailing edge (TE). During cell migration governed by inhibitory G protein (G_i)-coupled receptors (GPCRs), G protein βγ (Gβγ) subunits control the LE signaling. Interestingly, TE retraction has been linked to the activation of the small GTPase Ras homolog family member A (RhoA) by the Gα_12/13 pathway. However, it is not clear how the activation of G_i-coupled GPCRs at the LE orchestrates the TE retraction in RAW264.7 macrophages. Here, using an optogenetic approach involving an opsin to activate the G_i pathway in defined subcellular regions of RAW cells, we show that in addition to their LE activities, free Gβγ subunits also govern TE retraction by operating two independent, yet synchronized, pathways. The first pathway involves RhoA activation, which prevents dephosphorylation of the myosin light chain, allowing actomyosin contractility to proceed. The second pathway activates phospholipase Cβ and induces myosin light chain phosphorylation to enhance actomyosin contractility through increasing cytosolic calcium. We further show that both of these pathways are essential, and inhibition of either one is sufficient to abolish the G_i-coupled GPCR-governed TE retraction and subsequent migration of RAW cells.

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.

Calcium Dynamics of Ex Vivo Long-Term Cultured CD8+ T Cells Are Regulated by Changes in Redox Metabolism

T cells reach a state of replicative senescence characterized by a decreased ability to proliferate and respond to foreign antigens. Calcium release associated with TCR engagement is widely used as a surrogate measure of T cell response. Using an ex vivo culture model that partially replicates features of organismal aging, we observe that while the amplitude of Ca2+ signaling does not change with time in culture, older T cells exhibit faster Ca2+ rise and a faster decay. Gene expression analysis of Ca2+ channels and pumps expressed in T cells by RT-qPCR identified overexpression of the plasma membrane CRAC channel subunit ORAI1 and PMCA in older T cells. To test whether overexpression of the plasma membrane Ca2+ channel is sufficient to explain the kinetic information, we adapted a previously published computational model by Maurya and Subramaniam to include additional details on the store-operated calcium entry (SOCE) process to recapitulate Ca2+ dynamics after T cell receptor stimulation. Simulations demonstrated that upregulation of ORAI1 and PMCA channels is not sufficient to explain the observed alterations in Ca2+ signaling. Instead, modeling analysis identified kinetic parameters associated with the IP3R and STIM1 channels as potential causes for alterations in Ca2+ dynamics associated with the long term ex vivo culturing protocol. Due to these proteins having known cysteine residues susceptible to oxidation, we subsequently investigated and observed transcriptional remodeling of metabolic enzymes, a shift to more oxidized redox couples, and post-translational thiol oxidation of STIM1. The model-directed findings from this study highlight changes in the cellular redox environment that may ultimately lead to altered T cell calcium dynamics during immunosenescence or organismal aging.

Endothelial cells decode VEGF-mediated Ca2+ signaling patterns to produce distinct functional responses

A single extracellular stimulus can promote diverse behaviors among isogenic cells by differentially regulated signaling networks. We examined Ca(2+) signaling in response to VEGF (vascular endothelial growth factor), a growth factor that can stimulate different behaviors in endothelial cells. We found that altering the amount of VEGF signaling in endothelial cells by stimulating them with different VEGF concentrations triggered distinct and mutually exclusive dynamic Ca(2+) signaling responses that correlated with different cellular behaviors. These behaviors were cell proliferation involving the transcription factor NFAT (nuclear factor of activated T cells) and cell migration involving MLCK (myosin light chain kinase). Further analysis suggested that this signal decoding was robust to the noisy nature of the signal input. Using probabilistic modeling, we captured both the stochastic and deterministic aspects of Ca(2+) signal decoding and accurately predicted cell responses in VEGF gradients, which we used to simulate different amounts of VEGF signaling. Ca(2+) signaling patterns associated with proliferation and migration were detected during angiogenesis in developing zebrafish.

The macrophage and its role in inflammation and tissue repair: mathematical and systems biology approaches

Macrophages are central to the inflammatory response and its ability to resolve effectively. They are complex cells that adopt a range of subtypes depending on the tissue type and stimulus that they find themselves under. This flexibility allows them to play multiple, sometimes opposing, roles in inflammation and tissue repair. Their central role in the inflammatory process is reflected in macrophage dysfunction being implicated in chronic inflammation and poorly healing wounds. In this study, we discuss recent attempts to model mathematically and computationally the macrophage and how it partakes in the complex processes of inflammation and tissue repair. There are increasing data describing the variety of macrophage phenotypes and their underlying transcriptional programs. Dynamic mathematical and computational models are an ideal way to test biological hypotheses against experimental data and could aid in understanding this multi-functional cell and its potential role as an attractive therapeutic target for inflammatory conditions and tissue repair.

Immobilized IL-8 Triggers Phagocytosis and Dynamic Changes in Membrane Microtopology in Human Neutrophils

The interaction of leukocytes with surface bound ligands can be limited by the location of the molecules relative to the surface topology of the cell. In this report, we examine the dynamic response of neutrophils to IL-8-fractalkine chimera immobilized on bead surfaces, taking into account changes in receptor occupancy resulting from changes in surface topography. As a readout for receptor signaling, we observe the dynamics of calcium release in neutrophils following contact with the IL-8 coated surface. After a delay that depended on the initial area of contact and the surface density of IL-8, the cell began to phagocytose the IL-8 coated bead. This appeared to be a pre-requisite for release of calcium, which typically followed shortly after the initiation of phagocytosis. In separate experiments, effective kinetic coefficients for the formation of bonds between immobilized IL-8 and receptors on the cell surface were determined. Using these coefficients, we were able to estimate the number of bound receptors in the nascent contact zone. Kinetic modeling of the signaling response predicted that cell spreading and a concomitant increase in the density of occupied receptors would be required for the experimentally observed calcium dynamics. Postulating that there is an increase in receptor occupancy resulting from smoothing of the cell surface as it is stretched over the bead enabled us to obtain model predictions consistent with experimental observations. This study reveals the likely importance of membrane microtopology as a rate-limiting property and potential means of regulation of cell responses stimulated by two-dimensional surface interactions.

Modulation of the cAMP response by Gαi and Gβγ: a computational study of G protein signaling in immune cells

Cyclic AMP is important for the resolution of inflammation, as it promotes anti-inflammatory signaling in several immune cell lines. In this paper, we present an immune cell specific model of the cAMP signaling cascade, paying close attention to the specific isoforms of adenylyl cyclase (AC) and phosphodiesterase that control cAMP production and degradation, respectively, in these cells. The model describes the role that G protein subunits, including Gαs, Gαi, and Gβγ, have in regulating cAMP production. Previously, Gαi activation has been shown to increase the level of cAMP in certain immune cell types. This increase in cAMP is thought to be mediated by βγ subunits which are released upon Gα activation and can directly stimulate specific isoforms of AC. We conduct numerical experiments in order to explore the mechanisms through which Gαi activation can increase cAMP production. An important conclusion of our analysis is that the relative abundance of different G protein subunits is an essential determinant of the cAMP profile in immune cells. In particular, our model predicts that limited availability of βγ subunits may both (i) enable immune cells to link inflammatory Gαi signaling to anti-inflammatory cAMP production thereby creating a balanced immune response to stimulation with low concentrations of PGE2, and (ii) prohibit robust anti-inflammatory cAMP signaling in response to stimulation with high concentrations of PGE2.

Microfluidic interrogation and mathematical modeling of multi-regime calcium signaling dynamics

Through microfluidic interrogation we analyzed real-time calcium responses of HEK293 cells stimulated with short pulses of the M3 muscarinic receptor ligand carbachol in two different concentration regimes. Lower ligand concentrations elicit oscillatory calcium signals while higher concentrations trigger a rapid rise that eventually settles down at a steady-state slightly above pre-stimulus levels, referred to as an acute signal. Cells were periodically pulsed with carbachol at these two concentration regimes using a custom-made microfluidic platform, and the resulting calcium signals were measured with a single fluorescent readout. Pulsed stimulations at these two concentration regimes resulted in multiple types of response patterns that each delivered complementary information about the M3 muscarinic receptor signaling pathway. These multiple types of calcium response patterns enabled development of a comprehensive mathematical model of multi-regime calcium signaling. The resulting model suggests that dephosphorylation of deactivated receptors is rate limiting for recovery of calcium signals in the acute regime (high ligand concentration), while calcium replenishment and IP3 production determine signal recovery in the oscillatory regime (low ligand concentration). This study not only provides mechanistic insight into multi-regime signaling of the M3 muscarinic receptor pathway, but also provides a general strategy for analyzing multi-regime pathways using only one fluorescent readout.

Functional classification of skeletal muscle networks. I. Normal physiology

Extensive measurements of the parts list of human skeletal muscle through transcriptomics and other phenotypic assays offer the opportunity to reconstruct detailed functional models. Through integration of vast amounts of data present in databases and extant knowledge of muscle function combined with robust analyses that include a clustering approach, we present both a protein parts list and network models for skeletal muscle function. The model comprises the four key functional family networks that coexist within a functional space; namely, excitation-activation family (forward pathways that transmit a motoneuronal command signal into the spatial volume of the cell and then use Ca(2+) fluxes to bind Ca(2+) to troponin C sites on F-actin filaments, plus transmembrane pumps that maintain transmission capacity); mechanical transmission family (a sophisticated three-dimensional mechanical apparatus that bidirectionally couples the millions of actin-myosin nanomotors with external axial tensile forces at insertion sites); metabolic and bioenergetics family (pathways that supply energy for the skeletal muscle function under widely varying demands and provide for other cellular processes); and signaling-production family (which represents various sensing, signal transduction, and nuclear infrastructure that controls the turn over and structural integrity and regulates the maintenance, regeneration, and remodeling of the muscle). Within each family, we identify subfamilies that function as a unit through analysis of large-scale transcription profiles of muscle and other tissues. This comprehensive network model provides a framework for exploring functional mechanisms of the skeletal muscle in normal and pathophysiology, as well as for quantitative modeling.

An integrated stochastic model of "inside-out" integrin activation and selective T-lymphocyte recruitment

The pattern of T-lymphocyte homing is hypothesized to be controlled by combinations of chemokine receptors and complementary chemokines. Here, we use numerical simulation to explore the relationship among chemokine potency and concentration, signal transduction, and adhesion. We have developed a form of adhesive dynamics-a mechanically accurate stochastic simulation of adhesion-that incorporates stochastic signal transduction using the next subvolume method. We show that using measurable parameter estimates derived from a variety of sources, including signaling measurements that allow us to test parameter values, we can readily simulate approximate time scales for T-lymphocyte arrest. We find that adhesion correlates with total chemokine receptor occupancy, not the frequency of occupation, when multiple chemokine receptors feed through a single G-protein. A general strategy for selective T-lymphocyte recruitment appears to require low affinity chemokine receptors. For a single chemokine receptor, increases in multiple cross-reactive chemokines can lead to an overwhelming increase in adhesion. Overall, the methods presented here provide a predictive framework for understanding chemokine control of T-lymphocyte recruitment.

High-throughput analysis of calcium signalling kinetics in astrocytes stimulated with different neurotransmitters

Astrocytes express a wide range of receptors for neurotransmitters and hormones that are coupled to increases in intracellular Ca²⁺ concentration, enabling them to detect activity in both neuronal and vascular networks. There is increasing evidence that astrocytes are able to discriminate between different Ca²⁺-linked stimuli, as the efficiency of some Ca²⁺ dependent processes – notably release of gliotransmitters – depends on the stimulus that initiates the Ca²⁺ signal. The spatiotemporal complexity of Ca²⁺ signals is substantial, and we here tested the hypothesis that variation in the kinetics of Ca²⁺ responses could offer a means of selectively engaging downstream targets, if agonists exhibited a “signature shape” in evoked Ca²⁺ response. To test this, astrocytes were exposed to three different receptor agonists (ATP, glutamate and histamine) and the resultant Ca²⁺ signals were analysed for systematic differences in kinetics that depended on the initiating stimulus. We found substantial heterogeneity between cells in the time course of Ca²⁺ responses, but the variation did not correlate with the type or concentration of the stimulus. Using a simple metric to quantify the extent of difference between populations, it was found that the variation between agonists was insufficient to allow signal discrimination. We conclude that the time course of global intracellular Ca²⁺ signals does not offer the cells a means for distinguishing between different neurotransmitters.

Designing optimal calcium phosphate scaffold-cell combinations using an integrative model-based approach

Bone formation is a very complex physiological process, involving the participation of many different cell types and regulated by countless biochemical, physical and mechanical factors, including naturally occurring or synthetic biomaterials. For the latter, calcium phosphate (CaP)-based scaffolds have proven to stimulate bone formation, but at present still result in a wide range of in vivo outcomes, which is partly related to the suboptimal use and combination with osteogenic cells. To optimize CaP scaffold selection and make their use in combination with cells more clinically relevant, this study uses an integrative approach in which mathematical modeling is combined with experimental research. This paper describes the development and implementation of an experimentally informed bioregulatory model of the effect of calcium ions released from CaP-based biomaterials on the activity of osteogenic cells and mesenchymal stem cell driven ectopic bone formation. The amount of bone formation predicted by the mathematical model corresponds to the amount measured experimentally under similar conditions. Moreover, the model is also able to qualitatively predict the experimentally observed impaired bone formation under conditions such as insufficient cell seeding and scaffold decalcification. A strategy was designed in silico to overcome the negative influence of a low initial cell density on the bone formation process. Finally, the model was applied to design optimal combinations of calcium-based biomaterials and cell culture conditions with the aim of maximizing the amount of bone formation. This work illustrates the potential of mathematical models as research tools to design more efficient and cell-customized CaP scaffolds for bone tissue engineering applications.

Exploring phospholipase C-coupled Ca(2+) signalling networks using Boolean modelling

In this study, the authors explored the utility of a descriptive and predictive bionetwork model for phospholipase C-coupled calcium signalling pathways, built with non-kinetic experimental information. Boolean models generated from these data yield oscillatory activity patterns for both the endoplasmic reticulum resident inositol-1,4,5-trisphosphate receptor (IP(3)R) and the plasma-membrane resident canonical transient receptor potential channel 3 (TRPC3). These results are specific as randomisation of the Boolean operators ablates oscillatory pattern formation. Furthermore, knock-out simulations of the IP(3)R, TRPC3 and multiple other proteins recapitulate experimentally derived results. The potential of this approach can be observed by its ability to predict previously undescribed cellular phenotypes using in vitro experimental data. Indeed, our cellular analysis of the developmental and calcium-regulatory protein, DANGER1a, confirms the counter-intuitive predictions from our Boolean models in two highly relevant cellular models. Based on these results, the authors theorise that with sufficient legacy knowledge and/or computational biology predictions, Boolean networks can provide a robust method for predictive modelling of any biological system. [Includes supplementary material].

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)).

Integration of lipidomics and transcriptomics data towards a systems biology model of sphingolipid metabolism

Background

Sphingolipids play important roles in cell structure and function as well as in the pathophysiology of many diseases. Many of the intermediates of sphingolipid biosynthesis are highly bioactive and sometimes have antagonistic activities, for example, ceramide promotes apoptosis whereas sphingosine-1-phosphate can inhibit apoptosis and induce cell growth; therefore, quantification of the metabolites and modeling of the sphingolipid network is imperative for an understanding of sphingolipid biology.

Results

In this direction, the LIPID MAPS Consortium is developing methods to quantitate the sphingolipid metabolites in mammalian cells and is investigating their application to studies of the activation of the RAW264.7 macrophage cell by a chemically defined endotoxin, Kdo₂-Lipid A. Herein, we describe a model for the C₁₆-branch of sphingolipid metabolism (i.e., for ceramides with palmitate as the N-acyl-linked fatty acid, which is selected because it is a major subspecies for all categories of complex sphingolipids in RAW264.7 cells) integrating lipidomics and transcriptomics data and using a two-step matrix-based approach to estimate the rate constants from experimental data. The rate constants obtained from the first step are further refined using generalized constrained nonlinear optimization. The resulting model fits the experimental data for all species. The robustness of the model is validated through parametric sensitivity analysis.

Conclusions

A quantitative model of the sphigolipid pathway is developed by integrating metabolomics and transcriptomics data with legacy knowledge. The model could be used to design experimental studies of how genetic and pharmacological perturbations alter the flux through this important lipid biosynthetic pathway.

Variability in G-protein-coupled signaling studied with microfluidic devices

Different cells, even those that are genetically identical, can respond differently to identical stimuli, but the precise source of this variability remains obscure. To study this problem, we built a microfluidic experimental system which can track responses of individual cells across multiple stimulations. We used this system to determine that amplitude variation in G-protein-activated calcium release in RAW264.7 macrophages is generally extrinsic, i.e., they arise from long-lived variations between cells and not from stochastic activation of signaling components. In the case of responses linked to P2Y family purine receptors, we estimate that approximately one-third of the observed variability in calcium release is receptor-specific. We further demonstrate that the signaling apparatus downstream of P2Y6 receptor activation is moderately saturable. These observations will be useful in constructing and constraining single-cell models of G protein-coupled calcium dynamics.

Importance of cell variability for calcium signaling in rat airway myocytes

Calcium signaling controls several essential physiological functions in different cell types. Hence, it is not surprising that different aspects of Ca(2+) dynamics are in the focus of in-depth and extensive investigations. Efforts concentrate on the development of proper theoretical models that would provide a unified description of Ca(2+) signaling. Remarkably, experimentally recorded Ca(2+) signals exhibit a rather large diversity, which can be observed irrespective of the cell type, measuring techniques, or the nature of the signal. Our goal in the present study therefore is to present a theoretical explanation for the variability observed in experiments, whereby we focus on caffeine-induced Ca(2+) responses in isolated airway myocytes. By employing a stochastic model, we first test whether the observed variability can be attributed to intrinsic fluctuations that are a common feature of biochemical reactions that govern Ca(2+) signalization. We find that stochastic effects, within ranges that correspond to actual conditions in the cell, are far too modest to explain the large diversity observed in experimental data. Foremost, we reveal that only cell variability in theoretical modeling can appropriately describe the observed diversity in single-cell responses.

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.

Lipid raft-mediated regulation of G-protein coupled receptor signaling by ligands which influence receptor dimerization: a computational study

G-protein coupled receptors (GPCRs) are the largest family of cell surface receptors; they activate heterotrimeric G-proteins in response to ligand stimulation. Although many GPCRs have been shown to form homo- and/or heterodimers on the cell membrane, the purpose of this dimerization is not known. Recent research has shown that receptor dimerization may have a role in organization of receptors on the cell surface. In addition, microdomains on the cell membrane termed lipid rafts have been shown to play a role in GPCR localization. Using a combination of stochastic (Monte Carlo) and deterministic modeling, we propose a novel mechanism for lipid raft partitioning of GPCRs based on reversible dimerization of receptors and then demonstrate that such localization can affect GPCR signaling. Modeling results are consistent with a variety of experimental data indicating that lipid rafts have a role in amplification or attenuation of G-protein signaling. Thus our work suggests a new mechanism by which dimerization-inducing or inhibiting characteristics of ligands can influence GPCR signaling by controlling receptor organization on the cell membrane.

An integrated model of eicosanoid metabolism and signaling based on lipidomics flux analysis

There is increasing evidence for a major and critical involvement of lipids in signal transduction and cellular trafficking, and this has motivated large-scale studies on lipid pathways. The Lipid Metabolites and Pathways Strategy consortium is actively investigating lipid metabolism in mammalian cells and has made available time-course data on various lipids in response to treatment with KDO(2)-lipid A (a lipopolysaccharide analog) of macrophage RAW 264.7 cells. The lipids known as eicosanoids play an important role in inflammation. We have reconstructed an integrated network of eicosanoid metabolism and signaling based on the KEGG pathway database and the literature and have developed a kinetic model. A matrix-based approach was used to estimate the rate constants from experimental data and these were further refined using generalized constrained nonlinear optimization. The resulting model fits the experimental data well for all species, and simulated enzyme activities were similar to their literature values. The quantitative model for eicosanoid metabolism that we have developed can be used to design experimental studies utilizing genetic and pharmacological perturbations to probe fluxes in lipid pathways.

Mixed-integer nonlinear optimisation approach to coarse-graining biochemical networks

Quantitative modelling and analysis of biochemical networks is challenging because of the inherent complexities and nonlinearities of the system and the limited availability of parameter values. Even if a mathematical model of the network can be developed, the lack of large-scale good-quality data makes accurate estimation of a large number of parameters impossible. Hence, coarse-grained models (CGMs) consisting of essential biochemical mechanisms are more suitable for computational analysis and for studying important systemic functions. The central question in constructing a CGM is which mechanisms should be deemed 'essential' and which can be ignored. Also, how should parameter values be defined when data are sparse? A mixed-integer nonlinear-programming (MINLP) based optimisation approach to coarse-graining is presented. Starting with a detailed biochemical model with associated computational details (reaction network and mathematical description) and data on the biochemical system, the structure and the parameters of a CGM can be determined simultaneously. In this optimisation problem, the authors use a genetic algorithm to simultaneously identify parameter values and remove unimportant reactions. The methodology is exemplified by developing two CGMs for the GTPase-cycle module of M1 muscarinic acetylcholine receptor, Gq, and regulator of G protein signalling 4 [RGS4, a GTPase-activating protein (GAP)] starting from a detailed model of 48 reactions. Both the CGMs have only 17 reactions, fit experimental data well and predict, as does the detailed model, four limiting signalling regimes (LSRs) corresponding to the extremes of receptor and GAP concentration. The authors demonstrate that coarse-graining, in addition to resulting in a reduced-order model, also provides insights into the mechanisms in the network. The best CGM obtained for the GTPase cycle also contains an unconventional mechanism and its predictions explain an old problem in pharmacology, the biphasic (bell-shaped) response to certain drugs. The MINLP methodology is broadly applicable to larger and complex (dense) biochemical modules.

Temporal switching and cell-to-cell variability in Ca2+ release activity in mammalian cells

Genetically identical cells in a uniform external environment can exhibit different phenotypes, which are often masked by conventional measurements that average over cell populations. Although most studies on this topic have used microorganisms, differentiated mammalian cells have rarely been explored. Here, we report that only approximately 40% of clonal human embryonic kidney 293 cells respond with an intracellular Ca²⁺ increase when ryanodine receptor Ca²⁺ release channels in the endoplasmic reticulum are maximally activated by caffeine. On the other hand, the expression levels of ryanodine receptor showed a unimodal distribution. We showed that the difference in the caffeine sensitivity depends on a critical balance between Ca²⁺ release and Ca²⁺ uptake activities, which is amplified by the regenerative nature of the Ca²⁺ release mechanism. Furthermore, individual cells switched between the caffeine-sensitive and caffeine-insensitive states with an average transition time of approximately 65 h, suggestive of temporal fluctuation in endogenous protein expression levels associated with caffeine response. These results suggest the significance of regenerative mechanisms that amplify protein expression noise and induce cell-to-cell phenotypic variation in mammalian cells.

Real-time detection of the early event of cytotoxicity of herbal ingredients on single leukemia cells studied in a microfluidic biochip

A microfluidic approach has been developed for the real-time detection of drug effects, based on the quantitative measurement of calibrated cytosolic calcium ([Ca(2+)](i)) on single cancer cells. This microfluidic method is rapid by detecting the early event of cytotoxicity of drug candidates on cancer cells, without waiting for a couple of days needed for cell seeding and drug treatment by conventional assays. The miniaturized biochip consists of a V-shaped structure for the single-cell selection and retention. Various test reagents such as the chemotherapy drug (daunorubicin), an ionophore (ionomycin), and herbal ingredients from licorice (isoliquiritigenin or IQ) were investigated for their abilities to stimulate sustained cellular [Ca(2+)](i) elevations. The microfluidic results obtained in hours have been confirmed by conventional cytotoxicity assays which take days to complete. Moreover, any color or chemical interference problems found in the conventional assays of herbal compounds could be resolved. Using the microfluidic approach, IQ (50 microM) has been found to cause a sustained [Ca(2+)](i) elevation and cytotoxic effects on leukemia cells. The microfluidic single-cell analysis not only reduces reagent cost, and demands less cells, but also reveals some phenomena due to cellular heterogeneity that cannot be observed in bulk analysis.

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.

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?