Integrating intracellular dynamics using CompuCell3D and Bionetsolver: applications to multiscale modelling of cancer cell growth and invasion

In this paper we present a multiscale, individual-based simulation environment that integrates CompuCell3D for lattice-based modelling on the cellular level and Bionetsolver for intracellular modelling. CompuCell3D or CC3D provides an implementation of the lattice-based Cellular Potts Model or CPM (also known as the Glazier-Graner-Hogeweg or GGH model) and a Monte Carlo method based on the metropolis algorithm for system evolution. The integration of CC3D for cellular systems with Bionetsolver for subcellular systems enables us to develop a multiscale mathematical model and to study the evolution of cell behaviour due to the dynamics inside of the cells, capturing aspects of cell behaviour and interaction that is not possible using continuum approaches. We then apply this multiscale modelling technique to a model of cancer growth and invasion, based on a previously published model of Ramis-Conde et al. (2008) where individual cell behaviour is driven by a molecular network describing the dynamics of E-cadherin and β-catenin. In this model, which we refer to as the centre-based model, an alternative individual-based modelling technique was used, namely, a lattice-free approach. In many respects, the GGH or CPM methodology and the approach of the centre-based model have the same overall goal, that is to mimic behaviours and interactions of biological cells. Although the mathematical foundations and computational implementations of the two approaches are very different, the results of the presented simulations are compatible with each other, suggesting that by using individual-based approaches we can formulate a natural way of describing complex multi-cell, multiscale models. The ability to easily reproduce results of one modelling approach using an alternative approach is also essential from a model cross-validation standpoint and also helps to identify any modelling artefacts specific to a given computational approach.     

β2- and β3-, but not β1-adrenergic receptors are involved in osteogenesis of mouse mesenchymal stem cells via cAMP/PKA signaling

The osteogenic capacity of mesenchymal stem cells (MSCs) and the importance of β-adrenergic signals in bone formation and resorption have been well investigated. However, little is known about the development of β-adrenergic receptor (β-AR) systems and the role of β-adrenergic signals in osteogenic differentiation of MSCs, which is critically important in bone physiology and pharmacology. In this study, we demonstrated that both the mRNA and protein levels of β2- and β3-AR are up-regulated following osteogenesis of mouse MSCs. We also established that β-AR agonists negatively while antagonists positively affect MSC osteogenesis. Both β2- and β3-AR are involved in MSC osteogenesis, with β2-AR being dominant. The effect of β-ARs on MSC osteogenesis is partly mediated via the cAMP/PKA signaling. These findings suggest that MSC is also a target for β-adrenergic regulation and β-adrenergic signaling plays a role in MSC osteogenesis.     

Cross-talk between integrin α6β4 and insulin-like growth factor-1 receptor (IGF1R) through direct α6β4 binding to IGF1 and subsequent α6β4-IGF1-IGF1R ternary complex formation in anchorage-independent conditions

Integrin αvβ3 plays a role in insulin-like growth factor-1 (IGF1) signaling (integrin-IGF1 receptor (IGF1R) cross-talk). The specifics of the cross-talk are, however, unclear. In a current model, "ligand occupancy" of αvβ3 (i.e. the binding of extracellular matrix proteins) enhances signaling induced by IGF1 binding to IGF1R. We recently reported that IGF1 directly binds to αvβ3 and induces αvβ3-IGF1-IGF1R ternary complex formation. Consistently, the integrin binding-defective IGF1 mutant (R36E/R37E) is defective in inducing ternary complex formation and IGF signaling, but it still binds to IGF1R. Like αvβ3, integrin α6β4 is overexpressed in many cancers and is implicated in cancer progression. Here, we discovered that α6β4 directly bound to IGF1, but not to R36E/R37E. Grafting the β4 sequence WPNSDP (residues 167-172), which corresponds to the specificity loop of β3, to integrin β1 markedly enhanced IGF1 binding to β1, suggesting that the WPNSDP sequence is involved in IGF1 recognition. WT IGF1 induced α6β4-IGF1-IGF1R ternary complex formation, whereas R36E/R37E did not. When cells were attached to matrix, exogenous IGF1 or α6β4 expression had little or no effect on intracellular signaling. When cell-matrix adhesion was reduced (in poly(2-hydroxyethyl methacrylate-coated plates), IGF1 induced intracellular signaling and enhanced cell survival in an α6β4-dependent manner. Also IGF1 enhanced colony formation in soft agar in an α6β4-dependent manner. These results suggest that IGF binding to α6β4 plays a major role in IGF signaling in anchorage-independent conditions, which mimic the in vivo environment, and is a novel therapeutic target.     

Integrating cardiac PIP3 and cAMP signaling through a PKA anchoring function of p110γ

Adrenergic stimulation of the heart engages cAMP and phosphoinositide second messenger signaling cascades. Cardiac phosphoinositide 3-kinase p110γ participates in these processes by sustaining β-adrenergic receptor internalization through its catalytic function and by controlling phosphodiesterase 3B (PDE3B) activity via an unknown kinase-independent mechanism. We have discovered that p110γ anchors protein kinase A (PKA) through a site in its N-terminal region. Anchored PKA activates PDE3B to enhance cAMP degradation and phosphorylates p110γ to inhibit PIP(3) production. This provides local feedback control of PIP(3) and cAMP signaling events. In congestive heart failure, p110γ is upregulated and escapes PKA-mediated inhibition, contributing to a reduction in β-adrenergic receptor density. Pharmacological inhibition of p110γ normalizes β-adrenergic receptor density and improves contractility in failing hearts.     

Petri net-based method for the analysis of the dynamics of signal propagation in signaling pathways

MOTIVATION: Cellular signaling networks are dynamic systems that propagate and process information, and, ultimately, cause phenotypical responses. Understanding the circuitry of the information flow in cells is one of the keys to understanding complex cellular processes. The development of computational quantitative models is a promising avenue for attaining this goal. Not only does the analysis of the simulation data based on the concentration variations of biological compounds yields information about systemic state changes, but it is also very helpful for obtaining information about the dynamics of signal propagation. RESULTS: This article introduces a new method for analyzing the dynamics of signal propagation in signaling pathways using Petri net theory. The method is demonstrated with the Ca(2+)/calmodulin-dependent protein kinase II (CaMKII) regulation network. The results constitute temporal information about signal propagation in the network, a simplified graphical representation of the network and of the signal propagation dynamics and a characterization of some signaling routes as regulation motifs.     

Modeling GPCR active state conformations: the β(2)-adrenergic receptor

The recent publication of several G protein-coupled receptor (GPCR) structures has increased the information available for homology modeling inactive class A GPCRs. Moreover, the opsin crystal structure shows some active features. We have therefore combined information from these two sources to generate an extensively validated model of the active conformation of the β(2)-adrenergic receptor. Experimental information on fully active GPCRs from zinc binding studies, site-directed spin labeling, and other spectroscopic techniques has been used in molecular dynamics simulations. The observed conformational changes reside mainly in transmembrane helix 6 (TM6), with additional small but significant changes in TM5 and TM7. The active model has been validated by manual docking and is in agreement with a large amount of experimental work, including site-directed mutagenesis information. Virtual screening experiments show that the models are selective for β-adrenergic agonists over other GPCR ligands, for (R)- over (S)-β-hydroxy agonists and for β(2)-selective agonists over β(1)-selective agonists. The virtual screens reproduce interactions similar to those generated by manual docking. The C-terminal peptide from a model of the stimulatory G protein, readily docks into the active model in a similar manner to which the C-terminal peptide from transducin, docks into opsin, as shown in a recent opsin crystal structure. This GPCR-G protein model has been used to explain site-directed mutagenesis data on activation. The agreement with experiment suggests a robust model of an active state of the β(2)-adrenergic receptor has been produced. The methodology used here should be transferable to modeling the active state of other GPCRs.     

The A-kinase Anchoring Protein Yotiao Facilitates Complex Formation between Adenylyl Cyclase Type 9 and the IKs Potassium Channel in Heart

The scaffolding protein Yotiao is a member of a large family of protein A-kinase anchoring proteins with important roles in the organization of spatial and temporal signaling. In heart, Yotiao directly associates with the slow outward potassium ion current (I(Ks)) and recruits both PKA and PP1 to regulate I(Ks) phosphorylation and gating. Human mutations that disrupt I(Ks)-Yotiao interaction result in reduced PKA-dependent phosphorylation of the I(Ks) subunit KCNQ1 and inhibition of sympathetic stimulation of I(Ks), which can give rise to long-QT syndrome. We have previously identified a subset of adenylyl cyclase (AC) isoforms that interact with Yotiao, including AC1-3 and AC9, but surprisingly, this group did not include the major cardiac isoforms AC5 and AC6. We now show that either AC2 or AC9 can associate with KCNQ1 in a complex mediated by Yotiao. In transgenic mouse heart expressing KCNQ1-KCNE1, AC activity was specifically associated with the I(Ks)-Yotiao complex and could be disrupted by addition of the AC9 N terminus. A survey of all AC isoforms by RT-PCR indicated expression of AC4-6 and AC9 in adult mouse cardiac myocytes. Of these, the only Yotiao-interacting isoform was AC9. Furthermore, the endogenous I(Ks)-Yotiao complex from guinea pig also contained AC9. Finally, AC9 association with the KCNQ1-Yotiao complex sensitized PKA phosphorylation of KCNQ1 to β-adrenergic stimulation. Thus, in heart, Yotiao brings together PKA, PP1, PDE4D3, AC9, and the I(Ks) channel to achieve localized temporal regulation of β-adrenergic stimulation.     

Dissection and reduction of a modeled bursting neuron

An 11-variable Hodgkin-Huxley type model of a bursting neuron was investigated using numerical bifurcation analysis and computer simulations. The results were applied to develop a reduced model of the underlying subthreshold oscillations (slow-wave) in membrane potential. Two different low-order models were developed: one 3-variable model, which mimicked the slow-wave of the full model in the absence of action potentials and a second 4-variable model, which included expressions accounting for the perturbational effects of action potentials on the slow-wave. The 4-variable model predicted more accurately the activity mode (bursting, beating, or silence) in response to application of extrinsic stimulus current or modulatory agents. The 4-variable model also possessed a phase-response curve that was very similar to that of the original 11-variable model. The results suggest that low-order models of bursting cells that do not consider the effects of action potentials may erroneously predict modes of activity and transient responses of the full model on which the reductions are based. These results also show that it is possible to develop low-order models that retain many of the characteristics of the activity of the higher-order system.     

β₁-Adrenergic receptors increase UCP1 in human MADS brown adipocytes and rescue cold-acclimated β₃-adrenergic receptor-knockout mice via nonshivering thermogenesis

With the finding that brown adipose tissue is present and negatively correlated to obesity in adult man, finding the mechanism(s) of how to activate brown adipose tissue in humans could be important in combating obesity, type 2 diabetes, and their complications. In mice, the main regulator of nonshivering thermogenesis in brown adipose tissue is norepinephrine acting predominantly via β(3)-adrenergic receptors. However, vast majorities of β(3)-adrenergic agonists have so far not been able to stimulate human β(3)-adrenergic receptors or brown adipose tissue activity, and it was postulated that human brown adipose tissue could be regulated instead by β(1)-adrenergic receptors. Therefore, we have investigated the signaling pathways, specifically pathways to nonshivering thermogenesis, in mice lacking β(3)-adrenergic receptors. Wild-type and β(3)-knockout mice were either exposed to acute cold (up to 12 h) or acclimated for 7 wk to cold, and parameters related to metabolism and brown adipose tissue function were investigated. β(3)-knockout mice were able to survive both acute and prolonged cold exposure due to activation of β(1)-adrenergic receptors. Thus, in the absence of β(3)-adrenergic receptors, β(1)-adrenergic receptors are effectively able to signal via cAMP to elicit cAMP-mediated responses and to recruit and activate brown adipose tissue. In addition, we found that in human multipotent adipose-derived stem cells differentiated into functional brown adipocytes, activation of either β(1)-adrenergic receptors or β(3)-adrenergic receptors was able to increase UCP1 mRNA and protein levels. Thus, in humans, β(1)-adrenergic receptors could play an important role in regulating nonshivering thermogenesis.     

Finding single copy genes out of sequenced genomes for multilocus phylogenetics in non-model fungi

Historically, fungal multigene phylogenies have been reconstructed based on a small number of commonly used genes. The availability of complete fungal genomes has given rise to a new wave of model organisms that provide large number of genes potentially useful for building robust gene genealogies. Unfortunately, cross-utilization of these resources to study phylogenetic relationships in the vast majority of non-model fungi (i.e. "orphan" species) remains an unexamined question. To address this problem, we developed a method coupled with a program named "PHYLORPH" (PHYLogenetic markers for ORPHans). The method screens fungal genomic databases (107 fungal genomes fully sequenced) for single copy genes that might be easily transferable and well suited for studies at low taxonomic levels (for example, in species complexes) in non-model fungal species. To maximize the chance to target genes with informative regions, PHYLORPH displays a graphical evaluation system based on the estimation of nucleotide divergence relative to substitution type. The usefulness of this approach was tested by developing markers in four non-model groups of fungal pathogens. For each pathogen considered, 7 to 40% of the 10-15 best candidate genes proposed by PHYLORPH yielded sequencing success. Levels of polymorphism of these genes were compared with those obtained for some genes traditionally used to build fungal phylogenies (e.g. nuclear rDNA, β-tubulin, γ-actin, Elongation factor EF-1α). These genes were ranked among the best-performing ones and resolved accurately taxa relationships in each of the four non-model groups of fungi considered. We envision that PHYLORPH will constitute a useful tool for obtaining new and accurate phylogenetic markers to resolve relationships between closely related non-model fungal species.     

Beta-adrenoceptor-mediated cyclic AMP signal in different types of cultured nerve cells in normoxic and hypoxic conditions

β-adrenergic neurotransmission is an important factor regulating brain activity such as neuronal and glial survival, plasticity, membrane transport or cellular metabolism. Intracellular β-adrenergic signaling, via a stimulatory G protein (G_s), activates two major down-stream effectors, i.e., adenylyl cyclase (AC) and cAMP-dependent protein kinase A (PKA). The aim of this work was to study the ability of endogenous (adrenaline and noradrenaline) and exogenous (isoprenaline) β-adrenergic receptor agonists to increase cAMP in different types of nerve cells. Moreover, we wanted to precisely identify the receptor isoform involved in the observed phenomenon using selective β₁-, β₂- β₃-adrenoceptor blockers. In an additional study, the negative influence of hypoxia on the AC/cAMP intracellular signaling system was tested. The study was conducted in parallel on rat primary glial (astrocytes) cultures, primary neuronal cultures, C6 glioma cells and human T98G glioma cells. The formation of [³H] cAMP by agonists and antagonists was measured in [³H] adenine prelabeled cells under normoxic and hypoxic conditions. The obtained results revealed that adrenaline, noradrenaline and isoprenaline strongly stimulated cAMP production in all tested cell types (with highest potency in C6 glioma cells). In glial and neuronal cells the adrenaline-evoked cAMP effect was mediated mainly by the β₁-adrenoceptor, whereas in tumor cells the effect was probably mediated by all three β-subtype specific drugs. The AC/cAMP intracellular signaling system is affected by hypoxic conditions. Considering both physiological and therapeutic importance of β-family receptors the present work characterized the β-adrenoceptor-mediated cAMP signal transduction pathway in different nerve cells in normoxic and hypoxic conditions. The proposed in vitro model of hypoxic conditions may serve as a good model system to study the biological effects of endogenous catecholamines as well as potential therapeutics targeting adrenergic receptors, which are impaired during ischemia in vivo.     

Biased agonism at β-adrenergic receptors

The β-adrenergic receptors (βARs) include three subtypes, β₁, β₂ and β₃. These receptors are widely expressed and regulate numerous physiological processes including cardiovascular and metabolic functions and airway tone. The βARs are also important targets in the treatment of many diseases including hypertension, heart failure and asthma. In some cases, the use of current βAR ligands to treat a disease is suboptimal and can lead to severe side effects. One strategy to potentially improve such treatments is the development of biased agonists that selectively regulate a subset of βAR signaling pathways and responses. Here we discuss the compounds identified to date that preferentially activate a G_s- or β-arrestin-mediated signaling pathway through βARs. Mechanistic insight on how these compounds bias signaling sheds light on the potential development of even more selective compounds that should have increased utility in treating disease.     

Adrenergic regulation of HCN4 channel requires protein association with β2-adrenergic receptor

β(1)- and β(2)-adrenergic receptors utilize different signaling mechanisms to control cardiac function. Recent studies demonstrated that β(2)-adrenergic receptors (β(2)ARs) colocalize with some ion channels that are critical for proper cardiac function. Here, we demonstrate that β(2)ARs form protein complexes with the pacemaker HCN4 channel, as well as with other subtypes of HCN channels. The adrenergic receptor-binding site was identified at a proximal region of the N-terminal tail of the HCN4 channel. A synthetic peptide derived from the β(2)AR-binding domain of the HCN4 channel disrupted interaction between HCN4 and β(2)AR. In addition, treatment with this peptide prevented adrenergic augmentation of pacemaker currents and spontaneous contraction rates but did not affect adrenergic regulation of voltage-gated calcium currents. These results suggest that the ion channel-receptor complex is a critical mechanism in ion channel regulation.     

A three-dimensional multiscale model for the prediction of thrombus growth under flow with single-platelet resolution

Modeling thrombus growth in pathological flows allows evaluation of risk under patient-specific pharmacological, hematological, and hemodynamical conditions. We have developed a 3D multiscale framework for the prediction of thrombus growth under flow on a spatially resolved surface presenting collagen and tissue factor (TF). The multiscale framework is composed of four coupled modules: a Neural Network (NN) that accounts for platelet signaling, a Lattice Kinetic Monte Carlo (LKMC) simulation for tracking platelet positions, a Finite Volume Method (FVM) simulator for solving convection-diffusion-reaction equations describing agonist release and transport, and a Lattice Boltzmann (LB) flow solver for computing the blood flow field over the growing thrombus. A reduced model of the coagulation cascade was embedded into the framework to account for TF-driven thrombin production. The 3D model was first tested against in vitro microfluidics experiments of whole blood perfusion with various antiplatelet agents targeting COX-1, P₂Y₁, or the IP receptor. The model was able to accurately capture the evolution and morphology of the growing thrombus. Certain problems of 2D models for thrombus growth (artifactual dendritic growth) were naturally avoided with realistic trajectories of platelets in 3D flow. The generalizability of the 3D multiscale solver enabled simulations of important clinical situations, such as cylindrical blood vessels and acute flow narrowing (stenosis). Enhanced platelet-platelet bonding at pathologically high shear rates (e.g., von Willebrand factor unfolding) was required for accurately describing thrombus growth in stenotic flows. Overall, the approach allows consideration of patient-specific platelet signaling and vascular geometry for the prediction of thrombotic episodes.     

An approach to multiscale modelling with graph grammars

Background and Aims

Functional–structural plant models (FSPMs) simulate biological processes at different spatial scales. Methods exist for multiscale data representation and modification, but the advantages of using multiple scales in the dynamic aspects of FSPMs remain unclear. Results from multiscale models in various other areas of science that share fundamental modelling issues with FSPMs suggest that potential advantages do exist, and this study therefore aims to introduce an approach to multiscale modelling in FSPMs.

Methods

A three-part graph data structure and grammar is revisited, and presented with a conceptual framework for multiscale modelling. The framework is used for identifying roles, categorizing and describing scale-to-scale interactions, thus allowing alternative approaches to model development as opposed to correlation-based modelling at a single scale. Reverse information flow (from macro- to micro-scale) is catered for in the framework. The methods are implemented within the programming language XL.

Key Results

Three example models are implemented using the proposed multiscale graph model and framework. The first illustrates the fundamental usage of the graph data structure and grammar, the second uses probabilistic modelling for organs at the fine scale in order to derive crown growth, and the third combines multiscale plant topology with ozone trends and metabolic network simulations in order to model juvenile beech stands under exposure to a toxic trace gas.

Conclusions

The graph data structure supports data representation and grammar operations at multiple scales. The results demonstrate that multiscale modelling is a viable method in FSPM and an alternative to correlation-based modelling. Advantages and disadvantages of multiscale modelling are illustrated by comparisons with single-scale implementations, leading to motivations for further research in sensitivity analysis and run-time efficiency for these models.