Modeling cardiac β-adrenergic signaling with normalized-Hill differential equations: comparison with a biochemical model

Computational Models of Reactive Oxygen Species as Metabolic Byproducts and Signal-Transduction Modulators

Reactive oxygen species (ROS) are widely involved in intracellular signaling and human pathologies, but their precise roles have been difficult to enumerate and integrate holistically. The context- and dose-dependent intracellular effects of ROS can lead to contradictory experimental results and confounded interpretations. For example, lower levels of ROS promote cell signaling and proliferation, whereas abundant ROS cause overwhelming damage to biomolecules and cellular apoptosis or senescence. These complexities raise the question of whether the many facets of ROS biology can be joined under a common mechanistic framework using computational modeling. Here, we take inventory of some current models for ROS production or ROS regulation of signaling pathways. Several models captured non-intuitive observations or made predictions that were later verified by experiment. There remains a need for systems-level analyses that jointly incorporate ROS production, handling, and modulation of multiple signal-transduction cascades.

Knowledge gaps to understanding cardiac macrophage polarization following myocardial infarction

Following myocardial infarction (MI), macrophages coordinate both pro-inflammatory and reparative responses of the left ventricle (LV) by reacting to and secreting cytokines, chemokines, and growth factors and by stimulating endothelial cells and fibroblasts to modulate neovascularization and scar formation. Healing of the infarcted LV can be divided into three distinct, but overlapping phases: inflammatory, proliferative, and maturation. Macrophages are involved in all phases. Despite macrophages being a major leukocyte cell type in the post-MI LV, how this cell type regulates LV remodeling over the post-MI time continuum is not completely understood. In this review, we summarize the current literature as a foundation to discuss the major knowledge gaps that remain. Defining the post-MI temporal macrophage phenotypes to establish a classification system is the first step in exploring how macrophage phenotypes are regulated, how temporal stimulation and secretion profiles evolve, and how best to modify stimuli to yield predictable cell responses. This article is part of a Special Issue entitled: The role of post-translational protein modifications on heart and vascular metabolism edited by Jason R.B. Dyck & Jan F.C. Glatz.

Multi-scale Modeling of the Cardiovascular System: Disease Development, Progression, and Clinical Intervention

Cardiovascular diseases (CVDs) are the leading cause of death in the western world. With the current development of clinical diagnostics to more accurately measure the extent and specifics of CVDs, a laudable goal is a better understanding of the structure-function relation in the cardiovascular system. Much of this fundamental understanding comes from the development and study of models that integrate biology, medicine, imaging, and biomechanics. Information from these models provides guidance for developing diagnostics, and implementation of these diagnostics to the clinical setting, in turn, provides data for refining the models. In this review, we introduce multi-scale and multi-physical models for understanding disease development, progression, and designing clinical interventions. We begin with multi-scale models of cardiac electrophysiology and mechanics for diagnosis, clinical decision support, personalized and precision medicine in cardiology with examples in arrhythmia and heart failure. We then introduce computational models of vasculature mechanics and associated mechanical forces for understanding vascular disease progression, designing clinical interventions, and elucidating mechanisms that underlie diverse vascular conditions. We conclude with a discussion of barriers that must be overcome to provide enhanced insights, predictions, and decisions in pre-clinical and clinical applications.

A computational model of cardiac fibroblast signaling predicts context-dependent drivers of myofibroblast differentiation

Cardiac fibroblasts support heart function, and aberrant fibroblast signaling can lead to fibrosis and cardiac dysfunction. Yet how signaling molecules drive myofibroblast differentiation and fibrosis in the complex signaling environment of cardiac injury remains unclear. We developed a large-scale computational model of cardiac fibroblast signaling in order to identify regulators of fibrosis under diverse signaling contexts. The model network integrates 10 signaling pathways, including 91 nodes and 134 reactions, and it correctly predicted 80% of independent previous experiments. The model predicted key fibrotic signaling regulators (e.g. reactive oxygen species, tissue growth factor β (TGFβ) receptor), whose function varied depending on the extracellular environment. We characterized how network structure relates to function, identified functional modules, and predicted cross-talk between TGFβ and mechanical signaling, which was validated experimentally in adult cardiac fibroblasts. This study provides a systems framework for predicting key regulators of fibroblast signaling across diverse signaling contexts.

Spatially transformed fluorescence image data for ERK-MAPK and selected proteins within human epidermis

Background

Phosphoprotein signalling pathways have been intensively studied in vitro, yet their role in regulating tissue homeostasis is not fully understood. In the skin, interfollicular keratinocytes differentiate over approximately 2 weeks as they traverse the epidermis. The extracellular signal-regulated kinase (ERK) branch of the mitogen-activated protein kinase (MAPK) pathway has been implicated in this process. Therefore, we examined ERK-MAPK activity within human epidermal keratinocytes in situ.

Findings

We used confocal microscopy and immunofluorescence labelling to measure the relative abundances of Raf-1, MEK1/2 and ERK1/2, and their phosphorylated (active) forms within three human skin samples. Additionally, we measured the abundance of selected proteins thought to modulate ERK-MAPK activity, including calmodulin, β1 integrin and stratifin (14-3-3σ); and of transcription factors known to act as effectors of ERK1/2, including the AP-1 components Jun-B, Fra2 and c-Fos. Imaging was performed with sufficient resolution to identify the plasma membrane, cytoplasm and nucleus as distinct domains within cells across the epidermis. The image field of view was also sufficiently large to capture the entire epidermis in cross-section, and thus the full range of keratinocyte differentiation in a single observation. Image processing methods were developed to quantify image data for mathematical and statistical analysis. Here, we provide raw image data and processed outputs.

Conclusions

These data indicate coordinated changes in ERK-MAPK signalling activity throughout the depth of the epidermis, with changes in relative phosphorylation-mediated signalling activity occurring along the gradient of cellular differentiation. We believe these data provide unique information about intracellular signalling as they are obtained from a homeostatic human tissue, and they might be useful for investigating intercellular heterogeneity.

Electronic supplementary material

The online version of this article (doi:10.1186/s13742-015-0102-5) contains supplementary material, which is available to authorized users.

Interaction between phosphodiesterases in the regulation of the cardiac β-adrenergic pathway

In cardiac myocytes, the second messenger cAMP is synthesized within the β-adrenergic signaling pathway upon sympathetic activation. It activates Protein Kinase A (PKA) mediated phosphorylation of multiple target proteins that are functionally critical to cardiac contractility. The dynamics of cAMP are also controlled indirectly by cGMP-mediated regulation of phosphodiesterase isoenzymes (PDEs). The nature of the interactions between cGMP and the PDEs, as well as between PDE isoforms, and how these ultimately transduce the cGMP signal to regulate cAMP remains unclear. To better understand this, we have developed mechanistically detailed models of PDEs 1-4, the primary cAMP-hydrolyzing PDEs in cardiac myocytes, and integrated them into a model of the β-adrenergic signaling pathway. The PDE models are based on experimental studies performed on purified PDEs which have demonstrated that cAMP and cGMP bind competitively to the cyclic nucleotide (cN)-binding domains of PDEs 1, 2, and 3, while PDE4 regulation occurs via PKA-mediated phosphorylation. Individual PDE models reproduce experimentally measured cAMP hydrolysis rates with dose-dependent cGMP regulation. The fully integrated model replicates experimentally observed whole-cell cAMP activation-response relationships and temporal dynamics upon varying degrees of β-adrenergic stimulation in cardiac myocytes. Simulations reveal that as a result of network interactions, reduction in the level of one PDE is partially compensated for by increased activation of others. PDE2 and PDE4 exert the strongest compensatory roles among all PDEs. In addition, PDE2 competes with other PDEs to bind and hydrolyze cAMP and is a strong regulator of PDE interactions. Finally, an increasing level of cGMP gradually out-competes cAMP for the catalytic sites of PDEs 1, 2, and 3, suppresses their cAMP hydrolysis rates, and results in amplified cAMP signaling. These results provide insights into how PDEs transduce cGMP signals to regulate cAMP and how PDE interactions affect cardiac β-adrenergic response.

Regulation of ERK-MAPK signaling in human epidermis

Background

The skin is largely comprised of keratinocytes within the interfollicular epidermis. Over approximately two weeks these cells differentiate and traverse the thickness of the skin. The stage of differentiation is therefore reflected in the positions of cells within the tissue, providing a convenient axis along which to study the signaling events that occur in situ during keratinocyte terminal differentiation, over this extended two-week timescale. The canonical ERK-MAPK signaling cascade (Raf-1, MEK-1/2 and ERK-1/2) has been implicated in controlling diverse cellular behaviors, including proliferation and differentiation. While the molecular interactions involved in signal transduction through this cascade have been well characterized in cell culture experiments, our understanding of how this sequence of events unfolds to determine cell fate within a homeostatic tissue environment has not been fully characterized.

Methods

We measured the abundance of total and phosphorylated ERK-MAPK signaling proteins within interfollicular keratinocytes in transverse cross-sections of human epidermis using immunofluorescence microscopy. To investigate these data we developed a mathematical model of the signaling cascade using a normalized-Hill differential equation formalism.

Results

These data show coordinated variation in the abundance of phosphorylated ERK-MAPK components across the epidermis. Statistical analysis of these data shows that associations between phosphorylated ERK-MAPK components which correspond to canonical molecular interactions are dependent upon spatial position within the epidermis. The model demonstrates that the spatial profile of activation for ERK-MAPK signaling components across the epidermis may be maintained in a cell-autonomous fashion by an underlying spatial gradient in calcium signaling.

Conclusions

Our data demonstrate an extended phospho-protein profile of ERK-MAPK signaling cascade components across the epidermis in situ, and statistical associations in these data indicate canonical ERK-MAPK interactions underlie this spatial profile of ERK-MAPK activation. Using mathematical modelling we have demonstrated that spatially varying calcium signaling components across the epidermis may be sufficient to maintain the spatial profile of ERK-MAPK signaling cascade components in a cell-autonomous manner. These findings may have significant implications for the wide range of cancer drugs which therapeutically target ERK-MAPK signaling components.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-015-0187-6) contains supplementary material, which is available to authorized users.

Systems biology approaches for advancing the discovery of effective drug combinations

Complex diseases like cancer are regulated by large, interconnected networks with many pathways affecting cell proliferation, invasion, and drug resistance. However, current cancer therapy predominantly relies on the reductionist approach of one gene-one disease. Combinations of drugs may overcome drug resistance by limiting mutations and induction of escape pathways, but given the enormous number of possible drug combinations, strategies to reduce the search space and prioritize experiments are needed. In this review, we focus on the use of computational modeling, bioinformatics and high-throughput experimental methods for discovery of drug combinations. We highlight cutting-edge systems approaches, including large-scale modeling of cell signaling networks, network motif analysis, statistical association-based models, identifying correlations in gene signatures, functional genomics, and high-throughput combination screens. We also present a list of publicly available data and resources to aid in discovery of drug combinations. Integration of these systems approaches will enable faster discovery and translation of clinically relevant drug combinations.

Graphical abstract

Energy-based analysis of biochemical cycles using bond graphs

Thermodynamic aspects of chemical reactions have a long history in the physical chemistry literature. In particular, biochemical cycles require a source of energy to function. However, although fundamental, the role of chemical potential and Gibb's free energy in the analysis of biochemical systems is often overlooked leading to models which are physically impossible. The bond graph approach was developed for modelling engineering systems, where energy generation, storage and transmission are fundamental. The method focuses on how power flows between components and how energy is stored, transmitted or dissipated within components. Based on the early ideas of network thermodynamics, we have applied this approach to biochemical systems to generate models which automatically obey the laws of thermodynamics. We illustrate the method with examples of biochemical cycles. We have found that thermodynamically compliant models of simple biochemical cycles can easily be developed using this approach. In particular, both stoichiometric information and simulation models can be developed directly from the bond graph. Furthermore, model reduction and approximation while retaining structural and thermodynamic properties is facilitated. Because the bond graph approach is also modular and scaleable, we believe that it provides a secure foundation for building thermodynamically compliant models of large biochemical networks.

Calcium and IP3 dynamics in cardiac myocytes: experimental and computational perspectives and approaches

Calcium plays a crucial role in excitation-contraction coupling (ECC), but it is also a pivotal second messenger activating Ca²⁺-dependent transcription factors in a process termed excitation-transcription coupling (ETC). Evidence accumulated over the past decade indicates a pivotal role of inositol 1,4,5-trisphosphate receptor (IP₃R)-mediated Ca²⁺ release in the regulation of cytosolic and nuclear Ca²⁺ signals. IP₃ is generated by stimulation of plasma membrane receptors that couple to phospholipase C (PLC), liberating IP₃ from phosphatidylinositol 4,5-bisphosphate (PIP₂). An intriguing aspect of IP₃ signaling is the presence of the entire PIP₂-PLC-IP₃ signaling cascade as well as the presence of IP₃Rs at the inner and outer membranes of the nuclear envelope (NE) which functions as a Ca²⁺ store. The observation that the nucleus is surrounded by its own putative Ca²⁺ store raises the possibility that nuclear IP₃-dependent Ca²⁺ release plays a critical role in ETC. This provides a potential mechanism of regulation that acts locally and autonomously from the global cytosolic Ca²⁺ signal underlying ECC. Moreover, there is evidence that: (i) the sarcoplasmic reticulum (SR) and NE are a single contiguous Ca²⁺ store; (ii) the nuclear pore complex is the major gateway for Ca²⁺ and macromolecules to pass between the cytosol and the nucleoplasm; (iii) the inner membrane of the NE hosts key Ca²⁺ handling proteins including the Na⁺/Ca²⁺ exchanger (NCX)/GM1 complex, ryanodine receptors (RyRs), nicotinic acid adenine dinucleotide phosphate receptors (NAADPRs), Na⁺/K⁺ ATPase, and Na⁺/H⁺ exchanger. Thus, it appears that the nucleus represents a Ca²⁺ signaling domain equipped with its own ion channels and transporters that allow for complex local Ca²⁺ signals. Many experimental and modeling approaches have been used for the study of intracellular Ca²⁺ signaling but the key to the understanding of the dual role of Ca²⁺ mediating ECC and ECT lays in quantitative differences of local [Ca²⁺] in the nuclear and cytosolic compartment. In this review, we discuss the state of knowledge regarding the origin and the physiological implications of nuclear Ca²⁺ transients in different cardiac cell types (adult atrial and ventricular myocytes) as well as experimental and mathematical approaches to study Ca²⁺ and IP₃ signaling in the cytosol and nucleus. In particular, we focus on the concept that highly localized Ca²⁺ signals are required to translocate and activate Ca²⁺-dependent transcription factors (e.g., nuclear factor of activated T-cells, NFAT; histone deacetylase, HDAC) through phosphorylation/dephosphorylation processes.

Analysis of transcription factor network underlying 3T3-L1 adipocyte differentiation

Lipid accumulation in adipocytes reflects a balance between enzymatic pathways leading to the formation and breakdown of esterified lipids, primarily triglycerides. This balance is extremely important, as both high and low lipid levels in adipocytes can have deleterious consequences. The enzymes responsible for lipid synthesis and breakdown (lipogenesis and lipolysis, respectively) are regulated through the coordinated actions of several transcription factors (TFs). In this study, we examined the dynamics of several key transcription factors (TFs) - PPARγ, C/EBPβ, CREB, NFAT, FoxO1, and SREBP-1c - during adipogenic differentiation (week 1) and ensuing lipid accumulation. The activation profiles of these TFs at different times following induction of adipogenic differentiation were quantified using 3T3-L1 reporter cell lines constructed to secrete the Gaussia luciferase enzyme upon binding of a TF to its DNA binding element. The dynamics of the TFs was also modeled using a combination of logical gates and ordinary differential equations, where the logical gates were used to explore different combinations of activating inputs for PPARγ, C/EBPβ, and SREBP-1c. Comparisons of the experimental profiles and model simulations suggest that SREBP-1c could be independently activated by either insulin or PPARγ, whereas PPARγ activation required both C/EBPβ as well as a putative ligand. Parameter estimation and sensitivity analysis indicate that feedback activation of SREBP-1c by PPARγ is negligible in comparison to activation of SREBP-1c by insulin. On the other hand, the production of an activating ligand could quantitatively contribute to a sustained elevation in PPARγ activity.

Transfer functions for protein signal transduction: application to a model of striatal neural plasticity

We present a novel formulation for biochemical reaction networks in the context of protein signal transduction. The model consists of input-output transfer functions, which are derived from differential equations, using stable equilibria. We select a set of “source” species, which are interpreted as input signals. Signals are transmitted to all other species in the system (the “target” species) with a specific delay and with a specific transmission strength. The delay is computed as the maximal reaction time until a stable equilibrium for the target species is reached, in the context of all other reactions in the system. The transmission strength is the concentration change of the target species. The computed input-output transfer functions can be stored in a matrix, fitted with parameters, and even recalled to build dynamical models on the basis of state changes. By separating the temporal and the magnitudinal domain we can greatly simplify the computational model, circumventing typical problems of complex dynamical systems. The transfer function transformation of biochemical reaction systems can be applied to mass-action kinetic models of signal transduction. The paper shows that this approach yields significant novel insights while remaining a fully testable and executable dynamical model for signal transduction. In particular we can deconstruct the complex system into local transfer functions between individual species. As an example, we examine modularity and signal integration using a published model of striatal neural plasticity. The modularizations that emerge correspond to a known biological distinction between calcium-dependent and cAMP-dependent pathways. Remarkably, we found that overall interconnectedness depends on the magnitude of inputs, with higher connectivity at low input concentrations and significant modularization at moderate to high input concentrations. This general result, which directly follows from the properties of individual transfer functions, contradicts notions of ubiquitous complexity by showing input-dependent signal transmission inactivation.

Network reconstruction and systems analysis of cardiac myocyte hypertrophy signaling

Cardiac hypertrophy is managed by a dense web of signaling pathways with many pathways influencing myocyte growth. A quantitative understanding of the contributions of individual pathways and their interactions is needed to better understand hypertrophy signaling and to develop more effective therapies for heart failure. We developed a computational model of the cardiac myocyte hypertrophy signaling network to determine how the components and network topology lead to differential regulation of transcription factors, gene expression, and myocyte size. Our computational model of the hypertrophy signaling network contains 106 species and 193 reactions, integrating 14 established pathways regulating cardiac myocyte growth. 109 of 114 model predictions were validated using published experimental data testing the effects of receptor activation on transcription factors and myocyte phenotypic outputs. Network motif analysis revealed an enrichment of bifan and biparallel cross-talk motifs. Sensitivity analysis was used to inform clustering of the network into modules and to identify species with the greatest effects on cell growth. Many species influenced hypertrophy, but only a few nodes had large positive or negative influences. Ras, a network hub, had the greatest effect on cell area and influenced more species than any other protein in the network. We validated this model prediction in cultured cardiac myocytes. With this integrative computational model, we identified the most influential species in the cardiac hypertrophy signaling network and demonstrate how different levels of network organization affect myocyte size, transcription factors, and gene expression.

Bigger, better, faster: principles and models of AKAP anchoring protein signaling

A kinase anchoring proteins (AKAPs) bind multiple signaling proteins and have subcellular targeting domains that allow them to greatly impact cellular signaling. AKAPs localize, specify, amplify, and accelerate signal transduction within the cell by bringing signaling proteins together in space and time. AKAPs also organize higher-order network motifs such as feed forward and feedback loops that may create complex network responses, including adaptation, oscillation, and ultrasensitivity. Computational models have begun to provide an insight into how AKAPs regulate signaling dynamics and cardiovascular pathophysiology. Models of mitogen-activated protein kinase and epidermal growth factor receptor scaffolds have revealed additional design principles and new methods for representing signaling scaffolds mathematically. Coupling computational modeling with quantitative experimental approaches will be increasingly necessary for dissecting the diverse information processing functions performed by AKAP signaling complexes.